Subgroups — C₂₃×#62820 #19210446

Order 5888.

7382 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3535	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3534	C₂	1	8	yes	maximal, complemented
3	C₂₃×#3533	C₂	1	8	yes	maximal, complemented
4	C₂₃×#3513	C₂	1	16	yes	maximal, complemented
5	C₂₃×#3492	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3491	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3490	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3490	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3485	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3484	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#525	C₂	1	2	yes	maximal, complemented
12	C₂²×C₂₃×#123	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	complemented
14	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
15	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
17	C₂₃×#563	C₂²	1	8	yes	complemented
18	C₂₃×#562	C₂²	1	16	yes	complemented
19	C₂₃×#560	C₂²	1	8	yes	complemented
20	C₂₃×#559	C₂²	1	8	yes	complemented
21	C₂₃×#554	C₂²	1	16	yes	complemented
22	C₂₃×#553	C₂²	1	16	yes	complemented
23	C₂₃×#553	C₂²	1	16	yes	complemented
24	C₂₃×#552	C₂²	1	16	yes	complemented
25	C₂₃×#552	C₂²	1	16	yes	complemented
26	C₂₃×#551	C₂²	1	16	yes	complemented
27	C₂₃×#551	C₂²	1	16	yes	complemented
28	C₂₃×#551	C₂²	1	16	yes	complemented
29	C₂₃×#551	C₂²	1	16	yes	complemented
30	C₂₃×#551	C₂²	1	8	yes	complemented
31	C₂₃×#547	C₂²	1	16	yes	complemented
32	C₂₃×#547	C₂²	1	16	yes	complemented
33	C₂₃×#546	C₂²	1	16	yes	complemented
34	C₂₃×#546	C₂²	1	16	yes	complemented
35	C₂₃×#546	C₂²	1	16	yes	complemented
36	C₂₃×#546	C₂²	1	16	yes	complemented
37	C₂₃×#546	C₂²	1	16	yes	complemented
38	D₄²×C₂₃	C₂²	1	16	yes	complemented
39	C₂₃×#544	C₂²	1	4	yes	complemented
40	C₂₃×#543	C₂²	1	2	yes	complemented
41	C₂₃×#543	C₂²	1	4	yes	complemented
42	C₂₃×#542	C₂²	1	16	yes	complemented
43	C₂₃×#540	C₂²	1	16	yes	complemented
44	C₂₃×#539	C₂²	1	8	yes	complemented
45	C₂₃×#539	C₂²	1	8	yes	complemented
46	C₂₃×#539	C₂²	1	16	yes	complemented
47	C₂₃×#539	C₂²	1	16	yes	complemented
48	C₂₃×#538	C₂²	1	8	yes	complemented
49	C₂₃×#538	C₂²	1	8	yes	complemented
50	C₂₃×#538	C₂²	1	8	yes	complemented
51	C₂₃×#538	C₂²	1	16	yes	complemented
52	C₂₃×#537	C₂²	1	4	yes	complemented
53	C₂₃×#536	C₂²	1	8	yes	complemented
54	C₂₃×#535	C₂²	1	4	yes	complemented
55	C₂₃×#534	C₂²	1	4	yes	—
56	C₂₃×#534	C₂²	1	4	yes	complemented
57	C₂₃×#534	C₂²	1	2	yes	complemented
58	C₂₃×#534	C₂²	1	4	yes	complemented
59	C₂₃×#534	C₂²	1	8	yes	complemented
60	C₂₃×#529	C₂²	1	16	yes	complemented
61	C₂₃×#525	C₂²	1	8	yes	complemented
62	C₂₃×#525	C₂²	1	4	yes	complemented
63	C₂₃×#525	C₂²	1	8	yes	complemented
64	C₂₃×#525	C₂²	1	8	yes	complemented
65	C₂₃×#525	C₂²	1	8	yes	complemented
66	C₂₃×#525	C₂²	1	8	yes	complemented
67	C₂₃×#525	C₂²	1	8	yes	complemented
68	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
69	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
70	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
71	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
72	C₂×C₂₃×#123	C₂²	1	4	yes	complemented
73	C₂×C₂₃×#123	C₂²	1	8	yes	complemented
74	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
75	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
76	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
77	C₂×C₂₃×#120	C₂²	1	4	yes	complemented
78	C₂₃×#520	C₂²	1	8	yes	complemented
79	C₂₃×#518	C₂²	1	2	yes	complemented
80	C₂₃×#518	C₂²	1	4	yes	complemented
81	C₂₃×#518	C₂²	1	8	yes	complemented
82	C₂×C₄×D₄×C₂₃	C₂²	1	8	yes	complemented
83	C₂×C₂₃×#117	C₂²	1	2	yes	complemented
84	C₂²×C₄⋊C₄×C₂₃	C₂²	1	2	yes	complemented
85	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	1	yes	characteristic, complemented
86	C₂²×C₂²⋊C₄×C₂₃	C₂²	1	2	yes	complemented
87	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
88	C₂⁵×C₂₃	C₂³	1	1	yes	characteristic
89	C₂₃×H(5,𝔽₂)	—	4	8	no	—
90	C₂×#41×C₂₃	—	4	8	no	—
91	C₂×#41×C₂₃	C₂³	1	4	yes	—
92	C₂×#41×C₂₃	C₂³	1	8	yes	—
93	C₂×#41×C₂₃	C₂³	1	8	yes	—
94	C₂×#41×C₂₃	C₂³	1	8	yes	—
95	C₂×#41×C₂₃	C₂³	1	8	yes	complemented
96	C₂²×Q₈×C₂₃	C₂³	1	2	yes	complemented
97	C₂²×D₄×C₂₃	—	4	4	no	—
98	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
99	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
101	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
102	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
103	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
104	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
105	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
106	C₂²×D₄×C₂₃	C₂³	1	2	yes	complemented
107	C₂³×C₄×C₂₃	—	4	4	no	—
108	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
110	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
111	C₂³×C₄×C₂₃	C₂³	1	4	yes	—
112	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
113	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
115	C₂³×C₄×C₂₃	C₂³	1	4	yes	complemented
116	C₂₃×C₄⋊Q₈	C₂³	1	16	yes	complemented
117	C₂₃×#127	C₂³	1	8	yes	—
118	C₂₃×#126	C₂³	1	16	yes	complemented
119	C₂₃×#126	C₂³	1	16	yes	complemented
120	C₂₃×#126	C₂³	1	16	yes	complemented
121	C₂₃×#126	C₂³	1	16	yes	complemented
122	C₂₃×#126	C₂³	1	16	yes	complemented
123	C₂₃×#125	C₂³	1	16	yes	complemented
124	C₂₃×#125	C₂³	1	16	yes	complemented
125	C₂₃×#125	C₂³	1	16	yes	complemented
126	C₂₃×#124	C₂³	1	8	yes	—
127	C₂₃×#124	C₂³	1	16	yes	complemented
128	C₂₃×#124	C₂³	1	16	yes	complemented
129	C₂₃×#124	C₂³	1	16	yes	complemented
130	C₂₃×#123	C₂³	1	8	yes	—
131	C₂₃×#123	C₂³	1	16	yes	—
132	C₂₃×#123	C₂³	1	16	yes	—
133	C₂₃×#123	C₂³	1	16	yes	—
134	C₂₃×#123	C₂³	1	8	yes	—
135	C₂₃×#123	C₂³	1	8	yes	—
136	C₂₃×#123	C₂³	1	8	yes	—
137	C₂₃×#123	C₂³	1	8	yes	—
138	C₂₃×#123	C₂³	1	8	yes	—
139	C₂₃×#123	C₂³	1	8	yes	—
140	C₂₃×#123	C₂³	1	16	yes	—
141	C₂₃×#123	C₂³	1	8	yes	complemented
142	C₂₃×#123	C₂³	1	16	yes	complemented
143	C₂₃×#123	C₂³	1	16	yes	complemented
144	C₂₃×#123	C₂³	1	16	yes	complemented
145	C₂₃×#123	C₂³	1	16	yes	complemented
146	C₂₃×#123	C₂³	1	16	yes	complemented
147	C₂₃×#123	C₂³	1	16	yes	complemented
148	C₂₃×#123	C₂³	1	8	yes	complemented
149	C₂₃×#123	C₂³	1	8	yes	complemented
150	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
151	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
152	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
153	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
154	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
155	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
156	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
157	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
158	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
159	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
160	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
161	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
162	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
163	C₂₃×#121	C₂³	1	8	yes	—
164	C₂₃×#121	C₂³	1	16	yes	—
165	C₂₃×#121	C₂³	1	8	yes	—
166	C₂₃×#121	C₂³	1	8	yes	—
167	C₂₃×#121	C₂³	1	8	yes	—
168	C₂₃×#121	C₂³	1	16	yes	—
169	C₂₃×#121	C₂³	1	16	yes	—
170	C₂₃×#121	C₂³	1	8	yes	—
171	C₂₃×#121	C₂³	1	16	yes	complemented
172	C₂₃×#121	C₂³	1	16	yes	complemented
173	C₂₃×#121	C₂³	1	16	yes	complemented
174	C₂₃×#121	C₂³	1	16	yes	complemented
175	C₂₃×#121	C₂³	1	8	yes	complemented
176	C₂₃×#121	C₂³	1	8	yes	complemented
177	C₂₃×#120	C₂³	1	8	yes	—
178	C₂₃×#120	C₂³	1	8	yes	—
179	C₂₃×#120	C₂³	1	8	yes	—
180	C₂₃×#120	C₂³	1	16	yes	—
181	C₂₃×#120	C₂³	1	16	yes	—
182	C₂₃×#120	C₂³	1	8	yes	—
183	C₂₃×#120	C₂³	1	8	yes	—
184	C₂₃×#120	C₂³	1	16	yes	complemented
185	C₂₃×#120	C₂³	1	8	yes	complemented
186	C₄×Q₈×C₂₃	C₂³	1	16	yes	complemented
187	C₄×D₄×C₂₃	C₂³	1	16	yes	—
188	C₄×D₄×C₂₃	C₂³	1	16	yes	—
189	C₄×D₄×C₂₃	C₂³	1	16	yes	—
190	C₄×D₄×C₂₃	C₂³	1	16	yes	—
191	C₄×D₄×C₂₃	C₂³	1	16	yes	—
192	C₄×D₄×C₂₃	C₂³	1	16	yes	—
193	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
194	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
195	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
196	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
197	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
198	C₄×D₄×C₂₃	C₂³	1	16	yes	complemented
199	C₂₃×#117	C₂³	1	8	yes	—
200	C₂₃×#117	C₂³	1	8	yes	—
201	C₂₃×#117	C₂³	1	4	yes	—
202	C₂₃×#117	C₂³	1	8	yes	complemented
203	C₂₃×#117	C₂³	1	8	yes	complemented
204	C₂₃×#117	C₂³	1	16	yes	complemented
205	C₂₃×#117	C₂³	1	16	yes	complemented
206	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
207	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
208	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
209	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
210	C₂×C₄⋊C₄×C₂₃	C₂³	1	8	yes	complemented
211	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	complemented
212	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	complemented
213	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
214	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
215	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
216	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
217	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
218	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
219	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄×C₂₃	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄×C₂₃	C₂³	1	4	yes	—
224	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
225	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	complemented
226	C₂×C₂²⋊C₄×C₂₃	C₂³	1	16	yes	complemented
227	C₂×C₄²×C₂₃	C₂³	1	4	yes	complemented
228	C₂⁴×C₂₃	—	2	4	no	—
229	C₂⁴×C₂₃	—	4	4	no	—
230	C₂⁴×C₂₃	—	4	2	no	—
231	C₂⁴×C₂₃	—	4	4	no	—
232	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
233	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
234	C₂⁴×C₂₃	C₂⁴	1	2	yes	—
235	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
236	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
237	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
238	C₂⁴×C₂₃	C₂⁴	1	4	yes	—
239	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
240	#41×C₂₃	—	4	16	no	—
241	#41×C₂₃	—	4	16	no	—
242	#41×C₂₃	—	4	16	no	—
243	#41×C₂₃	—	4	8	no	—
244	#41×C₂₃	—	4	16	no	—
245	C₂×Q₈×C₂₃	—	4	4	no	—
246	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
247	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
248	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
249	C₂×D₄×C₂₃	—	2	8	no	—
250	C₂×D₄×C₂₃	—	2	16	no	—
251	C₂×D₄×C₂₃	—	4	4	no	—
252	C₂×D₄×C₂₃	—	4	4	no	—
253	C₂×D₄×C₂₃	—	4	16	no	—
254	C₂×D₄×C₂₃	—	4	16	no	—
255	C₂×D₄×C₂₃	—	4	16	no	—
256	C₂×D₄×C₂₃	—	4	16	no	—
257	C₂×D₄×C₂₃	—	4	8	no	—
258	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
259	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
260	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
261	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
262	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
263	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
264	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
265	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
266	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
267	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
268	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₂₃	—	2	8	no	—
270	C₂²×C₄×C₂₃	—	4	8	no	—
271	C₂²×C₄×C₂₃	—	4	8	no	—
272	C₂²×C₄×C₂₃	—	4	4	no	—
273	C₂²×C₄×C₂₃	—	4	4	no	—
274	C₂²×C₄×C₂₃	—	4	4	no	—
275	C₂²×C₄×C₂₃	—	4	2	no	—
276	C₂²×C₄×C₂₃	—	4	8	no	—
277	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
279	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
280	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
281	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
282	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
284	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
285	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
286	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
287	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
288	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
289	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
291	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
293	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
294	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
295	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
296	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
297	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
298	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
299	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
300	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
301	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
303	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
305	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
306	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
307	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
308	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
309	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
310	C₄⋊C₄×C₂₃	C₂⁴	1	16	yes	—
311	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
312	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
313	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
314	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
315	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
316	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
317	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
318	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
319	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
320	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
321	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
322	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
323	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
324	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
325	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
326	C₄²×C₂₃	C₂⁴	1	16	yes	—
327	C₄²×C₂₃	C₂⁴	1	8	yes	—
328	C₄²×C₂₃	C₂⁴	1	16	yes	—
329	#62820	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂³×C₂₃	—	2	2	no	—
331	C₂³×C₂₃	—	2	4	no	—
332	C₂³×C₂₃	—	2	8	no	—
333	C₂³×C₂₃	—	2	2	no	—
334	C₂³×C₂₃	—	2	8	no	—
335	C₂³×C₂₃	—	2	8	no	—
336	C₂³×C₂₃	—	2	4	no	—
337	C₂³×C₂₃	—	2	8	no	—
338	C₂³×C₂₃	—	4	2	no	—
339	C₂³×C₂₃	—	4	4	no	—
340	C₂³×C₂₃	—	4	2	no	—
341	C₂³×C₂₃	—	4	4	no	—
342	C₂³×C₂₃	—	4	8	no	—
343	C₂³×C₂₃	—	4	4	no	—
344	C₂³×C₂₃	—	4	4	no	—
345	C₂³×C₂₃	—	4	4	no	—
346	C₂³×C₂₃	—	4	8	no	—
347	C₂³×C₂₃	—	4	16	no	—
348	C₂³×C₂₃	—	8	8	no	—
349	C₂³×C₂₃	H(5,𝔽₂)	1	4	yes	—
350	C₂³×C₂₃	C₂⁵	1	4	yes	—
351	C₂³×C₂₃	C₂⁵	1	2	yes	—
352	C₂³×C₂₃	C₂⁵	1	8	yes	—
353	C₂³×C₂₃	C₂⁵	1	2	yes	—
354	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
355	C₂³×C₂₃	C₂⁵	1	2	yes	—
356	Q₈×C₂₃	—	4	8	no	—
357	Q₈×C₂₃	—	4	8	no	—
358	Q₈×C₂₃	—	4	4	no	—
359	D₄×C₂₃	—	2	16	no	—
360	D₄×C₂₃	—	2	16	no	—
361	D₄×C₂₃	—	2	16	no	—
362	D₄×C₂₃	—	2	32	no	—
363	D₄×C₂₃	—	4	8	no	—
364	D₄×C₂₃	—	4	4	no	—
365	D₄×C₂₃	—	4	8	no	—
366	D₄×C₂₃	—	4	16	no	—
367	D₄×C₂₃	—	4	16	no	—
368	D₄×C₂₃	—	4	8	no	—
369	D₄×C₂₃	—	4	8	no	—
370	C₂×C₄×C₂₃	—	2	4	no	—
371	C₂×C₄×C₂₃	—	2	4	no	—
372	C₂×C₄×C₂₃	—	2	8	no	—
373	C₂×C₄×C₂₃	—	2	8	no	—
374	C₂×C₄×C₂₃	—	2	4	no	—
375	C₂×C₄×C₂₃	—	2	8	no	—
376	C₂×C₄×C₂₃	—	2	8	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	2	no	—
379	C₂×C₄×C₂₃	—	4	4	no	—
380	C₂×C₄×C₂₃	—	4	4	no	—
381	C₂×C₄×C₂₃	—	4	2	no	—
382	C₂×C₄×C₂₃	—	4	2	no	—
383	C₂×C₄×C₂₃	—	4	4	no	—
384	C₂×C₄×C₂₃	—	4	4	no	—
385	C₂×C₄×C₂₃	—	4	4	no	—
386	C₂×C₄×C₂₃	—	4	16	no	—
387	C₂×C₄×C₂₃	—	4	8	no	—
388	C₂×C₄×C₂₃	—	4	8	no	—
389	C₂×C₄×C₂₃	—	4	8	no	—
390	C₂×C₄×C₂₃	—	4	4	no	—
391	C₂×C₄×C₂₃	—	4	16	no	—
392	C₂×C₄×C₂₃	C₂⁵	1	16	yes	—
393	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
394	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
395	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
396	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
397	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
398	#3535	C₂×C₂₃	1	8	yes	complemented
399	#3534	C₂×C₂₃	1	8	yes	complemented
400	#3533	C₂×C₂₃	1	8	yes	complemented
401	#3513	C₂×C₂₃	1	16	yes	complemented
402	#3492	C₂×C₂₃	1	4	yes	complemented
403	#3491	C₂×C₂₃	1	4	yes	complemented
404	#3490	C₂×C₂₃	1	2	yes	complemented
405	#3490	C₂×C₂₃	1	4	yes	complemented
406	#3485	C₂×C₂₃	1	4	yes	complemented
407	#3484	C₂×C₂₃	1	2	yes	complemented
408	C₂×#525	C₂×C₂₃	1	2	yes	complemented
409	C₂²×#123	C₂×C₂₃	1	1	yes	characteristic, complemented
410	C₂²×C₂₃	—	2	8	no	—
411	C₂²×C₂₃	—	2	2	no	—
412	C₂²×C₂₃	—	2	2	no	—
413	C₂²×C₂₃	—	2	2	no	—
414	C₂²×C₂₃	—	2	4	no	—
415	C₂²×C₂₃	—	2	2	no	—
416	C₂²×C₂₃	—	2	8	no	—
417	C₂²×C₂₃	—	2	4	no	—
418	C₂²×C₂₃	—	2	16	no	—
419	C₂²×C₂₃	—	2	8	no	—
420	C₂²×C₂₃	—	2	4	no	—
421	C₂²×C₂₃	—	4	4	no	—
422	C₂²×C₂₃	—	4	16	no	—
423	C₂²×C₂₃	—	4	4	no	—
424	C₂²×C₂₃	—	8	8	no	—
425	C₂²×C₂₃	—	8	4	no	—
426	C₂²×C₂₃	—	8	8	no	—
427	C₂²×C₂₃	—	16	4	no	—
428	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
430	C₂²×C₂₃	#585	1	4	yes	—
431	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
432	C₄×C₂₃	—	2	4	no	—
433	C₄×C₂₃	—	2	4	no	—
434	C₄×C₂₃	—	2	4	no	—
435	C₄×C₂₃	—	2	8	no	—
436	C₄×C₂₃	—	2	8	no	—
437	C₄×C₂₃	—	2	16	no	—
438	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	complemented
439	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
440	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
441	C₂⁴×C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
442	#563	C₂²×C₂₃	1	8	yes	complemented
443	#562	C₂²×C₂₃	1	16	yes	complemented
444	#560	C₂²×C₂₃	1	8	yes	complemented
445	#559	C₂²×C₂₃	1	8	yes	complemented
446	#554	C₂²×C₂₃	1	16	yes	complemented
447	#553	C₂²×C₂₃	1	16	yes	complemented
448	#553	C₂²×C₂₃	1	16	yes	complemented
449	#552	C₂²×C₂₃	1	16	yes	complemented
450	#552	C₂²×C₂₃	1	16	yes	complemented
451	#551	C₂²×C₂₃	1	16	yes	complemented
452	#551	C₂²×C₂₃	1	16	yes	complemented
453	#551	C₂²×C₂₃	1	16	yes	complemented
454	#551	C₂²×C₂₃	1	16	yes	complemented
455	#551	C₂²×C₂₃	1	8	yes	complemented
456	#547	C₂²×C₂₃	1	16	yes	complemented
457	#547	C₂²×C₂₃	1	16	yes	complemented
458	#546	C₂²×C₂₃	1	16	yes	complemented
459	#546	C₂²×C₂₃	1	16	yes	complemented
460	#546	C₂²×C₂₃	1	16	yes	complemented
461	#546	C₂²×C₂₃	1	16	yes	complemented
462	#546	C₂²×C₂₃	1	16	yes	complemented
463	D₄²	C₂²×C₂₃	1	16	yes	complemented
464	#544	C₂²×C₂₃	1	4	yes	complemented
465	#543	C₂²×C₂₃	1	2	yes	complemented
466	#543	C₂²×C₂₃	1	4	yes	complemented
467	#542	C₂²×C₂₃	1	16	yes	complemented
468	#540	C₂²×C₂₃	1	16	yes	complemented
469	#539	C₂²×C₂₃	1	8	yes	complemented
470	#539	C₂²×C₂₃	1	8	yes	complemented
471	#539	C₂²×C₂₃	1	16	yes	complemented
472	#539	C₂²×C₂₃	1	16	yes	complemented
473	#538	C₂²×C₂₃	1	8	yes	complemented
474	#538	C₂²×C₂₃	1	8	yes	complemented
475	#538	C₂²×C₂₃	1	8	yes	complemented
476	#538	C₂²×C₂₃	1	16	yes	complemented
477	#537	C₂²×C₂₃	1	4	yes	complemented
478	#536	C₂²×C₂₃	1	8	yes	complemented
479	#535	C₂²×C₂₃	1	4	yes	complemented
480	#534	C₂²×C₂₃	1	4	yes	—
481	#534	C₂²×C₂₃	1	4	yes	complemented
482	#534	C₂²×C₂₃	1	2	yes	complemented
483	#534	C₂²×C₂₃	1	4	yes	complemented
484	#534	C₂²×C₂₃	1	8	yes	complemented
485	#529	C₂²×C₂₃	1	16	yes	complemented
486	#525	C₂²×C₂₃	1	8	yes	complemented
487	#525	C₂²×C₂₃	1	4	yes	complemented
488	#525	C₂²×C₂₃	1	8	yes	complemented
489	#525	C₂²×C₂₃	1	8	yes	complemented
490	#525	C₂²×C₂₃	1	8	yes	complemented
491	#525	C₂²×C₂₃	1	8	yes	complemented
492	#525	C₂²×C₂₃	1	8	yes	complemented
493	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
494	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
495	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
496	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
497	C₂×#123	C₂²×C₂₃	1	4	yes	complemented
498	C₂×#123	C₂²×C₂₃	1	8	yes	complemented
499	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	4	yes	complemented
500	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
501	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
502	C₂×#120	C₂²×C₂₃	1	4	yes	complemented
503	#520	C₂²×C₂₃	1	8	yes	complemented
504	#518	C₂²×C₂₃	1	2	yes	complemented
505	#518	C₂²×C₂₃	1	4	yes	complemented
506	#518	C₂²×C₂₃	1	8	yes	complemented
507	C₂×C₄×D₄	C₂²×C₂₃	1	8	yes	complemented
508	C₂×#117	C₂²×C₂₃	1	2	yes	complemented
509	C₂²×C₄⋊C₄	C₂²×C₂₃	1	2	yes	complemented
510	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	C₂²×C₂²⋊C₄	C₂²×C₂₃	1	2	yes	complemented
512	C₂×C₂₃	—	2	2	no	—
513	C₂×C₂₃	—	2	4	no	—
514	C₂×C₂₃	—	2	4	no	—
515	C₂×C₂₃	—	4	2	no	—
516	C₂×C₂₃	—	4	4	no	—
517	C₂×C₂₃	—	4	8	no	—
518	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
519	C₂×C₂₃	C₂×#585	1	2	yes	—
520	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
521	C₂⁵	C₂³×C₂₃	1	1	yes	characteristic
522	H(5,𝔽₂)	—	4	8	no	—
523	C₂×#41	—	4	8	no	—
524	C₂×#41	C₂³×C₂₃	1	8	yes	—
525	C₂×#41	C₂³×C₂₃	1	8	yes	—
526	C₂×#41	C₂³×C₂₃	1	4	yes	—
527	C₂×#41	C₂³×C₂₃	1	8	yes	—
528	C₂×#41	C₂³×C₂₃	1	8	yes	complemented
529	C₂²×Q₈	C₂³×C₂₃	1	2	yes	complemented
530	C₂²×D₄	—	4	4	no	—
531	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
532	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
533	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
534	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
535	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
536	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
537	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
538	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
539	C₂²×D₄	C₂³×C₂₃	1	2	yes	complemented
540	C₂³×C₄	—	4	4	no	—
541	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
542	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
543	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
544	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
546	C₂³×C₄	C₂³×C₂₃	1	4	yes	—
547	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
548	C₂³×C₄	C₂³×C₂₃	1	4	yes	complemented
549	C₄⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
550	#127	C₂³×C₂₃	1	8	yes	—
551	#126	C₂³×C₂₃	1	16	yes	complemented
552	#126	C₂³×C₂₃	1	16	yes	complemented
553	#126	C₂³×C₂₃	1	16	yes	complemented
554	#126	C₂³×C₂₃	1	16	yes	complemented
555	#126	C₂³×C₂₃	1	16	yes	complemented
556	#125	C₂³×C₂₃	1	16	yes	complemented
557	#125	C₂³×C₂₃	1	16	yes	complemented
558	#125	C₂³×C₂₃	1	16	yes	complemented
559	#124	C₂³×C₂₃	1	8	yes	—
560	#124	C₂³×C₂₃	1	16	yes	complemented
561	#124	C₂³×C₂₃	1	16	yes	complemented
562	#124	C₂³×C₂₃	1	16	yes	complemented
563	#123	C₂³×C₂₃	1	8	yes	—
564	#123	C₂³×C₂₃	1	8	yes	—
565	#123	C₂³×C₂₃	1	16	yes	—
566	#123	C₂³×C₂₃	1	16	yes	—
567	#123	C₂³×C₂₃	1	8	yes	—
568	#123	C₂³×C₂₃	1	8	yes	—
569	#123	C₂³×C₂₃	1	16	yes	—
570	#123	C₂³×C₂₃	1	8	yes	—
571	#123	C₂³×C₂₃	1	8	yes	—
572	#123	C₂³×C₂₃	1	16	yes	—
573	#123	C₂³×C₂₃	1	8	yes	—
574	#123	C₂³×C₂₃	1	8	yes	complemented
575	#123	C₂³×C₂₃	1	8	yes	complemented
576	#123	C₂³×C₂₃	1	8	yes	complemented
577	#123	C₂³×C₂₃	1	16	yes	complemented
578	#123	C₂³×C₂₃	1	16	yes	complemented
579	#123	C₂³×C₂₃	1	16	yes	complemented
580	#123	C₂³×C₂₃	1	16	yes	complemented
581	#123	C₂³×C₂₃	1	16	yes	complemented
582	#123	C₂³×C₂₃	1	16	yes	complemented
583	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
584	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
585	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
586	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
587	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
588	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
589	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
590	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
591	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
592	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
593	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
594	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
595	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	complemented
596	#121	C₂³×C₂₃	1	8	yes	—
597	#121	C₂³×C₂₃	1	8	yes	—
598	#121	C₂³×C₂₃	1	8	yes	—
599	#121	C₂³×C₂₃	1	8	yes	—
600	#121	C₂³×C₂₃	1	8	yes	—
601	#121	C₂³×C₂₃	1	16	yes	—
602	#121	C₂³×C₂₃	1	16	yes	—
603	#121	C₂³×C₂₃	1	16	yes	—
604	#121	C₂³×C₂₃	1	8	yes	complemented
605	#121	C₂³×C₂₃	1	8	yes	complemented
606	#121	C₂³×C₂₃	1	16	yes	complemented
607	#121	C₂³×C₂₃	1	16	yes	complemented
608	#121	C₂³×C₂₃	1	16	yes	complemented
609	#121	C₂³×C₂₃	1	16	yes	complemented
610	#120	C₂³×C₂₃	1	8	yes	—
611	#120	C₂³×C₂₃	1	8	yes	—
612	#120	C₂³×C₂₃	1	16	yes	—
613	#120	C₂³×C₂₃	1	8	yes	—
614	#120	C₂³×C₂₃	1	16	yes	—
615	#120	C₂³×C₂₃	1	8	yes	—
616	#120	C₂³×C₂₃	1	8	yes	—
617	#120	C₂³×C₂₃	1	8	yes	complemented
618	#120	C₂³×C₂₃	1	16	yes	complemented
619	C₄×Q₈	C₂³×C₂₃	1	16	yes	complemented
620	C₄×D₄	C₂³×C₂₃	1	16	yes	—
621	C₄×D₄	C₂³×C₂₃	1	16	yes	—
622	C₄×D₄	C₂³×C₂₃	1	16	yes	—
623	C₄×D₄	C₂³×C₂₃	1	16	yes	—
624	C₄×D₄	C₂³×C₂₃	1	16	yes	—
625	C₄×D₄	C₂³×C₂₃	1	16	yes	—
626	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
627	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
628	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
629	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
630	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
631	C₄×D₄	C₂³×C₂₃	1	16	yes	complemented
632	#117	C₂³×C₂₃	1	8	yes	—
633	#117	C₂³×C₂₃	1	4	yes	—
634	#117	C₂³×C₂₃	1	8	yes	—
635	#117	C₂³×C₂₃	1	8	yes	complemented
636	#117	C₂³×C₂₃	1	8	yes	complemented
637	#117	C₂³×C₂₃	1	16	yes	complemented
638	#117	C₂³×C₂₃	1	16	yes	complemented
639	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
640	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
641	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
642	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	—
643	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	complemented
644	C₂×C₄⋊C₄	C₂³×C₂₃	1	8	yes	complemented
645	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	complemented
646	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
647	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
648	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
649	C₂×C₂²⋊C₄	C₂³×C₂₃	1	2	yes	—
650	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
651	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
652	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
653	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
654	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
655	C₂×C₂²⋊C₄	C₂³×C₂₃	1	4	yes	—
656	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
657	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
658	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	complemented
659	C₂×C₂²⋊C₄	C₂³×C₂₃	1	16	yes	complemented
660	C₂×C₄²	C₂³×C₂₃	1	4	yes	complemented
661	C₂₃	#62820	1	1	yes	characteristic, direct product factor, Sylow
662	C₂⁴	—	2	4	no	—
663	C₂⁴	—	4	4	no	—
664	C₂⁴	—	4	2	no	—
665	C₂⁴	—	4	4	no	—
666	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
667	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
668	C₂⁴	C₂⁴×C₂₃	1	2	yes	—
669	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
670	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
671	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
672	C₂⁴	C₂⁴×C₂₃	1	4	yes	—
673	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
674	#41	—	4	16	no	—
675	#41	—	4	16	no	—
676	#41	—	4	8	no	—
677	#41	—	4	16	no	—
678	#41	—	4	16	no	—
679	C₂×Q₈	—	4	4	no	—
680	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
681	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
682	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
683	C₂×D₄	—	2	8	no	—
684	C₂×D₄	—	2	16	no	—
685	C₂×D₄	—	4	4	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	16	no	—
688	C₂×D₄	—	4	16	no	—
689	C₂×D₄	—	4	8	no	—
690	C₂×D₄	—	4	16	no	—
691	C₂×D₄	—	4	16	no	—
692	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
693	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
694	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
695	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
696	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
697	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
698	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
699	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
700	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
701	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
702	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	4	8	no	—
705	C₂²×C₄	—	4	8	no	—
706	C₂²×C₄	—	4	4	no	—
707	C₂²×C₄	—	4	4	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	4	no	—
710	C₂²×C₄	—	4	8	no	—
711	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
713	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
714	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
715	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
716	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
717	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
718	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
719	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
720	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
721	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
722	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
723	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
724	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
725	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
726	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
727	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
728	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
729	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
730	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
731	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
732	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
734	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
735	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
736	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
737	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
738	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
739	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
740	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
741	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
742	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
743	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
744	C₄⋊C₄	C₂⁴×C₂₃	1	16	yes	—
745	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
746	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
747	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
748	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
749	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
750	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
751	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
752	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
753	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
754	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
755	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
756	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
757	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
758	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
759	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
760	C₄²	C₂⁴×C₂₃	1	16	yes	—
761	C₄²	C₂⁴×C₂₃	1	8	yes	—
762	C₄²	C₂⁴×C₂₃	1	16	yes	—
763	C₂³	—	2	2	no	—
764	C₂³	—	2	4	no	—
765	C₂³	—	2	8	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	8	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	4	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	4	2	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	8	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	4	no	—
778	C₂³	—	4	4	no	—
779	C₂³	—	4	8	no	—
780	C₂³	—	4	16	no	—
781	C₂³	—	8	8	no	—
782	C₂³	C₂₃×H(5,𝔽₂)	1	4	yes	—
783	C₂³	C₂⁵×C₂₃	1	4	yes	—
784	C₂³	C₂⁵×C₂₃	1	2	yes	—
785	C₂³	C₂⁵×C₂₃	1	8	yes	—
786	C₂³	C₂⁵×C₂₃	1	2	yes	—
787	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
788	C₂³	C₂⁵×C₂₃	1	2	yes	—
789	Q₈	—	4	8	no	—
790	Q₈	—	4	4	no	—
791	Q₈	—	4	8	no	—
792	D₄	—	2	16	no	—
793	D₄	—	2	16	no	—
794	D₄	—	2	16	no	—
795	D₄	—	2	32	no	—
796	D₄	—	4	8	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	8	no	—
799	D₄	—	4	8	no	—
800	D₄	—	4	16	no	—
801	D₄	—	4	16	no	—
802	D₄	—	4	8	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	4	no	—
805	C₂×C₄	—	2	8	no	—
806	C₂×C₄	—	2	8	no	—
807	C₂×C₄	—	2	4	no	—
808	C₂×C₄	—	2	8	no	—
809	C₂×C₄	—	2	8	no	—
810	C₂×C₄	—	4	2	no	—
811	C₂×C₄	—	4	2	no	—
812	C₂×C₄	—	4	4	no	—
813	C₂×C₄	—	4	4	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	16	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	4	no	—
820	C₂×C₄	—	4	8	no	—
821	C₂×C₄	—	4	4	no	—
822	C₂×C₄	—	4	8	no	—
823	C₂×C₄	—	4	8	no	—
824	C₂×C₄	—	4	16	no	—
825	C₂×C₄	C₂⁵×C₂₃	1	16	yes	—
826	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
827	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
828	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
829	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
830	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
831	C₂²	—	2	8	no	—
832	C₂²	—	2	2	no	—
833	C₂²	—	2	2	no	—
834	C₂²	—	2	2	no	—
835	C₂²	—	2	4	no	—
836	C₂²	—	2	2	no	—
837	C₂²	—	2	8	no	—
838	C₂²	—	2	4	no	—
839	C₂²	—	2	16	no	—
840	C₂²	—	2	8	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	16	no	—
844	C₂²	—	4	4	no	—
845	C₂²	—	8	4	no	—
846	C₂²	—	8	8	no	—
847	C₂²	—	8	8	no	—
848	C₂²	—	16	4	no	—
849	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
850	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
851	C₂²	C₂₃×#585	1	4	yes	—
852	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	8	no	—
857	C₄	—	2	8	no	—
858	C₄	—	2	16	no	—
859	C₂	—	2	2	no	—
860	C₂	—	2	4	no	—
861	C₂	—	2	4	no	—
862	C₂	—	4	2	no	—
863	C₂	—	4	4	no	—
864	C₂	—	4	8	no	—
865	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
866	C₂	C₂×C₂₃×#585	1	2	yes	—

	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×#3535	C₂	semidirect
2. C₂₃×#3534	C₂	semidirect
3. C₂₃×#3533	C₂	semidirect
4. C₂₃×#3513	C₂	semidirect
5. C₂₃×#3492	C₂	semidirect
6. C₂₃×#3491	C₂	semidirect
7. C₂₃×#3490	C₂	semidirect
8. C₂₃×#3490	C₂	semidirect
9. C₂₃×#3485	C₂	semidirect
10. C₂₃×#3484	C₂	semidirect
11. C₂×C₂₃×#525	C₂	semidirect
12. C₂²×C₂₃×#123	C₂	semidirect
13. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
14. C₂²×#41×C₂₃	C₂²	semidirect
16. C₂⁴×C₄×C₂₃	C₂²	semidirect
17. C₂₃×#563	C₂²	semidirect
18. C₂₃×#562	C₂²	semidirect
19. C₂₃×#560	C₂²	semidirect
20. C₂₃×#559	C₂²	semidirect
21. C₂₃×#554	C₂²	semidirect
22. C₂₃×#553	C₂²	semidirect
23. C₂₃×#553	C₂²	semidirect
24. C₂₃×#552	C₂²	semidirect
25. C₂₃×#552	C₂²	semidirect
26. C₂₃×#551	C₂²	semidirect
27. C₂₃×#551	C₂²	semidirect
28. C₂₃×#551	C₂²	semidirect
29. C₂₃×#551	C₂²	semidirect
30. C₂₃×#551	C₂²	semidirect
31. C₂₃×#547	C₂²	semidirect
32. C₂₃×#547	C₂²	semidirect
33. C₂₃×#546	C₂²	semidirect
34. C₂₃×#546	C₂²	semidirect
35. C₂₃×#546	C₂²	semidirect
36. C₂₃×#546	C₂²	semidirect
37. C₂₃×#546	C₂²	semidirect
38. D₄²×C₂₃	C₂²	semidirect
39. C₂₃×#544	C₂²	semidirect
40. C₂₃×#543	C₂²	semidirect
41. C₂₃×#543	C₂²	semidirect
42. C₂₃×#542	C₂²	semidirect
43. C₂₃×#540	C₂²	semidirect
44. C₂₃×#539	C₂²	semidirect
45. C₂₃×#539	C₂²	semidirect
46. C₂₃×#539	C₂²	semidirect
47. C₂₃×#539	C₂²	semidirect
48. C₂₃×#538	C₂²	semidirect
49. C₂₃×#538	C₂²	semidirect
50. C₂₃×#538	C₂²	semidirect
51. C₂₃×#538	C₂²	semidirect
52. C₂₃×#537	C₂²	semidirect
53. C₂₃×#536	C₂²	semidirect
54. C₂₃×#535	C₂²	semidirect
56. C₂₃×#534	C₂²	semidirect
57. C₂₃×#534	C₂²	semidirect
58. C₂₃×#534	C₂²	semidirect
59. C₂₃×#534	C₂²	semidirect
60. C₂₃×#529	C₂²	semidirect
61. C₂₃×#525	C₂²	semidirect
62. C₂₃×#525	C₂²	semidirect
63. C₂₃×#525	C₂²	semidirect
64. C₂₃×#525	C₂²	semidirect
65. C₂₃×#525	C₂²	semidirect
66. C₂₃×#525	C₂²	semidirect
67. C₂₃×#525	C₂²	semidirect
68. C₂×C₂₃×#123	C₂²	semidirect
69. C₂×C₂₃×#123	C₂²	semidirect
70. C₂×C₂₃×#123	C₂²	semidirect
71. C₂×C₂₃×#123	C₂²	semidirect
72. C₂×C₂₃×#123	C₂²	semidirect
73. C₂×C₂₃×#123	C₂²	semidirect
74. C₂×C₂₃×C₂²⋊Q₈	C₂²	semidirect
75. C₂×C₂₃×#121	C₂²	semidirect
76. C₂×C₂₃×#120	C₂²	semidirect
77. C₂×C₂₃×#120	C₂²	semidirect
78. C₂₃×#520	C₂²	semidirect
79. C₂₃×#518	C₂²	semidirect
80. C₂₃×#518	C₂²	semidirect
81. C₂₃×#518	C₂²	semidirect
82. C₂×C₄×D₄×C₂₃	C₂²	semidirect
83. C₂×C₂₃×#117	C₂²	semidirect
84. C₂²×C₄⋊C₄×C₂₃	C₂²	semidirect
85. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
86. C₂²×C₂²⋊C₄×C₂₃	C₂²	semidirect
95. C₂×#41×C₂₃	C₂³	semidirect
96. C₂²×Q₈×C₂₃	C₂³	semidirect
106. C₂²×D₄×C₂₃	C₂³	semidirect
115. C₂³×C₄×C₂₃	C₂³	semidirect
116. C₂₃×C₄⋊Q₈	C₂³	semidirect
118. C₂₃×#126	C₂³	semidirect
119. C₂₃×#126	C₂³	semidirect
120. C₂₃×#126	C₂³	semidirect
121. C₂₃×#126	C₂³	semidirect
122. C₂₃×#126	C₂³	semidirect
123. C₂₃×#125	C₂³	semidirect
124. C₂₃×#125	C₂³	semidirect
125. C₂₃×#125	C₂³	semidirect
127. C₂₃×#124	C₂³	semidirect
128. C₂₃×#124	C₂³	semidirect
129. C₂₃×#124	C₂³	semidirect
141. C₂₃×#123	C₂³	semidirect
142. C₂₃×#123	C₂³	semidirect
143. C₂₃×#123	C₂³	semidirect
144. C₂₃×#123	C₂³	semidirect
145. C₂₃×#123	C₂³	semidirect
146. C₂₃×#123	C₂³	semidirect
147. C₂₃×#123	C₂³	semidirect
148. C₂₃×#123	C₂³	semidirect
149. C₂₃×#123	C₂³	semidirect
155. C₂₃×C₂²⋊Q₈	C₂³	semidirect
156. C₂₃×C₂²⋊Q₈	C₂³	semidirect
157. C₂₃×C₂²⋊Q₈	C₂³	semidirect
158. C₂₃×C₂²⋊Q₈	C₂³	semidirect
159. C₂₃×C₂²⋊Q₈	C₂³	semidirect
160. C₂₃×C₂²⋊Q₈	C₂³	semidirect
161. C₂₃×C₂²⋊Q₈	C₂³	semidirect
162. C₂₃×C₂²⋊Q₈	C₂³	semidirect
171. C₂₃×#121	C₂³	semidirect
172. C₂₃×#121	C₂³	semidirect
173. C₂₃×#121	C₂³	semidirect
174. C₂₃×#121	C₂³	semidirect
175. C₂₃×#121	C₂³	semidirect
176. C₂₃×#121	C₂³	semidirect
184. C₂₃×#120	C₂³	semidirect
185. C₂₃×#120	C₂³	semidirect
186. C₄×Q₈×C₂₃	C₂³	semidirect
193. C₄×D₄×C₂₃	C₂³	semidirect
194. C₄×D₄×C₂₃	C₂³	semidirect
195. C₄×D₄×C₂₃	C₂³	semidirect
196. C₄×D₄×C₂₃	C₂³	semidirect
197. C₄×D₄×C₂₃	C₂³	semidirect
198. C₄×D₄×C₂₃	C₂³	semidirect
202. C₂₃×#117	C₂³	semidirect
203. C₂₃×#117	C₂³	semidirect
204. C₂₃×#117	C₂³	semidirect
205. C₂₃×#117	C₂³	semidirect
210. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
211. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
212. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
224. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
225. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
226. C₂×C₂²⋊C₄×C₂₃	C₂³	semidirect
227. C₂×C₄²×C₂₃	C₂³	semidirect
329. #62820	C₂₃	direct (N × H)
398. #3535	C₂×C₂₃	semidirect
399. #3534	C₂×C₂₃	semidirect
400. #3533	C₂×C₂₃	semidirect
401. #3513	C₂×C₂₃	semidirect
402. #3492	C₂×C₂₃	semidirect
403. #3491	C₂×C₂₃	semidirect
404. #3490	C₂×C₂₃	semidirect
405. #3490	C₂×C₂₃	semidirect
406. #3485	C₂×C₂₃	semidirect
407. #3484	C₂×C₂₃	semidirect
408. C₂×#525	C₂×C₂₃	semidirect
409. C₂²×#123	C₂×C₂₃	semidirect
438. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
439. C₂²×#41	C₂²×C₂₃	semidirect
441. C₂⁴×C₄	C₂²×C₂₃	semidirect
442. #563	C₂²×C₂₃	semidirect
443. #562	C₂²×C₂₃	semidirect
444. #560	C₂²×C₂₃	semidirect
445. #559	C₂²×C₂₃	semidirect
446. #554	C₂²×C₂₃	semidirect
447. #553	C₂²×C₂₃	semidirect
448. #553	C₂²×C₂₃	semidirect
449. #552	C₂²×C₂₃	semidirect
450. #552	C₂²×C₂₃	semidirect
451. #551	C₂²×C₂₃	semidirect
452. #551	C₂²×C₂₃	semidirect
453. #551	C₂²×C₂₃	semidirect
454. #551	C₂²×C₂₃	semidirect
455. #551	C₂²×C₂₃	semidirect
456. #547	C₂²×C₂₃	semidirect
457. #547	C₂²×C₂₃	semidirect
458. #546	C₂²×C₂₃	semidirect
459. #546	C₂²×C₂₃	semidirect
460. #546	C₂²×C₂₃	semidirect
461. #546	C₂²×C₂₃	semidirect
462. #546	C₂²×C₂₃	semidirect
463. D₄²	C₂²×C₂₃	semidirect
464. #544	C₂²×C₂₃	semidirect
465. #543	C₂²×C₂₃	semidirect
466. #543	C₂²×C₂₃	semidirect
467. #542	C₂²×C₂₃	semidirect
468. #540	C₂²×C₂₃	semidirect
469. #539	C₂²×C₂₃	semidirect
470. #539	C₂²×C₂₃	semidirect
471. #539	C₂²×C₂₃	semidirect
472. #539	C₂²×C₂₃	semidirect
473. #538	C₂²×C₂₃	semidirect
474. #538	C₂²×C₂₃	semidirect
475. #538	C₂²×C₂₃	semidirect
476. #538	C₂²×C₂₃	semidirect
477. #537	C₂²×C₂₃	semidirect
478. #536	C₂²×C₂₃	semidirect
479. #535	C₂²×C₂₃	semidirect
481. #534	C₂²×C₂₃	semidirect
482. #534	C₂²×C₂₃	semidirect
483. #534	C₂²×C₂₃	semidirect
484. #534	C₂²×C₂₃	semidirect
485. #529	C₂²×C₂₃	semidirect
486. #525	C₂²×C₂₃	semidirect
487. #525	C₂²×C₂₃	semidirect
488. #525	C₂²×C₂₃	semidirect
489. #525	C₂²×C₂₃	semidirect
490. #525	C₂²×C₂₃	semidirect
491. #525	C₂²×C₂₃	semidirect
492. #525	C₂²×C₂₃	semidirect
493. C₂×#123	C₂²×C₂₃	semidirect
494. C₂×#123	C₂²×C₂₃	semidirect
495. C₂×#123	C₂²×C₂₃	semidirect
496. C₂×#123	C₂²×C₂₃	semidirect
497. C₂×#123	C₂²×C₂₃	semidirect
498. C₂×#123	C₂²×C₂₃	semidirect
499. C₂×C₂²⋊Q₈	C₂²×C₂₃	semidirect
500. C₂×#121	C₂²×C₂₃	semidirect
501. C₂×#120	C₂²×C₂₃	semidirect
502. C₂×#120	C₂²×C₂₃	semidirect
503. #520	C₂²×C₂₃	semidirect
504. #518	C₂²×C₂₃	semidirect
505. #518	C₂²×C₂₃	semidirect
506. #518	C₂²×C₂₃	semidirect
507. C₂×C₄×D₄	C₂²×C₂₃	semidirect
508. C₂×#117	C₂²×C₂₃	semidirect
509. C₂²×C₄⋊C₄	C₂²×C₂₃	semidirect
510. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
511. C₂²×C₂²⋊C₄	C₂²×C₂₃	semidirect
528. C₂×#41	C₂³×C₂₃	semidirect
529. C₂²×Q₈	C₂³×C₂₃	semidirect
539. C₂²×D₄	C₂³×C₂₃	semidirect
548. C₂³×C₄	C₂³×C₂₃	semidirect
549. C₄⋊Q₈	C₂³×C₂₃	semidirect
551. #126	C₂³×C₂₃	semidirect
552. #126	C₂³×C₂₃	semidirect
553. #126	C₂³×C₂₃	semidirect
554. #126	C₂³×C₂₃	semidirect
555. #126	C₂³×C₂₃	semidirect
556. #125	C₂³×C₂₃	semidirect
557. #125	C₂³×C₂₃	semidirect
558. #125	C₂³×C₂₃	semidirect
560. #124	C₂³×C₂₃	semidirect
561. #124	C₂³×C₂₃	semidirect
562. #124	C₂³×C₂₃	semidirect
574. #123	C₂³×C₂₃	semidirect
575. #123	C₂³×C₂₃	semidirect
576. #123	C₂³×C₂₃	semidirect
577. #123	C₂³×C₂₃	semidirect
578. #123	C₂³×C₂₃	semidirect
579. #123	C₂³×C₂₃	semidirect
580. #123	C₂³×C₂₃	semidirect
581. #123	C₂³×C₂₃	semidirect
582. #123	C₂³×C₂₃	semidirect
588. C₂²⋊Q₈	C₂³×C₂₃	semidirect
589. C₂²⋊Q₈	C₂³×C₂₃	semidirect
590. C₂²⋊Q₈	C₂³×C₂₃	semidirect
591. C₂²⋊Q₈	C₂³×C₂₃	semidirect
592. C₂²⋊Q₈	C₂³×C₂₃	semidirect
593. C₂²⋊Q₈	C₂³×C₂₃	semidirect
594. C₂²⋊Q₈	C₂³×C₂₃	semidirect
595. C₂²⋊Q₈	C₂³×C₂₃	semidirect
604. #121	C₂³×C₂₃	semidirect
605. #121	C₂³×C₂₃	semidirect
606. #121	C₂³×C₂₃	semidirect
607. #121	C₂³×C₂₃	semidirect
608. #121	C₂³×C₂₃	semidirect
609. #121	C₂³×C₂₃	semidirect
617. #120	C₂³×C₂₃	semidirect
618. #120	C₂³×C₂₃	semidirect
619. C₄×Q₈	C₂³×C₂₃	semidirect
626. C₄×D₄	C₂³×C₂₃	semidirect
627. C₄×D₄	C₂³×C₂₃	semidirect
628. C₄×D₄	C₂³×C₂₃	semidirect
629. C₄×D₄	C₂³×C₂₃	semidirect
630. C₄×D₄	C₂³×C₂₃	semidirect
631. C₄×D₄	C₂³×C₂₃	semidirect
635. #117	C₂³×C₂₃	semidirect
636. #117	C₂³×C₂₃	semidirect
637. #117	C₂³×C₂₃	semidirect
638. #117	C₂³×C₂₃	semidirect
643. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
644. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
645. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
657. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
658. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
659. C₂×C₂²⋊C₄	C₂³×C₂₃	semidirect
660. C₂×C₄²	C₂³×C₂₃	semidirect
661. C₂₃	#62820	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂₃×#3535	2
C₂₃×#3534	2
C₂₃×#3533	2
C₂₃×#3513	2
C₂₃×#3492	2
C₂₃×#3491	2
C₂₃×#3490	2
C₂₃×#3485	2
C₂₃×#3484	2
C₂×C₂₃×#525	2
C₂²×C₂₃×#123	2
#62820	23

Subgroups — C23×#62820 #19210446

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62820 #19210446