Subgroups — C₂₃×#61200 #19208826

Order 5888.

2152 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂₃×#3496	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3331	C₂	1	2	yes	maximal, complemented
4	C₂₃×#3325	C₂	1	2	yes	maximal, complemented
5	C₂₃×#3311	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3306	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3303	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3295	C₂	1	2	yes	maximal, complemented
9	C₂₃×#3141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3099	C₂	1	2	yes	maximal, complemented
11	C₂×C₂₃×#476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#3060	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3035	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3012	C₂	1	2	yes	maximal, complemented
15	C₄×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂₃×#2935	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂₃×#2897	C₂	1	2	yes	maximal, complemented
18	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#135	C₂²	1	2	yes	complemented
21	C₂×C₂₃×#131	C₂²	1	2	yes	complemented
22	C₂₃×#556	C₂²	1	2	yes	complemented
23	C₂₃×#555	C₂²	1	2	yes	complemented
24	C₂₃×#554	C₂²	1	2	yes	complemented
25	C₂₃×#553	—	2	2	no	—
26	C₂₃×#548	—	2	2	no	—
27	C₂₃×#547	—	2	1	no	—
28	C₂₃×#547	C₂²	1	2	yes	—
29	C₂₃×#547	C₂²	1	2	yes	complemented
30	C₂₃×#546	—	2	2	no	—
31	C₂₃×#546	C₂²	1	4	yes	—
32	D₄²×C₂₃	—	2	1	no	—
33	D₄²×C₂₃	C₂²	1	2	yes	—
34	C₂₃×#542	—	2	2	no	—
35	C₂₃×#537	C₂²	1	2	yes	—
36	C₂₃×#537	C₂²	1	2	yes	complemented
37	C₂₃×#534	—	2	2	no	—
38	C₂₃×#533	—	2	1	no	—
39	C₂₃×#532	—	2	1	no	—
40	C₂₃×#532	C₂²	1	1	yes	characteristic
41	C₂₃×#532	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₂₃×#121	—	2	2	no	—
44	C₂₃×#520	C₂²	1	2	yes	complemented
45	C₄×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#489	C₂²	1	4	yes	complemented
48	C₂₃×#487	C₂²	1	2	yes	complemented
49	C₂₃×#486	C₂²	1	2	yes	complemented
50	C₂₃×#485	C₂²	1	4	yes	complemented
51	C₂₃×#483	C₂²	1	4	yes	complemented
52	C₂₃×#482	C₂²	1	4	yes	complemented
53	C₂₃×#481	C₂²	1	4	yes	complemented
54	C₂₃×#476	C₂²	1	2	yes	complemented
55	C₂₃×#476	C₂²	1	4	yes	complemented
56	C₂₃×#476	C₂²	1	2	yes	complemented
57	C₂₃×#470	C₂²	1	4	yes	complemented
58	C₂₃×#469	C₂²	1	4	yes	complemented
59	C₂₃×#465	C₂²	1	4	yes	complemented
60	C₂₃×#465	C₂²	1	4	yes	complemented
61	C₂₃×#464	C₂²	1	2	yes	complemented
62	C₂₃×#463	C₂²	1	2	yes	complemented
63	C₂₃×#462	C₂²	1	1	yes	characteristic, complemented
64	C₂₃×#461	C₂²	1	1	yes	characteristic, complemented
65	C₂₃×#460	C₂²	1	1	yes	characteristic, complemented
66	C₂₃×#459	C₂²	1	1	yes	characteristic, complemented
67	C₂₃×#452	C₂²	1	4	yes	complemented
68	C₂₃×#450	C₂²	1	4	yes	complemented
69	C₂₃×#449	C₂²	1	4	yes	complemented
70	C₂₃×#447	C₂²	1	4	yes	complemented
71	C₂₃×#442	C₂²	1	2	yes	complemented
72	C₂₃×#440	C₂²	1	2	yes	complemented
73	C₄×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
74	C₄×D₈×C₂₃	C₂²	1	2	yes	complemented
75	C₂₃×#436	C₂²	1	2	yes	complemented
76	C₂₃×#435	C₂²	1	4	yes	complemented
77	C₈×D₄×C₂₃	C₂²	1	2	yes	complemented
78	C₂₃×#428	C₂²	1	1	yes	characteristic, complemented
79	C₂×C₂₃×#106	C₂²	1	2	yes	complemented
80	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
81	C₂₃×#418	C₂²	1	1	yes	characteristic
82	C₂₃×#418	C₂²	1	4	yes	complemented
83	C₂₃×#417	C₂²	1	1	yes	characteristic, complemented
84	C₂₃×#417	C₂²	1	2	yes	complemented
85	C₂₃×#417	C₂²	1	4	yes	complemented
86	C₂₃×#417	C₂²	1	2	yes	complemented
87	C₂₃×#416	C₂²	1	2	yes	complemented
88	C₂₃×#416	C₂²	1	4	yes	complemented
89	C₂×C₂₃×#102	C₂²	1	2	yes	—
90	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
91	C₂₃×#408	C₂²	1	2	yes	complemented
92	C₄×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
93	C₂₃×H(5,𝔽₂)	—	2	8	no	—
94	C₂₃×H(5,𝔽₂)	—	4	4	no	—
95	C₂×#41×C₂₃	—	2	2	no	—
96	C₂×#41×C₂₃	—	2	2	no	—
97	C₂×#41×C₂₃	C₂³	1	1	yes	characteristic
98	C₂×#41×C₂₃	C₂³	1	2	yes	—
99	C₂×#41×C₂₃	C₂³	1	4	yes	—
100	C₂×#41×C₂₃	C₂³	1	2	yes	—
101	C₂²×Q₈×C₂₃	—	2	1	no	—
102	C₂²×D₄×C₂₃	—	2	4	no	—
103	C₂²×D₄×C₂₃	—	2	2	no	—
104	C₂²×D₄×C₂₃	—	2	2	no	—
105	C₂²×D₄×C₂₃	C₂³	1	4	yes	—
106	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₂₃	—	2	1	no	—
108	C₂₃×AGL(1,ℤ/8)	—	2	4	no	—
109	C₂₃×#135	—	4	4	no	—
110	C₂×Q₁₆×C₂₃	C₂³	1	2	yes	—
111	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
112	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
113	C₂×SD₁₆×C₂₃	C₂³	1	2	yes	—
114	C₂×D₈×C₂₃	C₂³	1	2	yes	—
115	C₂×D₈×C₂₃	C₂³	1	2	yes	—
116	C₂₃×#131	—	4	4	no	—
117	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
118	C₂×M₁₆×C₂₃	C₂³	1	1	yes	characteristic
119	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
120	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
121	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
122	C₂₃×C₄⋊Q₈	—	2	1	no	—
123	C₂₃×C₄⋊Q₈	—	2	1	no	—
124	C₂₃×C₄⋊Q₈	D₄	1	1	yes	characteristic
125	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
126	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
127	C₂₃×C₄⋊Q₈	C₂³	1	2	yes	—
128	C₂₃×#127	D₄	1	1	yes	characteristic
129	C₂₃×#127	C₂³	1	1	yes	characteristic
130	C₂₃×#126	—	2	4	no	—
131	C₂₃×#125	—	2	2	no	—
132	C₂₃×#124	—	2	2	no	—
133	C₂₃×#124	—	2	4	no	—
134	C₂₃×#124	D₄	1	2	yes	—
135	C₂₃×#124	C₂³	1	2	yes	—
136	C₂₃×#123	—	2	4	no	—
137	C₂₃×#123	—	2	4	no	—
138	C₂₃×#123	—	2	4	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	—	2	2	no	—
142	C₂₃×C₂²⋊Q₈	—	2	4	no	—
143	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
144	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
145	C₂₃×#121	—	2	2	no	—
146	C₂₃×#121	—	2	4	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	4	no	—
149	C₂₃×#121	—	2	2	no	—
150	C₂₃×#121	—	2	2	no	—
151	C₂₃×#121	—	2	1	no	—
152	C₂₃×#121	—	2	1	no	—
153	C₂₃×#121	—	2	2	no	—
154	C₂₃×#121	—	2	4	no	—
155	C₂₃×#121	D₄	1	2	yes	—
156	C₂₃×#121	D₄	1	2	yes	—
157	C₂₃×#121	C₂³	1	4	yes	—
158	C₂₃×#121	C₂³	1	4	yes	—
159	C₂₃×#120	—	2	4	no	—
160	C₂₃×#120	—	2	4	no	—
161	C₄×Q₈×C₂₃	—	2	2	no	—
162	C₄×Q₈×C₂₃	—	2	2	no	—
163	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
164	C₄×Q₈×C₂₃	C₂³	1	1	yes	characteristic
165	C₄×D₄×C₂₃	—	2	4	no	—
166	C₄×D₄×C₂₃	—	2	2	no	—
167	C₄×D₄×C₂₃	—	2	2	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	—	2	1	no	—
170	C₄×D₄×C₂₃	—	2	1	no	—
171	C₄×D₄×C₂₃	—	2	1	no	—
172	C₄×D₄×C₂₃	—	2	1	no	—
173	C₄×D₄×C₂₃	—	2	1	no	—
174	C₄×D₄×C₂₃	C₂³	1	2	yes	—
175	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
176	C₄×D₄×C₂₃	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₂₃	C₂³	1	2	yes	—
178	C₄×D₄×C₂₃	C₂³	1	2	yes	—
179	C₄×D₄×C₂₃	C₂³	1	2	yes	—
180	C₂₃×#117	—	2	2	no	—
181	C₂₃×#117	—	2	1	no	—
182	C₂₃×#117	C₂³	1	4	yes	—
183	C₂₃×#117	C₂³	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
185	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
186	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
187	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
188	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
191	C₂×C₄²×C₂₃	—	2	1	no	—
192	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
193	C₂₃×#107	C₂³	1	2	yes	—
194	C₂₃×#106	C₂³	1	4	yes	—
195	C₂₃×#106	C₂³	1	4	yes	—
196	C₂₃×#106	C₂³	1	2	yes	—
197	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
198	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
199	C₂₃×C₄⋊C₈	C₂³	1	1	yes	characteristic
200	C₂₃×#103	C₂³	1	2	yes	—
201	C₂₃×#103	C₂³	1	2	yes	—
202	C₂₃×#103	C₂³	1	4	yes	—
203	C₂₃×#103	C₂³	1	2	yes	—
204	C₂₃×#103	C₂³	1	4	yes	—
205	C₂₃×#102	C₂³	1	4	yes	—
206	C₂₃×#102	C₂³	1	4	yes	—
207	C₂₃×#102	C₂³	1	2	yes	—
208	C₂₃×#102	C₂³	1	2	yes	—
209	C₂₃×#102	C₂³	1	4	yes	—
210	C₂₃×#102	C₂³	1	2	yes	—
211	C₂₃×#102	C₂³	1	2	yes	—
212	C₂₃×#102	C₂³	1	2	yes	—
213	C₂₃×#102	C₂³	1	4	yes	—
214	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
215	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
216	C₂₃×#97	C₂³	1	2	yes	—
217	C₄×C₈×C₂₃	C₂³	1	2	yes	—
218	C₂⁴×C₂₃	—	2	1	no	—
219	C₂⁴×C₂₃	—	2	4	no	—
220	#41×C₂₃	—	2	4	no	—
221	#41×C₂₃	—	2	4	no	—
222	#41×C₂₃	—	2	8	no	—
223	#41×C₂₃	—	2	2	no	—
224	#41×C₂₃	—	2	4	no	—
225	#41×C₂₃	—	2	2	no	—
226	#41×C₂₃	—	2	4	no	—
227	#41×C₂₃	—	4	4	no	—
228	#41×C₂₃	—	4	8	no	—
229	#41×C₂₃	—	8	4	no	—
230	C₂×Q₈×C₂₃	—	2	2	no	—
231	C₂×Q₈×C₂₃	—	2	2	no	—
232	C₂×Q₈×C₂₃	—	8	2	no	—
233	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
234	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
235	C₂×Q₈×C₂₃	C₂⁴	1	1	yes	characteristic
236	C₂×D₄×C₂₃	—	2	8	no	—
237	C₂×D₄×C₂₃	—	2	1	no	—
238	C₂×D₄×C₂₃	—	2	4	no	—
239	C₂×D₄×C₂₃	—	2	2	no	—
240	C₂×D₄×C₂₃	—	2	4	no	—
241	C₂×D₄×C₂₃	—	2	4	no	—
242	C₂×D₄×C₂₃	—	2	1	no	—
243	C₂×D₄×C₂₃	—	2	1	no	—
244	C₂×D₄×C₂₃	—	2	4	no	—
245	C₂×D₄×C₂₃	—	2	1	no	—
246	C₂×D₄×C₂₃	—	2	2	no	—
247	C₂×D₄×C₂₃	—	4	4	no	—
248	C₂×D₄×C₂₃	—	4	8	no	—
249	C₂×D₄×C₂₃	—	4	16	no	—
250	C₂×D₄×C₂₃	—	8	4	no	—
251	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
252	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
253	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
254	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
255	C₂×D₄×C₂₃	#41	1	4	yes	complemented
256	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
257	C₂×D₄×C₂₃	C₂⁴	1	1	yes	characteristic
258	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₂₃	—	2	1	no	—
260	C₂²×C₄×C₂₃	—	2	2	no	—
261	C₂²×C₄×C₂₃	—	2	4	no	—
262	C₂²×C₄×C₂₃	—	2	1	no	—
263	C₂²×C₄×C₂₃	—	2	1	no	—
264	C₂²×C₄×C₂₃	—	2	1	no	—
265	C₂²×C₄×C₂₃	—	2	4	no	—
266	C₂²×C₄×C₂₃	—	2	2	no	—
267	C₂²×C₄×C₂₃	—	2	2	no	—
268	C₂²×C₄×C₂₃	—	2	2	no	—
269	C₂²×C₄×C₂₃	—	8	2	no	—
270	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
271	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
272	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
273	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
274	Q₁₆×C₂₃	—	4	2	no	—
275	SD₁₆×C₂₃	—	2	4	no	—
276	SD₁₆×C₂₃	—	4	2	no	—
277	SD₁₆×C₂₃	—	4	2	no	—
278	D₈×C₂₃	—	2	4	no	—
279	D₈×C₂₃	—	4	2	no	—
280	M₁₆×C₂₃	—	2	2	no	—
281	M₁₆×C₂₃	—	2	2	no	—
282	M₁₆×C₂₃	—	4	4	no	—
283	C₂×C₈×C₂₃	—	2	4	no	—
284	C₂×C₈×C₂₃	—	4	4	no	—
285	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
286	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
287	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
288	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
289	C₄⋊C₄×C₂₃	—	2	1	no	—
290	C₄⋊C₄×C₂₃	—	2	2	no	—
291	C₄⋊C₄×C₂₃	—	2	4	no	—
292	C₄⋊C₄×C₂₃	—	2	2	no	—
293	C₄⋊C₄×C₂₃	—	2	1	no	—
294	C₄⋊C₄×C₂₃	—	2	2	no	—
295	C₄⋊C₄×C₂₃	—	2	4	no	—
296	C₄⋊C₄×C₂₃	—	2	1	no	—
297	C₄⋊C₄×C₂₃	—	2	1	no	—
298	C₄⋊C₄×C₂₃	—	2	1	no	—
299	C₄⋊C₄×C₂₃	—	2	4	no	—
300	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
301	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
302	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
303	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
304	C₄⋊C₄×C₂₃	C₂⁴	1	1	yes	characteristic
305	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
306	C₂²⋊C₄×C₂₃	—	2	4	no	—
307	C₂²⋊C₄×C₂₃	—	2	1	no	—
308	C₂²⋊C₄×C₂₃	—	2	4	no	—
309	C₂²⋊C₄×C₂₃	—	2	4	no	—
310	C₂²⋊C₄×C₂₃	—	2	2	no	—
311	C₂²⋊C₄×C₂₃	—	2	2	no	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	4	no	—
314	C₂²⋊C₄×C₂₃	—	2	1	no	—
315	C₂²⋊C₄×C₂₃	—	2	1	no	—
316	C₂²⋊C₄×C₂₃	—	2	4	no	—
317	C₂²⋊C₄×C₂₃	—	2	2	no	—
318	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
319	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
320	C₄²×C₂₃	—	2	1	no	—
321	C₄²×C₂₃	—	2	1	no	—
322	C₄²×C₂₃	—	2	1	no	—
323	C₄²×C₂₃	—	2	4	no	—
324	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
325	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
326	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
327	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
328	#61200	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
329	C₂³×C₂₃	—	2	2	no	—
330	C₂³×C₂₃	—	2	4	no	—
331	C₂³×C₂₃	—	2	1	no	—
332	C₂³×C₂₃	—	2	2	no	—
333	C₂³×C₂₃	—	4	8	no	—
334	C₂³×C₂₃	—	8	1	no	—
335	C₂³×C₂₃	—	8	1	no	—
336	C₂³×C₂₃	—	8	4	no	—
337	C₂³×C₂₃	—	8	4	no	—
338	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
339	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
340	Q₈×C₂₃	—	2	4	no	—
341	Q₈×C₂₃	—	2	1	no	—
342	Q₈×C₂₃	—	2	2	no	—
343	Q₈×C₂₃	—	2	1	no	—
344	Q₈×C₂₃	—	2	2	no	—
345	Q₈×C₂₃	—	4	4	no	—
346	Q₈×C₂₃	—	8	2	no	—
347	D₄×C₂₃	—	2	8	no	—
348	D₄×C₂₃	—	2	4	no	—
349	D₄×C₂₃	—	2	4	no	—
350	D₄×C₂₃	—	2	4	no	—
351	D₄×C₂₃	—	2	1	no	—
352	D₄×C₂₃	—	2	2	no	—
353	D₄×C₂₃	—	2	2	no	—
354	D₄×C₂₃	—	2	1	no	—
355	D₄×C₂₃	—	2	2	no	—
356	D₄×C₂₃	—	4	2	no	—
357	D₄×C₂₃	—	4	8	no	—
358	D₄×C₂₃	—	4	8	no	—
359	D₄×C₂₃	—	4	4	no	—
360	D₄×C₂₃	—	4	2	no	—
361	D₄×C₂₃	—	4	2	no	—
362	D₄×C₂₃	—	8	1	no	—
363	D₄×C₂₃	—	8	4	no	—
364	D₄×C₂₃	—	8	4	no	—
365	D₄×C₂₃	C₂×#41	1	4	yes	—
366	C₂×C₄×C₂₃	—	2	2	no	—
367	C₂×C₄×C₂₃	—	2	4	no	—
368	C₂×C₄×C₂₃	—	2	4	no	—
369	C₂×C₄×C₂₃	—	2	1	no	—
370	C₂×C₄×C₂₃	—	2	1	no	—
371	C₂×C₄×C₂₃	—	2	1	no	—
372	C₂×C₄×C₂₃	—	2	4	no	—
373	C₂×C₄×C₂₃	—	2	2	no	—
374	C₂×C₄×C₂₃	—	2	2	no	—
375	C₂×C₄×C₂₃	—	4	1	no	—
376	C₂×C₄×C₂₃	—	4	8	no	—
377	C₂×C₄×C₂₃	—	4	2	no	—
378	C₂×C₄×C₂₃	—	4	4	no	—
379	C₂×C₄×C₂₃	—	4	2	no	—
380	C₂×C₄×C₂₃	—	4	2	no	—
381	C₂×C₄×C₂₃	—	4	4	no	—
382	C₂×C₄×C₂₃	—	8	2	no	—
383	C₂×C₄×C₂₃	—	8	1	no	—
384	C₂×C₄×C₂₃	—	8	2	no	—
385	C₂×C₄×C₂₃	—	8	4	no	—
386	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
391	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
393	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
394	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
395	C₈×C₂₃	—	2	2	no	—
396	C₈×C₂₃	—	2	2	no	—
397	C₈×C₂₃	—	2	2	no	—
398	C₈×C₂₃	—	2	2	no	—
399	#3511	C₂×C₂₃	1	1	yes	characteristic, complemented
400	#3496	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3331	C₂×C₂₃	1	2	yes	complemented
402	#3325	C₂×C₂₃	1	2	yes	complemented
403	#3311	C₂×C₂₃	1	4	yes	complemented
404	#3306	C₂×C₂₃	1	4	yes	complemented
405	#3303	C₂×C₂₃	1	2	yes	complemented
406	#3295	C₂×C₂₃	1	2	yes	complemented
407	#3141	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3099	C₂×C₂₃	1	2	yes	complemented
409	C₂×#476	C₂×C₂₃	1	1	yes	characteristic, complemented
410	#3060	C₂×C₂₃	1	2	yes	complemented
411	#3035	C₂×C₂₃	1	1	yes	characteristic, complemented
412	#3012	C₂×C₂₃	1	2	yes	complemented
413	C₄×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
414	#2935	C₂×C₂₃	1	1	yes	characteristic, complemented
415	#2897	C₂×C₂₃	1	2	yes	complemented
416	C₂²×C₂₃	—	2	1	no	—
417	C₂²×C₂₃	—	2	1	no	—
418	C₂²×C₂₃	—	2	4	no	—
419	C₂²×C₂₃	—	2	4	no	—
420	C₂²×C₂₃	—	2	4	no	—
421	C₂²×C₂₃	—	2	4	no	—
422	C₂²×C₂₃	—	4	2	no	—
423	C₂²×C₂₃	—	4	2	no	—
424	C₂²×C₂₃	—	4	1	no	—
425	C₂²×C₂₃	—	4	2	no	—
426	C₂²×C₂₃	—	4	2	no	—
427	C₂²×C₂₃	—	4	1	no	—
428	C₂²×C₂₃	—	4	1	no	—
429	C₂²×C₂₃	—	4	2	no	—
430	C₂²×C₂₃	—	8	4	no	—
431	C₂²×C₂₃	—	16	8	no	—
432	C₂²×C₂₃	#546	1	2	yes	—
433	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
434	C₄×C₂₃	—	2	1	no	—
435	C₄×C₂₃	—	2	1	no	—
436	C₄×C₂₃	—	2	4	no	—
437	C₄×C₂₃	—	2	1	no	—
438	C₄×C₂₃	—	4	1	no	—
439	C₄×C₂₃	—	4	4	no	—
440	C₄×C₂₃	—	4	2	no	—
441	C₄×C₂₃	—	4	1	no	—
442	C₄×C₂₃	—	4	1	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	#546	1	2	yes	—
445	C₄×C₂₃	#577	1	2	yes	—
446	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
447	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	2	yes	—
449	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×#135	C₂²×C₂₃	1	2	yes	complemented
451	C₂×#131	C₂²×C₂₃	1	2	yes	complemented
452	#556	C₂²×C₂₃	1	2	yes	complemented
453	#555	C₂²×C₂₃	1	2	yes	complemented
454	#554	C₂²×C₂₃	1	2	yes	complemented
455	#553	—	2	2	no	—
456	#548	—	2	2	no	—
457	#547	—	2	1	no	—
458	#547	C₂²×C₂₃	1	2	yes	—
459	#547	C₂²×C₂₃	1	2	yes	complemented
460	#546	—	2	2	no	—
461	#546	C₂²×C₂₃	1	4	yes	—
462	D₄²	—	2	1	no	—
463	D₄²	C₂²×C₂₃	1	2	yes	—
464	#542	—	2	2	no	—
465	#537	C₂²×C₂₃	1	2	yes	—
466	#537	C₂²×C₂₃	1	2	yes	complemented
467	#534	—	2	2	no	—
468	#533	—	2	1	no	—
469	#532	—	2	1	no	—
470	#532	C₂²×C₂₃	1	1	yes	characteristic
471	#532	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
473	C₂×#121	—	2	2	no	—
474	#520	C₂²×C₂₃	1	2	yes	complemented
475	C₄×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
477	#489	C₂²×C₂₃	1	4	yes	complemented
478	#487	C₂²×C₂₃	1	2	yes	complemented
479	#486	C₂²×C₂₃	1	2	yes	complemented
480	#485	C₂²×C₂₃	1	4	yes	complemented
481	#483	C₂²×C₂₃	1	4	yes	complemented
482	#482	C₂²×C₂₃	1	4	yes	complemented
483	#481	C₂²×C₂₃	1	4	yes	complemented
484	#476	C₂²×C₂₃	1	2	yes	complemented
485	#476	C₂²×C₂₃	1	2	yes	complemented
486	#476	C₂²×C₂₃	1	4	yes	complemented
487	#470	C₂²×C₂₃	1	4	yes	complemented
488	#469	C₂²×C₂₃	1	4	yes	complemented
489	#465	C₂²×C₂₃	1	4	yes	complemented
490	#465	C₂²×C₂₃	1	4	yes	complemented
491	#464	C₂²×C₂₃	1	2	yes	complemented
492	#463	C₂²×C₂₃	1	2	yes	complemented
493	#462	C₂²×C₂₃	1	1	yes	characteristic, complemented
494	#461	C₂²×C₂₃	1	1	yes	characteristic, complemented
495	#460	C₂²×C₂₃	1	1	yes	characteristic, complemented
496	#459	C₂²×C₂₃	1	1	yes	characteristic, complemented
497	#452	C₂²×C₂₃	1	4	yes	complemented
498	#450	C₂²×C₂₃	1	4	yes	complemented
499	#449	C₂²×C₂₃	1	4	yes	complemented
500	#447	C₂²×C₂₃	1	4	yes	complemented
501	#442	C₂²×C₂₃	1	2	yes	complemented
502	#440	C₂²×C₂₃	1	2	yes	complemented
503	C₄×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
504	C₄×D₈	C₂²×C₂₃	1	2	yes	complemented
505	#436	C₂²×C₂₃	1	2	yes	complemented
506	#435	C₂²×C₂₃	1	4	yes	complemented
507	C₈×D₄	C₂²×C₂₃	1	2	yes	complemented
508	#428	C₂²×C₂₃	1	1	yes	characteristic, complemented
509	C₂×#106	C₂²×C₂₃	1	2	yes	complemented
510	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic, complemented
511	#418	C₂²×C₂₃	1	1	yes	characteristic
512	#418	C₂²×C₂₃	1	4	yes	complemented
513	#417	C₂²×C₂₃	1	4	yes	complemented
514	#417	C₂²×C₂₃	1	2	yes	complemented
515	#417	C₂²×C₂₃	1	2	yes	complemented
516	#417	C₂²×C₂₃	1	1	yes	characteristic, complemented
517	#416	C₂²×C₂₃	1	2	yes	complemented
518	#416	C₂²×C₂₃	1	4	yes	complemented
519	C₂×#102	C₂²×C₂₃	1	2	yes	—
520	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
521	#408	C₂²×C₂₃	1	2	yes	complemented
522	C₄×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
523	C₂×C₂₃	—	2	2	no	—
524	C₂×C₂₃	—	4	4	no	—
525	C₂×C₂₃	—	4	4	no	—
526	C₂×C₂₃	—	8	1	no	—
527	C₂×C₂₃	—	8	2	no	—
528	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
529	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
530	C₂×C₂₃	#3585	1	1	yes	characteristic
531	H(5,𝔽₂)	—	2	8	no	—
532	H(5,𝔽₂)	—	4	4	no	—
533	C₂×#41	—	2	2	no	—
534	C₂×#41	—	2	2	no	—
535	C₂×#41	C₂³×C₂₃	1	1	yes	characteristic
536	C₂×#41	C₂³×C₂₃	1	2	yes	—
537	C₂×#41	C₂³×C₂₃	1	4	yes	—
538	C₂×#41	C₂³×C₂₃	1	2	yes	—
539	C₂²×Q₈	—	2	1	no	—
540	C₂²×D₄	—	2	4	no	—
541	C₂²×D₄	—	2	2	no	—
542	C₂²×D₄	—	2	2	no	—
543	C₂²×D₄	C₂³×C₂₃	1	4	yes	—
544	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
545	C₂³×C₄	—	2	1	no	—
546	AGL(1,ℤ/8)	—	2	4	no	—
547	#135	—	4	4	no	—
548	C₂×Q₁₆	C₂³×C₂₃	1	2	yes	—
549	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
550	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
551	C₂×SD₁₆	C₂³×C₂₃	1	2	yes	—
552	C₂×D₈	C₂³×C₂₃	1	2	yes	—
553	C₂×D₈	C₂³×C₂₃	1	2	yes	—
554	#131	—	4	4	no	—
555	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
556	C₂×M₁₆	C₂³×C₂₃	1	1	yes	characteristic
557	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
558	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
559	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
560	C₄⋊Q₈	—	2	1	no	—
561	C₄⋊Q₈	—	2	1	no	—
562	C₄⋊Q₈	D₄×C₂₃	1	1	yes	characteristic
563	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
564	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
565	C₄⋊Q₈	C₂³×C₂₃	1	2	yes	—
566	#127	D₄×C₂₃	1	1	yes	characteristic
567	#127	C₂³×C₂₃	1	1	yes	characteristic
568	#126	—	2	4	no	—
569	#125	—	2	2	no	—
570	#124	—	2	2	no	—
571	#124	—	2	4	no	—
572	#124	D₄×C₂₃	1	2	yes	—
573	#124	C₂³×C₂₃	1	2	yes	—
574	#123	—	2	4	no	—
575	#123	—	2	4	no	—
576	#123	—	2	4	no	—
577	C₂²⋊Q₈	—	2	2	no	—
578	C₂²⋊Q₈	—	2	2	no	—
579	C₂²⋊Q₈	—	2	2	no	—
580	C₂²⋊Q₈	—	2	4	no	—
581	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
582	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
583	#121	—	2	4	no	—
584	#121	—	2	2	no	—
585	#121	—	2	2	no	—
586	#121	—	2	2	no	—
587	#121	—	2	2	no	—
588	#121	—	2	4	no	—
589	#121	—	2	1	no	—
590	#121	—	2	1	no	—
591	#121	—	2	2	no	—
592	#121	—	2	4	no	—
593	#121	D₄×C₂₃	1	2	yes	—
594	#121	D₄×C₂₃	1	2	yes	—
595	#121	C₂³×C₂₃	1	4	yes	—
596	#121	C₂³×C₂₃	1	4	yes	—
597	#120	—	2	4	no	—
598	#120	—	2	4	no	—
599	C₄×Q₈	—	2	2	no	—
600	C₄×Q₈	—	2	2	no	—
601	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
602	C₄×Q₈	C₂³×C₂₃	1	1	yes	characteristic
603	C₄×D₄	—	2	2	no	—
604	C₄×D₄	—	2	4	no	—
605	C₄×D₄	—	2	2	no	—
606	C₄×D₄	—	2	1	no	—
607	C₄×D₄	—	2	1	no	—
608	C₄×D₄	—	2	1	no	—
609	C₄×D₄	—	2	1	no	—
610	C₄×D₄	—	2	1	no	—
611	C₄×D₄	—	2	1	no	—
612	C₄×D₄	C₂³×C₂₃	1	2	yes	—
613	C₄×D₄	C₂³×C₂₃	1	2	yes	—
614	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
615	C₄×D₄	C₂³×C₂₃	1	1	yes	characteristic
616	C₄×D₄	C₂³×C₂₃	1	2	yes	—
617	C₄×D₄	C₂³×C₂₃	1	2	yes	—
618	#117	—	2	2	no	—
619	#117	—	2	1	no	—
620	#117	C₂³×C₂₃	1	1	yes	characteristic
621	#117	C₂³×C₂₃	1	4	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
626	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
627	C₂×C₂²⋊C₄	—	2	1	no	—
628	C₂×C₂²⋊C₄	—	2	4	no	—
629	C₂×C₄²	—	2	1	no	—
630	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
631	#107	C₂³×C₂₃	1	2	yes	—
632	#106	C₂³×C₂₃	1	4	yes	—
633	#106	C₂³×C₂₃	1	4	yes	—
634	#106	C₂³×C₂₃	1	2	yes	—
635	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
636	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
637	C₄⋊C₈	C₂³×C₂₃	1	1	yes	characteristic
638	#103	C₂³×C₂₃	1	2	yes	—
639	#103	C₂³×C₂₃	1	2	yes	—
640	#103	C₂³×C₂₃	1	4	yes	—
641	#103	C₂³×C₂₃	1	2	yes	—
642	#103	C₂³×C₂₃	1	4	yes	—
643	#102	C₂³×C₂₃	1	4	yes	—
644	#102	C₂³×C₂₃	1	4	yes	—
645	#102	C₂³×C₂₃	1	2	yes	—
646	#102	C₂³×C₂₃	1	2	yes	—
647	#102	C₂³×C₂₃	1	4	yes	—
648	#102	C₂³×C₂₃	1	2	yes	—
649	#102	C₂³×C₂₃	1	2	yes	—
650	#102	C₂³×C₂₃	1	2	yes	—
651	#102	C₂³×C₂₃	1	4	yes	—
652	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
653	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
654	#97	C₂³×C₂₃	1	2	yes	—
655	C₄×C₈	C₂³×C₂₃	1	2	yes	—
656	C₂₃	#61200	1	1	yes	characteristic, direct product factor, Sylow
657	C₂⁴	—	2	1	no	—
658	C₂⁴	—	2	4	no	—
659	#41	—	2	4	no	—
660	#41	—	2	4	no	—
661	#41	—	2	8	no	—
662	#41	—	2	2	no	—
663	#41	—	2	4	no	—
664	#41	—	2	2	no	—
665	#41	—	2	4	no	—
666	#41	—	4	4	no	—
667	#41	—	4	8	no	—
668	#41	—	8	4	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	2	no	—
671	C₂×Q₈	—	8	2	no	—
672	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
673	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₂₃	1	1	yes	characteristic
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	4	no	—
678	C₂×D₄	—	2	2	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	1	no	—
683	C₂×D₄	—	2	4	no	—
684	C₂×D₄	—	2	1	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	4	4	no	—
687	C₂×D₄	—	4	8	no	—
688	C₂×D₄	—	4	16	no	—
689	C₂×D₄	—	8	4	no	—
690	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
691	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
692	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
693	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
694	C₂×D₄	#41×C₂₃	1	4	yes	complemented
695	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
696	C₂×D₄	C₂⁴×C₂₃	1	1	yes	characteristic
697	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
698	C₂²×C₄	—	2	1	no	—
699	C₂²×C₄	—	2	2	no	—
700	C₂²×C₄	—	2	4	no	—
701	C₂²×C₄	—	2	1	no	—
702	C₂²×C₄	—	2	1	no	—
703	C₂²×C₄	—	2	1	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	2	no	—
708	C₂²×C₄	—	8	2	no	—
709	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
710	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
711	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
712	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
713	Q₁₆	—	4	2	no	—
714	SD₁₆	—	2	4	no	—
715	SD₁₆	—	4	2	no	—
716	SD₁₆	—	4	2	no	—
717	D₈	—	2	4	no	—
718	D₈	—	4	2	no	—
719	M₁₆	—	2	2	no	—
720	M₁₆	—	2	2	no	—
721	M₁₆	—	4	4	no	—
722	C₂×C₈	—	2	4	no	—
723	C₂×C₈	—	4	4	no	—
724	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
725	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
726	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
727	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
728	C₄⋊C₄	—	2	1	no	—
729	C₄⋊C₄	—	2	2	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	2	no	—
732	C₄⋊C₄	—	2	1	no	—
733	C₄⋊C₄	—	2	2	no	—
734	C₄⋊C₄	—	2	4	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	4	no	—
739	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
740	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
741	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
742	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
743	C₄⋊C₄	C₂⁴×C₂₃	1	1	yes	characteristic
744	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
745	C₂²⋊C₄	—	2	4	no	—
746	C₂²⋊C₄	—	2	1	no	—
747	C₂²⋊C₄	—	2	4	no	—
748	C₂²⋊C₄	—	2	4	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	1	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₂²⋊C₄	—	2	2	no	—
757	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
758	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
759	C₄²	—	2	1	no	—
760	C₄²	—	2	1	no	—
761	C₄²	—	2	1	no	—
762	C₄²	—	2	4	no	—
763	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
764	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
765	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
766	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
767	C₂³	—	2	2	no	—
768	C₂³	—	2	4	no	—
769	C₂³	—	2	1	no	—
770	C₂³	—	2	2	no	—
771	C₂³	—	4	8	no	—
772	C₂³	—	8	1	no	—
773	C₂³	—	8	1	no	—
774	C₂³	—	8	4	no	—
775	C₂³	—	8	4	no	—
776	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
777	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
778	Q₈	—	2	4	no	—
779	Q₈	—	2	1	no	—
780	Q₈	—	2	2	no	—
781	Q₈	—	2	1	no	—
782	Q₈	—	2	2	no	—
783	Q₈	—	4	4	no	—
784	Q₈	—	8	2	no	—
785	D₄	—	2	8	no	—
786	D₄	—	2	4	no	—
787	D₄	—	2	1	no	—
788	D₄	—	2	2	no	—
789	D₄	—	2	2	no	—
790	D₄	—	2	1	no	—
791	D₄	—	2	2	no	—
792	D₄	—	2	4	no	—
793	D₄	—	2	4	no	—
794	D₄	—	4	2	no	—
795	D₄	—	4	8	no	—
796	D₄	—	4	8	no	—
797	D₄	—	4	4	no	—
798	D₄	—	4	2	no	—
799	D₄	—	4	2	no	—
800	D₄	—	8	1	no	—
801	D₄	—	8	4	no	—
802	D₄	—	8	4	no	—
803	D₄	C₂×#41×C₂₃	1	4	yes	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	4	no	—
806	C₂×C₄	—	2	4	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	1	no	—
810	C₂×C₄	—	2	4	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	4	1	no	—
814	C₂×C₄	—	4	8	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	4	no	—
817	C₂×C₄	—	4	2	no	—
818	C₂×C₄	—	4	4	no	—
819	C₂×C₄	—	4	2	no	—
820	C₂×C₄	—	8	2	no	—
821	C₂×C₄	—	8	1	no	—
822	C₂×C₄	—	8	2	no	—
823	C₂×C₄	—	8	4	no	—
824	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
825	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
826	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
827	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
828	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
829	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
830	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
831	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
832	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
833	C₈	—	2	2	no	—
834	C₈	—	2	2	no	—
835	C₈	—	2	2	no	—
836	C₈	—	2	2	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	2	4	no	—
840	C₂²	—	2	4	no	—
841	C₂²	—	2	4	no	—
842	C₂²	—	2	4	no	—
843	C₂²	—	4	2	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	1	no	—
847	C₂²	—	4	1	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	1	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	8	4	no	—
852	C₂²	—	16	8	no	—
853	C₂²	C₂₃×#546	1	2	yes	—
854	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
855	C₄	—	2	4	no	—
856	C₄	—	2	1	no	—
857	C₄	—	2	1	no	—
858	C₄	—	2	1	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	1	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	1	no	—
863	C₄	—	4	1	no	—
864	C₄	—	4	4	no	—
865	C₄	C₂₃×#546	1	2	yes	—
866	C₄	C₂₃×#577	1	2	yes	—
867	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
868	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
869	C₂	—	2	2	no	—
870	C₂	—	4	4	no	—
871	C₂	—	4	4	no	—
872	C₂	—	8	2	no	—
873	C₂	—	8	1	no	—
874	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
875	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
876	C₂	C₂₃×#3585	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×#3511	C₂	semidirect
2. C₂₃×#3496	C₂	semidirect
3. C₂₃×#3331	C₂	semidirect
4. C₂₃×#3325	C₂	semidirect
5. C₂₃×#3311	C₂	semidirect
6. C₂₃×#3306	C₂	semidirect
7. C₂₃×#3303	C₂	semidirect
8. C₂₃×#3295	C₂	semidirect
9. C₂₃×#3141	C₂	semidirect
10. C₂₃×#3099	C₂	semidirect
11. C₂×C₂₃×#476	C₂	semidirect
12. C₂₃×#3060	C₂	semidirect
13. C₂₃×#3035	C₂	semidirect
14. C₂₃×#3012	C₂	semidirect
15. C₄×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
16. C₂₃×#2935	C₂	semidirect
17. C₂₃×#2897	C₂	semidirect
20. C₂×C₂₃×#135	C₂²	semidirect
21. C₂×C₂₃×#131	C₂²	semidirect
22. C₂₃×#556	C₂²	semidirect
23. C₂₃×#555	C₂²	semidirect
24. C₂₃×#554	C₂²	semidirect
29. C₂₃×#547	C₂²	semidirect
36. C₂₃×#537	C₂²	semidirect
42. C₂×C₂₃×C₄⋊Q₈	C₂²	semidirect
44. C₂₃×#520	C₂²	semidirect
45. C₄×#41×C₂₃	C₂²	semidirect
47. C₂₃×#489	C₂²	semidirect
48. C₂₃×#487	C₂²	semidirect
49. C₂₃×#486	C₂²	semidirect
50. C₂₃×#485	C₂²	semidirect
51. C₂₃×#483	C₂²	semidirect
52. C₂₃×#482	C₂²	semidirect
53. C₂₃×#481	C₂²	semidirect
54. C₂₃×#476	C₂²	semidirect
55. C₂₃×#476	C₂²	semidirect
56. C₂₃×#476	C₂²	semidirect
57. C₂₃×#470	C₂²	semidirect
58. C₂₃×#469	C₂²	semidirect
59. C₂₃×#465	C₂²	semidirect
60. C₂₃×#465	C₂²	semidirect
61. C₂₃×#464	C₂²	semidirect
62. C₂₃×#463	C₂²	semidirect
63. C₂₃×#462	C₂²	semidirect
64. C₂₃×#461	C₂²	semidirect
65. C₂₃×#460	C₂²	semidirect
66. C₂₃×#459	C₂²	semidirect
67. C₂₃×#452	C₂²	semidirect
68. C₂₃×#450	C₂²	semidirect
69. C₂₃×#449	C₂²	semidirect
70. C₂₃×#447	C₂²	semidirect
71. C₂₃×#442	C₂²	semidirect
72. C₂₃×#440	C₂²	semidirect
73. C₄×SD₁₆×C₂₃	C₂²	semidirect
74. C₄×D₈×C₂₃	C₂²	semidirect
75. C₂₃×#436	C₂²	semidirect
76. C₂₃×#435	C₂²	semidirect
77. C₈×D₄×C₂₃	C₂²	semidirect
78. C₂₃×#428	C₂²	semidirect
79. C₂×C₂₃×#106	C₂²	semidirect
80. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
82. C₂₃×#418	C₂²	semidirect
83. C₂₃×#417	C₂²	semidirect
84. C₂₃×#417	C₂²	semidirect
85. C₂₃×#417	C₂²	semidirect
86. C₂₃×#417	C₂²	semidirect
87. C₂₃×#416	C₂²	semidirect
88. C₂₃×#416	C₂²	semidirect
90. C₂×C₂₃×#102	C₂²	semidirect
91. C₂₃×#408	C₂²	semidirect
92. C₄×M₁₆×C₂₃	C₂²	semidirect
255. C₂×D₄×C₂₃	#41	semidirect
328. #61200	C₂₃	direct (N × H)
399. #3511	C₂×C₂₃	semidirect
400. #3496	C₂×C₂₃	semidirect
401. #3331	C₂×C₂₃	semidirect
402. #3325	C₂×C₂₃	semidirect
403. #3311	C₂×C₂₃	semidirect
404. #3306	C₂×C₂₃	semidirect
405. #3303	C₂×C₂₃	semidirect
406. #3295	C₂×C₂₃	semidirect
407. #3141	C₂×C₂₃	semidirect
408. #3099	C₂×C₂₃	semidirect
409. C₂×#476	C₂×C₂₃	semidirect
410. #3060	C₂×C₂₃	semidirect
411. #3035	C₂×C₂₃	semidirect
412. #3012	C₂×C₂₃	semidirect
413. C₄×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
414. #2935	C₂×C₂₃	semidirect
415. #2897	C₂×C₂₃	semidirect
450. C₂×#135	C₂²×C₂₃	semidirect
451. C₂×#131	C₂²×C₂₃	semidirect
452. #556	C₂²×C₂₃	semidirect
453. #555	C₂²×C₂₃	semidirect
454. #554	C₂²×C₂₃	semidirect
459. #547	C₂²×C₂₃	semidirect
466. #537	C₂²×C₂₃	semidirect
472. C₂×C₄⋊Q₈	C₂²×C₂₃	semidirect
474. #520	C₂²×C₂₃	semidirect
475. C₄×#41	C₂²×C₂₃	semidirect
477. #489	C₂²×C₂₃	semidirect
478. #487	C₂²×C₂₃	semidirect
479. #486	C₂²×C₂₃	semidirect
480. #485	C₂²×C₂₃	semidirect
481. #483	C₂²×C₂₃	semidirect
482. #482	C₂²×C₂₃	semidirect
483. #481	C₂²×C₂₃	semidirect
484. #476	C₂²×C₂₃	semidirect
485. #476	C₂²×C₂₃	semidirect
486. #476	C₂²×C₂₃	semidirect
487. #470	C₂²×C₂₃	semidirect
488. #469	C₂²×C₂₃	semidirect
489. #465	C₂²×C₂₃	semidirect
490. #465	C₂²×C₂₃	semidirect
491. #464	C₂²×C₂₃	semidirect
492. #463	C₂²×C₂₃	semidirect
493. #462	C₂²×C₂₃	semidirect
494. #461	C₂²×C₂₃	semidirect
495. #460	C₂²×C₂₃	semidirect
496. #459	C₂²×C₂₃	semidirect
497. #452	C₂²×C₂₃	semidirect
498. #450	C₂²×C₂₃	semidirect
499. #449	C₂²×C₂₃	semidirect
500. #447	C₂²×C₂₃	semidirect
501. #442	C₂²×C₂₃	semidirect
502. #440	C₂²×C₂₃	semidirect
503. C₄×SD₁₆	C₂²×C₂₃	semidirect
504. C₄×D₈	C₂²×C₂₃	semidirect
505. #436	C₂²×C₂₃	semidirect
506. #435	C₂²×C₂₃	semidirect
507. C₈×D₄	C₂²×C₂₃	semidirect
508. #428	C₂²×C₂₃	semidirect
509. C₂×#106	C₂²×C₂₃	semidirect
510. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
512. #418	C₂²×C₂₃	semidirect
513. #417	C₂²×C₂₃	semidirect
514. #417	C₂²×C₂₃	semidirect
515. #417	C₂²×C₂₃	semidirect
516. #417	C₂²×C₂₃	semidirect
517. #416	C₂²×C₂₃	semidirect
518. #416	C₂²×C₂₃	semidirect
520. C₂×#102	C₂²×C₂₃	semidirect
521. #408	C₂²×C₂₃	semidirect
522. C₄×M₁₆	C₂²×C₂₃	semidirect
656. C₂₃	#61200	direct (N × H)
694. C₂×D₄	#41×C₂₃	semidirect

Maximal subgroups

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

subgroup	index
C₂₃×#3511	2
C₂₃×#3496	2
C₂₃×#3331	2
C₂₃×#3325	2
C₂₃×#3311	2
C₂₃×#3306	2
C₂₃×#3303	2
C₂₃×#3295	2
C₂₃×#3141	2
C₂₃×#3099	2
C₂×C₂₃×#476	2
C₂₃×#3060	2
C₂₃×#3035	2
C₂₃×#3012	2
C₄×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#2935	2
C₂₃×#2897	2
#61200	23

Subgroups — C23×#61200 #19208826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#61200 #19208826