Subgroups — C₂₃×#61684 #19209310

Order 5888.

2152 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3548	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3330	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3314	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3294	C₂	1	2	yes	maximal, complemented
6	C₂₃×#3283	C₂	1	2	yes	maximal, complemented
7	C₂₃×#3272	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3268	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3214	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂₃×#3203	C₂	1	4	yes	maximal, complemented
12	C₂₃×#3110	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂₃×#3100	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3012	C₂	1	4	yes	maximal, complemented
15	C₂₃×#2981	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
18	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
19	C₂₃×#562	—	2	2	no	—
20	C₂₃×#554	—	2	1	no	—
21	C₂₃×#554	C₂²	1	2	yes	complemented
22	C₂₃×#550	—	2	1	no	—
23	C₂₃×#550	C₂²	1	2	yes	complemented
24	C₂₃×#547	—	2	1	no	—
25	C₂₃×#547	C₂²	1	2	yes	—
26	C₂₃×#547	C₂²	1	2	yes	complemented
27	C₂₃×#547	C₂²	1	2	yes	complemented
28	C₂₃×#546	—	2	2	no	—
29	C₂₃×#546	C₂²	1	4	yes	—
30	D₄²×C₂₃	—	2	1	no	—
31	D₄²×C₂₃	C₂²	1	2	yes	—
32	C₂₃×#540	—	2	2	no	—
33	C₂₃×#537	—	2	2	no	—
34	C₂₃×#537	C₂²	1	2	yes	—
35	C₂₃×#537	C₂²	1	4	yes	complemented
36	C₂₃×#534	—	2	2	no	—
37	C₂₃×#533	C₂²	1	1	yes	characteristic, complemented
38	C₂₃×#532	C₂²	1	1	yes	characteristic
39	C₂₃×#532	C₂²	1	1	yes	characteristic
40	C₂₃×#532	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₂₃×#121	—	2	2	no	—
42	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
43	C₂₃×#496	C₂²	1	2	yes	complemented
44	C₂₃×#494	C₂²	1	1	yes	characteristic, complemented
45	C₂₃×#492	C₂²	1	1	yes	characteristic, complemented
46	C₂₃×#489	C₂²	1	2	yes	complemented
47	C₂₃×#487	C₂²	1	1	yes	characteristic, complemented
48	C₂₃×#486	C₂²	1	1	yes	characteristic, complemented
49	C₂₃×#484	C₂²	1	2	yes	complemented
50	C₂₃×#484	C₂²	1	4	yes	complemented
51	C₂₃×#480	C₂²	1	2	yes	complemented
52	C₂₃×#480	C₂²	1	4	yes	complemented
53	C₂₃×#474	C₂²	1	2	yes	complemented
54	C₂₃×#474	C₂²	1	2	yes	complemented
55	C₂₃×#468	C₂²	1	4	yes	complemented
56	C₂₃×#468	C₂²	1	4	yes	complemented
57	C₂₃×#467	C₂²	1	4	yes	complemented
58	C₂₃×#466	C₂²	1	4	yes	complemented
59	C₂₃×#464	C₂²	1	4	yes	complemented
60	C₂₃×#461	C₂²	1	2	yes	complemented
61	C₂₃×#461	C₂²	1	2	yes	complemented
62	C₂₃×#459	C₂²	1	2	yes	complemented
63	C₂₃×#459	C₂²	1	2	yes	complemented
64	C₂₃×#452	C₂²	1	4	yes	complemented
65	C₂₃×#452	C₂²	1	4	yes	complemented
66	C₂₃×#452	C₂²	1	4	yes	complemented
67	C₂₃×#450	C₂²	1	2	yes	—
68	C₂₃×#450	C₂²	1	4	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#449	C₂²	1	4	yes	complemented
71	C₂₃×#449	C₂²	1	4	yes	complemented
72	C₂₃×#447	C₂²	1	2	yes	—
73	C₂₃×#447	C₂²	1	4	yes	complemented
74	C₂₃×#440	C₂²	1	4	yes	complemented
75	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
76	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
77	C₂₃×#436	C₂²	1	2	yes	complemented
78	C₂₃×#435	C₂²	1	4	yes	complemented
79	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
80	C₂₃×#432	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#431	C₂²	1	1	yes	characteristic, complemented
82	C₂₃×#417	C₂²	1	4	yes	complemented
83	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
84	C₂₃×#408	C₂²	1	4	yes	complemented
85	C₂₃×H(5,𝔽₂)	—	4	8	no	—
86	C₂×#41×C₂₃	—	2	2	no	—
87	C₂×#41×C₂₃	—	2	2	no	—
88	C₂×#41×C₂₃	—	2	1	no	—
89	C₂×#41×C₂₃	C₂³	1	4	yes	—
90	C₂×#41×C₂₃	C₂³	1	4	yes	—
91	C₂×#41×C₂₃	C₂³	1	2	yes	—
92	C₂×#41×C₂₃	C₂³	1	2	yes	—
93	C₂²×D₄×C₂₃	—	2	4	no	—
94	C₂²×D₄×C₂₃	—	2	2	no	—
95	C₂²×D₄×C₂₃	—	2	2	no	—
96	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
98	C₂³×C₄×C₂₃	—	2	1	no	—
99	C₂₃×AGL(1,ℤ/8)	—	4	8	no	—
100	C₂₃×#135	—	4	8	no	—
101	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
102	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
105	C₂×D₈×C₂₃	C₂³	1	2	yes	—
106	C₂×D₈×C₂₃	C₂³	1	2	yes	—
107	C₂×D₈×C₂₃	C₂³	1	4	yes	—
108	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
110	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
111	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
112	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
113	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
114	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
115	C₂₃×#127	—	2	2	no	—
116	C₂₃×#127	D₄	1	1	yes	characteristic
117	C₂₃×#127	C₂³	1	1	yes	characteristic
118	C₂₃×#127	C₂³	1	1	yes	characteristic
119	C₂₃×#125	—	2	2	no	—
120	C₂₃×#125	—	2	1	no	—
121	C₂₃×#124	—	2	1	no	—
122	C₂₃×#124	D₄	1	2	yes	—
123	C₂₃×#124	C₂³	1	2	yes	—
124	C₂₃×#123	—	2	4	no	—
125	C₂₃×#123	—	2	4	no	—
126	C₂₃×#123	—	2	4	no	—
127	C₂₃×#123	—	2	4	no	—
128	C₂₃×C₂²⋊Q₈	—	2	2	no	—
129	C₂₃×C₂²⋊Q₈	—	2	4	no	—
130	C₂₃×C₂²⋊Q₈	—	2	1	no	—
131	C₂₃×C₂²⋊Q₈	—	2	2	no	—
132	C₂₃×C₂²⋊Q₈	—	2	4	no	—
133	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
134	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
135	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
136	C₂₃×#121	—	2	2	no	—
137	C₂₃×#121	—	2	2	no	—
138	C₂₃×#121	—	2	4	no	—
139	C₂₃×#121	—	2	4	no	—
140	C₂₃×#121	—	2	4	no	—
141	C₂₃×#121	—	2	4	no	—
142	C₂₃×#121	—	2	2	no	—
143	C₂₃×#121	—	2	1	no	—
144	C₂₃×#121	—	2	1	no	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	2	no	—
147	C₂₃×#121	—	2	4	no	—
148	C₂₃×#121	—	2	4	no	—
149	C₂₃×#121	D₄	1	2	yes	—
150	C₂₃×#121	D₄	1	2	yes	—
151	C₂₃×#121	C₂³	1	4	yes	—
152	C₂₃×#121	C₂³	1	2	yes	—
153	C₂₃×#121	C₂³	1	4	yes	—
154	C₂₃×#120	—	2	4	no	—
155	C₂₃×#120	—	2	4	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
158	C₄×D₄×C₂₃	—	2	2	no	—
159	C₄×D₄×C₂₃	—	2	2	no	—
160	C₄×D₄×C₂₃	—	2	1	no	—
161	C₄×D₄×C₂₃	—	2	1	no	—
162	C₄×D₄×C₂₃	—	2	1	no	—
163	C₄×D₄×C₂₃	—	2	1	no	—
164	C₄×D₄×C₂₃	—	2	1	no	—
165	C₄×D₄×C₂₃	C₂³	1	2	yes	—
166	C₄×D₄×C₂₃	C₂³	1	2	yes	—
167	C₄×D₄×C₂₃	C₂³	1	2	yes	—
168	C₄×D₄×C₂₃	C₂³	1	2	yes	—
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₂₃×#117	—	2	1	no	—
171	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
172	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
174	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
175	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
176	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
177	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
178	C₂₃×#107	C₂³	1	2	yes	—
179	C₂₃×#107	C₂³	1	2	yes	—
180	C₂₃×#107	C₂³	1	4	yes	—
181	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
182	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
183	C₂₃×#103	C₂³	1	4	yes	—
184	C₂₃×#103	C₂³	1	4	yes	—
185	C₂₃×#103	C₂³	1	4	yes	—
186	C₂₃×#102	C₂³	1	2	yes	—
187	C₂₃×#102	C₂³	1	4	yes	—
188	C₂₃×#102	C₂³	1	4	yes	—
189	C₂₃×#102	C₂³	1	4	yes	—
190	C₂₃×#102	C₂³	1	2	yes	—
191	C₂₃×#102	C₂³	1	2	yes	—
192	C₂₃×#102	C₂³	1	2	yes	—
193	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
194	C₂₃×C₂²⋊C₈	C₂³	1	2	yes	—
195	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
196	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
197	C₂₃×#97	C₂³	1	2	yes	—
198	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
199	C₄×C₈×C₂₃	C₂³	1	1	yes	characteristic
200	C₂⁴×C₂₃	—	2	1	no	—
201	C₂⁴×C₂₃	—	2	4	no	—
202	#41×C₂₃	—	2	8	no	—
203	#41×C₂₃	—	4	4	no	—
204	#41×C₂₃	—	4	4	no	—
205	#41×C₂₃	—	4	4	no	—
206	#41×C₂₃	—	4	4	no	—
207	#41×C₂₃	—	4	4	no	—
208	#41×C₂₃	—	4	8	no	—
209	#41×C₂₃	—	8	2	no	—
210	#41×C₂₃	—	8	4	no	—
211	C₂×Q₈×C₂₃	—	2	1	no	—
212	C₂×Q₈×C₂₃	—	2	1	no	—
213	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
214	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
215	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
216	C₂×D₄×C₂₃	—	2	4	no	—
217	C₂×D₄×C₂₃	—	2	8	no	—
218	C₂×D₄×C₂₃	—	2	4	no	—
219	C₂×D₄×C₂₃	—	2	2	no	—
220	C₂×D₄×C₂₃	—	2	4	no	—
221	C₂×D₄×C₂₃	—	2	2	no	—
222	C₂×D₄×C₂₃	—	2	4	no	—
223	C₂×D₄×C₂₃	—	2	4	no	—
224	C₂×D₄×C₂₃	—	2	1	no	—
225	C₂×D₄×C₂₃	—	2	1	no	—
226	C₂×D₄×C₂₃	—	2	1	no	—
227	C₂×D₄×C₂₃	—	2	4	no	—
228	C₂×D₄×C₂₃	—	2	1	no	—
229	C₂×D₄×C₂₃	—	2	1	no	—
230	C₂×D₄×C₂₃	—	4	4	no	—
231	C₂×D₄×C₂₃	—	4	8	no	—
232	C₂×D₄×C₂₃	—	4	16	no	—
233	C₂×D₄×C₂₃	—	8	4	no	—
234	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
235	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
236	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
237	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₂₃	—	2	1	no	—
242	C₂²×C₄×C₂₃	—	2	4	no	—
243	C₂²×C₄×C₂₃	—	2	4	no	—
244	C₂²×C₄×C₂₃	—	2	2	no	—
245	C₂²×C₄×C₂₃	—	2	2	no	—
246	C₂²×C₄×C₂₃	—	2	2	no	—
247	C₂²×C₄×C₂₃	—	2	2	no	—
248	C₂²×C₄×C₂₃	—	2	4	no	—
249	C₂²×C₄×C₂₃	—	8	2	no	—
250	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
253	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
254	Q₁₆×C₂₃	—	4	4	no	—
255	SD₁₆×C₂₃	—	2	8	no	—
256	SD₁₆×C₂₃	—	4	4	no	—
257	SD₁₆×C₂₃	—	4	4	no	—
258	D₈×C₂₃	—	2	4	no	—
259	D₈×C₂₃	—	2	4	no	—
260	D₈×C₂₃	—	4	4	no	—
261	M₁₆×C₂₃	—	4	4	no	—
262	C₂×C₈×C₂₃	—	4	4	no	—
263	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
264	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
265	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
266	C₄⋊C₄×C₂₃	—	2	1	no	—
267	C₄⋊C₄×C₂₃	—	2	1	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	1	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	1	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	1	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	2	no	—
278	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
279	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
280	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
281	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
282	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	—	2	2	no	—
285	C₂²⋊C₄×C₂₃	—	2	4	no	—
286	C₂²⋊C₄×C₂₃	—	2	2	no	—
287	C₂²⋊C₄×C₂₃	—	2	2	no	—
288	C₂²⋊C₄×C₂₃	—	2	2	no	—
289	C₂²⋊C₄×C₂₃	—	2	4	no	—
290	C₂²⋊C₄×C₂₃	—	2	2	no	—
291	C₂²⋊C₄×C₂₃	—	2	4	no	—
292	C₂²⋊C₄×C₂₃	—	2	2	no	—
293	C₂²⋊C₄×C₂₃	—	2	2	no	—
294	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
295	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
296	C₄²×C₂₃	—	2	2	no	—
297	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
298	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
299	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
300	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
301	#61684	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
302	C₂³×C₂₃	—	2	4	no	—
303	C₂³×C₂₃	—	2	2	no	—
304	C₂³×C₂₃	—	2	2	no	—
305	C₂³×C₂₃	—	2	2	no	—
306	C₂³×C₂₃	—	4	8	no	—
307	C₂³×C₂₃	—	8	1	no	—
308	C₂³×C₂₃	—	8	1	no	—
309	C₂³×C₂₃	—	8	4	no	—
310	C₂³×C₂₃	—	8	4	no	—
311	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
312	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
313	Q₈×C₂₃	—	2	4	no	—
314	Q₈×C₂₃	—	2	4	no	—
315	Q₈×C₂₃	—	4	2	no	—
316	Q₈×C₂₃	—	4	2	no	—
317	Q₈×C₂₃	—	8	1	no	—
318	D₄×C₂₃	—	2	4	no	—
319	D₄×C₂₃	—	2	4	no	—
320	D₄×C₂₃	—	2	2	no	—
321	D₄×C₂₃	—	2	2	no	—
322	D₄×C₂₃	—	2	2	no	—
323	D₄×C₂₃	—	2	4	no	—
324	D₄×C₂₃	—	4	2	no	—
325	D₄×C₂₃	—	4	4	no	—
326	D₄×C₂₃	—	4	2	no	—
327	D₄×C₂₃	—	4	8	no	—
328	D₄×C₂₃	—	4	2	no	—
329	D₄×C₂₃	—	4	8	no	—
330	D₄×C₂₃	—	4	4	no	—
331	D₄×C₂₃	—	4	2	no	—
332	D₄×C₂₃	—	8	1	no	—
333	D₄×C₂₃	—	8	1	no	—
334	D₄×C₂₃	—	8	4	no	—
335	D₄×C₂₃	—	8	4	no	—
336	D₄×C₂₃	—	8	2	no	—
337	D₄×C₂₃	—	8	4	no	—
338	D₄×C₂₃	H(5,𝔽₂)	1	4	yes	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	4	no	—
341	C₂×C₄×C₂₃	—	2	4	no	—
342	C₂×C₄×C₂₃	—	2	2	no	—
343	C₂×C₄×C₂₃	—	2	2	no	—
344	C₂×C₄×C₂₃	—	2	2	no	—
345	C₂×C₄×C₂₃	—	2	2	no	—
346	C₂×C₄×C₂₃	—	2	2	no	—
347	C₂×C₄×C₂₃	—	2	2	no	—
348	C₂×C₄×C₂₃	—	4	1	no	—
349	C₂×C₄×C₂₃	—	4	8	no	—
350	C₂×C₄×C₂₃	—	4	4	no	—
351	C₂×C₄×C₂₃	—	4	4	no	—
352	C₂×C₄×C₂₃	—	4	4	no	—
353	C₂×C₄×C₂₃	—	8	2	no	—
354	C₂×C₄×C₂₃	—	8	4	no	—
355	C₂×C₄×C₂₃	—	8	1	no	—
356	C₂×C₄×C₂₃	—	8	4	no	—
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
359	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
360	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
361	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
362	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
363	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
364	C₈×C₂₃	—	2	2	no	—
365	C₈×C₂₃	—	2	4	no	—
366	C₈×C₂₃	—	2	2	no	—
367	#3548	C₂×C₂₃	1	1	yes	characteristic, complemented
368	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
369	#3330	C₂×C₂₃	1	2	yes	complemented
370	#3314	C₂×C₂₃	1	4	yes	complemented
371	#3294	C₂×C₂₃	1	2	yes	complemented
372	#3283	C₂×C₂₃	1	2	yes	complemented
373	#3272	C₂×C₂₃	1	2	yes	complemented
374	#3268	C₂×C₂₃	1	4	yes	complemented
375	#3214	C₂×C₂₃	1	1	yes	characteristic, complemented
376	#3210	C₂×C₂₃	1	1	yes	characteristic, complemented
377	#3203	C₂×C₂₃	1	4	yes	complemented
378	#3110	C₂×C₂₃	1	1	yes	characteristic, complemented
379	#3100	C₂×C₂₃	1	1	yes	characteristic, complemented
380	#3012	C₂×C₂₃	1	4	yes	complemented
381	#2981	C₂×C₂₃	1	1	yes	characteristic, complemented
382	C₂²×C₂₃	—	2	1	no	—
383	C₂²×C₂₃	—	2	4	no	—
384	C₂²×C₂₃	—	2	1	no	—
385	C₂²×C₂₃	—	2	4	no	—
386	C₂²×C₂₃	—	2	4	no	—
387	C₂²×C₂₃	—	2	1	no	—
388	C₂²×C₂₃	—	2	4	no	—
389	C₂²×C₂₃	—	4	2	no	—
390	C₂²×C₂₃	—	4	2	no	—
391	C₂²×C₂₃	—	4	2	no	—
392	C₂²×C₂₃	—	4	2	no	—
393	C₂²×C₂₃	—	4	2	no	—
394	C₂²×C₂₃	—	4	2	no	—
395	C₂²×C₂₃	—	4	2	no	—
396	C₂²×C₂₃	—	4	2	no	—
397	C₂²×C₂₃	—	8	4	no	—
398	C₂²×C₂₃	—	16	8	no	—
399	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
400	C₄×C₂₃	—	2	1	no	—
401	C₄×C₂₃	—	2	1	no	—
402	C₄×C₂₃	—	2	1	no	—
403	C₄×C₂₃	—	2	4	no	—
404	C₄×C₂₃	—	2	1	no	—
405	C₄×C₂₃	—	4	2	no	—
406	C₄×C₂₃	—	4	2	no	—
407	C₄×C₂₃	—	4	2	no	—
408	C₄×C₂₃	—	4	2	no	—
409	C₄×C₂₃	—	4	2	no	—
410	C₄×C₂₃	#576	1	2	yes	—
411	C₄×C₂₃	C₂×H(5,𝔽₂)	1	2	yes	—
412	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
413	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
414	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
415	#562	—	2	2	no	—
416	#554	—	2	1	no	—
417	#554	C₂²×C₂₃	1	2	yes	complemented
418	#550	—	2	1	no	—
419	#550	C₂²×C₂₃	1	2	yes	complemented
420	#547	—	2	1	no	—
421	#547	C₂²×C₂₃	1	2	yes	—
422	#547	C₂²×C₂₃	1	2	yes	complemented
423	#547	C₂²×C₂₃	1	2	yes	complemented
424	#546	—	2	2	no	—
425	#546	C₂²×C₂₃	1	4	yes	—
426	D₄²	—	2	1	no	—
427	D₄²	C₂²×C₂₃	1	2	yes	—
428	#540	—	2	2	no	—
429	#537	—	2	2	no	—
430	#537	C₂²×C₂₃	1	2	yes	—
431	#537	C₂²×C₂₃	1	4	yes	complemented
432	#534	—	2	2	no	—
433	#533	C₂²×C₂₃	1	1	yes	characteristic, complemented
434	#532	C₂²×C₂₃	1	1	yes	characteristic
435	#532	C₂²×C₂₃	1	1	yes	characteristic
436	#532	C₂²×C₂₃	1	1	yes	characteristic, complemented
437	C₂×#121	—	2	2	no	—
438	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
439	#496	C₂²×C₂₃	1	2	yes	complemented
440	#494	C₂²×C₂₃	1	1	yes	characteristic, complemented
441	#492	C₂²×C₂₃	1	1	yes	characteristic, complemented
442	#489	C₂²×C₂₃	1	2	yes	complemented
443	#487	C₂²×C₂₃	1	1	yes	characteristic, complemented
444	#486	C₂²×C₂₃	1	1	yes	characteristic, complemented
445	#484	C₂²×C₂₃	1	4	yes	complemented
446	#484	C₂²×C₂₃	1	2	yes	complemented
447	#480	C₂²×C₂₃	1	2	yes	complemented
448	#480	C₂²×C₂₃	1	4	yes	complemented
449	#474	C₂²×C₂₃	1	2	yes	complemented
450	#474	C₂²×C₂₃	1	2	yes	complemented
451	#468	C₂²×C₂₃	1	4	yes	complemented
452	#468	C₂²×C₂₃	1	4	yes	complemented
453	#467	C₂²×C₂₃	1	4	yes	complemented
454	#466	C₂²×C₂₃	1	4	yes	complemented
455	#464	C₂²×C₂₃	1	4	yes	complemented
456	#461	C₂²×C₂₃	1	2	yes	complemented
457	#461	C₂²×C₂₃	1	2	yes	complemented
458	#459	C₂²×C₂₃	1	2	yes	complemented
459	#459	C₂²×C₂₃	1	2	yes	complemented
460	#452	C₂²×C₂₃	1	4	yes	complemented
461	#452	C₂²×C₂₃	1	4	yes	complemented
462	#452	C₂²×C₂₃	1	4	yes	complemented
463	#450	C₂²×C₂₃	1	2	yes	—
464	#450	C₂²×C₂₃	1	4	yes	complemented
465	#449	C₂²×C₂₃	1	4	yes	complemented
466	#449	C₂²×C₂₃	1	4	yes	complemented
467	#449	C₂²×C₂₃	1	4	yes	complemented
468	#447	C₂²×C₂₃	1	2	yes	—
469	#447	C₂²×C₂₃	1	4	yes	complemented
470	#440	C₂²×C₂₃	1	4	yes	complemented
471	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
472	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
473	#436	C₂²×C₂₃	1	2	yes	complemented
474	#435	C₂²×C₂₃	1	4	yes	complemented
475	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
476	#432	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	#431	C₂²×C₂₃	1	1	yes	characteristic, complemented
478	#417	C₂²×C₂₃	1	4	yes	complemented
479	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
480	#408	C₂²×C₂₃	1	4	yes	complemented
481	C₂×C₂₃	—	4	1	no	—
482	C₂×C₂₃	—	4	4	no	—
483	C₂×C₂₃	—	4	4	no	—
484	C₂×C₂₃	—	8	2	no	—
485	C₂×C₂₃	—	8	2	no	—
486	C₂×C₂₃	#3484	1	1	yes	characteristic
487	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
488	C₂×C₂₃	#3586	1	1	yes	characteristic
489	H(5,𝔽₂)	—	4	8	no	—
490	C₂×#41	—	2	2	no	—
491	C₂×#41	—	2	2	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	C₂³×C₂₃	1	4	yes	—
494	C₂×#41	C₂³×C₂₃	1	2	yes	—
495	C₂×#41	C₂³×C₂₃	1	4	yes	—
496	C₂×#41	C₂³×C₂₃	1	2	yes	—
497	C₂²×D₄	—	2	4	no	—
498	C₂²×D₄	—	2	2	no	—
499	C₂²×D₄	—	2	2	no	—
500	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
502	C₂³×C₄	—	2	1	no	—
503	AGL(1,ℤ/8)	—	4	8	no	—
504	#135	—	4	8	no	—
505	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
506	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
507	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
509	C₂×D₈	C₂³×C₂₃	1	2	yes	—
510	C₂×D₈	C₂³×C₂₃	1	2	yes	—
511	C₂×D₈	C₂³×C₂₃	1	4	yes	—
512	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
513	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
514	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
515	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
518	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
519	#127	—	2	2	no	—
520	#127	D₄×C₂₃	1	1	yes	characteristic
521	#127	C₂³×C₂₃	1	1	yes	characteristic
522	#127	C₂³×C₂₃	1	1	yes	characteristic
523	#125	—	2	2	no	—
524	#125	—	2	1	no	—
525	#124	—	2	1	no	—
526	#124	D₄×C₂₃	1	2	yes	—
527	#124	C₂³×C₂₃	1	2	yes	—
528	#123	—	2	4	no	—
529	#123	—	2	4	no	—
530	#123	—	2	4	no	—
531	#123	—	2	4	no	—
532	C₂²⋊Q₈	—	2	2	no	—
533	C₂²⋊Q₈	—	2	4	no	—
534	C₂²⋊Q₈	—	2	1	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	—	2	4	no	—
537	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
538	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
539	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
540	#121	—	2	4	no	—
541	#121	—	2	2	no	—
542	#121	—	2	4	no	—
543	#121	—	2	4	no	—
544	#121	—	2	2	no	—
545	#121	—	2	2	no	—
546	#121	—	2	4	no	—
547	#121	—	2	1	no	—
548	#121	—	2	1	no	—
549	#121	—	2	1	no	—
550	#121	—	2	2	no	—
551	#121	—	2	4	no	—
552	#121	—	2	4	no	—
553	#121	D₄×C₂₃	1	2	yes	—
554	#121	D₄×C₂₃	1	2	yes	—
555	#121	C₂³×C₂₃	1	2	yes	—
556	#121	C₂³×C₂₃	1	4	yes	—
557	#121	C₂³×C₂₃	1	4	yes	—
558	#120	—	2	4	no	—
559	#120	—	2	4	no	—
560	C₄×Q₈	—	2	1	no	—
561	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
562	C₄×D₄	—	2	2	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	1	no	—
566	C₄×D₄	—	2	1	no	—
567	C₄×D₄	—	2	1	no	—
568	C₄×D₄	—	2	1	no	—
569	C₄×D₄	C₂³×C₂₃	1	2	yes	—
570	C₄×D₄	C₂³×C₂₃	1	2	yes	—
571	C₄×D₄	C₂³×C₂₃	1	2	yes	—
572	C₄×D₄	C₂³×C₂₃	1	2	yes	—
573	C₄×D₄	C₂³×C₂₃	1	2	yes	—
574	#117	—	2	1	no	—
575	C₂×C₄⋊C₄	—	2	2	no	—
576	C₂×C₄⋊C₄	—	2	2	no	—
577	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
578	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
579	C₂×C₂²⋊C₄	—	2	1	no	—
580	C₂×C₂²⋊C₄	—	2	4	no	—
581	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
582	#107	C₂³×C₂₃	1	2	yes	—
583	#107	C₂³×C₂₃	1	2	yes	—
584	#107	C₂³×C₂₃	1	4	yes	—
585	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
586	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
587	#103	C₂³×C₂₃	1	4	yes	—
588	#103	C₂³×C₂₃	1	4	yes	—
589	#103	C₂³×C₂₃	1	4	yes	—
590	#102	C₂³×C₂₃	1	2	yes	—
591	#102	C₂³×C₂₃	1	4	yes	—
592	#102	C₂³×C₂₃	1	4	yes	—
593	#102	C₂³×C₂₃	1	4	yes	—
594	#102	C₂³×C₂₃	1	2	yes	—
595	#102	C₂³×C₂₃	1	2	yes	—
596	#102	C₂³×C₂₃	1	2	yes	—
597	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
598	C₂²⋊C₈	C₂³×C₂₃	1	2	yes	—
599	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
600	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
601	#97	C₂³×C₂₃	1	2	yes	—
602	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
603	C₄×C₈	C₂³×C₂₃	1	1	yes	characteristic
604	C₂₃	#61684	1	1	yes	characteristic, direct product factor, Sylow
605	C₂⁴	—	2	1	no	—
606	C₂⁴	—	2	4	no	—
607	#41	—	2	8	no	—
608	#41	—	4	4	no	—
609	#41	—	4	4	no	—
610	#41	—	4	4	no	—
611	#41	—	4	4	no	—
612	#41	—	4	4	no	—
613	#41	—	4	8	no	—
614	#41	—	8	2	no	—
615	#41	—	8	4	no	—
616	C₂×Q₈	—	2	1	no	—
617	C₂×Q₈	—	2	1	no	—
618	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
619	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
620	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
621	C₂×D₄	—	2	4	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	4	no	—
624	C₂×D₄	—	2	2	no	—
625	C₂×D₄	—	2	4	no	—
626	C₂×D₄	—	2	2	no	—
627	C₂×D₄	—	2	4	no	—
628	C₂×D₄	—	2	4	no	—
629	C₂×D₄	—	2	1	no	—
630	C₂×D₄	—	2	1	no	—
631	C₂×D₄	—	2	1	no	—
632	C₂×D₄	—	2	4	no	—
633	C₂×D₄	—	2	1	no	—
634	C₂×D₄	—	2	1	no	—
635	C₂×D₄	—	4	4	no	—
636	C₂×D₄	—	4	8	no	—
637	C₂×D₄	—	4	16	no	—
638	C₂×D₄	—	8	4	no	—
639	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
640	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
641	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
642	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
643	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
644	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
645	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
646	C₂²×C₄	—	2	1	no	—
647	C₂²×C₄	—	2	4	no	—
648	C₂²×C₄	—	2	4	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	4	no	—
654	C₂²×C₄	—	8	2	no	—
655	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
656	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
657	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
658	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
659	Q₁₆	—	4	4	no	—
660	SD₁₆	—	2	8	no	—
661	SD₁₆	—	4	4	no	—
662	SD₁₆	—	4	4	no	—
663	D₈	—	2	4	no	—
664	D₈	—	2	4	no	—
665	D₈	—	4	4	no	—
666	M₁₆	—	4	4	no	—
667	C₂×C₈	—	4	4	no	—
668	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
669	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
670	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
671	C₄⋊C₄	—	2	1	no	—
672	C₄⋊C₄	—	2	1	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	1	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	1	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	—	2	1	no	—
681	C₄⋊C₄	—	2	2	no	—
682	C₄⋊C₄	—	2	2	no	—
683	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
685	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
686	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
687	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	2	no	—
690	C₂²⋊C₄	—	2	4	no	—
691	C₂²⋊C₄	—	2	2	no	—
692	C₂²⋊C₄	—	2	2	no	—
693	C₂²⋊C₄	—	2	2	no	—
694	C₂²⋊C₄	—	2	4	no	—
695	C₂²⋊C₄	—	2	2	no	—
696	C₂²⋊C₄	—	2	4	no	—
697	C₂²⋊C₄	—	2	2	no	—
698	C₂²⋊C₄	—	2	2	no	—
699	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
700	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
701	C₄²	—	2	2	no	—
702	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
703	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
704	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
705	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
706	C₂³	—	2	4	no	—
707	C₂³	—	2	2	no	—
708	C₂³	—	2	2	no	—
709	C₂³	—	2	2	no	—
710	C₂³	—	4	8	no	—
711	C₂³	—	8	1	no	—
712	C₂³	—	8	1	no	—
713	C₂³	—	8	4	no	—
714	C₂³	—	8	4	no	—
715	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
716	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
717	Q₈	—	2	4	no	—
718	Q₈	—	2	4	no	—
719	Q₈	—	4	2	no	—
720	Q₈	—	4	2	no	—
721	Q₈	—	8	1	no	—
722	D₄	—	2	4	no	—
723	D₄	—	2	4	no	—
724	D₄	—	2	2	no	—
725	D₄	—	2	2	no	—
726	D₄	—	2	2	no	—
727	D₄	—	2	4	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	4	no	—
730	D₄	—	4	2	no	—
731	D₄	—	4	8	no	—
732	D₄	—	4	2	no	—
733	D₄	—	4	8	no	—
734	D₄	—	4	4	no	—
735	D₄	—	4	2	no	—
736	D₄	—	8	1	no	—
737	D₄	—	8	1	no	—
738	D₄	—	8	4	no	—
739	D₄	—	8	4	no	—
740	D₄	—	8	2	no	—
741	D₄	—	8	4	no	—
742	D₄	C₂₃×H(5,𝔽₂)	1	4	yes	—
743	C₂×C₄	—	2	2	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	4	no	—
746	C₂×C₄	—	2	2	no	—
747	C₂×C₄	—	2	2	no	—
748	C₂×C₄	—	2	2	no	—
749	C₂×C₄	—	2	2	no	—
750	C₂×C₄	—	2	2	no	—
751	C₂×C₄	—	2	2	no	—
752	C₂×C₄	—	4	1	no	—
753	C₂×C₄	—	4	8	no	—
754	C₂×C₄	—	4	4	no	—
755	C₂×C₄	—	4	4	no	—
756	C₂×C₄	—	4	4	no	—
757	C₂×C₄	—	8	2	no	—
758	C₂×C₄	—	8	4	no	—
759	C₂×C₄	—	8	1	no	—
760	C₂×C₄	—	8	4	no	—
761	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
762	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
763	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
764	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
765	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
766	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
767	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
768	C₈	—	2	2	no	—
769	C₈	—	2	4	no	—
770	C₈	—	2	2	no	—
771	C₂²	—	2	1	no	—
772	C₂²	—	2	4	no	—
773	C₂²	—	2	4	no	—
774	C₂²	—	2	1	no	—
775	C₂²	—	2	4	no	—
776	C₂²	—	2	1	no	—
777	C₂²	—	2	4	no	—
778	C₂²	—	4	2	no	—
779	C₂²	—	4	2	no	—
780	C₂²	—	4	2	no	—
781	C₂²	—	4	2	no	—
782	C₂²	—	4	2	no	—
783	C₂²	—	4	2	no	—
784	C₂²	—	4	2	no	—
785	C₂²	—	4	2	no	—
786	C₂²	—	8	4	no	—
787	C₂²	—	16	8	no	—
788	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
789	C₄	—	2	1	no	—
790	C₄	—	2	4	no	—
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	1	no	—
794	C₄	—	4	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	C₂₃×#576	1	2	yes	—
800	C₄	C₂×C₂₃×H(5,𝔽₂)	1	2	yes	—
801	C₂	—	4	1	no	—
802	C₂	—	4	4	no	—
803	C₂	—	4	4	no	—
804	C₂	—	8	2	no	—
805	C₂	—	8	2	no	—
806	C₂	C₂₃×#3484	1	1	yes	characteristic
807	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
808	C₂	C₂₃×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂₃×#532 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3548	C₂	semidirect
2. C₂₃×#3496	C₂	semidirect
3. C₂₃×#3330	C₂	semidirect
4. C₂₃×#3314	C₂	semidirect
5. C₂₃×#3294	C₂	semidirect
6. C₂₃×#3283	C₂	semidirect
7. C₂₃×#3272	C₂	semidirect
8. C₂₃×#3268	C₂	semidirect
9. C₂₃×#3214	C₂	semidirect
10. C₂₃×#3210	C₂	semidirect
11. C₂₃×#3203	C₂	semidirect
12. C₂₃×#3110	C₂	semidirect
13. C₂₃×#3100	C₂	semidirect
14. C₂₃×#3012	C₂	semidirect
15. C₂₃×#2981	C₂	semidirect
17. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
18. C₂×C₂₃×#135	C₂²	semidirect
21. C₂₃×#554	C₂²	semidirect
23. C₂₃×#550	C₂²	semidirect
26. C₂₃×#547	C₂²	semidirect
27. C₂₃×#547	C₂²	semidirect
35. C₂₃×#537	C₂²	semidirect
37. C₂₃×#533	C₂²	semidirect
40. C₂₃×#532	C₂²	semidirect
43. C₂₃×#496	C₂²	semidirect
44. C₂₃×#494	C₂²	semidirect
45. C₂₃×#492	C₂²	semidirect
46. C₂₃×#489	C₂²	semidirect
47. C₂₃×#487	C₂²	semidirect
48. C₂₃×#486	C₂²	semidirect
49. C₂₃×#484	C₂²	semidirect
50. C₂₃×#484	C₂²	semidirect
51. C₂₃×#480	C₂²	semidirect
52. C₂₃×#480	C₂²	semidirect
53. C₂₃×#474	C₂²	semidirect
54. C₂₃×#474	C₂²	semidirect
55. C₂₃×#468	C₂²	semidirect
56. C₂₃×#468	C₂²	semidirect
57. C₂₃×#467	C₂²	semidirect
58. C₂₃×#466	C₂²	semidirect
59. C₂₃×#464	C₂²	semidirect
60. C₂₃×#461	C₂²	semidirect
61. C₂₃×#461	C₂²	semidirect
62. C₂₃×#459	C₂²	semidirect
63. C₂₃×#459	C₂²	semidirect
64. C₂₃×#452	C₂²	semidirect
65. C₂₃×#452	C₂²	semidirect
66. C₂₃×#452	C₂²	semidirect
68. C₂₃×#450	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
70. C₂₃×#449	C₂²	semidirect
71. C₂₃×#449	C₂²	semidirect
73. C₂₃×#447	C₂²	semidirect
74. C₂₃×#440	C₂²	semidirect
75. C₄×D₈×C₂₃	C₂²	semidirect
76. C₄×D₈×C₂₃	C₂²	semidirect
77. C₂₃×#436	C₂²	semidirect
78. C₂₃×#435	C₂²	semidirect
79. C₈×D₄×C₂₃	C₂²	semidirect
80. C₂₃×#432	C₂²	semidirect
81. C₂₃×#431	C₂²	semidirect
82. C₂₃×#417	C₂²	semidirect
83. C₂×C₂₃×#102	C₂²	semidirect
84. C₂₃×#408	C₂²	semidirect
301. #61684	C₂₃	direct (N × H)
367. #3548	C₂×C₂₃	semidirect
368. #3496	C₂×C₂₃	semidirect
369. #3330	C₂×C₂₃	semidirect
370. #3314	C₂×C₂₃	semidirect
371. #3294	C₂×C₂₃	semidirect
372. #3283	C₂×C₂₃	semidirect
373. #3272	C₂×C₂₃	semidirect
374. #3268	C₂×C₂₃	semidirect
375. #3214	C₂×C₂₃	semidirect
376. #3210	C₂×C₂₃	semidirect
377. #3203	C₂×C₂₃	semidirect
378. #3110	C₂×C₂₃	semidirect
379. #3100	C₂×C₂₃	semidirect
380. #3012	C₂×C₂₃	semidirect
381. #2981	C₂×C₂₃	semidirect
413. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
414. C₂×#135	C₂²×C₂₃	semidirect
417. #554	C₂²×C₂₃	semidirect
419. #550	C₂²×C₂₃	semidirect
422. #547	C₂²×C₂₃	semidirect
423. #547	C₂²×C₂₃	semidirect
431. #537	C₂²×C₂₃	semidirect
433. #533	C₂²×C₂₃	semidirect
436. #532	C₂²×C₂₃	semidirect
439. #496	C₂²×C₂₃	semidirect
440. #494	C₂²×C₂₃	semidirect
441. #492	C₂²×C₂₃	semidirect
442. #489	C₂²×C₂₃	semidirect
443. #487	C₂²×C₂₃	semidirect
444. #486	C₂²×C₂₃	semidirect
445. #484	C₂²×C₂₃	semidirect
446. #484	C₂²×C₂₃	semidirect
447. #480	C₂²×C₂₃	semidirect
448. #480	C₂²×C₂₃	semidirect
449. #474	C₂²×C₂₃	semidirect
450. #474	C₂²×C₂₃	semidirect
451. #468	C₂²×C₂₃	semidirect
452. #468	C₂²×C₂₃	semidirect
453. #467	C₂²×C₂₃	semidirect
454. #466	C₂²×C₂₃	semidirect
455. #464	C₂²×C₂₃	semidirect
456. #461	C₂²×C₂₃	semidirect
457. #461	C₂²×C₂₃	semidirect
458. #459	C₂²×C₂₃	semidirect
459. #459	C₂²×C₂₃	semidirect
460. #452	C₂²×C₂₃	semidirect
461. #452	C₂²×C₂₃	semidirect
462. #452	C₂²×C₂₃	semidirect
464. #450	C₂²×C₂₃	semidirect
465. #449	C₂²×C₂₃	semidirect
466. #449	C₂²×C₂₃	semidirect
467. #449	C₂²×C₂₃	semidirect
469. #447	C₂²×C₂₃	semidirect
470. #440	C₂²×C₂₃	semidirect
471. C₄×D₈	C₂²×C₂₃	semidirect
472. C₄×D₈	C₂²×C₂₃	semidirect
473. #436	C₂²×C₂₃	semidirect
474. #435	C₂²×C₂₃	semidirect
475. C₈×D₄	C₂²×C₂₃	semidirect
476. #432	C₂²×C₂₃	semidirect
477. #431	C₂²×C₂₃	semidirect
478. #417	C₂²×C₂₃	semidirect
479. C₂×#102	C₂²×C₂₃	semidirect
480. #408	C₂²×C₂₃	semidirect
604. C₂₃	#61684	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×#3548	2
C₂₃×#3496	2
C₂₃×#3330	2
C₂₃×#3314	2
C₂₃×#3294	2
C₂₃×#3283	2
C₂₃×#3272	2
C₂₃×#3268	2
C₂₃×#3214	2
C₂₃×#3210	2
C₂₃×#3203	2
C₂₃×#3110	2
C₂₃×#3100	2
C₂₃×#3012	2
C₂₃×#2981	2
#61684	23

Subgroups — C23×#61684 #19209310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61684 #19209310