Subgroups — C₂₃×#62834 #19210460

Order 5888.

7900 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3558	C₂	1	8	yes	maximal, complemented
2	C₂₃×#3549	C₂	1	2	yes	maximal, complemented
3	C₂₃×#3548	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3546	C₂	1	8	yes	maximal, complemented
5	C₂₃×#3537	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3519	C₂	1	8	yes	maximal, complemented
7	C₂₃×#3511	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3508	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3506	C₂	1	4	yes	maximal, complemented
10	C₂₃×#3498	C₂	1	4	yes	maximal, complemented
11	C₂₃×#3496	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3488	C₂	1	8	yes	maximal, complemented
13	C₂₃×#3444	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#532	C₂	1	2	yes	maximal, complemented
15	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	8	yes	complemented
16	C₂²×#41×C₂₃	C₂²	1	4	yes	complemented
17	C₂₃×#562	C₂²	1	8	yes	complemented
18	C₂₃×H(3,𝔽₄)	C₂²	1	8	yes	complemented
19	C₂₃×#560	C₂²	1	16	yes	complemented
20	C₂₃×#559	C₂²	1	16	yes	complemented
21	C₂₃×#556	C₂²	1	8	yes	complemented
22	C₂₃×#555	C₂²	1	4	yes	complemented
23	C₂₃×#555	C₂²	1	8	yes	complemented
24	C₂₃×#554	C₂²	1	8	yes	complemented
25	C₂₃×#553	C₂²	1	16	yes	complemented
26	C₂₃×#553	C₂²	1	16	yes	complemented
27	C₂₃×#550	C₂²	1	16	yes	complemented
28	C₂₃×#550	C₂²	1	8	yes	complemented
29	C₂₃×#550	C₂²	1	8	yes	complemented
30	C₂₃×#548	C₂²	1	16	yes	complemented
31	C₂₃×#547	C₂²	1	8	yes	complemented
32	C₂₃×#547	C₂²	1	8	yes	complemented
33	C₂₃×#546	C₂²	1	16	yes	complemented
34	C₂₃×#546	C₂²	1	32	yes	complemented
35	C₂₃×#546	C₂²	1	16	yes	complemented
36	C₂₃×#546	C₂²	1	16	yes	complemented
37	D₄²×C₂₃	C₂²	1	16	yes	complemented
38	D₄²×C₂₃	C₂²	1	16	yes	complemented
39	D₄²×C₂₃	C₂²	1	4	yes	complemented
40	D₄²×C₂₃	C₂²	1	8	yes	complemented
41	D₄²×C₂₃	C₂²	1	16	yes	complemented
42	D₄²×C₂₃	C₂²	1	8	yes	complemented
43	C₂₃×#542	C₂²	1	16	yes	complemented
44	C₂₃×#540	C₂²	1	8	yes	complemented
45	C₂₃×#540	C₂²	1	8	yes	complemented
46	C₂₃×#538	C₂²	1	16	yes	complemented
47	C₂₃×#538	C₂²	1	32	yes	complemented
48	C₂₃×#537	C₂²	1	8	yes	complemented
49	C₂₃×#537	C₂²	1	16	yes	complemented
50	C₂₃×#535	C₂²	1	8	yes	complemented
51	C₂₃×#535	C₂²	1	16	yes	complemented
52	C₂₃×#535	C₂²	1	16	yes	complemented
53	C₂₃×#535	C₂²	1	8	yes	complemented
54	C₂₃×#534	C₂²	1	16	yes	complemented
55	C₂₃×#533	C₂²	1	2	yes	complemented
56	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
57	C₂₃×#533	C₂²	1	4	yes	complemented
58	C₂₃×#532	C₂²	1	4	yes	complemented
59	C₂₃×#532	C₂²	1	4	yes	complemented
60	C₂₃×#532	C₂²	1	4	yes	complemented
61	C₂₃×#532	C₂²	1	4	yes	complemented
62	C₂₃×#532	C₂²	1	4	yes	complemented
63	C₂₃×#532	C₂²	1	4	yes	complemented
64	C₂₃×#532	C₂²	1	4	yes	complemented
65	C₂₃×#532	C₂²	1	4	yes	complemented
66	C₂₃×#532	C₂²	1	2	yes	complemented
67	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
68	C₂₃×#532	C₂²	1	8	yes	complemented
69	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
70	C₂×C₂₃×#127	C₂²	1	2	yes	complemented
71	C₂×C₂₃×#127	C₂²	1	4	yes	complemented
72	C₂₃×#529	C₂²	1	4	yes	complemented
73	C₂₃×#529	C₂²	1	4	yes	complemented
74	C₂₃×#529	C₂²	1	4	yes	complemented
75	C₂×C₂₃×#124	C₂²	1	4	yes	complemented
76	C₂₃×#525	C₂²	1	4	yes	complemented
77	C₂₃×#525	C₂²	1	2	yes	complemented
78	C₂₃×#525	C₂²	1	16	yes	complemented
79	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
80	C₂×C₂₃×#121	C₂²	1	4	yes	complemented
81	C₂×C₂₃×#121	C₂²	1	16	yes	complemented
82	C₂₃×#520	C₂²	1	8	yes	complemented
83	C₂₃×#518	C₂²	1	8	yes	complemented
84	C₄×#41×C₂₃	C₂²	1	4	yes	complemented
85	C₄×#41×C₂₃	C₂²	1	2	yes	complemented
86	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
87	C₂×C₄×D₄×C₂₃	C₂²	1	4	yes	complemented
88	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic, complemented
89	C₂₃×H(5,𝔽₂)	—	4	32	no	—
90	C₂×#41×C₂₃	—	4	16	no	—
91	C₂×#41×C₂₃	C₂³	1	8	yes	—
92	C₂×#41×C₂₃	C₂³	1	4	yes	—
93	C₂×#41×C₂₃	C₂³	1	16	yes	—
94	C₂×#41×C₂₃	C₂³	1	16	yes	—
95	C₂×#41×C₂₃	C₂³	1	8	yes	—
96	C₂×#41×C₂₃	C₂³	1	8	yes	—
97	C₂×#41×C₂₃	C₂³	1	8	yes	—
98	C₂×#41×C₂₃	C₂³	1	2	yes	—
99	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
100	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
101	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
102	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
103	C₂²×D₄×C₂₃	C₂³	1	32	yes	—
104	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
105	C₂²×D₄×C₂₃	C₂³	1	16	yes	—
106	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
107	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
108	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
109	C₂³×C₄×C₂₃	C₂³	1	8	yes	—
110	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
113	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
116	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
117	C₂₃×#127	C₂³	1	16	yes	—
118	C₂₃×#127	C₂³	1	16	yes	—
119	C₂₃×#127	C₂³	1	4	yes	—
120	C₂₃×#127	C₂³	1	4	yes	—
121	C₂₃×#127	C₂³	1	8	yes	—
122	C₂₃×#127	C₂³	1	4	yes	—
123	C₂₃×#127	C₂³	1	4	yes	—
124	C₂₃×#127	C₂³	1	1	yes	characteristic
125	C₂₃×#126	C₂³	1	32	yes	—
126	C₂₃×#126	C₂³	1	8	yes	—
127	C₂₃×#125	C₂³	1	4	yes	—
128	C₂₃×#125	C₂³	1	8	yes	—
129	C₂₃×#125	C₂³	1	2	yes	—
130	C₂₃×#124	C₂³	1	32	yes	—
131	C₂₃×#124	C₂³	1	16	yes	—
132	C₂₃×#124	C₂³	1	16	yes	—
133	C₂₃×#124	C₂³	1	8	yes	—
134	C₂₃×#124	C₂³	1	2	yes	—
135	C₂₃×#124	C₂³	1	8	yes	—
136	C₂₃×#124	C₂³	1	8	yes	—
137	C₂₃×#124	C₂³	1	8	yes	—
138	C₂₃×#124	C₂³	1	4	yes	—
139	C₂₃×#123	C₂³	1	32	yes	—
140	C₂₃×#123	C₂³	1	32	yes	—
141	C₂₃×#123	C₂³	1	32	yes	—
142	C₂₃×#123	C₂³	1	4	yes	—
143	C₂₃×#123	C₂³	1	8	yes	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
145	C₂₃×C₂²⋊Q₈	C₂³	1	16	yes	—
146	C₂₃×C₂²⋊Q₈	C₂³	1	32	yes	—
147	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
150	C₂₃×#121	C₂³	1	16	yes	—
151	C₂₃×#121	C₂³	1	16	yes	—
152	C₂₃×#121	C₂³	1	8	yes	—
153	C₂₃×#121	C₂³	1	32	yes	—
154	C₂₃×#121	C₂³	1	8	yes	—
155	C₂₃×#121	C₂³	1	16	yes	—
156	C₂₃×#121	C₂³	1	32	yes	—
157	C₂₃×#121	C₂³	1	32	yes	—
158	C₂₃×#121	C₂³	1	32	yes	—
159	C₂₃×#121	C₂³	1	32	yes	—
160	C₂₃×#121	C₂³	1	16	yes	—
161	C₂₃×#121	C₂³	1	8	yes	—
162	C₂₃×#121	C₂³	1	16	yes	—
163	C₂₃×#121	C₂³	1	8	yes	—
164	C₂₃×#121	C₂³	1	4	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	8	yes	—
169	C₂₃×#121	C₂³	1	4	yes	—
170	C₂₃×#121	C₂³	1	4	yes	—
171	C₂₃×#120	C₂³	1	32	yes	—
172	C₂₃×#120	C₂³	1	16	yes	—
173	C₂₃×#120	C₂³	1	16	yes	—
174	C₂₃×#120	C₂³	1	32	yes	—
175	C₂₃×#120	C₂³	1	4	yes	—
176	C₂₃×#120	C₂³	1	32	yes	—
177	C₄×Q₈×C₂₃	C₂³	1	16	yes	—
178	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
179	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
180	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
181	C₄×D₄×C₂₃	C₂³	1	8	yes	—
182	C₄×D₄×C₂₃	C₂³	1	4	yes	—
183	C₄×D₄×C₂₃	C₂³	1	8	yes	—
184	C₄×D₄×C₂₃	C₂³	1	8	yes	—
185	C₄×D₄×C₂₃	C₂³	1	32	yes	—
186	C₄×D₄×C₂₃	C₂³	1	8	yes	—
187	C₄×D₄×C₂₃	C₂³	1	16	yes	—
188	C₄×D₄×C₂₃	C₂³	1	32	yes	—
189	C₄×D₄×C₂₃	C₂³	1	8	yes	—
190	C₄×D₄×C₂₃	C₂³	1	16	yes	—
191	C₄×D₄×C₂₃	C₂³	1	8	yes	—
192	C₄×D₄×C₂₃	C₂³	1	8	yes	—
193	C₄×D₄×C₂₃	C₂³	1	8	yes	—
194	C₄×D₄×C₂₃	C₂³	1	4	yes	—
195	C₄×D₄×C₂₃	C₂³	1	8	yes	—
196	C₄×D₄×C₂₃	C₂³	1	8	yes	—
197	C₄×D₄×C₂₃	C₂³	1	8	yes	—
198	C₄×D₄×C₂₃	C₂³	1	4	yes	—
199	C₂₃×#117	C₂³	1	8	yes	—
200	C₂₃×#117	C₂³	1	16	yes	—
201	C₂₃×#117	C₂³	1	4	yes	—
202	C₂₃×#117	C₂³	1	4	yes	—
203	C₂₃×#117	C₂³	1	2	yes	—
204	C₂₃×#117	C₂³	1	8	yes	—
205	C₂×C₄⋊C₄×C₂₃	C₂³	1	16	yes	—
206	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
209	C₂×C₂²⋊C₄×C₂₃	C₂³	1	8	yes	—
210	C₂×C₂²⋊C₄×C₂₃	C₂³	1	32	yes	—
211	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
212	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
213	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
214	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
216	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
217	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
219	C₂⁴×C₂₃	C₂⁴	1	1	yes	characteristic
220	C₂⁴×C₂₃	C₂⁴	1	8	yes	—
221	C₂⁴×C₂₃	C₂⁴	1	16	yes	—
222	#41×C₂₃	—	2	32	no	—
223	#41×C₂₃	—	2	16	no	—
224	#41×C₂₃	—	4	16	no	—
225	#41×C₂₃	—	4	4	no	—
226	#41×C₂₃	—	4	16	no	—
227	#41×C₂₃	—	4	16	no	—
228	#41×C₂₃	—	4	32	no	—
229	#41×C₂₃	—	4	32	no	—
230	C₂×Q₈×C₂₃	—	4	8	no	—
231	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
232	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
233	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
234	C₂×Q₈×C₂₃	C₂⁴	1	8	yes	—
235	C₂×D₄×C₂₃	—	2	16	no	—
236	C₂×D₄×C₂₃	—	4	8	no	—
237	C₂×D₄×C₂₃	—	4	16	no	—
238	C₂×D₄×C₂₃	—	4	8	no	—
239	C₂×D₄×C₂₃	—	4	32	no	—
240	C₂×D₄×C₂₃	—	4	32	no	—
241	C₂×D₄×C₂₃	—	4	16	no	—
242	C₂×D₄×C₂₃	—	4	64	no	—
243	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
244	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
245	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
246	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
247	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
248	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
249	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
250	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
251	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
252	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
253	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
254	C₂×D₄×C₂₃	C₂⁴	1	8	yes	—
255	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
256	C₂×D₄×C₂₃	C₂⁴	1	16	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	32	yes	—
258	C₂²×C₄×C₂₃	—	2	8	no	—
259	C₂²×C₄×C₂₃	—	4	2	no	—
260	C₂²×C₄×C₂₃	—	4	16	no	—
261	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
264	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
265	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
266	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
267	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
268	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
269	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
270	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
271	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
272	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
273	C₂²×C₄×C₂₃	C₂⁴	1	8	yes	—
274	C₂²×C₄×C₂₃	C₂⁴	1	16	yes	—
275	C₂²×C₄×C₂₃	C₂⁴	1	32	yes	—
276	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
278	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
279	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	32	yes	—
283	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
284	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
285	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
286	C₄⋊C₄×C₂₃	C₂⁴	1	8	yes	—
287	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
288	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
289	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
290	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
291	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
292	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
293	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
294	C₂²⋊C₄×C₂₃	C₂⁴	1	16	yes	—
295	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
296	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
297	C₂²⋊C₄×C₂₃	C₂⁴	1	8	yes	—
298	C₂²⋊C₄×C₂₃	C₂⁴	1	32	yes	—
299	C₂²⋊C₄×C₂₃	C₂⁴	1	4	yes	—
300	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
301	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
302	C₄²×C₂₃	C₂⁴	1	2	yes	—
303	C₄²×C₂₃	C₂⁴	1	2	yes	—
304	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₄²×C₂₃	C₂⁴	1	2	yes	—
306	C₄²×C₂₃	C₂⁴	1	2	yes	—
307	C₄²×C₂₃	C₂⁴	1	2	yes	—
308	C₄²×C₂₃	C₂⁴	1	2	yes	—
309	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
310	C₄²×C₂₃	C₂⁴	1	4	yes	—
311	C₄²×C₂₃	C₂⁴	1	8	yes	—
312	C₄²×C₂₃	C₂⁴	1	16	yes	—
313	#62834	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
314	C₂³×C₂₃	—	2	4	no	—
315	C₂³×C₂₃	—	2	16	no	—
316	C₂³×C₂₃	—	4	1	no	—
317	C₂³×C₂₃	—	4	8	no	—
318	C₂³×C₂₃	—	4	8	no	—
319	C₂³×C₂₃	—	4	32	no	—
320	C₂³×C₂₃	—	4	16	no	—
321	C₂³×C₂₃	C₂⁵	1	4	yes	—
322	C₂³×C₂₃	C₂⁵	1	16	yes	—
323	C₂³×C₂₃	C₂⁵	1	1	yes	characteristic
324	C₂³×C₂₃	C₂⁵	1	2	yes	—
325	Q₈×C₂₃	—	2	16	no	—
326	Q₈×C₂₃	—	2	8	no	—
327	Q₈×C₂₃	—	4	8	no	—
328	Q₈×C₂₃	—	4	2	no	—
329	D₄×C₂₃	—	2	16	no	—
330	D₄×C₂₃	—	2	32	no	—
331	D₄×C₂₃	—	2	16	no	—
332	D₄×C₂₃	—	2	16	no	—
333	D₄×C₂₃	—	2	8	no	—
334	D₄×C₂₃	—	2	16	no	—
335	D₄×C₂₃	—	2	16	no	—
336	D₄×C₂₃	—	4	32	no	—
337	D₄×C₂₃	—	4	32	no	—
338	D₄×C₂₃	—	4	8	no	—
339	D₄×C₂₃	—	4	16	no	—
340	D₄×C₂₃	—	4	8	no	—
341	D₄×C₂₃	—	4	16	no	—
342	D₄×C₂₃	—	4	2	no	—
343	D₄×C₂₃	—	4	4	no	—
344	C₂×C₄×C₂₃	—	2	4	no	—
345	C₂×C₄×C₂₃	—	2	4	no	—
346	C₂×C₄×C₂₃	—	2	4	no	—
347	C₂×C₄×C₂₃	—	2	4	no	—
348	C₂×C₄×C₂₃	—	2	4	no	—
349	C₂×C₄×C₂₃	—	2	32	no	—
350	C₂×C₄×C₂₃	—	2	16	no	—
351	C₂×C₄×C₂₃	—	2	4	no	—
352	C₂×C₄×C₂₃	—	2	2	no	—
353	C₂×C₄×C₂₃	—	2	8	no	—
354	C₂×C₄×C₂₃	—	4	1	no	—
355	C₂×C₄×C₂₃	—	4	2	no	—
356	C₂×C₄×C₂₃	—	4	8	no	—
357	C₂×C₄×C₂₃	—	4	16	no	—
358	C₂×C₄×C₂₃	—	4	32	no	—
359	C₂×C₄×C₂₃	H(5,𝔽₂)	1	8	yes	complemented
360	C₂×C₄×C₂₃	C₂⁵	1	4	yes	—
361	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
362	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
363	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
364	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
365	C₂×C₄×C₂₃	C₂⁵	1	16	yes	—
366	C₂×C₄×C₂₃	C₂⁵	1	8	yes	—
367	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
368	C₂×C₄×C₂₃	C₂⁵	1	2	yes	—
369	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
370	#3558	C₂×C₂₃	1	8	yes	complemented
371	#3549	C₂×C₂₃	1	2	yes	complemented
372	#3548	C₂×C₂₃	1	2	yes	complemented
373	#3546	C₂×C₂₃	1	8	yes	complemented
374	#3537	C₂×C₂₃	1	4	yes	complemented
375	#3519	C₂×C₂₃	1	8	yes	complemented
376	#3511	C₂×C₂₃	1	4	yes	complemented
377	#3508	C₂×C₂₃	1	4	yes	complemented
378	#3506	C₂×C₂₃	1	4	yes	complemented
379	#3498	C₂×C₂₃	1	4	yes	complemented
380	#3496	C₂×C₂₃	1	4	yes	complemented
381	#3488	C₂×C₂₃	1	8	yes	complemented
382	#3444	C₂×C₂₃	1	1	yes	characteristic, complemented
383	C₂×#532	C₂×C₂₃	1	2	yes	complemented
384	C₂²×C₂₃	—	2	2	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	2	16	no	—
388	C₂²×C₂₃	—	2	8	no	—
389	C₂²×C₂₃	—	2	16	no	—
390	C₂²×C₂₃	—	2	1	no	—
391	C₂²×C₂₃	—	2	4	no	—
392	C₂²×C₂₃	—	2	16	no	—
393	C₂²×C₂₃	—	4	4	no	—
394	C₂²×C₂₃	—	8	16	no	—
395	C₂²×C₂₃	—	16	16	no	—
396	C₂²×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
397	C₂²×C₂₃	C₂⁶	1	1	yes	characteristic
398	C₄×C₂₃	—	2	2	no	—
399	C₄×C₂₃	—	2	2	no	—
400	C₄×C₂₃	—	2	8	no	—
401	C₄×C₂₃	—	2	16	no	—
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	2	1	no	—
404	C₄×C₂₃	—	2	4	no	—
405	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
406	C₄×C₂₃	C₂×H(5,𝔽₂)	1	4	yes	—
407	C₄×C₂₃	#585	1	2	yes	—
408	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	8	yes	complemented
409	C₂²×#41	C₂²×C₂₃	1	4	yes	complemented
410	#562	C₂²×C₂₃	1	8	yes	complemented
411	H(3,𝔽₄)	C₂²×C₂₃	1	8	yes	complemented
412	#560	C₂²×C₂₃	1	16	yes	complemented
413	#559	C₂²×C₂₃	1	16	yes	complemented
414	#556	C₂²×C₂₃	1	8	yes	complemented
415	#555	C₂²×C₂₃	1	4	yes	complemented
416	#555	C₂²×C₂₃	1	8	yes	complemented
417	#554	C₂²×C₂₃	1	8	yes	complemented
418	#553	C₂²×C₂₃	1	16	yes	complemented
419	#553	C₂²×C₂₃	1	16	yes	complemented
420	#550	C₂²×C₂₃	1	16	yes	complemented
421	#550	C₂²×C₂₃	1	8	yes	complemented
422	#550	C₂²×C₂₃	1	8	yes	complemented
423	#548	C₂²×C₂₃	1	16	yes	complemented
424	#547	C₂²×C₂₃	1	8	yes	complemented
425	#547	C₂²×C₂₃	1	8	yes	complemented
426	#546	C₂²×C₂₃	1	16	yes	complemented
427	#546	C₂²×C₂₃	1	32	yes	complemented
428	#546	C₂²×C₂₃	1	16	yes	complemented
429	#546	C₂²×C₂₃	1	16	yes	complemented
430	D₄²	C₂²×C₂₃	1	16	yes	complemented
431	D₄²	C₂²×C₂₃	1	16	yes	complemented
432	D₄²	C₂²×C₂₃	1	4	yes	complemented
433	D₄²	C₂²×C₂₃	1	8	yes	complemented
434	D₄²	C₂²×C₂₃	1	16	yes	complemented
435	D₄²	C₂²×C₂₃	1	8	yes	complemented
436	#542	C₂²×C₂₃	1	16	yes	complemented
437	#540	C₂²×C₂₃	1	8	yes	complemented
438	#540	C₂²×C₂₃	1	8	yes	complemented
439	#538	C₂²×C₂₃	1	16	yes	complemented
440	#538	C₂²×C₂₃	1	32	yes	complemented
441	#537	C₂²×C₂₃	1	8	yes	complemented
442	#537	C₂²×C₂₃	1	16	yes	complemented
443	#535	C₂²×C₂₃	1	8	yes	complemented
444	#535	C₂²×C₂₃	1	16	yes	complemented
445	#535	C₂²×C₂₃	1	16	yes	complemented
446	#535	C₂²×C₂₃	1	8	yes	complemented
447	#534	C₂²×C₂₃	1	16	yes	complemented
448	#533	C₂²×C₂₃	1	2	yes	complemented
449	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
450	#533	C₂²×C₂₃	1	4	yes	complemented
451	#532	C₂²×C₂₃	1	4	yes	complemented
452	#532	C₂²×C₂₃	1	4	yes	complemented
453	#532	C₂²×C₂₃	1	4	yes	complemented
454	#532	C₂²×C₂₃	1	4	yes	complemented
455	#532	C₂²×C₂₃	1	4	yes	complemented
456	#532	C₂²×C₂₃	1	4	yes	complemented
457	#532	C₂²×C₂₃	1	4	yes	complemented
458	#532	C₂²×C₂₃	1	4	yes	complemented
459	#532	C₂²×C₂₃	1	2	yes	complemented
460	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
461	#532	C₂²×C₂₃	1	8	yes	complemented
462	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	complemented
463	C₂×#127	C₂²×C₂₃	1	2	yes	complemented
464	C₂×#127	C₂²×C₂₃	1	4	yes	complemented
465	#529	C₂²×C₂₃	1	4	yes	complemented
466	#529	C₂²×C₂₃	1	4	yes	complemented
467	#529	C₂²×C₂₃	1	4	yes	complemented
468	C₂×#124	C₂²×C₂₃	1	4	yes	complemented
469	#525	C₂²×C₂₃	1	4	yes	complemented
470	#525	C₂²×C₂₃	1	2	yes	complemented
471	#525	C₂²×C₂₃	1	16	yes	complemented
472	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
473	C₂×#121	C₂²×C₂₃	1	4	yes	complemented
474	C₂×#121	C₂²×C₂₃	1	16	yes	complemented
475	#520	C₂²×C₂₃	1	8	yes	complemented
476	#518	C₂²×C₂₃	1	8	yes	complemented
477	C₄×#41	C₂²×C₂₃	1	4	yes	complemented
478	C₄×#41	C₂²×C₂₃	1	2	yes	complemented
479	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
480	C₂×C₄×D₄	C₂²×C₂₃	1	4	yes	complemented
481	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic, complemented
482	C₂×C₂₃	—	2	4	no	—
483	C₂×C₂₃	—	4	1	no	—
484	C₂×C₂₃	—	4	16	no	—
485	C₂×C₂₃	—	4	4	no	—
486	C₂×C₂₃	C₂²×H(5,𝔽₂)	1	2	yes	—
487	C₂×C₂₃	C₂×#585	1	1	yes	characteristic
488	H(5,𝔽₂)	—	4	32	no	—
489	C₂×#41	—	4	16	no	—
490	C₂×#41	C₂³×C₂₃	1	4	yes	—
491	C₂×#41	C₂³×C₂₃	1	8	yes	—
492	C₂×#41	C₂³×C₂₃	1	2	yes	—
493	C₂×#41	C₂³×C₂₃	1	16	yes	—
494	C₂×#41	C₂³×C₂₃	1	8	yes	—
495	C₂×#41	C₂³×C₂₃	1	8	yes	—
496	C₂×#41	C₂³×C₂₃	1	8	yes	—
497	C₂×#41	C₂³×C₂₃	1	16	yes	—
498	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
499	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
500	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
501	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
502	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
503	C₂²×D₄	C₂³×C₂₃	1	32	yes	—
504	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
505	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
506	C₂²×D₄	C₂³×C₂₃	1	16	yes	—
507	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
508	C₂³×C₄	C₂³×C₂₃	1	8	yes	—
509	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
510	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
511	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
512	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
513	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
514	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
515	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
516	#127	C₂³×C₂₃	1	4	yes	—
517	#127	C₂³×C₂₃	1	4	yes	—
518	#127	C₂³×C₂₃	1	4	yes	—
519	#127	C₂³×C₂₃	1	4	yes	—
520	#127	C₂³×C₂₃	1	16	yes	—
521	#127	C₂³×C₂₃	1	8	yes	—
522	#127	C₂³×C₂₃	1	1	yes	characteristic
523	#127	C₂³×C₂₃	1	16	yes	—
524	#126	C₂³×C₂₃	1	8	yes	—
525	#126	C₂³×C₂₃	1	32	yes	—
526	#125	C₂³×C₂₃	1	4	yes	—
527	#125	C₂³×C₂₃	1	2	yes	—
528	#125	C₂³×C₂₃	1	8	yes	—
529	#124	C₂³×C₂₃	1	8	yes	—
530	#124	C₂³×C₂₃	1	8	yes	—
531	#124	C₂³×C₂₃	1	8	yes	—
532	#124	C₂³×C₂₃	1	8	yes	—
533	#124	C₂³×C₂₃	1	4	yes	—
534	#124	C₂³×C₂₃	1	2	yes	—
535	#124	C₂³×C₂₃	1	16	yes	—
536	#124	C₂³×C₂₃	1	16	yes	—
537	#124	C₂³×C₂₃	1	32	yes	—
538	#123	C₂³×C₂₃	1	8	yes	—
539	#123	C₂³×C₂₃	1	4	yes	—
540	#123	C₂³×C₂₃	1	32	yes	—
541	#123	C₂³×C₂₃	1	32	yes	—
542	#123	C₂³×C₂₃	1	32	yes	—
543	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
544	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
545	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
546	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
547	C₂²⋊Q₈	C₂³×C₂₃	1	16	yes	—
548	C₂²⋊Q₈	C₂³×C₂₃	1	32	yes	—
549	#121	C₂³×C₂₃	1	4	yes	—
550	#121	C₂³×C₂₃	1	8	yes	—
551	#121	C₂³×C₂₃	1	8	yes	—
552	#121	C₂³×C₂₃	1	8	yes	—
553	#121	C₂³×C₂₃	1	8	yes	—
554	#121	C₂³×C₂₃	1	8	yes	—
555	#121	C₂³×C₂₃	1	8	yes	—
556	#121	C₂³×C₂₃	1	8	yes	—
557	#121	C₂³×C₂₃	1	8	yes	—
558	#121	C₂³×C₂₃	1	32	yes	—
559	#121	C₂³×C₂₃	1	16	yes	—
560	#121	C₂³×C₂₃	1	16	yes	—
561	#121	C₂³×C₂₃	1	32	yes	—
562	#121	C₂³×C₂₃	1	4	yes	—
563	#121	C₂³×C₂₃	1	4	yes	—
564	#121	C₂³×C₂₃	1	16	yes	—
565	#121	C₂³×C₂₃	1	16	yes	—
566	#121	C₂³×C₂₃	1	16	yes	—
567	#121	C₂³×C₂₃	1	32	yes	—
568	#121	C₂³×C₂₃	1	32	yes	—
569	#121	C₂³×C₂₃	1	32	yes	—
570	#120	C₂³×C₂₃	1	4	yes	—
571	#120	C₂³×C₂₃	1	32	yes	—
572	#120	C₂³×C₂₃	1	16	yes	—
573	#120	C₂³×C₂₃	1	32	yes	—
574	#120	C₂³×C₂₃	1	16	yes	—
575	#120	C₂³×C₂₃	1	32	yes	—
576	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
577	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
578	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
579	C₄×Q₈	C₂³×C₂₃	1	16	yes	—
580	C₄×D₄	C₂³×C₂₃	1	8	yes	—
581	C₄×D₄	C₂³×C₂₃	1	8	yes	—
582	C₄×D₄	C₂³×C₂₃	1	8	yes	—
583	C₄×D₄	C₂³×C₂₃	1	8	yes	—
584	C₄×D₄	C₂³×C₂₃	1	8	yes	—
585	C₄×D₄	C₂³×C₂₃	1	8	yes	—
586	C₄×D₄	C₂³×C₂₃	1	8	yes	—
587	C₄×D₄	C₂³×C₂₃	1	8	yes	—
588	C₄×D₄	C₂³×C₂₃	1	8	yes	—
589	C₄×D₄	C₂³×C₂₃	1	8	yes	—
590	C₄×D₄	C₂³×C₂₃	1	8	yes	—
591	C₄×D₄	C₂³×C₂₃	1	4	yes	—
592	C₄×D₄	C₂³×C₂₃	1	4	yes	—
593	C₄×D₄	C₂³×C₂₃	1	4	yes	—
594	C₄×D₄	C₂³×C₂₃	1	32	yes	—
595	C₄×D₄	C₂³×C₂₃	1	16	yes	—
596	C₄×D₄	C₂³×C₂₃	1	32	yes	—
597	C₄×D₄	C₂³×C₂₃	1	16	yes	—
598	#117	C₂³×C₂₃	1	4	yes	—
599	#117	C₂³×C₂₃	1	4	yes	—
600	#117	C₂³×C₂₃	1	2	yes	—
601	#117	C₂³×C₂₃	1	8	yes	—
602	#117	C₂³×C₂₃	1	8	yes	—
603	#117	C₂³×C₂₃	1	16	yes	—
604	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
605	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
606	C₂×C₄⋊C₄	C₂³×C₂₃	1	16	yes	—
607	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
608	C₂×C₂²⋊C₄	C₂³×C₂₃	1	8	yes	—
609	C₂×C₂²⋊C₄	C₂³×C₂₃	1	32	yes	—
610	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
611	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
612	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
613	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
614	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
615	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
616	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
617	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
618	C₂₃	#62834	1	1	yes	characteristic, direct product factor, Sylow
619	C₂⁴	C₂⁴×C₂₃	1	1	yes	characteristic
620	C₂⁴	C₂⁴×C₂₃	1	8	yes	—
621	C₂⁴	C₂⁴×C₂₃	1	16	yes	—
622	#41	—	2	32	no	—
623	#41	—	2	16	no	—
624	#41	—	4	16	no	—
625	#41	—	4	4	no	—
626	#41	—	4	16	no	—
627	#41	—	4	16	no	—
628	#41	—	4	32	no	—
629	#41	—	4	32	no	—
630	C₂×Q₈	—	4	8	no	—
631	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
632	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
633	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
634	C₂×Q₈	C₂⁴×C₂₃	1	8	yes	—
635	C₂×D₄	—	2	16	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	32	no	—
638	C₂×D₄	—	4	32	no	—
639	C₂×D₄	—	4	8	no	—
640	C₂×D₄	—	4	16	no	—
641	C₂×D₄	—	4	16	no	—
642	C₂×D₄	—	4	64	no	—
643	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
644	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
645	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
646	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
647	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
648	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
649	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
650	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
651	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
652	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
653	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
654	C₂×D₄	C₂⁴×C₂₃	1	8	yes	—
655	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
656	C₂×D₄	C₂⁴×C₂₃	1	16	yes	—
657	C₂×D₄	C₂⁴×C₂₃	1	32	yes	—
658	C₂²×C₄	—	2	8	no	—
659	C₂²×C₄	—	4	16	no	—
660	C₂²×C₄	—	4	2	no	—
661	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
662	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
663	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
664	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
665	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
666	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
667	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
668	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
669	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
670	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
671	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
672	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
673	C₂²×C₄	C₂⁴×C₂₃	1	8	yes	—
674	C₂²×C₄	C₂⁴×C₂₃	1	16	yes	—
675	C₂²×C₄	C₂⁴×C₂₃	1	32	yes	—
676	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
677	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
678	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
679	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
680	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
681	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
682	C₄⋊C₄	C₂⁴×C₂₃	1	32	yes	—
683	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
685	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
686	C₄⋊C₄	C₂⁴×C₂₃	1	8	yes	—
687	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
688	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
689	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
690	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
691	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
692	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
693	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
694	C₂²⋊C₄	C₂⁴×C₂₃	1	16	yes	—
695	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
696	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
697	C₂²⋊C₄	C₂⁴×C₂₃	1	8	yes	—
698	C₂²⋊C₄	C₂⁴×C₂₃	1	32	yes	—
699	C₂²⋊C₄	C₂⁴×C₂₃	1	4	yes	—
700	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
701	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
702	C₄²	C₂⁴×C₂₃	1	2	yes	—
703	C₄²	C₂⁴×C₂₃	1	2	yes	—
704	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
705	C₄²	C₂⁴×C₂₃	1	2	yes	—
706	C₄²	C₂⁴×C₂₃	1	2	yes	—
707	C₄²	C₂⁴×C₂₃	1	2	yes	—
708	C₄²	C₂⁴×C₂₃	1	2	yes	—
709	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
710	C₄²	C₂⁴×C₂₃	1	4	yes	—
711	C₄²	C₂⁴×C₂₃	1	8	yes	—
712	C₄²	C₂⁴×C₂₃	1	16	yes	—
713	C₂³	—	2	4	no	—
714	C₂³	—	2	16	no	—
715	C₂³	—	4	1	no	—
716	C₂³	—	4	8	no	—
717	C₂³	—	4	8	no	—
718	C₂³	—	4	32	no	—
719	C₂³	—	4	16	no	—
720	C₂³	C₂⁵×C₂₃	1	4	yes	—
721	C₂³	C₂⁵×C₂₃	1	16	yes	—
722	C₂³	C₂⁵×C₂₃	1	1	yes	characteristic
723	C₂³	C₂⁵×C₂₃	1	2	yes	—
724	Q₈	—	2	16	no	—
725	Q₈	—	2	8	no	—
726	Q₈	—	4	8	no	—
727	Q₈	—	4	2	no	—
728	D₄	—	2	16	no	—
729	D₄	—	2	32	no	—
730	D₄	—	2	16	no	—
731	D₄	—	2	16	no	—
732	D₄	—	2	8	no	—
733	D₄	—	2	16	no	—
734	D₄	—	2	16	no	—
735	D₄	—	4	32	no	—
736	D₄	—	4	32	no	—
737	D₄	—	4	8	no	—
738	D₄	—	4	16	no	—
739	D₄	—	4	8	no	—
740	D₄	—	4	16	no	—
741	D₄	—	4	2	no	—
742	D₄	—	4	4	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	4	no	—
747	C₂×C₄	—	2	4	no	—
748	C₂×C₄	—	2	32	no	—
749	C₂×C₄	—	2	16	no	—
750	C₂×C₄	—	2	4	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	2	8	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	16	no	—
755	C₂×C₄	—	4	1	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	32	no	—
758	C₂×C₄	C₂₃×H(5,𝔽₂)	1	8	yes	complemented
759	C₂×C₄	C₂⁵×C₂₃	1	4	yes	—
760	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
761	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
762	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
763	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
764	C₂×C₄	C₂⁵×C₂₃	1	16	yes	—
765	C₂×C₄	C₂⁵×C₂₃	1	8	yes	—
766	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
767	C₂×C₄	C₂⁵×C₂₃	1	2	yes	—
768	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
769	C₂²	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	16	no	—
773	C₂²	—	2	8	no	—
774	C₂²	—	2	16	no	—
775	C₂²	—	2	1	no	—
776	C₂²	—	2	4	no	—
777	C₂²	—	2	16	no	—
778	C₂²	—	4	4	no	—
779	C₂²	—	8	16	no	—
780	C₂²	—	16	16	no	—
781	C₂²	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
782	C₂²	C₂⁶×C₂₃	1	1	yes	characteristic
783	C₄	—	2	2	no	—
784	C₄	—	2	2	no	—
785	C₄	—	2	8	no	—
786	C₄	—	2	16	no	—
787	C₄	—	2	2	no	—
788	C₄	—	2	1	no	—
789	C₄	—	2	4	no	—
790	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
791	C₄	C₂×C₂₃×H(5,𝔽₂)	1	4	yes	—
792	C₄	C₂₃×#585	1	2	yes	—
793	C₂	—	2	4	no	—
794	C₂	—	4	1	no	—
795	C₂	—	4	16	no	—
796	C₂	—	4	4	no	—
797	C₂	C₂²×C₂₃×H(5,𝔽₂)	1	2	yes	—
798	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×#3558	C₂	semidirect
2. C₂₃×#3549	C₂	semidirect
3. C₂₃×#3548	C₂	semidirect
4. C₂₃×#3546	C₂	semidirect
5. C₂₃×#3537	C₂	semidirect
6. C₂₃×#3519	C₂	semidirect
7. C₂₃×#3511	C₂	semidirect
8. C₂₃×#3508	C₂	semidirect
9. C₂₃×#3506	C₂	semidirect
10. C₂₃×#3498	C₂	semidirect
11. C₂₃×#3496	C₂	semidirect
12. C₂₃×#3488	C₂	semidirect
13. C₂₃×#3444	C₂	semidirect
14. C₂×C₂₃×#532	C₂	semidirect
15. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
16. C₂²×#41×C₂₃	C₂²	semidirect
17. C₂₃×#562	C₂²	semidirect
18. C₂₃×H(3,𝔽₄)	C₂²	semidirect
19. C₂₃×#560	C₂²	semidirect
20. C₂₃×#559	C₂²	semidirect
21. C₂₃×#556	C₂²	semidirect
22. C₂₃×#555	C₂²	semidirect
23. C₂₃×#555	C₂²	semidirect
24. C₂₃×#554	C₂²	semidirect
25. C₂₃×#553	C₂²	semidirect
26. C₂₃×#553	C₂²	semidirect
27. C₂₃×#550	C₂²	semidirect
28. C₂₃×#550	C₂²	semidirect
29. C₂₃×#550	C₂²	semidirect
30. C₂₃×#548	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. D₄²×C₂₃	C₂²	semidirect
38. D₄²×C₂₃	C₂²	semidirect
39. D₄²×C₂₃	C₂²	semidirect
40. D₄²×C₂₃	C₂²	semidirect
41. D₄²×C₂₃	C₂²	semidirect
42. D₄²×C₂₃	C₂²	semidirect
43. C₂₃×#542	C₂²	semidirect
44. C₂₃×#540	C₂²	semidirect
45. C₂₃×#540	C₂²	semidirect
46. C₂₃×#538	C₂²	semidirect
47. C₂₃×#538	C₂²	semidirect
48. C₂₃×#537	C₂²	semidirect
49. C₂₃×#537	C₂²	semidirect
50. C₂₃×#535	C₂²	semidirect
51. C₂₃×#535	C₂²	semidirect
52. C₂₃×#535	C₂²	semidirect
53. C₂₃×#535	C₂²	semidirect
54. C₂₃×#534	C₂²	semidirect
55. C₂₃×#533	C₂²	semidirect
56. C₂₃×#533	C₂²	semidirect
57. C₂₃×#533	C₂²	semidirect
58. C₂₃×#532	C₂²	semidirect
59. C₂₃×#532	C₂²	semidirect
60. C₂₃×#532	C₂²	semidirect
61. C₂₃×#532	C₂²	semidirect
62. C₂₃×#532	C₂²	semidirect
63. C₂₃×#532	C₂²	semidirect
64. C₂₃×#532	C₂²	semidirect
65. C₂₃×#532	C₂²	semidirect
66. C₂₃×#532	C₂²	semidirect
67. C₂₃×#532	C₂²	semidirect
68. C₂₃×#532	C₂²	semidirect
69. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
70. C₂×C₂₃×#127	C₂²	semidirect
71. C₂×C₂₃×#127	C₂²	semidirect
72. C₂₃×#529	C₂²	semidirect
73. C₂₃×#529	C₂²	semidirect
74. C₂₃×#529	C₂²	semidirect
75. C₂×C₂₃×#124	C₂²	semidirect
76. C₂₃×#525	C₂²	semidirect
77. C₂₃×#525	C₂²	semidirect
78. C₂₃×#525	C₂²	semidirect
79. C₂×C₂₃×#121	C₂²	semidirect
80. C₂×C₂₃×#121	C₂²	semidirect
81. C₂×C₂₃×#121	C₂²	semidirect
82. C₂₃×#520	C₂²	semidirect
83. C₂₃×#518	C₂²	semidirect
84. C₄×#41×C₂₃	C₂²	semidirect
85. C₄×#41×C₂₃	C₂²	semidirect
86. C₂×C₄×D₄×C₂₃	C₂²	semidirect
87. C₂×C₄×D₄×C₂₃	C₂²	semidirect
88. C₂²×C₄²×C₂₃	C₂²	semidirect
313. #62834	C₂₃	direct (N × H)
359. C₂×C₄×C₂₃	H(5,𝔽₂)	semidirect
370. #3558	C₂×C₂₃	semidirect
371. #3549	C₂×C₂₃	semidirect
372. #3548	C₂×C₂₃	semidirect
373. #3546	C₂×C₂₃	semidirect
374. #3537	C₂×C₂₃	semidirect
375. #3519	C₂×C₂₃	semidirect
376. #3511	C₂×C₂₃	semidirect
377. #3508	C₂×C₂₃	semidirect
378. #3506	C₂×C₂₃	semidirect
379. #3498	C₂×C₂₃	semidirect
380. #3496	C₂×C₂₃	semidirect
381. #3488	C₂×C₂₃	semidirect
382. #3444	C₂×C₂₃	semidirect
383. C₂×#532	C₂×C₂₃	semidirect
408. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
409. C₂²×#41	C₂²×C₂₃	semidirect
410. #562	C₂²×C₂₃	semidirect
411. H(3,𝔽₄)	C₂²×C₂₃	semidirect
412. #560	C₂²×C₂₃	semidirect
413. #559	C₂²×C₂₃	semidirect
414. #556	C₂²×C₂₃	semidirect
415. #555	C₂²×C₂₃	semidirect
416. #555	C₂²×C₂₃	semidirect
417. #554	C₂²×C₂₃	semidirect
418. #553	C₂²×C₂₃	semidirect
419. #553	C₂²×C₂₃	semidirect
420. #550	C₂²×C₂₃	semidirect
421. #550	C₂²×C₂₃	semidirect
422. #550	C₂²×C₂₃	semidirect
423. #548	C₂²×C₂₃	semidirect
424. #547	C₂²×C₂₃	semidirect
425. #547	C₂²×C₂₃	semidirect
426. #546	C₂²×C₂₃	semidirect
427. #546	C₂²×C₂₃	semidirect
428. #546	C₂²×C₂₃	semidirect
429. #546	C₂²×C₂₃	semidirect
430. D₄²	C₂²×C₂₃	semidirect
431. D₄²	C₂²×C₂₃	semidirect
432. D₄²	C₂²×C₂₃	semidirect
433. D₄²	C₂²×C₂₃	semidirect
434. D₄²	C₂²×C₂₃	semidirect
435. D₄²	C₂²×C₂₃	semidirect
436. #542	C₂²×C₂₃	semidirect
437. #540	C₂²×C₂₃	semidirect
438. #540	C₂²×C₂₃	semidirect
439. #538	C₂²×C₂₃	semidirect
440. #538	C₂²×C₂₃	semidirect
441. #537	C₂²×C₂₃	semidirect
442. #537	C₂²×C₂₃	semidirect
443. #535	C₂²×C₂₃	semidirect
444. #535	C₂²×C₂₃	semidirect
445. #535	C₂²×C₂₃	semidirect
446. #535	C₂²×C₂₃	semidirect
447. #534	C₂²×C₂₃	semidirect
448. #533	C₂²×C₂₃	semidirect
449. #533	C₂²×C₂₃	semidirect
450. #533	C₂²×C₂₃	semidirect
451. #532	C₂²×C₂₃	semidirect
452. #532	C₂²×C₂₃	semidirect
453. #532	C₂²×C₂₃	semidirect
454. #532	C₂²×C₂₃	semidirect
455. #532	C₂²×C₂₃	semidirect
456. #532	C₂²×C₂₃	semidirect
457. #532	C₂²×C₂₃	semidirect
458. #532	C₂²×C₂₃	semidirect
459. #532	C₂²×C₂₃	semidirect
460. #532	C₂²×C₂₃	semidirect
461. #532	C₂²×C₂₃	semidirect
462. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
463. C₂×#127	C₂²×C₂₃	semidirect
464. C₂×#127	C₂²×C₂₃	semidirect
465. #529	C₂²×C₂₃	semidirect
466. #529	C₂²×C₂₃	semidirect
467. #529	C₂²×C₂₃	semidirect
468. C₂×#124	C₂²×C₂₃	semidirect
469. #525	C₂²×C₂₃	semidirect
470. #525	C₂²×C₂₃	semidirect
471. #525	C₂²×C₂₃	semidirect
472. C₂×#121	C₂²×C₂₃	semidirect
473. C₂×#121	C₂²×C₂₃	semidirect
474. C₂×#121	C₂²×C₂₃	semidirect
475. #520	C₂²×C₂₃	semidirect
476. #518	C₂²×C₂₃	semidirect
477. C₄×#41	C₂²×C₂₃	semidirect
478. C₄×#41	C₂²×C₂₃	semidirect
479. C₂×C₄×D₄	C₂²×C₂₃	semidirect
480. C₂×C₄×D₄	C₂²×C₂₃	semidirect
481. C₂²×C₄²	C₂²×C₂₃	semidirect
618. C₂₃	#62834	direct (N × H)
758. 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×#3558	2
C₂₃×#3549	2
C₂₃×#3548	2
C₂₃×#3546	2
C₂₃×#3537	2
C₂₃×#3519	2
C₂₃×#3511	2
C₂₃×#3508	2
C₂₃×#3506	2
C₂₃×#3498	2
C₂₃×#3496	2
C₂₃×#3488	2
C₂₃×#3444	2
C₂×C₂₃×#532	2
#62834	23

Subgroups — C23×#62834 #19210460

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#62834 #19210460