Subgroups — C₂₃×#62818 #19210444

Order 5888.

8042 conjugacy classes of subgroups.

The subgroup lattice has 1110 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3542	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3537	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3536	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3534	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3519	C₂	1	8	yes	maximal, complemented
6	C₂₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3496	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3494	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3492	C₂	1	2	yes	maximal, complemented
10	C₂₃×#3490	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3488	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3484	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3484	C₂	1	4	yes	maximal, complemented
14	C₂×C₂₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₂₃×#121	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
17	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
19	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
20	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
21	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
22	C₂₃×#562	C₂²	1	16	yes	complemented
23	C₂₃×#560	C₂²	1	16	yes	complemented
24	C₂₃×#555	C₂²	1	8	yes	complemented
25	C₂₃×#554	C₂²	1	8	yes	complemented
26	C₂₃×#553	C₂²	1	8	yes	complemented
27	C₂₃×#553	C₂²	1	8	yes	complemented
28	C₂₃×#553	C₂²	1	8	yes	complemented
29	C₂₃×#553	C₂²	1	16	yes	complemented
30	C₂₃×#552	C₂²	1	8	yes	complemented
31	C₂₃×#551	C₂²	1	16	yes	complemented
32	C₂₃×#551	C₂²	1	16	yes	complemented
33	C₂₃×#550	C₂²	1	8	yes	complemented
34	C₂₃×#548	C₂²	1	8	yes	complemented
35	C₂₃×#547	C₂²	1	8	yes	complemented
36	C₂₃×#547	C₂²	1	8	yes	complemented
37	C₂₃×#546	C₂²	1	16	yes	complemented
38	C₂₃×#546	C₂²	1	8	yes	complemented
39	C₂₃×#546	C₂²	1	16	yes	complemented
40	C₂₃×#546	C₂²	1	8	yes	complemented
41	C₂₃×#546	C₂²	1	16	yes	complemented
42	C₂₃×#546	C₂²	1	16	yes	complemented
43	C₂₃×#546	C₂²	1	8	yes	complemented
44	C₂₃×#546	C₂²	1	16	yes	complemented
45	D₄²×C₂₃	C₂²	1	16	yes	complemented
46	D₄²×C₂₃	C₂²	1	8	yes	complemented
47	D₄²×C₂₃	C₂²	1	8	yes	complemented
48	D₄²×C₂₃	C₂²	1	16	yes	complemented
49	D₄²×C₂₃	C₂²	1	8	yes	complemented
50	C₂₃×#544	C₂²	1	2	yes	complemented
51	C₂₃×#543	C₂²	1	4	yes	complemented
52	C₂₃×#542	C₂²	1	8	yes	complemented
53	C₂₃×#540	C₂²	1	8	yes	complemented
54	C₂₃×#540	C₂²	1	16	yes	complemented
55	C₂₃×#539	C₂²	1	8	yes	complemented
56	C₂₃×#539	C₂²	1	8	yes	complemented
57	C₂₃×#538	C₂²	1	8	yes	complemented
58	C₂₃×#538	C₂²	1	8	yes	complemented
59	C₂₃×#538	C₂²	1	8	yes	complemented
60	C₂₃×#538	C₂²	1	16	yes	complemented
61	C₂₃×#537	C₂²	1	2	yes	complemented
62	C₂₃×#537	C₂²	1	8	yes	complemented
63	C₂₃×#537	C₂²	1	8	yes	complemented
64	C₂₃×#535	C₂²	1	4	yes	complemented
65	C₂₃×#535	C₂²	1	8	yes	complemented
66	C₂₃×#535	C₂²	1	8	yes	complemented
67	C₂₃×#534	C₂²	1	8	yes	complemented
68	C₂₃×#534	C₂²	1	8	yes	complemented
69	C₂₃×#534	C₂²	1	8	yes	complemented
70	C₂₃×#534	C₂²	1	4	yes	complemented
71	C₂₃×#534	C₂²	1	8	yes	complemented
72	C₂₃×#532	C₂²	1	8	yes	complemented
73	C₂₃×#529	C₂²	1	8	yes	complemented
74	C₂₃×#525	C₂²	1	4	yes	complemented
75	C₂₃×#525	C₂²	1	4	yes	complemented
76	C₂₃×#525	C₂²	1	8	yes	complemented
77	C₂₃×#525	C₂²	1	4	yes	complemented
78	C₂₃×#525	C₂²	1	4	yes	complemented
79	C₂₃×#525	C₂²	1	4	yes	complemented
80	C₂₃×#525	C₂²	1	4	yes	complemented
81	C₂₃×#525	C₂²	1	4	yes	complemented
82	C₂₃×#525	C₂²	1	4	yes	complemented
83	C₂₃×#525	C₂²	1	8	yes	complemented
84	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
85	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
86	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
87	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
88	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
89	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
90	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
91	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
92	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
93	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
94	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
95	C₂×C₂₃×#121	C₂²	1	8	yes	complemented
96	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
97	C₂×C₂₃×#120	C₂²	1	8	yes	complemented
98	C₂₃×#520	C₂²	1	4	yes	complemented
99	C₂₃×#518	C₂²	1	2	yes	complemented
100	C₂₃×#518	C₂²	1	4	yes	complemented
101	C₂₃×#518	C₂²	1	8	yes	complemented
102	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
103	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
104	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
105	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
106	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂⁵×C₂₃	C₂³	1	2	yes	—
109	C₂₃×H(5,𝔽₂)	—	4	16	no	—
110	C₂₃×H(5,𝔽₂)	—	4	8	no	—
111	C₂×#41×C₂₃	—	4	8	no	—
112	C₂×#41×C₂₃	C₂³	1	4	yes	—
113	C₂×#41×C₂₃	C₂³	1	8	yes	—
114	C₂×#41×C₂₃	C₂³	1	4	yes	—
115	C₂×#41×C₂₃	C₂³	1	16	yes	complemented
116	C₂×#41×C₂₃	C₂³	1	8	yes	complemented
117	C₂×#41×C₂₃	C₂³	1	4	yes	complemented
118	C₂×#41×C₂₃	C₂³	1	4	yes	complemented
119	C₂²×Q₈×C₂₃	C₂³	1	2	yes	complemented
120	C₂²×D₄×C₂₃	—	4	4	no	—
121	C₂²×D₄×C₂₃	—	4	8	no	—
122	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
123	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
127	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
128	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
129	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
130	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
131	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
132	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
133	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
134	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
135	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
136	C₂²×D₄×C₂₃	C₂³	1	2	yes	complemented
137	C₂²×D₄×C₂₃	C₂³	1	16	yes	complemented
138	C₂²×D₄×C₂₃	C₂³	1	8	yes	complemented
139	C₂³×C₄×C₂₃	—	4	4	no	—
140	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
142	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
144	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
145	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
146	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
147	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
148	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
149	C₂³×C₄×C₂₃	C₂³	1	4	yes	complemented
150	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
151	C₂₃×#127	C₂³	1	16	yes	complemented
152	C₂₃×#127	C₂³	1	8	yes	complemented
153	C₂₃×#126	C₂³	1	16	yes	complemented
154	C₂₃×#126	C₂³	1	16	yes	complemented
155	C₂₃×#126	C₂³	1	16	yes	complemented
156	C₂₃×#125	C₂³	1	8	yes	complemented
157	C₂₃×#125	C₂³	1	16	yes	complemented
158	C₂₃×#124	C₂³	1	16	yes	complemented
159	C₂₃×#124	C₂³	1	8	yes	complemented
160	C₂₃×#124	C₂³	1	16	yes	complemented
161	C₂₃×#124	C₂³	1	16	yes	complemented
162	C₂₃×#123	C₂³	1	16	yes	—
163	C₂₃×#123	C₂³	1	8	yes	—
164	C₂₃×#123	C₂³	1	8	yes	—
165	C₂₃×#123	C₂³	1	16	yes	complemented
166	C₂₃×#123	C₂³	1	16	yes	complemented
167	C₂₃×#123	C₂³	1	16	yes	complemented
168	C₂₃×#123	C₂³	1	16	yes	complemented
169	C₂₃×#123	C₂³	1	16	yes	complemented
170	C₂₃×#123	C₂³	1	16	yes	complemented
171	C₂₃×#123	C₂³	1	16	yes	complemented
172	C₂₃×#123	C₂³	1	8	yes	complemented
173	C₂₃×#123	C₂³	1	8	yes	complemented
174	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
175	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
176	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
178	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
180	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
181	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
182	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
183	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
184	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
185	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
186	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
187	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	complemented
188	C₂₃×#121	C₂³	1	4	yes	—
189	C₂₃×#121	C₂³	1	8	yes	—
190	C₂₃×#121	C₂³	1	8	yes	—
191	C₂₃×#121	C₂³	1	8	yes	—
192	C₂₃×#121	C₂³	1	4	yes	—
193	C₂₃×#121	C₂³	1	8	yes	—
194	C₂₃×#121	C₂³	1	8	yes	—
195	C₂₃×#121	C₂³	1	8	yes	—
196	C₂₃×#121	C₂³	1	8	yes	—
197	C₂₃×#121	C₂³	1	8	yes	—
198	C₂₃×#121	C₂³	1	8	yes	—
199	C₂₃×#121	C₂³	1	4	yes	—
200	C₂₃×#121	C₂³	1	4	yes	—
201	C₂₃×#121	C₂³	1	8	yes	—
202	C₂₃×#121	C₂³	1	8	yes	complemented
203	C₂₃×#121	C₂³	1	8	yes	complemented
204	C₂₃×#121	C₂³	1	16	yes	complemented
205	C₂₃×#121	C₂³	1	16	yes	complemented
206	C₂₃×#121	C₂³	1	16	yes	complemented
207	C₂₃×#121	C₂³	1	8	yes	complemented
208	C₂₃×#121	C₂³	1	16	yes	complemented
209	C₂₃×#121	C₂³	1	16	yes	complemented
210	C₂₃×#121	C₂³	1	16	yes	complemented
211	C₂₃×#121	C₂³	1	16	yes	complemented
212	C₂₃×#121	C₂³	1	4	yes	complemented
213	C₂₃×#121	C₂³	1	16	yes	complemented
214	C₂₃×#121	C₂³	1	16	yes	complemented
215	C₂₃×#121	C₂³	1	16	yes	complemented
216	C₂₃×#121	C₂³	1	4	yes	complemented
217	C₂₃×#121	C₂³	1	4	yes	complemented
218	C₂₃×#121	C₂³	1	4	yes	complemented
219	C₂₃×#120	C₂³	1	16	yes	—
220	C₂₃×#120	C₂³	1	16	yes	—
221	C₂₃×#120	C₂³	1	8	yes	—
222	C₂₃×#120	C₂³	1	8	yes	—
223	C₂₃×#120	C₂³	1	8	yes	—
224	C₂₃×#120	C₂³	1	8	yes	—
225	C₂₃×#120	C₂³	1	16	yes	—
226	C₂₃×#120	C₂³	1	16	yes	complemented
227	C₂₃×#120	C₂³	1	16	yes	complemented
228	C₂₃×#120	C₂³	1	16	yes	complemented
229	C₂₃×#120	C₂³	1	16	yes	complemented
230	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
231	C₄×D₄×C₂₃	C₂³	1	8	yes	—
232	C₄×D₄×C₂₃	C₂³	1	8	yes	—
233	C₄×D₄×C₂₃	C₂³	1	16	yes	—
234	C₄×D₄×C₂₃	C₂³	1	8	yes	—
235	C₄×D₄×C₂₃	C₂³	1	16	yes	—
236	C₄×D₄×C₂₃	C₂³	1	8	yes	—
237	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
238	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
239	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
240	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
241	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
242	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
243	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
244	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
245	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
246	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
247	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
248	C₂₃×#117	C₂³	1	4	yes	—
249	C₂₃×#117	C₂³	1	8	yes	—
250	C₂₃×#117	C₂³	1	4	yes	—
251	C₂₃×#117	C₂³	1	16	yes	complemented
252	C₂₃×#117	C₂³	1	8	yes	complemented
253	C₂₃×#117	C₂³	1	4	yes	complemented
254	C₂₃×#117	C₂³	1	4	yes	complemented
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
264	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
265	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
266	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
267	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
268	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
269	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
270	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
271	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
272	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
273	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
274	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
275	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	complemented
276	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	complemented
277	C₂×C₄²×C₂₃	C₂³	1	4	yes	complemented
278	C₂⁴×C₂₃	—	2	4	no	—
279	C₂⁴×C₂₃	—	4	2	no	—
280	C₂⁴×C₂₃	—	4	2	no	—
281	C₂⁴×C₂₃	—	4	4	no	—
282	C₂⁴×C₂₃	—	4	4	no	—
283	C₂⁴×C₂₃	—	4	4	no	—
284	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
285	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
286	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
287	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
288	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
289	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
290	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
291	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
292	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
293	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
294	#41×C₂₃	—	2	16	no	—
295	#41×C₂₃	—	4	8	no	—
296	#41×C₂₃	—	4	8	no	—
297	#41×C₂₃	—	4	16	no	—
298	#41×C₂₃	—	4	32	no	—
299	#41×C₂₃	—	4	8	no	—
300	#41×C₂₃	—	4	16	no	—
301	C₂×Q₈×C₂₃	—	4	4	no	—
302	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
304	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
305	C₂×D₄×C₂₃	—	2	16	no	—
306	C₂×D₄×C₂₃	—	2	16	no	—
307	C₂×D₄×C₂₃	—	2	8	no	—
308	C₂×D₄×C₂₃	—	4	8	no	—
309	C₂×D₄×C₂₃	—	4	8	no	—
310	C₂×D₄×C₂₃	—	4	4	no	—
311	C₂×D₄×C₂₃	—	4	16	no	—
312	C₂×D₄×C₂₃	—	4	4	no	—
313	C₂×D₄×C₂₃	—	4	8	no	—
314	C₂×D₄×C₂₃	—	4	16	no	—
315	C₂×D₄×C₂₃	—	4	16	no	—
316	C₂×D₄×C₂₃	—	4	8	no	—
317	C₂×D₄×C₂₃	—	4	16	no	—
318	C₂×D₄×C₂₃	—	4	8	no	—
319	C₂×D₄×C₂₃	—	4	16	no	—
320	C₂×D₄×C₂₃	—	4	16	no	—
321	C₂×D₄×C₂₃	—	4	32	no	—
322	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
323	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
324	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
325	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
326	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
327	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
328	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
329	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
330	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
331	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
332	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
333	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
334	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
335	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
336	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
337	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
338	C₂²×C₄×C₂₃	—	2	4	no	—
339	C₂²×C₄×C₂₃	—	2	8	no	—
340	C₂²×C₄×C₂₃	—	4	4	no	—
341	C₂²×C₄×C₂₃	—	4	4	no	—
342	C₂²×C₄×C₂₃	—	4	4	no	—
343	C₂²×C₄×C₂₃	—	4	4	no	—
344	C₂²×C₄×C₂₃	—	4	8	no	—
345	C₂²×C₄×C₂₃	—	4	4	no	—
346	C₂²×C₄×C₂₃	—	4	2	no	—
347	C₂²×C₄×C₂₃	—	4	4	no	—
348	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
350	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
351	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
352	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
355	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
357	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
359	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
360	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
361	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
362	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
363	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
364	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
365	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
367	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
369	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
370	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
371	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
372	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
373	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
374	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
375	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
378	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
379	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
380	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
381	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
382	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
383	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
384	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
385	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
386	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
387	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
388	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
389	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
390	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
391	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
393	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
394	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
395	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
396	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
397	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
398	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
399	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
400	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
401	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
402	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
403	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
404	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
405	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
406	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
407	C₄²×C₂₃	C₂⁴	1	8	yes	—
408	C₄²×C₂₃	C₂⁴	1	8	yes	—
409	C₄²×C₂₃	C₂⁴	1	16	yes	—
410	#62818	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
411	C₂³×C₂₃	—	2	2	no	—
412	C₂³×C₂₃	—	2	2	no	—
413	C₂³×C₂₃	—	2	2	no	—
414	C₂³×C₂₃	—	2	4	no	—
415	C₂³×C₂₃	—	2	4	no	—
416	C₂³×C₂₃	—	2	4	no	—
417	C₂³×C₂₃	—	2	2	no	—
418	C₂³×C₂₃	—	2	4	no	—
419	C₂³×C₂₃	—	2	8	no	—
420	C₂³×C₂₃	—	2	8	no	—
421	C₂³×C₂₃	—	2	8	no	—
422	C₂³×C₂₃	—	2	8	no	—
423	C₂³×C₂₃	—	4	1	no	—
424	C₂³×C₂₃	—	4	2	no	—
425	C₂³×C₂₃	—	4	1	no	—
426	C₂³×C₂₃	—	4	1	no	—
427	C₂³×C₂₃	—	4	2	no	—
428	C₂³×C₂₃	—	4	1	no	—
429	C₂³×C₂₃	—	4	4	no	—
430	C₂³×C₂₃	—	4	4	no	—
431	C₂³×C₂₃	—	4	4	no	—
432	C₂³×C₂₃	—	4	4	no	—
433	C₂³×C₂₃	—	4	4	no	—
434	C₂³×C₂₃	—	4	4	no	—
435	C₂³×C₂₃	—	4	4	no	—
436	C₂³×C₂₃	—	4	4	no	—
437	C₂³×C₂₃	—	4	8	no	—
438	C₂³×C₂₃	—	4	8	no	—
439	C₂³×C₂₃	—	4	8	no	—
440	C₂³×C₂₃	—	4	16	no	—
441	C₂³×C₂₃	—	8	16	no	—
442	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	complemented
443	C₂³×C₂₃	C₂⁵	1	8	yes	—
444	C₂³×C₂₃	C₂⁵	1	2	yes	—
445	C₂³×C₂₃	C₂⁵	1	8	yes	—
446	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
447	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
448	C₂³×C₂₃	C₂⁵	1	2	yes	—
449	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
450	Q₈×C₂₃	—	2	8	no	—
451	Q₈×C₂₃	—	4	4	no	—
452	Q₈×C₂₃	—	4	8	no	—
453	D₄×C₂₃	—	2	32	no	—
454	D₄×C₂₃	—	2	16	no	—
455	D₄×C₂₃	—	2	16	no	—
456	D₄×C₂₃	—	2	16	no	—
457	D₄×C₂₃	—	2	16	no	—
458	D₄×C₂₃	—	2	16	no	—
459	D₄×C₂₃	—	2	8	no	—
460	D₄×C₂₃	—	4	8	no	—
461	D₄×C₂₃	—	4	16	no	—
462	D₄×C₂₃	—	4	8	no	—
463	D₄×C₂₃	—	4	16	no	—
464	D₄×C₂₃	—	4	16	no	—
465	D₄×C₂₃	—	4	16	no	—
466	D₄×C₂₃	—	4	8	no	—
467	D₄×C₂₃	—	4	4	no	—
468	D₄×C₂₃	—	4	8	no	—
469	C₂×C₄×C₂₃	—	2	2	no	—
470	C₂×C₄×C₂₃	—	2	4	no	—
471	C₂×C₄×C₂₃	—	2	8	no	—
472	C₂×C₄×C₂₃	—	2	8	no	—
473	C₂×C₄×C₂₃	—	2	4	no	—
474	C₂×C₄×C₂₃	—	2	4	no	—
475	C₂×C₄×C₂₃	—	2	4	no	—
476	C₂×C₄×C₂₃	—	2	4	no	—
477	C₂×C₄×C₂₃	—	2	4	no	—
478	C₂×C₄×C₂₃	—	2	4	no	—
479	C₂×C₄×C₂₃	—	2	16	no	—
480	C₂×C₄×C₂₃	—	4	1	no	—
481	C₂×C₄×C₂₃	—	4	2	no	—
482	C₂×C₄×C₂₃	—	4	2	no	—
483	C₂×C₄×C₂₃	—	4	2	no	—
484	C₂×C₄×C₂₃	—	4	2	no	—
485	C₂×C₄×C₂₃	—	4	2	no	—
486	C₂×C₄×C₂₃	—	4	1	no	—
487	C₂×C₄×C₂₃	—	4	4	no	—
488	C₂×C₄×C₂₃	—	4	4	no	—
489	C₂×C₄×C₂₃	—	4	4	no	—
490	C₂×C₄×C₂₃	—	4	8	no	—
491	C₂×C₄×C₂₃	—	4	4	no	—
492	C₂×C₄×C₂₃	—	4	8	no	—
493	C₂×C₄×C₂₃	—	4	16	no	—
494	C₂×C₄×C₂₃	—	4	8	no	—
495	C₂×C₄×C₂₃	—	4	8	no	—
496	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	complemented
497	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
498	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
499	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
500	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
501	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
502	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
503	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
504	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
505	#3542	C₂×C₂₃	1	8	yes	complemented
506	#3537	C₂×C₂₃	1	4	yes	complemented
507	#3536	C₂×C₂₃	1	4	yes	complemented
508	#3534	C₂×C₂₃	1	8	yes	complemented
509	#3519	C₂×C₂₃	1	8	yes	complemented
510	#3505	C₂×C₂₃	1	4	yes	complemented
511	#3496	C₂×C₂₃	1	4	yes	complemented
512	#3494	C₂×C₂₃	1	4	yes	complemented
513	#3492	C₂×C₂₃	1	2	yes	complemented
514	#3490	C₂×C₂₃	1	4	yes	complemented
515	#3488	C₂×C₂₃	1	4	yes	complemented
516	#3484	C₂×C₂₃	1	2	yes	complemented
517	#3484	C₂×C₂₃	1	4	yes	complemented
518	C₂×#525	C₂×C₂₃	1	2	yes	complemented
519	C₂²×#121	C₂×C₂₃	1	1	yes	characteristic, complemented
520	C₂²×C₂₃	—	2	8	no	—
521	C₂²×C₂₃	—	2	2	no	—
522	C₂²×C₂₃	—	2	1	no	—
523	C₂²×C₂₃	—	2	1	no	—
524	C₂²×C₂₃	—	2	1	no	—
525	C₂²×C₂₃	—	2	1	no	—
526	C₂²×C₂₃	—	2	2	no	—
527	C₂²×C₂₃	—	2	1	no	—
528	C₂²×C₂₃	—	2	1	no	—
529	C₂²×C₂₃	—	2	2	no	—
530	C₂²×C₂₃	—	2	8	no	—
531	C₂²×C₂₃	—	2	8	no	—
532	C₂²×C₂₃	—	2	8	no	—
533	C₂²×C₂₃	—	2	8	no	—
534	C₂²×C₂₃	—	2	2	no	—
535	C₂²×C₂₃	—	2	8	no	—
536	C₂²×C₂₃	—	2	8	no	—
537	C₂²×C₂₃	—	2	2	no	—
538	C₂²×C₂₃	—	4	4	no	—
539	C₂²×C₂₃	—	4	8	no	—
540	C₂²×C₂₃	—	4	8	no	—
541	C₂²×C₂₃	—	4	4	no	—
542	C₂²×C₂₃	—	8	8	no	—
543	C₂²×C₂₃	—	8	8	no	—
544	C₂²×C₂₃	—	8	8	no	—
545	C₂²×C₂₃	—	8	8	no	—
546	C₂²×C₂₃	—	16	8	no	—
547	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
548	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
549	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
550	C₂²×C₂₃	#585	1	2	yes	—
551	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
552	C₄×C₂₃	—	2	2	no	—
553	C₄×C₂₃	—	2	2	no	—
554	C₄×C₂₃	—	2	2	no	—
555	C₄×C₂₃	—	2	8	no	—
556	C₄×C₂₃	—	2	8	no	—
557	C₄×C₂₃	—	2	8	no	—
558	C₄×C₂₃	—	2	8	no	—
559	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
560	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	complemented
561	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	4	yes	complemented
562	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
563	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
564	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
565	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
566	#562	C₂²×C₂₃	1	16	yes	complemented
567	#560	C₂²×C₂₃	1	16	yes	complemented
568	#555	C₂²×C₂₃	1	8	yes	complemented
569	#554	C₂²×C₂₃	1	8	yes	complemented
570	#553	C₂²×C₂₃	1	8	yes	complemented
571	#553	C₂²×C₂₃	1	8	yes	complemented
572	#553	C₂²×C₂₃	1	8	yes	complemented
573	#553	C₂²×C₂₃	1	16	yes	complemented
574	#552	C₂²×C₂₃	1	8	yes	complemented
575	#551	C₂²×C₂₃	1	16	yes	complemented
576	#551	C₂²×C₂₃	1	16	yes	complemented
577	#550	C₂²×C₂₃	1	8	yes	complemented
578	#548	C₂²×C₂₃	1	8	yes	complemented
579	#547	C₂²×C₂₃	1	8	yes	complemented
580	#547	C₂²×C₂₃	1	8	yes	complemented
581	#546	C₂²×C₂₃	1	16	yes	complemented
582	#546	C₂²×C₂₃	1	8	yes	complemented
583	#546	C₂²×C₂₃	1	16	yes	complemented
584	#546	C₂²×C₂₃	1	8	yes	complemented
585	#546	C₂²×C₂₃	1	16	yes	complemented
586	#546	C₂²×C₂₃	1	16	yes	complemented
587	#546	C₂²×C₂₃	1	8	yes	complemented
588	#546	C₂²×C₂₃	1	16	yes	complemented
589	D₄²	C₂²×C₂₃	1	16	yes	complemented
590	D₄²	C₂²×C₂₃	1	8	yes	complemented
591	D₄²	C₂²×C₂₃	1	8	yes	complemented
592	D₄²	C₂²×C₂₃	1	16	yes	complemented
593	D₄²	C₂²×C₂₃	1	8	yes	complemented
594	#544	C₂²×C₂₃	1	2	yes	complemented
595	#543	C₂²×C₂₃	1	4	yes	complemented
596	#542	C₂²×C₂₃	1	8	yes	complemented
597	#540	C₂²×C₂₃	1	8	yes	complemented
598	#540	C₂²×C₂₃	1	16	yes	complemented
599	#539	C₂²×C₂₃	1	8	yes	complemented
600	#539	C₂²×C₂₃	1	8	yes	complemented
601	#538	C₂²×C₂₃	1	8	yes	complemented
602	#538	C₂²×C₂₃	1	8	yes	complemented
603	#538	C₂²×C₂₃	1	8	yes	complemented
604	#538	C₂²×C₂₃	1	16	yes	complemented
605	#537	C₂²×C₂₃	1	2	yes	complemented
606	#537	C₂²×C₂₃	1	8	yes	complemented
607	#537	C₂²×C₂₃	1	8	yes	complemented
608	#535	C₂²×C₂₃	1	4	yes	complemented
609	#535	C₂²×C₂₃	1	8	yes	complemented
610	#535	C₂²×C₂₃	1	8	yes	complemented
611	#534	C₂²×C₂₃	1	8	yes	complemented
612	#534	C₂²×C₂₃	1	8	yes	complemented
613	#534	C₂²×C₂₃	1	8	yes	complemented
614	#534	C₂²×C₂₃	1	4	yes	complemented
615	#534	C₂²×C₂₃	1	8	yes	complemented
616	#532	C₂²×C₂₃	1	8	yes	complemented
617	#529	C₂²×C₂₃	1	8	yes	complemented
618	#525	C₂²×C₂₃	1	4	yes	complemented
619	#525	C₂²×C₂₃	1	4	yes	complemented
620	#525	C₂²×C₂₃	1	8	yes	complemented
621	#525	C₂²×C₂₃	1	4	yes	complemented
622	#525	C₂²×C₂₃	1	4	yes	complemented
623	#525	C₂²×C₂₃	1	4	yes	complemented
624	#525	C₂²×C₂₃	1	4	yes	complemented
625	#525	C₂²×C₂₃	1	4	yes	complemented
626	#525	C₂²×C₂₃	1	4	yes	complemented
627	#525	C₂²×C₂₃	1	8	yes	complemented
628	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
629	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
630	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
631	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
632	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
633	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
634	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
635	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
636	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
637	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
638	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
639	C₂×#121	C₂²×C₂₃	1	8	yes	complemented
640	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
641	C₂×#120	C₂²×C₂₃	1	8	yes	complemented
642	#520	C₂²×C₂₃	1	4	yes	complemented
643	#518	C₂²×C₂₃	1	2	yes	complemented
644	#518	C₂²×C₂₃	1	4	yes	complemented
645	#518	C₂²×C₂₃	1	8	yes	complemented
646	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
647	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
648	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
649	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
650	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
651	C₂×C₂₃	—	2	2	no	—
652	C₂×C₂₃	—	2	2	no	—
653	C₂×C₂₃	—	2	2	no	—
654	C₂×C₂₃	—	2	4	no	—
655	C₂×C₂₃	—	4	2	no	—
656	C₂×C₂₃	—	4	8	no	—
657	C₂×C₂₃	—	4	8	no	—
658	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
659	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
660	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
661	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
662	C₂⁵	C₂³×C₂₃	1	2	yes	—
663	H(5,𝔽₂)	—	4	16	no	—
664	H(5,𝔽₂)	—	4	8	no	—
665	C₂×#41	—	4	8	no	—
666	C₂×#41	C₂³×C₂₃	1	4	yes	—
667	C₂×#41	C₂³×C₂₃	1	4	yes	—
668	C₂×#41	C₂³×C₂₃	1	8	yes	—
669	C₂×#41	C₂³×C₂₃	1	4	yes	complemented
670	C₂×#41	C₂³×C₂₃	1	4	yes	complemented
671	C₂×#41	C₂³×C₂₃	1	8	yes	complemented
672	C₂×#41	C₂³×C₂₃	1	16	yes	complemented
673	C₂²×Q₈	C₂³×C₂₃	1	2	yes	complemented
674	C₂²×D₄	—	4	4	no	—
675	C₂²×D₄	—	4	8	no	—
676	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
677	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
678	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
679	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
680	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
681	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
682	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
683	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
684	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
685	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
686	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
687	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
688	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
689	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
690	C₂²×D₄	C₂³×C₂₃	1	2	yes	complemented
691	C₂²×D₄	C₂³×C₂₃	1	16	yes	complemented
692	C₂²×D₄	C₂³×C₂₃	1	8	yes	complemented
693	C₂³×C₄	—	4	4	no	—
694	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
695	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
696	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
697	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
698	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
699	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
700	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
701	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
702	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
703	C₂³×C₄	C₂³×C₂₃	1	4	yes	complemented
704	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
705	#127	C₂³×C₂₃	1	8	yes	complemented
706	#127	C₂³×C₂₃	1	16	yes	complemented
707	#126	C₂³×C₂₃	1	16	yes	complemented
708	#126	C₂³×C₂₃	1	16	yes	complemented
709	#126	C₂³×C₂₃	1	16	yes	complemented
710	#125	C₂³×C₂₃	1	8	yes	complemented
711	#125	C₂³×C₂₃	1	16	yes	complemented
712	#124	C₂³×C₂₃	1	8	yes	complemented
713	#124	C₂³×C₂₃	1	16	yes	complemented
714	#124	C₂³×C₂₃	1	16	yes	complemented
715	#124	C₂³×C₂₃	1	16	yes	complemented
716	#123	C₂³×C₂₃	1	8	yes	—
717	#123	C₂³×C₂₃	1	8	yes	—
718	#123	C₂³×C₂₃	1	16	yes	—
719	#123	C₂³×C₂₃	1	8	yes	complemented
720	#123	C₂³×C₂₃	1	8	yes	complemented
721	#123	C₂³×C₂₃	1	16	yes	complemented
722	#123	C₂³×C₂₃	1	16	yes	complemented
723	#123	C₂³×C₂₃	1	16	yes	complemented
724	#123	C₂³×C₂₃	1	16	yes	complemented
725	#123	C₂³×C₂₃	1	16	yes	complemented
726	#123	C₂³×C₂₃	1	16	yes	complemented
727	#123	C₂³×C₂₃	1	16	yes	complemented
728	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
729	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
730	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
731	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
732	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
733	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
734	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
735	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
736	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
737	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	complemented
738	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
739	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
740	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
741	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
742	#121	C₂³×C₂₃	1	8	yes	—
743	#121	C₂³×C₂₃	1	8	yes	—
744	#121	C₂³×C₂₃	1	8	yes	—
745	#121	C₂³×C₂₃	1	8	yes	—
746	#121	C₂³×C₂₃	1	8	yes	—
747	#121	C₂³×C₂₃	1	8	yes	—
748	#121	C₂³×C₂₃	1	8	yes	—
749	#121	C₂³×C₂₃	1	8	yes	—
750	#121	C₂³×C₂₃	1	4	yes	—
751	#121	C₂³×C₂₃	1	4	yes	—
752	#121	C₂³×C₂₃	1	4	yes	—
753	#121	C₂³×C₂₃	1	4	yes	—
754	#121	C₂³×C₂₃	1	8	yes	—
755	#121	C₂³×C₂₃	1	8	yes	—
756	#121	C₂³×C₂₃	1	4	yes	complemented
757	#121	C₂³×C₂₃	1	4	yes	complemented
758	#121	C₂³×C₂₃	1	4	yes	complemented
759	#121	C₂³×C₂₃	1	4	yes	complemented
760	#121	C₂³×C₂₃	1	16	yes	complemented
761	#121	C₂³×C₂₃	1	8	yes	complemented
762	#121	C₂³×C₂₃	1	8	yes	complemented
763	#121	C₂³×C₂₃	1	16	yes	complemented
764	#121	C₂³×C₂₃	1	8	yes	complemented
765	#121	C₂³×C₂₃	1	16	yes	complemented
766	#121	C₂³×C₂₃	1	16	yes	complemented
767	#121	C₂³×C₂₃	1	16	yes	complemented
768	#121	C₂³×C₂₃	1	16	yes	complemented
769	#121	C₂³×C₂₃	1	16	yes	complemented
770	#121	C₂³×C₂₃	1	16	yes	complemented
771	#121	C₂³×C₂₃	1	16	yes	complemented
772	#121	C₂³×C₂₃	1	16	yes	complemented
773	#120	C₂³×C₂₃	1	8	yes	—
774	#120	C₂³×C₂₃	1	8	yes	—
775	#120	C₂³×C₂₃	1	8	yes	—
776	#120	C₂³×C₂₃	1	8	yes	—
777	#120	C₂³×C₂₃	1	16	yes	—
778	#120	C₂³×C₂₃	1	16	yes	—
779	#120	C₂³×C₂₃	1	16	yes	—
780	#120	C₂³×C₂₃	1	16	yes	complemented
781	#120	C₂³×C₂₃	1	16	yes	complemented
782	#120	C₂³×C₂₃	1	16	yes	complemented
783	#120	C₂³×C₂₃	1	16	yes	complemented
784	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
785	C₄×D₄	C₂³×C₂₃	1	8	yes	—
786	C₄×D₄	C₂³×C₂₃	1	8	yes	—
787	C₄×D₄	C₂³×C₂₃	1	8	yes	—
788	C₄×D₄	C₂³×C₂₃	1	8	yes	—
789	C₄×D₄	C₂³×C₂₃	1	16	yes	—
790	C₄×D₄	C₂³×C₂₃	1	16	yes	—
791	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
792	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
793	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
794	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
795	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
796	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
797	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
798	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
799	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
800	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
801	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
802	#117	C₂³×C₂₃	1	4	yes	—
803	#117	C₂³×C₂₃	1	4	yes	—
804	#117	C₂³×C₂₃	1	8	yes	—
805	#117	C₂³×C₂₃	1	4	yes	complemented
806	#117	C₂³×C₂₃	1	4	yes	complemented
807	#117	C₂³×C₂₃	1	16	yes	complemented
808	#117	C₂³×C₂₃	1	8	yes	complemented
809	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
810	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
811	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
812	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
813	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
814	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
815	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
816	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
817	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
818	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
819	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
820	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
821	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
822	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
823	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
824	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
825	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
826	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
827	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
828	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
829	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	complemented
830	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	complemented
831	C₂×C₄²	C₂³×C₂₃	1	4	yes	complemented
832	C₂₃	#62818	1	1	yes	characteristic, direct product factor, Sylow
833	C₂⁴	—	2	4	no	—
834	C₂⁴	—	4	2	no	—
835	C₂⁴	—	4	2	no	—
836	C₂⁴	—	4	4	no	—
837	C₂⁴	—	4	4	no	—
838	C₂⁴	—	4	4	no	—
839	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
840	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
841	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
842	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
843	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
844	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
845	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
846	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
847	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
848	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
849	#41	—	2	16	no	—
850	#41	—	4	8	no	—
851	#41	—	4	8	no	—
852	#41	—	4	16	no	—
853	#41	—	4	32	no	—
854	#41	—	4	8	no	—
855	#41	—	4	16	no	—
856	C₂×Q₈	—	4	4	no	—
857	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
858	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
859	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
860	C₂×D₄	—	2	16	no	—
861	C₂×D₄	—	2	16	no	—
862	C₂×D₄	—	2	8	no	—
863	C₂×D₄	—	4	8	no	—
864	C₂×D₄	—	4	8	no	—
865	C₂×D₄	—	4	4	no	—
866	C₂×D₄	—	4	16	no	—
867	C₂×D₄	—	4	4	no	—
868	C₂×D₄	—	4	8	no	—
869	C₂×D₄	—	4	16	no	—
870	C₂×D₄	—	4	16	no	—
871	C₂×D₄	—	4	8	no	—
872	C₂×D₄	—	4	16	no	—
873	C₂×D₄	—	4	16	no	—
874	C₂×D₄	—	4	8	no	—
875	C₂×D₄	—	4	16	no	—
876	C₂×D₄	—	4	32	no	—
877	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
878	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
879	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
880	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
881	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
882	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
883	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
884	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
885	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
886	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
887	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
888	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
889	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
890	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
891	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
892	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
893	C₂²×C₄	—	2	4	no	—
894	C₂²×C₄	—	2	8	no	—
895	C₂²×C₄	—	4	4	no	—
896	C₂²×C₄	—	4	4	no	—
897	C₂²×C₄	—	4	4	no	—
898	C₂²×C₄	—	4	4	no	—
899	C₂²×C₄	—	4	8	no	—
900	C₂²×C₄	—	4	4	no	—
901	C₂²×C₄	—	4	2	no	—
902	C₂²×C₄	—	4	4	no	—
903	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
904	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
905	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
906	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
907	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
908	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
909	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
910	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
911	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
912	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
913	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
914	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
915	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
916	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
917	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
918	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
919	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
920	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
921	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
922	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
923	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
924	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
925	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
926	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
927	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
928	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
929	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
930	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
931	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
932	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
933	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
934	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
935	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
936	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
937	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
938	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
939	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
940	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
941	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
942	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
943	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
944	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
945	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
946	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
947	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
948	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
949	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
950	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
951	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
952	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
953	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
954	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
955	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
956	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
957	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
958	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
959	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
960	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
961	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
962	C₄²	C₂⁴×C₂₃	1	8	yes	—
963	C₄²	C₂⁴×C₂₃	1	8	yes	—
964	C₄²	C₂⁴×C₂₃	1	16	yes	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	4	no	—
969	C₂³	—	2	4	no	—
970	C₂³	—	2	4	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	4	no	—
973	C₂³	—	2	8	no	—
974	C₂³	—	2	8	no	—
975	C₂³	—	2	8	no	—
976	C₂³	—	2	8	no	—
977	C₂³	—	4	1	no	—
978	C₂³	—	4	2	no	—
979	C₂³	—	4	1	no	—
980	C₂³	—	4	1	no	—
981	C₂³	—	4	2	no	—
982	C₂³	—	4	1	no	—
983	C₂³	—	4	4	no	—
984	C₂³	—	4	4	no	—
985	C₂³	—	4	4	no	—
986	C₂³	—	4	4	no	—
987	C₂³	—	4	4	no	—
988	C₂³	—	4	4	no	—
989	C₂³	—	4	4	no	—
990	C₂³	—	4	4	no	—
991	C₂³	—	4	8	no	—
992	C₂³	—	4	8	no	—
993	C₂³	—	4	8	no	—
994	C₂³	—	4	16	no	—
995	C₂³	—	8	16	no	—
996	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	complemented
997	C₂³	C₂⁵×C₂₃	1	8	yes	—
998	C₂³	C₂⁵×C₂₃	1	2	yes	—
999	C₂³	C₂⁵×C₂₃	1	8	yes	—
1000	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1001	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1002	C₂³	C₂⁵×C₂₃	1	2	yes	—
1003	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
1004	Q₈	—	2	8	no	—
1005	Q₈	—	4	4	no	—
1006	Q₈	—	4	8	no	—
1007	D₄	—	2	32	no	—
1008	D₄	—	2	16	no	—
1009	D₄	—	2	16	no	—
1010	D₄	—	2	16	no	—
1011	D₄	—	2	16	no	—
1012	D₄	—	2	16	no	—
1013	D₄	—	2	8	no	—
1014	D₄	—	4	8	no	—
1015	D₄	—	4	16	no	—
1016	D₄	—	4	8	no	—
1017	D₄	—	4	16	no	—
1018	D₄	—	4	16	no	—
1019	D₄	—	4	4	no	—
1020	D₄	—	4	8	no	—
1021	D₄	—	4	16	no	—
1022	D₄	—	4	8	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	4	no	—
1025	C₂×C₄	—	2	8	no	—
1026	C₂×C₄	—	2	8	no	—
1027	C₂×C₄	—	2	4	no	—
1028	C₂×C₄	—	2	4	no	—
1029	C₂×C₄	—	2	4	no	—
1030	C₂×C₄	—	2	4	no	—
1031	C₂×C₄	—	2	4	no	—
1032	C₂×C₄	—	2	4	no	—
1033	C₂×C₄	—	2	16	no	—
1034	C₂×C₄	—	4	1	no	—
1035	C₂×C₄	—	4	2	no	—
1036	C₂×C₄	—	4	2	no	—
1037	C₂×C₄	—	4	2	no	—
1038	C₂×C₄	—	4	2	no	—
1039	C₂×C₄	—	4	2	no	—
1040	C₂×C₄	—	4	1	no	—
1041	C₂×C₄	—	4	4	no	—
1042	C₂×C₄	—	4	4	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	8	no	—
1045	C₂×C₄	—	4	16	no	—
1046	C₂×C₄	—	4	8	no	—
1047	C₂×C₄	—	4	8	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	4	8	no	—
1050	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	complemented
1051	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1052	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1053	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1054	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1055	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
1056	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1057	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1058	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
1059	C₂²	—	2	8	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	2	no	—
1069	C₂²	—	2	8	no	—
1070	C₂²	—	2	8	no	—
1071	C₂²	—	2	8	no	—
1072	C₂²	—	2	8	no	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	2	8	no	—
1075	C₂²	—	2	8	no	—
1076	C₂²	—	2	2	no	—
1077	C₂²	—	4	4	no	—
1078	C₂²	—	4	8	no	—
1079	C₂²	—	4	8	no	—
1080	C₂²	—	4	4	no	—
1081	C₂²	—	8	8	no	—
1082	C₂²	—	8	8	no	—
1083	C₂²	—	8	8	no	—
1084	C₂²	—	8	8	no	—
1085	C₂²	—	16	8	no	—
1086	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1087	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1088	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
1089	C₂²	C₂₃×#585	1	2	yes	—
1090	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
1091	C₄	—	2	2	no	—
1092	C₄	—	2	2	no	—
1093	C₄	—	2	2	no	—
1094	C₄	—	2	8	no	—
1095	C₄	—	2	8	no	—
1096	C₄	—	2	8	no	—
1097	C₄	—	2	8	no	—
1098	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
1099	C₂	—	2	2	no	—
1100	C₂	—	2	2	no	—
1101	C₂	—	2	2	no	—
1102	C₂	—	2	4	no	—
1103	C₂	—	4	2	no	—
1104	C₂	—	4	8	no	—
1105	C₂	—	4	8	no	—
1106	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1107	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1108	C₂	C₂×C₂₃×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂₃×#3542	C₂	semidirect
2. C₂₃×#3537	C₂	semidirect
3. C₂₃×#3536	C₂	semidirect
4. C₂₃×#3534	C₂	semidirect
5. C₂₃×#3519	C₂	semidirect
6. C₂₃×#3505	C₂	semidirect
7. C₂₃×#3496	C₂	semidirect
8. C₂₃×#3494	C₂	semidirect
9. C₂₃×#3492	C₂	semidirect
10. C₂₃×#3490	C₂	semidirect
11. C₂₃×#3488	C₂	semidirect
12. C₂₃×#3484	C₂	semidirect
13. C₂₃×#3484	C₂	semidirect
14. C₂×C₂₃×#525	C₂	semidirect
15. C₂²×C₂₃×#121	C₂	semidirect
16. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
18. C₂²×#41×C₂₃	C₂²	semidirect
19. C₂³×D₄×C₂₃	C₂²	semidirect
20. C₂³×D₄×C₂₃	C₂²	semidirect
21. C₂⁴×C₄×C₂₃	C₂²	semidirect
22. C₂₃×#562	C₂²	semidirect
23. C₂₃×#560	C₂²	semidirect
24. C₂₃×#555	C₂²	semidirect
25. C₂₃×#554	C₂²	semidirect
26. C₂₃×#553	C₂²	semidirect
27. C₂₃×#553	C₂²	semidirect
28. C₂₃×#553	C₂²	semidirect
29. C₂₃×#553	C₂²	semidirect
30. C₂₃×#552	C₂²	semidirect
31. C₂₃×#551	C₂²	semidirect
32. C₂₃×#551	C₂²	semidirect
33. C₂₃×#550	C₂²	semidirect
34. C₂₃×#548	C₂²	semidirect
35. C₂₃×#547	C₂²	semidirect
36. C₂₃×#547	C₂²	semidirect
37. C₂₃×#546	C₂²	semidirect
38. C₂₃×#546	C₂²	semidirect
39. C₂₃×#546	C₂²	semidirect
40. C₂₃×#546	C₂²	semidirect
41. C₂₃×#546	C₂²	semidirect
42. C₂₃×#546	C₂²	semidirect
43. C₂₃×#546	C₂²	semidirect
44. C₂₃×#546	C₂²	semidirect
45. D₄²×C₂₃	C₂²	semidirect
46. D₄²×C₂₃	C₂²	semidirect
47. D₄²×C₂₃	C₂²	semidirect
48. D₄²×C₂₃	C₂²	semidirect
49. D₄²×C₂₃	C₂²	semidirect
50. C₂₃×#544	C₂²	semidirect
51. C₂₃×#543	C₂²	semidirect
52. C₂₃×#542	C₂²	semidirect
53. C₂₃×#540	C₂²	semidirect
54. C₂₃×#540	C₂²	semidirect
55. C₂₃×#539	C₂²	semidirect
56. C₂₃×#539	C₂²	semidirect
57. C₂₃×#538	C₂²	semidirect
58. C₂₃×#538	C₂²	semidirect
59. C₂₃×#538	C₂²	semidirect
60. C₂₃×#538	C₂²	semidirect
61. C₂₃×#537	C₂²	semidirect
62. C₂₃×#537	C₂²	semidirect
63. C₂₃×#537	C₂²	semidirect
64. C₂₃×#535	C₂²	semidirect
65. C₂₃×#535	C₂²	semidirect
66. C₂₃×#535	C₂²	semidirect
67. C₂₃×#534	C₂²	semidirect
68. C₂₃×#534	C₂²	semidirect
69. C₂₃×#534	C₂²	semidirect
70. C₂₃×#534	C₂²	semidirect
71. C₂₃×#534	C₂²	semidirect
72. C₂₃×#532	C₂²	semidirect
73. C₂₃×#529	C₂²	semidirect
74. C₂₃×#525	C₂²	semidirect
75. C₂₃×#525	C₂²	semidirect
76. C₂₃×#525	C₂²	semidirect
77. C₂₃×#525	C₂²	semidirect
78. C₂₃×#525	C₂²	semidirect
79. C₂₃×#525	C₂²	semidirect
80. C₂₃×#525	C₂²	semidirect
81. C₂₃×#525	C₂²	semidirect
82. C₂₃×#525	C₂²	semidirect
83. C₂₃×#525	C₂²	semidirect
84. C₂×C₂₃×#123	C₂²	semidirect
85. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₂₃×#121	C₂²	semidirect
88. C₂×C₂₃×#121	C₂²	semidirect
89. C₂×C₂₃×#121	C₂²	semidirect
90. C₂×C₂₃×#121	C₂²	semidirect
91. C₂×C₂₃×#121	C₂²	semidirect
92. C₂×C₂₃×#121	C₂²	semidirect
93. C₂×C₂₃×#121	C₂²	semidirect
94. C₂×C₂₃×#121	C₂²	semidirect
95. C₂×C₂₃×#121	C₂²	semidirect
96. C₂×C₂₃×#120	C₂²	semidirect
97. C₂×C₂₃×#120	C₂²	semidirect
98. C₂₃×#520	C₂²	semidirect
99. C₂₃×#518	C₂²	semidirect
100. C₂₃×#518	C₂²	semidirect
101. C₂₃×#518	C₂²	semidirect
102. C₂×C₄×D₄×C₂₃	C₂²	semidirect
103. C₂×C₄×D₄×C₂₃	C₂²	semidirect
104. C₂×C₂₃×#117	C₂²	semidirect
105. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
106. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
115. C₂×#41×C₂₃	C₂³	semidirect
116. C₂×#41×C₂₃	C₂³	semidirect
117. C₂×#41×C₂₃	C₂³	semidirect
118. C₂×#41×C₂₃	C₂³	semidirect
119. C₂²×Q₈×C₂₃	C₂³	semidirect
136. C₂²×D₄×C₂₃	C₂³	semidirect
137. C₂²×D₄×C₂₃	C₂³	semidirect
138. C₂²×D₄×C₂₃	C₂³	semidirect
149. C₂³×C₄×C₂₃	C₂³	semidirect
150. C₂₃×C₄⋊Q₈	C₂³	semidirect
151. C₂₃×#127	C₂³	semidirect
152. C₂₃×#127	C₂³	semidirect
153. C₂₃×#126	C₂³	semidirect
154. C₂₃×#126	C₂³	semidirect
155. C₂₃×#126	C₂³	semidirect
156. C₂₃×#125	C₂³	semidirect
157. C₂₃×#125	C₂³	semidirect
158. C₂₃×#124	C₂³	semidirect
159. C₂₃×#124	C₂³	semidirect
160. C₂₃×#124	C₂³	semidirect
161. C₂₃×#124	C₂³	semidirect
165. C₂₃×#123	C₂³	semidirect
166. C₂₃×#123	C₂³	semidirect
167. C₂₃×#123	C₂³	semidirect
168. C₂₃×#123	C₂³	semidirect
169. C₂₃×#123	C₂³	semidirect
170. C₂₃×#123	C₂³	semidirect
171. C₂₃×#123	C₂³	semidirect
172. C₂₃×#123	C₂³	semidirect
173. C₂₃×#123	C₂³	semidirect
180. C₂₃×C₂²⋊Q₈	C₂³	semidirect
181. C₂₃×C₂²⋊Q₈	C₂³	semidirect
182. C₂₃×C₂²⋊Q₈	C₂³	semidirect
183. C₂₃×C₂²⋊Q₈	C₂³	semidirect
184. C₂₃×C₂²⋊Q₈	C₂³	semidirect
185. C₂₃×C₂²⋊Q₈	C₂³	semidirect
186. C₂₃×C₂²⋊Q₈	C₂³	semidirect
187. C₂₃×C₂²⋊Q₈	C₂³	semidirect
202. C₂₃×#121	C₂³	semidirect
203. C₂₃×#121	C₂³	semidirect
204. C₂₃×#121	C₂³	semidirect
205. C₂₃×#121	C₂³	semidirect
206. C₂₃×#121	C₂³	semidirect
207. C₂₃×#121	C₂³	semidirect
208. C₂₃×#121	C₂³	semidirect
209. C₂₃×#121	C₂³	semidirect
210. C₂₃×#121	C₂³	semidirect
211. C₂₃×#121	C₂³	semidirect
212. C₂₃×#121	C₂³	semidirect
213. C₂₃×#121	C₂³	semidirect
214. C₂₃×#121	C₂³	semidirect
215. C₂₃×#121	C₂³	semidirect
216. C₂₃×#121	C₂³	semidirect
217. C₂₃×#121	C₂³	semidirect
218. C₂₃×#121	C₂³	semidirect
226. C₂₃×#120	C₂³	semidirect
227. C₂₃×#120	C₂³	semidirect
228. C₂₃×#120	C₂³	semidirect
229. C₂₃×#120	C₂³	semidirect
230. C₄×Q₈×C₂₃	C₂³	semidirect
237. C₄×D₄×C₂₃	C₂³	semidirect
238. C₄×D₄×C₂₃	C₂³	semidirect
239. C₄×D₄×C₂₃	C₂³	semidirect
240. C₄×D₄×C₂₃	C₂³	semidirect
241. C₄×D₄×C₂₃	C₂³	semidirect
242. C₄×D₄×C₂₃	C₂³	semidirect
243. C₄×D₄×C₂₃	C₂³	semidirect
244. C₄×D₄×C₂₃	C₂³	semidirect
245. C₄×D₄×C₂₃	C₂³	semidirect
246. C₄×D₄×C₂₃	C₂³	semidirect
247. C₄×D₄×C₂₃	C₂³	semidirect
251. C₂₃×#117	C₂³	semidirect
252. C₂₃×#117	C₂³	semidirect
253. C₂₃×#117	C₂³	semidirect
254. C₂₃×#117	C₂³	semidirect
259. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
260. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
261. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
262. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
263. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
274. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
275. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
276. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
277. C₂×C₄²×C₂₃	C₂³	semidirect
410. #62818	C₂₃	direct (N × H)
442. C₂³×C₂₃	H(5,𝔽₂)	semidirect
496. C₂×C₄×C₂₃	H(5,𝔽₂)	semidirect
505. #3542	C₂×C₂₃	semidirect
506. #3537	C₂×C₂₃	semidirect
507. #3536	C₂×C₂₃	semidirect
508. #3534	C₂×C₂₃	semidirect
509. #3519	C₂×C₂₃	semidirect
510. #3505	C₂×C₂₃	semidirect
511. #3496	C₂×C₂₃	semidirect
512. #3494	C₂×C₂₃	semidirect
513. #3492	C₂×C₂₃	semidirect
514. #3490	C₂×C₂₃	semidirect
515. #3488	C₂×C₂₃	semidirect
516. #3484	C₂×C₂₃	semidirect
517. #3484	C₂×C₂₃	semidirect
518. C₂×#525	C₂×C₂₃	semidirect
519. C₂²×#121	C₂×C₂₃	semidirect
560. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
561. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
562. C₂²×#41	C₂²×C₂₃	semidirect
563. C₂³×D₄	C₂²×C₂₃	semidirect
564. C₂³×D₄	C₂²×C₂₃	semidirect
565. C₂⁴×C₄	C₂²×C₂₃	semidirect
566. #562	C₂²×C₂₃	semidirect
567. #560	C₂²×C₂₃	semidirect
568. #555	C₂²×C₂₃	semidirect
569. #554	C₂²×C₂₃	semidirect
570. #553	C₂²×C₂₃	semidirect
571. #553	C₂²×C₂₃	semidirect
572. #553	C₂²×C₂₃	semidirect
573. #553	C₂²×C₂₃	semidirect
574. #552	C₂²×C₂₃	semidirect
575. #551	C₂²×C₂₃	semidirect
576. #551	C₂²×C₂₃	semidirect
577. #550	C₂²×C₂₃	semidirect
578. #548	C₂²×C₂₃	semidirect
579. #547	C₂²×C₂₃	semidirect
580. #547	C₂²×C₂₃	semidirect
581. #546	C₂²×C₂₃	semidirect
582. #546	C₂²×C₂₃	semidirect
583. #546	C₂²×C₂₃	semidirect
584. #546	C₂²×C₂₃	semidirect
585. #546	C₂²×C₂₃	semidirect
586. #546	C₂²×C₂₃	semidirect
587. #546	C₂²×C₂₃	semidirect
588. #546	C₂²×C₂₃	semidirect
589. D₄²	C₂²×C₂₃	semidirect
590. D₄²	C₂²×C₂₃	semidirect
591. D₄²	C₂²×C₂₃	semidirect
592. D₄²	C₂²×C₂₃	semidirect
593. D₄²	C₂²×C₂₃	semidirect
594. #544	C₂²×C₂₃	semidirect
595. #543	C₂²×C₂₃	semidirect
596. #542	C₂²×C₂₃	semidirect
597. #540	C₂²×C₂₃	semidirect
598. #540	C₂²×C₂₃	semidirect
599. #539	C₂²×C₂₃	semidirect
600. #539	C₂²×C₂₃	semidirect
601. #538	C₂²×C₂₃	semidirect
602. #538	C₂²×C₂₃	semidirect
603. #538	C₂²×C₂₃	semidirect
604. #538	C₂²×C₂₃	semidirect
605. #537	C₂²×C₂₃	semidirect
606. #537	C₂²×C₂₃	semidirect
607. #537	C₂²×C₂₃	semidirect
608. #535	C₂²×C₂₃	semidirect
609. #535	C₂²×C₂₃	semidirect
610. #535	C₂²×C₂₃	semidirect
611. #534	C₂²×C₂₃	semidirect
612. #534	C₂²×C₂₃	semidirect
613. #534	C₂²×C₂₃	semidirect
614. #534	C₂²×C₂₃	semidirect
615. #534	C₂²×C₂₃	semidirect
616. #532	C₂²×C₂₃	semidirect
617. #529	C₂²×C₂₃	semidirect
618. #525	C₂²×C₂₃	semidirect
619. #525	C₂²×C₂₃	semidirect
620. #525	C₂²×C₂₃	semidirect
621. #525	C₂²×C₂₃	semidirect
622. #525	C₂²×C₂₃	semidirect
623. #525	C₂²×C₂₃	semidirect
624. #525	C₂²×C₂₃	semidirect
625. #525	C₂²×C₂₃	semidirect
626. #525	C₂²×C₂₃	semidirect
627. #525	C₂²×C₂₃	semidirect
628. C₂×#123	C₂²×C₂₃	semidirect
629. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
630. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
631. C₂×#121	C₂²×C₂₃	semidirect
632. C₂×#121	C₂²×C₂₃	semidirect
633. C₂×#121	C₂²×C₂₃	semidirect
634. C₂×#121	C₂²×C₂₃	semidirect
635. C₂×#121	C₂²×C₂₃	semidirect
636. C₂×#121	C₂²×C₂₃	semidirect
637. C₂×#121	C₂²×C₂₃	semidirect
638. C₂×#121	C₂²×C₂₃	semidirect
639. C₂×#121	C₂²×C₂₃	semidirect
640. C₂×#120	C₂²×C₂₃	semidirect
641. C₂×#120	C₂²×C₂₃	semidirect
642. #520	C₂²×C₂₃	semidirect
643. #518	C₂²×C₂₃	semidirect
644. #518	C₂²×C₂₃	semidirect
645. #518	C₂²×C₂₃	semidirect
646. C₂×C₄×D₄	C₂²×C₂₃	semidirect
647. C₂×C₄×D₄	C₂²×C₂₃	semidirect
648. C₂×#117	C₂²×C₂₃	semidirect
649. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
650. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
669. C₂×#41	C₂³×C₂₃	semidirect
670. C₂×#41	C₂³×C₂₃	semidirect
671. C₂×#41	C₂³×C₂₃	semidirect
672. C₂×#41	C₂³×C₂₃	semidirect
673. C₂²×Q₈	C₂³×C₂₃	semidirect
690. C₂²×D₄	C₂³×C₂₃	semidirect
691. C₂²×D₄	C₂³×C₂₃	semidirect
692. C₂²×D₄	C₂³×C₂₃	semidirect
703. C₂³×C₄	C₂³×C₂₃	semidirect
704. C₄⋊Q₈	C₂³×C₂₃	semidirect
705. #127	C₂³×C₂₃	semidirect
706. #127	C₂³×C₂₃	semidirect
707. #126	C₂³×C₂₃	semidirect
708. #126	C₂³×C₂₃	semidirect
709. #126	C₂³×C₂₃	semidirect
710. #125	C₂³×C₂₃	semidirect
711. #125	C₂³×C₂₃	semidirect
712. #124	C₂³×C₂₃	semidirect
713. #124	C₂³×C₂₃	semidirect
714. #124	C₂³×C₂₃	semidirect
715. #124	C₂³×C₂₃	semidirect
719. #123	C₂³×C₂₃	semidirect
720. #123	C₂³×C₂₃	semidirect
721. #123	C₂³×C₂₃	semidirect
722. #123	C₂³×C₂₃	semidirect
723. #123	C₂³×C₂₃	semidirect
724. #123	C₂³×C₂₃	semidirect
725. #123	C₂³×C₂₃	semidirect
726. #123	C₂³×C₂₃	semidirect
727. #123	C₂³×C₂₃	semidirect
734. C₂²⋊Q₈	C₂³×C₂₃	semidirect
735. C₂²⋊Q₈	C₂³×C₂₃	semidirect
736. C₂²⋊Q₈	C₂³×C₂₃	semidirect
737. C₂²⋊Q₈	C₂³×C₂₃	semidirect
738. C₂²⋊Q₈	C₂³×C₂₃	semidirect
739. C₂²⋊Q₈	C₂³×C₂₃	semidirect
740. C₂²⋊Q₈	C₂³×C₂₃	semidirect
741. C₂²⋊Q₈	C₂³×C₂₃	semidirect
756. #121	C₂³×C₂₃	semidirect
757. #121	C₂³×C₂₃	semidirect
758. #121	C₂³×C₂₃	semidirect
759. #121	C₂³×C₂₃	semidirect
760. #121	C₂³×C₂₃	semidirect
761. #121	C₂³×C₂₃	semidirect
762. #121	C₂³×C₂₃	semidirect
763. #121	C₂³×C₂₃	semidirect
764. #121	C₂³×C₂₃	semidirect
765. #121	C₂³×C₂₃	semidirect
766. #121	C₂³×C₂₃	semidirect
767. #121	C₂³×C₂₃	semidirect
768. #121	C₂³×C₂₃	semidirect
769. #121	C₂³×C₂₃	semidirect
770. #121	C₂³×C₂₃	semidirect
771. #121	C₂³×C₂₃	semidirect
772. #121	C₂³×C₂₃	semidirect
780. #120	C₂³×C₂₃	semidirect
781. #120	C₂³×C₂₃	semidirect
782. #120	C₂³×C₂₃	semidirect
783. #120	C₂³×C₂₃	semidirect
784. C₄×Q₈	C₂³×C₂₃	semidirect
791. C₄×D₄	C₂³×C₂₃	semidirect
792. C₄×D₄	C₂³×C₂₃	semidirect
793. C₄×D₄	C₂³×C₂₃	semidirect
794. C₄×D₄	C₂³×C₂₃	semidirect
795. C₄×D₄	C₂³×C₂₃	semidirect
796. C₄×D₄	C₂³×C₂₃	semidirect
797. C₄×D₄	C₂³×C₂₃	semidirect
798. C₄×D₄	C₂³×C₂₃	semidirect
799. C₄×D₄	C₂³×C₂₃	semidirect
800. C₄×D₄	C₂³×C₂₃	semidirect
801. C₄×D₄	C₂³×C₂₃	semidirect
805. #117	C₂³×C₂₃	semidirect
806. #117	C₂³×C₂₃	semidirect
807. #117	C₂³×C₂₃	semidirect
808. #117	C₂³×C₂₃	semidirect
813. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
814. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
815. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
816. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
817. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
828. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
829. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
830. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
831. C₂×C₄²	C₂³×C₂₃	semidirect
832. C₂₃	#62818	direct (N × H)
996. C₂³	C₂₃×H(5,𝔽₂)	semidirect
1050. C₂×C₄	C₂₃×H(5,𝔽₂)	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₃×#3542	2
C₂₃×#3537	2
C₂₃×#3536	2
C₂₃×#3534	2
C₂₃×#3519	2
C₂₃×#3505	2
C₂₃×#3496	2
C₂₃×#3494	2
C₂₃×#3492	2
C₂₃×#3490	2
C₂₃×#3488	2
C₂₃×#3484	2
C₂×C₂₃×#525	2
C₂²×C₂₃×#121	2
#62818	23

Subgroups — C23×#62818 #19210444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62818 #19210444