Subgroups — C₂₃×#62819 #19210445

Order 5888.

7242 conjugacy classes of subgroups.

The subgroup lattice has 1042 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3541	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3538	C₂	1	4	yes	maximal, complemented
3	C₂₃×#3536	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3535	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3520	C₂	1	8	yes	maximal, complemented
6	C₂₃×#3505	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3501	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3495	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3492	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3492	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3490	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3489	C₂	1	4	yes	maximal, complemented
13	C₂₃×#3486	C₂	1	2	yes	maximal, complemented
14	C₂×C₂₃×#525	C₂	1	2	yes	maximal, complemented
15	C₂²×C₂₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×2₋¹⁺⁴	C₂²	1	2	yes	complemented
17	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
18	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic, complemented
19	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#563	C₂²	1	16	yes	complemented
21	C₂₃×#562	C₂²	1	16	yes	complemented
22	C₂₃×#556	C₂²	1	8	yes	complemented
23	C₂₃×#554	C₂²	1	16	yes	complemented
24	C₂₃×#554	C₂²	1	8	yes	complemented
25	C₂₃×#554	C₂²	1	8	yes	complemented
26	C₂₃×#554	C₂²	1	16	yes	complemented
27	C₂₃×#553	C₂²	1	16	yes	complemented
28	C₂₃×#553	C₂²	1	8	yes	complemented
29	C₂₃×#552	C₂²	1	16	yes	complemented
30	C₂₃×#552	C₂²	1	8	yes	complemented
31	C₂₃×#552	C₂²	1	8	yes	complemented
32	C₂₃×#552	C₂²	1	8	yes	complemented
33	C₂₃×#551	C₂²	1	16	yes	complemented
34	C₂₃×#551	C₂²	1	16	yes	complemented
35	C₂₃×#551	C₂²	1	16	yes	complemented
36	D₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
37	D₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
38	D₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
39	C₂₃×#548	C₂²	1	8	yes	complemented
40	C₂₃×#548	C₂²	1	8	yes	complemented
41	C₂₃×#548	C₂²	1	8	yes	complemented
42	C₂₃×#547	C₂²	1	16	yes	complemented
43	C₂₃×#547	C₂²	1	8	yes	complemented
44	C₂₃×#547	C₂²	1	8	yes	complemented
45	C₂₃×#546	C₂²	1	16	yes	complemented
46	C₂₃×#546	C₂²	1	16	yes	complemented
47	C₂₃×#546	C₂²	1	8	yes	complemented
48	C₂₃×#544	C₂²	1	2	yes	complemented
49	C₂₃×#544	C₂²	1	4	yes	complemented
50	C₂₃×#544	C₂²	1	8	yes	complemented
51	C₂₃×#543	C₂²	1	4	yes	—
52	C₂₃×#543	C₂²	1	8	yes	complemented
53	C₂₃×#542	C₂²	1	8	yes	complemented
54	C₂₃×#542	C₂²	1	16	yes	complemented
55	C₂₃×#541	C₂²	1	8	yes	complemented
56	C₂₃×#539	C₂²	1	8	yes	complemented
57	C₂₃×#539	C₂²	1	8	yes	complemented
58	C₂₃×#539	C₂²	1	8	yes	complemented
59	C₂₃×#539	C₂²	1	8	yes	complemented
60	C₂₃×#539	C₂²	1	16	yes	complemented
61	C₂₃×#538	C₂²	1	8	yes	complemented
62	C₂₃×#538	C₂²	1	8	yes	complemented
63	C₂₃×#538	C₂²	1	8	yes	complemented
64	C₂₃×#537	C₂²	1	2	yes	complemented
65	C₂₃×#537	C₂²	1	4	yes	complemented
66	C₂₃×#537	C₂²	1	8	yes	complemented
67	C₂₃×#536	C₂²	1	4	yes	complemented
68	C₂₃×#536	C₂²	1	8	yes	complemented
69	C₂₃×#536	C₂²	1	8	yes	complemented
70	C₂₃×#534	C₂²	1	4	yes	—
71	C₂₃×#533	C₂²	1	8	yes	complemented
72	C₂₃×#529	C₂²	1	8	yes	complemented
73	C₂₃×#525	C₂²	1	4	yes	—
74	C₂₃×#525	C₂²	1	4	yes	—
75	C₂₃×#525	C₂²	1	4	yes	—
76	C₂₃×#525	C₂²	1	4	yes	—
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	8	yes	complemented
82	C₂₃×#525	C₂²	1	8	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	4	yes	—
86	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
87	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
88	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
89	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
90	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
91	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
92	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
93	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	8	yes	complemented
94	C₂×C₂₃×#121	C₂²	1	2	yes	—
95	C₂×C₂₃×#121	C₂²	1	2	yes	complemented
96	C₂×C₂₃×#120	C₂²	1	4	yes	—
97	C₂₃×#520	C₂²	1	4	yes	complemented
98	C₂₃×#520	C₂²	1	8	yes	complemented
99	C₂₃×#519	C₂²	1	2	yes	complemented
100	C₂₃×#518	C₂²	1	8	yes	—
101	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	—
102	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
103	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
104	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
105	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
106	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	—
107	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
108	C₂₃×2₋¹⁺⁴	—	4	8	no	—
109	C₂×#41×C₂₃	—	4	8	no	—
110	C₂×#41×C₂₃	C₂³	1	4	yes	—
111	C₂×#41×C₂₃	C₂³	1	4	yes	—
112	C₂×#41×C₂₃	C₂³	1	4	yes	—
113	C₂×#41×C₂₃	C₂³	1	8	yes	—
114	C₂×#41×C₂₃	C₂³	1	8	yes	—
115	C₂×#41×C₂₃	C₂³	1	4	yes	—
116	C₂×#41×C₂₃	C₂³	1	8	yes	complemented
117	C₂²×Q₈×C₂₃	—	4	4	no	—
118	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
119	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
120	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
121	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
122	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
123	C₂²×Q₈×C₂₃	C₂³	1	8	yes	complemented
124	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
126	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
127	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
128	C₂³×C₄×C₂₃	—	4	4	no	—
129	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
130	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
133	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
134	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
135	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
136	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
137	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
138	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
139	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
140	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
141	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
142	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
143	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
144	C₂₃×#126	C₂³	1	16	yes	—
145	C₂₃×#126	C₂³	1	16	yes	—
146	C₂₃×#126	C₂³	1	16	yes	complemented
147	C₂₃×#126	C₂³	1	16	yes	complemented
148	C₂₃×#126	C₂³	1	16	yes	complemented
149	C₂₃×#125	C₂³	1	8	yes	complemented
150	C₂₃×#125	C₂³	1	16	yes	complemented
151	C₂₃×#125	C₂³	1	16	yes	complemented
152	C₂₃×#125	C₂³	1	16	yes	complemented
153	C₂₃×#125	C₂³	1	16	yes	complemented
154	C₂₃×#124	C₂³	1	16	yes	—
155	C₂₃×#124	C₂³	1	16	yes	—
156	C₂₃×#124	C₂³	1	8	yes	complemented
157	C₂₃×#124	C₂³	1	16	yes	complemented
158	C₂₃×#123	C₂³	1	8	yes	—
159	C₂₃×#123	C₂³	1	16	yes	—
160	C₂₃×#123	C₂³	1	16	yes	—
161	C₂₃×#123	C₂³	1	16	yes	—
162	C₂₃×#123	C₂³	1	16	yes	—
163	C₂₃×#123	C₂³	1	16	yes	—
164	C₂₃×#123	C₂³	1	8	yes	—
165	C₂₃×#123	C₂³	1	8	yes	—
166	C₂₃×#123	C₂³	1	8	yes	—
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×C₂²⋊Q₈	C₂³	1	8	yes	—
171	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
172	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
173	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
174	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
175	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
176	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
177	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
179	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
180	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
181	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
182	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
183	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
184	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
185	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
186	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
187	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
188	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
189	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
190	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
191	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
192	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
193	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
194	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
195	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
196	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
197	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
198	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
199	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
200	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
201	C₂₃×#121	C₂³	1	4	yes	—
202	C₂₃×#121	C₂³	1	8	yes	—
203	C₂₃×#121	C₂³	1	16	yes	—
204	C₂₃×#121	C₂³	1	4	yes	—
205	C₂₃×#121	C₂³	1	8	yes	—
206	C₂₃×#121	C₂³	1	8	yes	—
207	C₂₃×#121	C₂³	1	16	yes	—
208	C₂₃×#121	C₂³	1	4	yes	—
209	C₂₃×#121	C₂³	1	8	yes	—
210	C₂₃×#121	C₂³	1	4	yes	—
211	C₂₃×#121	C₂³	1	4	yes	—
212	C₂₃×#121	C₂³	1	4	yes	—
213	C₂₃×#121	C₂³	1	4	yes	—
214	C₂₃×#121	C₂³	1	4	yes	—
215	C₂₃×#121	C₂³	1	8	yes	complemented
216	C₂₃×#121	C₂³	1	16	yes	complemented
217	C₂₃×#120	C₂³	1	8	yes	—
218	C₂₃×#120	C₂³	1	8	yes	—
219	C₂₃×#120	C₂³	1	16	yes	—
220	C₂₃×#120	C₂³	1	8	yes	—
221	C₂₃×#120	C₂³	1	8	yes	—
222	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
223	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
224	C₄×Q₈×C₂₃	C₂³	1	8	yes	complemented
225	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
226	C₄×D₄×C₂₃	C₂³	1	8	yes	—
227	C₄×D₄×C₂₃	C₂³	1	8	yes	—
228	C₄×D₄×C₂₃	C₂³	1	16	yes	—
229	C₄×D₄×C₂₃	C₂³	1	16	yes	—
230	C₄×D₄×C₂₃	C₂³	1	8	yes	—
231	C₄×D₄×C₂₃	C₂³	1	16	yes	—
232	C₄×D₄×C₂₃	C₂³	1	16	yes	—
233	C₄×D₄×C₂₃	C₂³	1	8	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	16	yes	—
238	C₄×D₄×C₂₃	C₂³	1	8	yes	—
239	C₄×D₄×C₂₃	C₂³	1	8	yes	—
240	C₄×D₄×C₂₃	C₂³	1	8	yes	complemented
241	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
242	C₂₃×#117	C₂³	1	16	yes	—
243	C₂₃×#117	C₂³	1	8	yes	—
244	C₂₃×#117	C₂³	1	8	yes	—
245	C₂₃×#117	C₂³	1	4	yes	—
246	C₂₃×#117	C₂³	1	4	yes	—
247	C₂₃×#117	C₂³	1	4	yes	—
248	C₂₃×#117	C₂³	1	4	yes	—
249	C₂₃×#117	C₂³	1	16	yes	complemented
250	C₂₃×#117	C₂³	1	8	yes	complemented
251	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
252	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
253	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
254	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
255	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
256	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
258	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
259	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
260	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
261	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
263	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	complemented
264	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
265	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
266	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
267	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
268	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
269	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
270	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	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	4	yes	—
274	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
275	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
276	C₂⁴×C₂₃	—	2	4	no	—
277	C₂⁴×C₂₃	—	4	2	no	—
278	C₂⁴×C₂₃	—	4	2	no	—
279	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
280	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
281	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
282	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
283	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
284	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
285	#41×C₂₃	—	2	16	no	—
286	#41×C₂₃	—	4	8	no	—
287	#41×C₂₃	—	4	8	no	—
288	#41×C₂₃	—	4	16	no	—
289	#41×C₂₃	—	4	16	no	—
290	#41×C₂₃	—	4	8	no	—
291	#41×C₂₃	—	4	16	no	—
292	C₂×Q₈×C₂₃	—	2	8	no	—
293	C₂×Q₈×C₂₃	—	4	4	no	—
294	C₂×Q₈×C₂₃	—	4	8	no	—
295	C₂×Q₈×C₂₃	—	4	8	no	—
296	C₂×Q₈×C₂₃	—	4	4	no	—
297	C₂×Q₈×C₂₃	—	4	16	no	—
298	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
299	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
300	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
301	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
302	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
303	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
304	C₂×D₄×C₂₃	—	2	16	no	—
305	C₂×D₄×C₂₃	—	4	4	no	—
306	C₂×D₄×C₂₃	—	4	8	no	—
307	C₂×D₄×C₂₃	—	4	8	no	—
308	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
309	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
310	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
311	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
312	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
313	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
314	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
315	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
316	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
317	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
318	C₂²×C₄×C₂₃	—	2	4	no	—
319	C₂²×C₄×C₂₃	—	2	8	no	—
320	C₂²×C₄×C₂₃	—	4	4	no	—
321	C₂²×C₄×C₂₃	—	4	4	no	—
322	C₂²×C₄×C₂₃	—	4	4	no	—
323	C₂²×C₄×C₂₃	—	4	4	no	—
324	C₂²×C₄×C₂₃	—	4	8	no	—
325	C₂²×C₄×C₂₃	—	4	4	no	—
326	C₂²×C₄×C₂₃	—	4	2	no	—
327	C₂²×C₄×C₂₃	—	4	4	no	—
328	C₂²×C₄×C₂₃	—	4	4	no	—
329	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
330	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
331	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
332	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
333	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
334	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
335	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
336	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
337	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
339	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
340	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
341	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
342	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
343	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
344	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
345	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
346	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
347	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
348	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
349	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
350	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
351	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
353	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
354	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
355	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
356	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
357	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
358	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
359	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
360	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
361	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
362	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
363	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
364	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
365	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
366	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
367	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
368	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
369	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
370	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
371	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
372	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
373	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
374	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
375	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
376	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
377	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
378	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
379	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
380	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
381	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
382	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
383	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
384	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
385	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
386	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
387	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
388	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
389	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
390	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
391	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
392	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
393	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
394	C₄²×C₂₃	C₂⁴	1	8	yes	—
395	C₄²×C₂₃	C₂⁴	1	8	yes	—
396	C₄²×C₂₃	C₂⁴	1	16	yes	—
397	C₄²×C₂₃	C₂⁴	1	16	yes	—
398	#62819	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
399	C₂³×C₂₃	—	2	2	no	—
400	C₂³×C₂₃	—	2	2	no	—
401	C₂³×C₂₃	—	2	2	no	—
402	C₂³×C₂₃	—	2	4	no	—
403	C₂³×C₂₃	—	2	4	no	—
404	C₂³×C₂₃	—	2	4	no	—
405	C₂³×C₂₃	—	2	2	no	—
406	C₂³×C₂₃	—	2	4	no	—
407	C₂³×C₂₃	—	2	8	no	—
408	C₂³×C₂₃	—	4	1	no	—
409	C₂³×C₂₃	—	4	2	no	—
410	C₂³×C₂₃	—	4	1	no	—
411	C₂³×C₂₃	—	4	1	no	—
412	C₂³×C₂₃	—	4	2	no	—
413	C₂³×C₂₃	—	4	1	no	—
414	C₂³×C₂₃	—	4	4	no	—
415	C₂³×C₂₃	—	4	4	no	—
416	C₂³×C₂₃	—	4	16	no	—
417	C₂³×C₂₃	2₋¹⁺⁴	1	4	yes	complemented
418	C₂³×C₂₃	C₂⁵	1	2	yes	—
419	C₂³×C₂₃	C₂⁵	1	8	yes	—
420	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
421	C₂³×C₂₃	C₂⁵	1	2	yes	—
422	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
423	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
424	Q₈×C₂₃	—	2	16	no	—
425	Q₈×C₂₃	—	2	8	no	—
426	Q₈×C₂₃	—	4	8	no	—
427	Q₈×C₂₃	—	4	8	no	—
428	Q₈×C₂₃	—	4	4	no	—
429	Q₈×C₂₃	—	4	8	no	—
430	D₄×C₂₃	—	2	16	no	—
431	D₄×C₂₃	—	2	16	no	—
432	D₄×C₂₃	—	2	16	no	—
433	D₄×C₂₃	—	2	16	no	—
434	D₄×C₂₃	—	2	8	no	—
435	D₄×C₂₃	—	4	8	no	—
436	D₄×C₂₃	—	4	4	no	—
437	D₄×C₂₃	—	4	8	no	—
438	D₄×C₂₃	—	4	8	no	—
439	D₄×C₂₃	—	4	8	no	—
440	C₂×C₄×C₂₃	—	2	2	no	—
441	C₂×C₄×C₂₃	—	2	4	no	—
442	C₂×C₄×C₂₃	—	2	8	no	—
443	C₂×C₄×C₂₃	—	2	8	no	—
444	C₂×C₄×C₂₃	—	2	8	no	—
445	C₂×C₄×C₂₃	—	2	4	no	—
446	C₂×C₄×C₂₃	—	2	4	no	—
447	C₂×C₄×C₂₃	—	2	4	no	—
448	C₂×C₄×C₂₃	—	2	4	no	—
449	C₂×C₄×C₂₃	—	2	4	no	—
450	C₂×C₄×C₂₃	—	2	4	no	—
451	C₂×C₄×C₂₃	—	2	16	no	—
452	C₂×C₄×C₂₃	—	4	1	no	—
453	C₂×C₄×C₂₃	—	4	2	no	—
454	C₂×C₄×C₂₃	—	4	2	no	—
455	C₂×C₄×C₂₃	—	4	2	no	—
456	C₂×C₄×C₂₃	—	4	1	no	—
457	C₂×C₄×C₂₃	—	4	2	no	—
458	C₂×C₄×C₂₃	—	4	2	no	—
459	C₂×C₄×C₂₃	—	4	4	no	—
460	C₂×C₄×C₂₃	—	4	4	no	—
461	C₂×C₄×C₂₃	—	4	4	no	—
462	C₂×C₄×C₂₃	—	4	4	no	—
463	C₂×C₄×C₂₃	—	4	4	no	—
464	C₂×C₄×C₂₃	—	4	8	no	—
465	C₂×C₄×C₂₃	—	4	4	no	—
466	C₂×C₄×C₂₃	—	4	16	no	—
467	C₂×C₄×C₂₃	—	4	16	no	—
468	C₂×C₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
469	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
470	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
471	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
472	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
473	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
474	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
475	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
476	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
477	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
478	#3541	C₂×C₂₃	1	8	yes	complemented
479	#3538	C₂×C₂₃	1	4	yes	complemented
480	#3536	C₂×C₂₃	1	4	yes	complemented
481	#3535	C₂×C₂₃	1	8	yes	complemented
482	#3520	C₂×C₂₃	1	8	yes	complemented
483	#3505	C₂×C₂₃	1	4	yes	complemented
484	#3501	C₂×C₂₃	1	4	yes	complemented
485	#3495	C₂×C₂₃	1	4	yes	complemented
486	#3492	C₂×C₂₃	1	2	yes	complemented
487	#3492	C₂×C₂₃	1	4	yes	complemented
488	#3490	C₂×C₂₃	1	4	yes	complemented
489	#3489	C₂×C₂₃	1	4	yes	complemented
490	#3486	C₂×C₂₃	1	2	yes	complemented
491	C₂×#525	C₂×C₂₃	1	2	yes	complemented
492	C₂²×C₂²⋊Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
493	C₂²×C₂₃	—	2	8	no	—
494	C₂²×C₂₃	—	2	1	no	—
495	C₂²×C₂₃	—	2	1	no	—
496	C₂²×C₂₃	—	2	2	no	—
497	C₂²×C₂₃	—	2	1	no	—
498	C₂²×C₂₃	—	2	1	no	—
499	C₂²×C₂₃	—	2	1	no	—
500	C₂²×C₂₃	—	2	1	no	—
501	C₂²×C₂₃	—	2	2	no	—
502	C₂²×C₂₃	—	2	2	no	—
503	C₂²×C₂₃	—	2	8	no	—
504	C₂²×C₂₃	—	2	8	no	—
505	C₂²×C₂₃	—	2	2	no	—
506	C₂²×C₂₃	—	2	8	no	—
507	C₂²×C₂₃	—	2	2	no	—
508	C₂²×C₂₃	—	4	4	no	—
509	C₂²×C₂₃	—	4	8	no	—
510	C₂²×C₂₃	—	4	8	no	—
511	C₂²×C₂₃	—	4	4	no	—
512	C₂²×C₂₃	—	8	8	no	—
513	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
514	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	4	yes	—
515	C₂²×C₂₃	C₂×2₋¹⁺⁴	1	2	yes	—
516	C₂²×C₂₃	#585	1	2	yes	—
517	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
518	C₄×C₂₃	—	2	2	no	—
519	C₄×C₂₃	—	2	2	no	—
520	C₄×C₂₃	—	2	2	no	—
521	C₄×C₂₃	—	2	8	no	—
522	C₄×C₂₃	—	2	8	no	—
523	C₄×C₂₃	—	2	8	no	—
524	C₄×C₂₃	—	2	8	no	—
525	C₄×C₂₃	—	2	8	no	—
526	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
527	C₂×2₋¹⁺⁴	C₂²×C₂₃	1	2	yes	complemented
528	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
529	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
530	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic
531	#563	C₂²×C₂₃	1	16	yes	complemented
532	#562	C₂²×C₂₃	1	16	yes	complemented
533	#556	C₂²×C₂₃	1	8	yes	complemented
534	#554	C₂²×C₂₃	1	8	yes	complemented
535	#554	C₂²×C₂₃	1	16	yes	complemented
536	#554	C₂²×C₂₃	1	8	yes	complemented
537	#554	C₂²×C₂₃	1	16	yes	complemented
538	#553	C₂²×C₂₃	1	8	yes	complemented
539	#553	C₂²×C₂₃	1	16	yes	complemented
540	#552	C₂²×C₂₃	1	16	yes	complemented
541	#552	C₂²×C₂₃	1	8	yes	complemented
542	#552	C₂²×C₂₃	1	8	yes	complemented
543	#552	C₂²×C₂₃	1	8	yes	complemented
544	#551	C₂²×C₂₃	1	16	yes	complemented
545	#551	C₂²×C₂₃	1	16	yes	complemented
546	#551	C₂²×C₂₃	1	16	yes	complemented
547	D₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
548	D₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
549	D₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
550	#548	C₂²×C₂₃	1	8	yes	complemented
551	#548	C₂²×C₂₃	1	8	yes	complemented
552	#548	C₂²×C₂₃	1	8	yes	complemented
553	#547	C₂²×C₂₃	1	16	yes	complemented
554	#547	C₂²×C₂₃	1	8	yes	complemented
555	#547	C₂²×C₂₃	1	8	yes	complemented
556	#546	C₂²×C₂₃	1	16	yes	complemented
557	#546	C₂²×C₂₃	1	16	yes	complemented
558	#546	C₂²×C₂₃	1	8	yes	complemented
559	#544	C₂²×C₂₃	1	2	yes	complemented
560	#544	C₂²×C₂₃	1	4	yes	complemented
561	#544	C₂²×C₂₃	1	8	yes	complemented
562	#543	C₂²×C₂₃	1	4	yes	—
563	#543	C₂²×C₂₃	1	8	yes	complemented
564	#542	C₂²×C₂₃	1	8	yes	complemented
565	#542	C₂²×C₂₃	1	16	yes	complemented
566	#541	C₂²×C₂₃	1	8	yes	complemented
567	#539	C₂²×C₂₃	1	8	yes	complemented
568	#539	C₂²×C₂₃	1	8	yes	complemented
569	#539	C₂²×C₂₃	1	8	yes	complemented
570	#539	C₂²×C₂₃	1	8	yes	complemented
571	#539	C₂²×C₂₃	1	16	yes	complemented
572	#538	C₂²×C₂₃	1	8	yes	complemented
573	#538	C₂²×C₂₃	1	8	yes	complemented
574	#538	C₂²×C₂₃	1	8	yes	complemented
575	#537	C₂²×C₂₃	1	2	yes	complemented
576	#537	C₂²×C₂₃	1	4	yes	complemented
577	#537	C₂²×C₂₃	1	8	yes	complemented
578	#536	C₂²×C₂₃	1	4	yes	complemented
579	#536	C₂²×C₂₃	1	8	yes	complemented
580	#536	C₂²×C₂₃	1	8	yes	complemented
581	#534	C₂²×C₂₃	1	4	yes	—
582	#533	C₂²×C₂₃	1	8	yes	complemented
583	#529	C₂²×C₂₃	1	8	yes	complemented
584	#525	C₂²×C₂₃	1	4	yes	—
585	#525	C₂²×C₂₃	1	4	yes	—
586	#525	C₂²×C₂₃	1	4	yes	—
587	#525	C₂²×C₂₃	1	4	yes	—
588	#525	C₂²×C₂₃	1	4	yes	complemented
589	#525	C₂²×C₂₃	1	4	yes	complemented
590	#525	C₂²×C₂₃	1	4	yes	complemented
591	#525	C₂²×C₂₃	1	4	yes	complemented
592	#525	C₂²×C₂₃	1	8	yes	complemented
593	#525	C₂²×C₂₃	1	8	yes	complemented
594	#525	C₂²×C₂₃	1	8	yes	complemented
595	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
596	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	—
597	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
598	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
599	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
600	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
601	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
602	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
603	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
604	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	8	yes	complemented
605	C₂×#121	C₂²×C₂₃	1	2	yes	—
606	C₂×#121	C₂²×C₂₃	1	2	yes	complemented
607	C₂×#120	C₂²×C₂₃	1	4	yes	—
608	#520	C₂²×C₂₃	1	4	yes	complemented
609	#520	C₂²×C₂₃	1	8	yes	complemented
610	#519	C₂²×C₂₃	1	2	yes	complemented
611	#518	C₂²×C₂₃	1	8	yes	—
612	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	—
613	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
614	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
615	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
616	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
617	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	—
618	C₂×C₂₃	—	2	2	no	—
619	C₂×C₂₃	—	2	2	no	—
620	C₂×C₂₃	—	2	2	no	—
621	C₂×C₂₃	—	2	4	no	—
622	C₂×C₂₃	—	4	2	no	—
623	C₂×C₂₃	—	4	8	no	—
624	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
625	C₂×C₂₃	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
626	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
627	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
628	2₋¹⁺⁴	—	4	8	no	—
629	C₂×#41	—	4	8	no	—
630	C₂×#41	C₂³×C₂₃	1	4	yes	—
631	C₂×#41	C₂³×C₂₃	1	8	yes	—
632	C₂×#41	C₂³×C₂₃	1	4	yes	—
633	C₂×#41	C₂³×C₂₃	1	4	yes	—
634	C₂×#41	C₂³×C₂₃	1	4	yes	—
635	C₂×#41	C₂³×C₂₃	1	8	yes	—
636	C₂×#41	C₂³×C₂₃	1	8	yes	complemented
637	C₂²×Q₈	—	4	4	no	—
638	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
639	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
640	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
641	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
642	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
643	C₂²×Q₈	C₂³×C₂₃	1	8	yes	complemented
644	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
645	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
646	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
647	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
648	C₂³×C₄	—	4	4	no	—
649	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
650	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
651	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
652	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
653	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
654	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
655	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
656	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
657	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
658	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
659	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
660	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
661	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
662	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
663	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
664	#126	C₂³×C₂₃	1	16	yes	—
665	#126	C₂³×C₂₃	1	16	yes	—
666	#126	C₂³×C₂₃	1	16	yes	complemented
667	#126	C₂³×C₂₃	1	16	yes	complemented
668	#126	C₂³×C₂₃	1	16	yes	complemented
669	#125	C₂³×C₂₃	1	8	yes	complemented
670	#125	C₂³×C₂₃	1	16	yes	complemented
671	#125	C₂³×C₂₃	1	16	yes	complemented
672	#125	C₂³×C₂₃	1	16	yes	complemented
673	#125	C₂³×C₂₃	1	16	yes	complemented
674	#124	C₂³×C₂₃	1	16	yes	—
675	#124	C₂³×C₂₃	1	16	yes	—
676	#124	C₂³×C₂₃	1	8	yes	complemented
677	#124	C₂³×C₂₃	1	16	yes	complemented
678	#123	C₂³×C₂₃	1	8	yes	—
679	#123	C₂³×C₂₃	1	8	yes	—
680	#123	C₂³×C₂₃	1	8	yes	—
681	#123	C₂³×C₂₃	1	8	yes	—
682	#123	C₂³×C₂₃	1	16	yes	—
683	#123	C₂³×C₂₃	1	16	yes	—
684	#123	C₂³×C₂₃	1	16	yes	—
685	#123	C₂³×C₂₃	1	16	yes	—
686	#123	C₂³×C₂₃	1	16	yes	—
687	#123	C₂³×C₂₃	1	16	yes	complemented
688	#123	C₂³×C₂₃	1	16	yes	complemented
689	#123	C₂³×C₂₃	1	16	yes	complemented
690	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
691	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
692	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
693	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
694	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
695	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
696	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
697	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
698	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
699	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
700	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
701	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
702	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
703	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
704	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
705	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
706	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
707	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
708	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
709	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
710	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
711	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
712	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
713	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
714	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
715	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
716	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
717	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
718	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
719	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
720	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
721	#121	C₂³×C₂₃	1	4	yes	—
722	#121	C₂³×C₂₃	1	4	yes	—
723	#121	C₂³×C₂₃	1	4	yes	—
724	#121	C₂³×C₂₃	1	4	yes	—
725	#121	C₂³×C₂₃	1	4	yes	—
726	#121	C₂³×C₂₃	1	4	yes	—
727	#121	C₂³×C₂₃	1	4	yes	—
728	#121	C₂³×C₂₃	1	4	yes	—
729	#121	C₂³×C₂₃	1	8	yes	—
730	#121	C₂³×C₂₃	1	8	yes	—
731	#121	C₂³×C₂₃	1	8	yes	—
732	#121	C₂³×C₂₃	1	8	yes	—
733	#121	C₂³×C₂₃	1	16	yes	—
734	#121	C₂³×C₂₃	1	16	yes	—
735	#121	C₂³×C₂₃	1	8	yes	complemented
736	#121	C₂³×C₂₃	1	16	yes	complemented
737	#120	C₂³×C₂₃	1	8	yes	—
738	#120	C₂³×C₂₃	1	8	yes	—
739	#120	C₂³×C₂₃	1	8	yes	—
740	#120	C₂³×C₂₃	1	8	yes	—
741	#120	C₂³×C₂₃	1	16	yes	—
742	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
743	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
744	C₄×Q₈	C₂³×C₂₃	1	8	yes	complemented
745	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
746	C₄×D₄	C₂³×C₂₃	1	8	yes	—
747	C₄×D₄	C₂³×C₂₃	1	8	yes	—
748	C₄×D₄	C₂³×C₂₃	1	8	yes	—
749	C₄×D₄	C₂³×C₂₃	1	8	yes	—
750	C₄×D₄	C₂³×C₂₃	1	8	yes	—
751	C₄×D₄	C₂³×C₂₃	1	8	yes	—
752	C₄×D₄	C₂³×C₂₃	1	8	yes	—
753	C₄×D₄	C₂³×C₂₃	1	8	yes	—
754	C₄×D₄	C₂³×C₂₃	1	16	yes	—
755	C₄×D₄	C₂³×C₂₃	1	16	yes	—
756	C₄×D₄	C₂³×C₂₃	1	16	yes	—
757	C₄×D₄	C₂³×C₂₃	1	16	yes	—
758	C₄×D₄	C₂³×C₂₃	1	16	yes	—
759	C₄×D₄	C₂³×C₂₃	1	16	yes	—
760	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
761	C₄×D₄	C₂³×C₂₃	1	8	yes	complemented
762	#117	C₂³×C₂₃	1	4	yes	—
763	#117	C₂³×C₂₃	1	4	yes	—
764	#117	C₂³×C₂₃	1	4	yes	—
765	#117	C₂³×C₂₃	1	4	yes	—
766	#117	C₂³×C₂₃	1	16	yes	—
767	#117	C₂³×C₂₃	1	8	yes	—
768	#117	C₂³×C₂₃	1	8	yes	—
769	#117	C₂³×C₂₃	1	8	yes	complemented
770	#117	C₂³×C₂₃	1	16	yes	complemented
771	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
772	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
773	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
774	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
775	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
776	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
777	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
778	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
779	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
780	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
781	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
782	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
783	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
784	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	complemented
785	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
786	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
787	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
788	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
789	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
790	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
791	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
792	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
793	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
794	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	—
795	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
796	C₂₃	#62819	1	1	yes	characteristic, direct product factor, Sylow
797	C₂⁴	—	2	4	no	—
798	C₂⁴	—	4	2	no	—
799	C₂⁴	—	4	2	no	—
800	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
801	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
802	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
803	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
804	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
805	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
806	#41	—	2	16	no	—
807	#41	—	4	8	no	—
808	#41	—	4	8	no	—
809	#41	—	4	16	no	—
810	#41	—	4	16	no	—
811	#41	—	4	8	no	—
812	#41	—	4	16	no	—
813	C₂×Q₈	—	2	8	no	—
814	C₂×Q₈	—	4	4	no	—
815	C₂×Q₈	—	4	8	no	—
816	C₂×Q₈	—	4	8	no	—
817	C₂×Q₈	—	4	4	no	—
818	C₂×Q₈	—	4	16	no	—
819	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
820	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
821	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
822	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
823	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
824	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
825	C₂×D₄	—	2	16	no	—
826	C₂×D₄	—	4	4	no	—
827	C₂×D₄	—	4	8	no	—
828	C₂×D₄	—	4	8	no	—
829	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
830	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
831	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
832	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
833	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
834	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
835	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
836	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
837	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
838	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
839	C₂²×C₄	—	2	4	no	—
840	C₂²×C₄	—	2	8	no	—
841	C₂²×C₄	—	4	4	no	—
842	C₂²×C₄	—	4	4	no	—
843	C₂²×C₄	—	4	4	no	—
844	C₂²×C₄	—	4	4	no	—
845	C₂²×C₄	—	4	8	no	—
846	C₂²×C₄	—	4	4	no	—
847	C₂²×C₄	—	4	2	no	—
848	C₂²×C₄	—	4	4	no	—
849	C₂²×C₄	—	4	4	no	—
850	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
851	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
852	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
853	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
854	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
855	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
856	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
857	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
858	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
859	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
860	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
861	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
862	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
863	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
864	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
865	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
866	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
867	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
868	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
869	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
870	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
871	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
872	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
873	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
874	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
876	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
877	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
879	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
880	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
881	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
882	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
883	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
884	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
885	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
886	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
887	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
888	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
889	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
890	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
891	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
892	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
893	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
894	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
895	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
896	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
897	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
898	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
899	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
900	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
901	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
902	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
903	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
905	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
907	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
908	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
909	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
910	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
911	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
912	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
913	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
914	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
915	C₄²	C₂⁴×C₂₃	1	8	yes	—
916	C₄²	C₂⁴×C₂₃	1	8	yes	—
917	C₄²	C₂⁴×C₂₃	1	16	yes	—
918	C₄²	C₂⁴×C₂₃	1	16	yes	—
919	C₂³	—	2	2	no	—
920	C₂³	—	2	2	no	—
921	C₂³	—	2	2	no	—
922	C₂³	—	2	4	no	—
923	C₂³	—	2	4	no	—
924	C₂³	—	2	4	no	—
925	C₂³	—	2	2	no	—
926	C₂³	—	2	4	no	—
927	C₂³	—	2	8	no	—
928	C₂³	—	4	1	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	1	no	—
931	C₂³	—	4	1	no	—
932	C₂³	—	4	2	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	4	no	—
935	C₂³	—	4	4	no	—
936	C₂³	—	4	16	no	—
937	C₂³	C₂₃×2₋¹⁺⁴	1	4	yes	complemented
938	C₂³	C₂⁵×C₂₃	1	2	yes	—
939	C₂³	C₂⁵×C₂₃	1	8	yes	—
940	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
941	C₂³	C₂⁵×C₂₃	1	2	yes	—
942	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
943	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
944	Q₈	—	2	16	no	—
945	Q₈	—	2	8	no	—
946	Q₈	—	4	8	no	—
947	Q₈	—	4	8	no	—
948	Q₈	—	4	4	no	—
949	Q₈	—	4	8	no	—
950	D₄	—	2	16	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	16	no	—
953	D₄	—	2	16	no	—
954	D₄	—	2	8	no	—
955	D₄	—	4	4	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	8	no	—
958	D₄	—	4	8	no	—
959	D₄	—	4	8	no	—
960	C₂×C₄	—	2	2	no	—
961	C₂×C₄	—	2	4	no	—
962	C₂×C₄	—	2	8	no	—
963	C₂×C₄	—	2	8	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	2	4	no	—
966	C₂×C₄	—	2	4	no	—
967	C₂×C₄	—	2	4	no	—
968	C₂×C₄	—	2	4	no	—
969	C₂×C₄	—	2	4	no	—
970	C₂×C₄	—	2	4	no	—
971	C₂×C₄	—	2	16	no	—
972	C₂×C₄	—	4	1	no	—
973	C₂×C₄	—	4	2	no	—
974	C₂×C₄	—	4	2	no	—
975	C₂×C₄	—	4	2	no	—
976	C₂×C₄	—	4	1	no	—
977	C₂×C₄	—	4	2	no	—
978	C₂×C₄	—	4	2	no	—
979	C₂×C₄	—	4	4	no	—
980	C₂×C₄	—	4	4	no	—
981	C₂×C₄	—	4	4	no	—
982	C₂×C₄	—	4	8	no	—
983	C₂×C₄	—	4	4	no	—
984	C₂×C₄	—	4	4	no	—
985	C₂×C₄	—	4	4	no	—
986	C₂×C₄	—	4	16	no	—
987	C₂×C₄	—	4	16	no	—
988	C₂×C₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
989	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
990	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
991	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
992	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
993	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
994	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
995	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
996	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
997	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
998	C₂²	—	2	8	no	—
999	C₂²	—	2	1	no	—
1000	C₂²	—	2	1	no	—
1001	C₂²	—	2	2	no	—
1002	C₂²	—	2	1	no	—
1003	C₂²	—	2	1	no	—
1004	C₂²	—	2	1	no	—
1005	C₂²	—	2	1	no	—
1006	C₂²	—	2	2	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	8	no	—
1009	C₂²	—	2	8	no	—
1010	C₂²	—	2	2	no	—
1011	C₂²	—	2	8	no	—
1012	C₂²	—	2	2	no	—
1013	C₂²	—	4	4	no	—
1014	C₂²	—	4	8	no	—
1015	C₂²	—	4	8	no	—
1016	C₂²	—	4	4	no	—
1017	C₂²	—	8	8	no	—
1018	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
1019	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	4	yes	—
1020	C₂²	C₂×C₂₃×2₋¹⁺⁴	1	2	yes	—
1021	C₂²	C₂₃×#585	1	2	yes	—
1022	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
1023	C₄	—	2	2	no	—
1024	C₄	—	2	2	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	8	no	—
1027	C₄	—	2	8	no	—
1028	C₄	—	2	8	no	—
1029	C₄	—	2	8	no	—
1030	C₄	—	2	8	no	—
1031	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
1032	C₂	—	2	2	no	—
1033	C₂	—	2	2	no	—
1034	C₂	—	2	2	no	—
1035	C₂	—	2	4	no	—
1036	C₂	—	4	2	no	—
1037	C₂	—	4	8	no	—
1038	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
1039	C₂	C₂²×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
1040	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×#3541	C₂	semidirect
2. C₂₃×#3538	C₂	semidirect
3. C₂₃×#3536	C₂	semidirect
4. C₂₃×#3535	C₂	semidirect
5. C₂₃×#3520	C₂	semidirect
6. C₂₃×#3505	C₂	semidirect
7. C₂₃×#3501	C₂	semidirect
8. C₂₃×#3495	C₂	semidirect
9. C₂₃×#3492	C₂	semidirect
10. C₂₃×#3492	C₂	semidirect
11. C₂₃×#3490	C₂	semidirect
12. C₂₃×#3489	C₂	semidirect
13. C₂₃×#3486	C₂	semidirect
14. C₂×C₂₃×#525	C₂	semidirect
15. C₂²×C₂₃×C₂²⋊Q₈	C₂	semidirect
16. C₂×C₂₃×2₋¹⁺⁴	C₂²	semidirect
17. C₂²×#41×C₂₃	C₂²	semidirect
18. C₂³×Q₈×C₂₃	C₂²	semidirect
20. C₂₃×#563	C₂²	semidirect
21. C₂₃×#562	C₂²	semidirect
22. C₂₃×#556	C₂²	semidirect
23. C₂₃×#554	C₂²	semidirect
24. C₂₃×#554	C₂²	semidirect
25. C₂₃×#554	C₂²	semidirect
26. C₂₃×#554	C₂²	semidirect
27. C₂₃×#553	C₂²	semidirect
28. C₂₃×#553	C₂²	semidirect
29. C₂₃×#552	C₂²	semidirect
30. C₂₃×#552	C₂²	semidirect
31. C₂₃×#552	C₂²	semidirect
32. C₂₃×#552	C₂²	semidirect
33. C₂₃×#551	C₂²	semidirect
34. C₂₃×#551	C₂²	semidirect
35. C₂₃×#551	C₂²	semidirect
36. D₄×Q₈×C₂₃	C₂²	semidirect
37. D₄×Q₈×C₂₃	C₂²	semidirect
38. D₄×Q₈×C₂₃	C₂²	semidirect
39. C₂₃×#548	C₂²	semidirect
40. C₂₃×#548	C₂²	semidirect
41. C₂₃×#548	C₂²	semidirect
42. C₂₃×#547	C₂²	semidirect
43. C₂₃×#547	C₂²	semidirect
44. C₂₃×#547	C₂²	semidirect
45. C₂₃×#546	C₂²	semidirect
46. C₂₃×#546	C₂²	semidirect
47. C₂₃×#546	C₂²	semidirect
48. C₂₃×#544	C₂²	semidirect
49. C₂₃×#544	C₂²	semidirect
50. C₂₃×#544	C₂²	semidirect
52. C₂₃×#543	C₂²	semidirect
53. C₂₃×#542	C₂²	semidirect
54. C₂₃×#542	C₂²	semidirect
55. C₂₃×#541	C₂²	semidirect
56. C₂₃×#539	C₂²	semidirect
57. C₂₃×#539	C₂²	semidirect
58. C₂₃×#539	C₂²	semidirect
59. C₂₃×#539	C₂²	semidirect
60. C₂₃×#539	C₂²	semidirect
61. C₂₃×#538	C₂²	semidirect
62. C₂₃×#538	C₂²	semidirect
63. C₂₃×#538	C₂²	semidirect
64. C₂₃×#537	C₂²	semidirect
65. C₂₃×#537	C₂²	semidirect
66. C₂₃×#537	C₂²	semidirect
67. C₂₃×#536	C₂²	semidirect
68. C₂₃×#536	C₂²	semidirect
69. C₂₃×#536	C₂²	semidirect
71. C₂₃×#533	C₂²	semidirect
72. C₂₃×#529	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
87. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
90. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
91. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
92. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
93. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
95. C₂×C₂₃×#121	C₂²	semidirect
97. C₂₃×#520	C₂²	semidirect
98. C₂₃×#520	C₂²	semidirect
99. C₂₃×#519	C₂²	semidirect
102. C₂×C₄×D₄×C₂₃	C₂²	semidirect
103. C₂×C₂₃×#117	C₂²	semidirect
104. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
105. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
116. C₂×#41×C₂₃	C₂³	semidirect
123. C₂²×Q₈×C₂₃	C₂³	semidirect
140. C₂₃×C₄⋊Q₈	C₂³	semidirect
141. C₂₃×C₄⋊Q₈	C₂³	semidirect
142. C₂₃×C₄⋊Q₈	C₂³	semidirect
143. C₂₃×C₄⋊Q₈	C₂³	semidirect
146. C₂₃×#126	C₂³	semidirect
147. C₂₃×#126	C₂³	semidirect
148. C₂₃×#126	C₂³	semidirect
149. C₂₃×#125	C₂³	semidirect
150. C₂₃×#125	C₂³	semidirect
151. C₂₃×#125	C₂³	semidirect
152. C₂₃×#125	C₂³	semidirect
153. C₂₃×#125	C₂³	semidirect
156. C₂₃×#124	C₂³	semidirect
157. C₂₃×#124	C₂³	semidirect
167. C₂₃×#123	C₂³	semidirect
168. C₂₃×#123	C₂³	semidirect
169. C₂₃×#123	C₂³	semidirect
192. C₂₃×C₂²⋊Q₈	C₂³	semidirect
193. C₂₃×C₂²⋊Q₈	C₂³	semidirect
194. C₂₃×C₂²⋊Q₈	C₂³	semidirect
195. C₂₃×C₂²⋊Q₈	C₂³	semidirect
196. C₂₃×C₂²⋊Q₈	C₂³	semidirect
197. C₂₃×C₂²⋊Q₈	C₂³	semidirect
198. C₂₃×C₂²⋊Q₈	C₂³	semidirect
199. C₂₃×C₂²⋊Q₈	C₂³	semidirect
200. C₂₃×C₂²⋊Q₈	C₂³	semidirect
215. C₂₃×#121	C₂³	semidirect
216. C₂₃×#121	C₂³	semidirect
222. C₄×Q₈×C₂₃	C₂³	semidirect
223. C₄×Q₈×C₂₃	C₂³	semidirect
224. C₄×Q₈×C₂₃	C₂³	semidirect
225. C₄×Q₈×C₂₃	C₂³	semidirect
240. C₄×D₄×C₂₃	C₂³	semidirect
241. C₄×D₄×C₂₃	C₂³	semidirect
249. C₂₃×#117	C₂³	semidirect
250. C₂₃×#117	C₂³	semidirect
263. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
264. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
398. #62819	C₂₃	direct (N × H)
417. C₂³×C₂₃	2₋¹⁺⁴	semidirect
478. #3541	C₂×C₂₃	semidirect
479. #3538	C₂×C₂₃	semidirect
480. #3536	C₂×C₂₃	semidirect
481. #3535	C₂×C₂₃	semidirect
482. #3520	C₂×C₂₃	semidirect
483. #3505	C₂×C₂₃	semidirect
484. #3501	C₂×C₂₃	semidirect
485. #3495	C₂×C₂₃	semidirect
486. #3492	C₂×C₂₃	semidirect
487. #3492	C₂×C₂₃	semidirect
488. #3490	C₂×C₂₃	semidirect
489. #3489	C₂×C₂₃	semidirect
490. #3486	C₂×C₂₃	semidirect
491. C₂×#525	C₂×C₂₃	semidirect
492. C₂²×C₂²⋊Q₈	C₂×C₂₃	semidirect
527. C₂×2₋¹⁺⁴	C₂²×C₂₃	semidirect
528. C₂²×#41	C₂²×C₂₃	semidirect
529. C₂³×Q₈	C₂²×C₂₃	semidirect
531. #563	C₂²×C₂₃	semidirect
532. #562	C₂²×C₂₃	semidirect
533. #556	C₂²×C₂₃	semidirect
534. #554	C₂²×C₂₃	semidirect
535. #554	C₂²×C₂₃	semidirect
536. #554	C₂²×C₂₃	semidirect
537. #554	C₂²×C₂₃	semidirect
538. #553	C₂²×C₂₃	semidirect
539. #553	C₂²×C₂₃	semidirect
540. #552	C₂²×C₂₃	semidirect
541. #552	C₂²×C₂₃	semidirect
542. #552	C₂²×C₂₃	semidirect
543. #552	C₂²×C₂₃	semidirect
544. #551	C₂²×C₂₃	semidirect
545. #551	C₂²×C₂₃	semidirect
546. #551	C₂²×C₂₃	semidirect
547. D₄×Q₈	C₂²×C₂₃	semidirect
548. D₄×Q₈	C₂²×C₂₃	semidirect
549. D₄×Q₈	C₂²×C₂₃	semidirect
550. #548	C₂²×C₂₃	semidirect
551. #548	C₂²×C₂₃	semidirect
552. #548	C₂²×C₂₃	semidirect
553. #547	C₂²×C₂₃	semidirect
554. #547	C₂²×C₂₃	semidirect
555. #547	C₂²×C₂₃	semidirect
556. #546	C₂²×C₂₃	semidirect
557. #546	C₂²×C₂₃	semidirect
558. #546	C₂²×C₂₃	semidirect
559. #544	C₂²×C₂₃	semidirect
560. #544	C₂²×C₂₃	semidirect
561. #544	C₂²×C₂₃	semidirect
563. #543	C₂²×C₂₃	semidirect
564. #542	C₂²×C₂₃	semidirect
565. #542	C₂²×C₂₃	semidirect
566. #541	C₂²×C₂₃	semidirect
567. #539	C₂²×C₂₃	semidirect
568. #539	C₂²×C₂₃	semidirect
569. #539	C₂²×C₂₃	semidirect
570. #539	C₂²×C₂₃	semidirect
571. #539	C₂²×C₂₃	semidirect
572. #538	C₂²×C₂₃	semidirect
573. #538	C₂²×C₂₃	semidirect
574. #538	C₂²×C₂₃	semidirect
575. #537	C₂²×C₂₃	semidirect
576. #537	C₂²×C₂₃	semidirect
577. #537	C₂²×C₂₃	semidirect
578. #536	C₂²×C₂₃	semidirect
579. #536	C₂²×C₂₃	semidirect
580. #536	C₂²×C₂₃	semidirect
582. #533	C₂²×C₂₃	semidirect
583. #529	C₂²×C₂₃	semidirect
588. #525	C₂²×C₂₃	semidirect
589. #525	C₂²×C₂₃	semidirect
590. #525	C₂²×C₂₃	semidirect
591. #525	C₂²×C₂₃	semidirect
592. #525	C₂²×C₂₃	semidirect
593. #525	C₂²×C₂₃	semidirect
594. #525	C₂²×C₂₃	semidirect
595. C₂×#123	C₂²×C₂₃	semidirect
598. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
599. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
600. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
601. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
602. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
603. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
604. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
606. C₂×#121	C₂²×C₂₃	semidirect
608. #520	C₂²×C₂₃	semidirect
609. #520	C₂²×C₂₃	semidirect
610. #519	C₂²×C₂₃	semidirect
613. C₂×C₄×D₄	C₂²×C₂₃	semidirect
614. C₂×#117	C₂²×C₂₃	semidirect
615. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
616. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
636. C₂×#41	C₂³×C₂₃	semidirect
643. C₂²×Q₈	C₂³×C₂₃	semidirect
660. C₄⋊Q₈	C₂³×C₂₃	semidirect
661. C₄⋊Q₈	C₂³×C₂₃	semidirect
662. C₄⋊Q₈	C₂³×C₂₃	semidirect
663. C₄⋊Q₈	C₂³×C₂₃	semidirect
666. #126	C₂³×C₂₃	semidirect
667. #126	C₂³×C₂₃	semidirect
668. #126	C₂³×C₂₃	semidirect
669. #125	C₂³×C₂₃	semidirect
670. #125	C₂³×C₂₃	semidirect
671. #125	C₂³×C₂₃	semidirect
672. #125	C₂³×C₂₃	semidirect
673. #125	C₂³×C₂₃	semidirect
676. #124	C₂³×C₂₃	semidirect
677. #124	C₂³×C₂₃	semidirect
687. #123	C₂³×C₂₃	semidirect
688. #123	C₂³×C₂₃	semidirect
689. #123	C₂³×C₂₃	semidirect
712. C₂²⋊Q₈	C₂³×C₂₃	semidirect
713. C₂²⋊Q₈	C₂³×C₂₃	semidirect
714. C₂²⋊Q₈	C₂³×C₂₃	semidirect
715. C₂²⋊Q₈	C₂³×C₂₃	semidirect
716. C₂²⋊Q₈	C₂³×C₂₃	semidirect
717. C₂²⋊Q₈	C₂³×C₂₃	semidirect
718. C₂²⋊Q₈	C₂³×C₂₃	semidirect
719. C₂²⋊Q₈	C₂³×C₂₃	semidirect
720. C₂²⋊Q₈	C₂³×C₂₃	semidirect
735. #121	C₂³×C₂₃	semidirect
736. #121	C₂³×C₂₃	semidirect
742. C₄×Q₈	C₂³×C₂₃	semidirect
743. C₄×Q₈	C₂³×C₂₃	semidirect
744. C₄×Q₈	C₂³×C₂₃	semidirect
745. C₄×Q₈	C₂³×C₂₃	semidirect
760. C₄×D₄	C₂³×C₂₃	semidirect
761. C₄×D₄	C₂³×C₂₃	semidirect
769. #117	C₂³×C₂₃	semidirect
770. #117	C₂³×C₂₃	semidirect
783. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
784. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
796. C₂₃	#62819	direct (N × H)
937. C₂³	C₂₃×2₋¹⁺⁴	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3541	2
C₂₃×#3538	2
C₂₃×#3536	2
C₂₃×#3535	2
C₂₃×#3520	2
C₂₃×#3505	2
C₂₃×#3501	2
C₂₃×#3495	2
C₂₃×#3492	2
C₂₃×#3490	2
C₂₃×#3489	2
C₂₃×#3486	2
C₂×C₂₃×#525	2
C₂²×C₂₃×C₂²⋊Q₈	2
#62819	23

Subgroups — C23×#62819 #19210445

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62819 #19210445