Subgroups — C₂₃×#60919 #19208545

Order 5888.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₃×#3455	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3263	C₂	1	4	yes	maximal, complemented
4	C₂₃×#3262	C₂	1	4	yes	maximal, complemented
5	C₂₃×#3258	C₂	1	4	yes	maximal, complemented
6	C₂₃×#3257	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3079	C₂	1	2	yes	maximal, complemented
8	C₂₃×#3078	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂₃×#3077	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂₃×#3056	C₂	1	2	yes	maximal, complemented
11	C₂₃×#3055	C₂	1	2	yes	maximal, complemented
12	C₂₃×#3040	C₂	1	2	yes	maximal, complemented
13	C₂₃×#3037	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂₃×#3036	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂₃×#2905	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#137	C₂²	1	2	yes	—
17	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	—
18	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
19	C₂₃×#542	—	2	2	no	—
20	C₂₃×#542	—	2	2	no	—
21	C₂₃×#542	C₂²	1	4	yes	—
22	C₂₃×#542	C₂²	1	4	yes	—
23	C₂₃×#542	C₂²	1	2	yes	complemented
24	C₂₃×#542	C₂²	1	2	yes	complemented
25	C₂₃×#541	C₂²	1	2	yes	complemented
26	C₂₃×#540	C₂²	1	2	yes	complemented
27	C₂₃×#539	—	2	1	no	—
28	C₂₃×#539	—	2	1	no	—
29	C₂₃×#538	—	2	1	no	—
30	C₂₃×#538	—	2	1	no	—
31	C₂₃×#533	C₂²	1	1	yes	characteristic
32	C₂₃×#532	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
34	C₂₃×#529	—	2	2	no	—
35	C₂₃×#529	—	2	2	no	—
36	C₂×C₂₃×#126	—	2	1	no	—
37	C₂×C₂₃×#124	—	2	1	no	—
38	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
39	C₂₃×#525	C₂²	1	2	yes	—
40	C₂×C₂₃×#123	—	2	1	no	—
41	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
42	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
44	C₄×#41×C₂₃	C₂²	1	2	yes	—
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
48	C₂₃×#479	C₂²	1	4	yes	complemented
49	C₂₃×#478	C₂²	1	4	yes	complemented
50	C₂₃×#477	C₂²	1	4	yes	complemented
51	C₂₃×#477	C₂²	1	2	yes	complemented
52	C₂₃×#476	C₂²	1	4	yes	complemented
53	C₂₃×#476	C₂²	1	2	yes	complemented
54	C₂₃×#475	C₂²	1	4	yes	complemented
55	C₂₃×#475	C₂²	1	2	yes	complemented
56	C₂₃×#474	C₂²	1	4	yes	complemented
57	C₂₃×#474	C₂²	1	2	yes	complemented
58	C₂₃×#470	C₂²	1	4	yes	complemented
59	C₂₃×#469	C₂²	1	4	yes	—
60	C₂₃×#468	C₂²	1	4	yes	—
61	C₂₃×#468	C₂²	1	4	yes	complemented
62	C₂₃×#467	C₂²	1	4	yes	complemented
63	C₂₃×#466	C₂²	1	4	yes	—
64	C₂₃×#465	C₂²	1	4	yes	—
65	C₂₃×#465	C₂²	1	4	yes	complemented
66	C₂₃×#464	C₂²	1	4	yes	complemented
67	C₂₃×#464	C₂²	1	4	yes	complemented
68	C₂₃×#464	C₂²	1	4	yes	complemented
69	C₂₃×#463	C₂²	1	4	yes	complemented
70	C₂₃×#463	C₂²	1	4	yes	complemented
71	C₂₃×#463	C₂²	1	4	yes	complemented
72	C₂₃×#462	C₂²	1	2	yes	complemented
73	C₂₃×#461	C₂²	1	2	yes	complemented
74	C₂₃×#460	C₂²	1	2	yes	complemented
75	C₂₃×#459	C₂²	1	2	yes	complemented
76	C₂₃×#428	C₂²	1	2	yes	—
77	C₂₃×#428	C₂²	1	2	yes	—
78	C₂₃×#424	C₂²	1	4	yes	complemented
79	C₂₃×#424	C₂²	1	4	yes	complemented
80	C₂₃×#423	C₂²	1	1	yes	characteristic
81	C₂₃×#423	C₂²	1	1	yes	characteristic
82	C₂₃×#423	C₂²	1	2	yes	—
83	C₂₃×#419	C₂²	1	2	yes	—
84	C₂₃×#418	C₂²	1	2	yes	—
85	C₂₃×#417	C₂²	1	2	yes	—
86	C₂₃×#417	C₂²	1	2	yes	—
87	C₂×#41×C₂₃	C₂³	1	2	yes	—
88	C₂²×Q₈×C₂₃	—	2	1	no	—
89	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₂₃	—	2	1	no	—
93	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
94	C₂₃×#137	—	4	4	no	—
95	C₂₃×AGL(1,ℤ/8)	—	4	4	no	—
96	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
98	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
99	C₂×D₈×C₂₃	C₂³	1	4	yes	—
100	C₂×M₁₆×C₂₃	—	4	4	no	—
101	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
102	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
103	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
105	C₂₃×C₄⋊Q₈	—	2	2	no	—
106	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
108	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₂₃×C₄⋊Q₈	C₂³	1	1	yes	characteristic
110	C₂₃×#127	C₂³	1	1	yes	characteristic
111	C₂₃×#126	—	2	4	no	—
112	C₂₃×#126	—	2	4	no	—
113	C₂₃×#126	—	2	2	no	—
114	C₂₃×#126	—	2	2	no	—
115	C₂₃×#126	—	2	2	no	—
116	C₂₃×#126	—	2	2	no	—
117	C₂₃×#125	—	2	2	no	—
118	C₂₃×#125	—	2	2	no	—
119	C₂₃×#125	C₂³	1	2	yes	—
120	C₂₃×#124	—	2	4	no	—
121	C₂₃×#124	—	2	4	no	—
122	C₂₃×#124	—	2	2	no	—
123	C₂₃×#124	—	2	2	no	—
124	C₂₃×#124	—	2	2	no	—
125	C₂₃×#124	C₂³	1	4	yes	—
126	C₂₃×#124	C₂³	1	2	yes	—
127	C₂₃×#123	—	2	2	no	—
128	C₂₃×#123	—	2	2	no	—
129	C₂₃×#123	—	2	2	no	—
130	C₂₃×#123	—	2	4	no	—
131	C₂₃×#123	—	2	4	no	—
132	C₂₃×#123	—	2	2	no	—
133	C₂₃×#123	—	2	2	no	—
134	C₂₃×C₂²⋊Q₈	—	2	2	no	—
135	C₂₃×C₂²⋊Q₈	—	2	1	no	—
136	C₂₃×C₂²⋊Q₈	—	2	1	no	—
137	C₂₃×C₂²⋊Q₈	—	2	4	no	—
138	C₂₃×C₂²⋊Q₈	—	2	4	no	—
139	C₂₃×C₂²⋊Q₈	—	2	2	no	—
140	C₂₃×C₂²⋊Q₈	—	2	2	no	—
141	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
142	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
143	C₂₃×C₂²⋊Q₈	C₂³	1	2	yes	—
144	C₂₃×#121	—	2	2	no	—
145	C₂₃×#121	—	2	1	no	—
146	C₂₃×#121	—	2	1	no	—
147	C₂₃×#121	—	2	2	no	—
148	C₂₃×#121	—	2	2	no	—
149	C₂₃×#121	C₂³	1	4	yes	—
150	C₂₃×#121	C₂³	1	2	yes	—
151	C₂₃×#121	C₂³	1	2	yes	—
152	C₂₃×#120	—	2	2	no	—
153	C₄×Q₈×C₂₃	—	2	1	no	—
154	C₄×Q₈×C₂₃	—	2	1	no	—
155	C₄×Q₈×C₂₃	—	2	1	no	—
156	C₄×Q₈×C₂₃	—	2	1	no	—
157	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
158	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
159	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
160	C₄×Q₈×C₂₃	C₂³	1	2	yes	—
161	C₄×D₄×C₂₃	—	2	2	no	—
162	C₄×D₄×C₂₃	—	2	2	no	—
163	C₄×D₄×C₂₃	—	2	2	no	—
164	C₄×D₄×C₂₃	—	2	2	no	—
165	C₄×D₄×C₂₃	—	2	1	no	—
166	C₄×D₄×C₂₃	—	2	1	no	—
167	C₄×D₄×C₂₃	—	2	1	no	—
168	C₄×D₄×C₂₃	—	2	1	no	—
169	C₄×D₄×C₂₃	C₂³	1	2	yes	—
170	C₄×D₄×C₂₃	C₂³	1	2	yes	—
171	C₄×D₄×C₂₃	C₂³	1	2	yes	—
172	C₄×D₄×C₂₃	C₂³	1	2	yes	—
173	C₂₃×#117	—	2	2	no	—
174	C₂₃×#117	D₄	1	2	yes	—
175	C₂₃×#117	D₄	1	2	yes	—
176	C₂₃×#117	C₂³	1	2	yes	—
177	C₂₃×#117	C₂³	1	2	yes	—
178	C₂₃×#117	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
180	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
181	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
182	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
183	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
184	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
186	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
187	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
188	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
189	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
190	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
191	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
192	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₂₃	—	2	1	no	—
194	C₂×C₄²×C₂₃	—	2	2	no	—
195	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
197	C₂₃×#107	C₂³	1	4	yes	—
198	C₂₃×#107	C₂³	1	4	yes	—
199	C₂₃×#106	C₂³	1	4	yes	—
200	C₂₃×#106	C₂³	1	4	yes	—
201	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
202	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
203	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
204	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
205	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
206	C₂₃×C₄⋊C₈	C₂³	1	2	yes	—
207	C₂₃×#103	C₂³	1	4	yes	—
208	C₂₃×#103	C₂³	1	4	yes	—
209	C₂₃×#103	C₂³	1	4	yes	—
210	C₂₃×#103	C₂³	1	4	yes	—
211	C₂₃×#102	C₂³	1	4	yes	—
212	C₂₃×#102	C₂³	1	4	yes	—
213	C₂₃×#102	C₂³	1	4	yes	—
214	C₂₃×#102	C₂³	1	4	yes	—
215	C₂⁴×C₂₃	—	2	1	no	—
216	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
217	#41×C₂₃	—	2	4	no	—
218	#41×C₂₃	—	2	4	no	—
219	C₂×Q₈×C₂₃	—	2	1	no	—
220	C₂×Q₈×C₂₃	—	2	1	no	—
221	C₂×Q₈×C₂₃	—	2	1	no	—
222	C₂×Q₈×C₂₃	—	2	4	no	—
223	C₂×Q₈×C₂₃	—	2	2	no	—
224	C₂×Q₈×C₂₃	—	2	2	no	—
225	C₂×Q₈×C₂₃	—	8	2	no	—
226	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
227	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
228	C₂×D₄×C₂₃	—	2	2	no	—
229	C₂×D₄×C₂₃	—	2	2	no	—
230	C₂×D₄×C₂₃	—	2	2	no	—
231	C₂×D₄×C₂₃	—	2	4	no	—
232	C₂×D₄×C₂₃	—	2	1	no	—
233	C₂×D₄×C₂₃	—	2	1	no	—
234	C₂×D₄×C₂₃	—	2	1	no	—
235	C₂×D₄×C₂₃	—	2	2	no	—
236	C₂×D₄×C₂₃	—	2	2	no	—
237	C₂×D₄×C₂₃	—	8	2	no	—
238	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
239	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₂₃	—	2	2	no	—
241	C₂²×C₄×C₂₃	—	2	2	no	—
242	C₂²×C₄×C₂₃	—	2	1	no	—
243	C₂²×C₄×C₂₃	—	2	1	no	—
244	C₂²×C₄×C₂₃	—	2	1	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	2	no	—
249	C₂²×C₄×C₂₃	—	2	2	no	—
250	C₂²×C₄×C₂₃	—	8	2	no	—
251	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
252	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
253	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
254	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
255	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
256	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
257	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
259	Q₁₆×C₂₃	—	4	4	no	—
260	SD₁₆×C₂₃	—	4	4	no	—
261	SD₁₆×C₂₃	—	4	4	no	—
262	D₈×C₂₃	—	4	4	no	—
263	M₁₆×C₂₃	—	2	4	no	—
264	M₁₆×C₂₃	—	2	4	no	—
265	M₁₆×C₂₃	—	4	4	no	—
266	C₂×C₈×C₂₃	—	4	4	no	—
267	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
268	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
269	C₄⋊C₄×C₂₃	—	2	2	no	—
270	C₄⋊C₄×C₂₃	—	2	2	no	—
271	C₄⋊C₄×C₂₃	—	2	4	no	—
272	C₄⋊C₄×C₂₃	—	2	4	no	—
273	C₄⋊C₄×C₂₃	—	2	1	no	—
274	C₄⋊C₄×C₂₃	—	2	1	no	—
275	C₄⋊C₄×C₂₃	—	2	2	no	—
276	C₄⋊C₄×C₂₃	—	2	2	no	—
277	C₄⋊C₄×C₂₃	—	2	1	no	—
278	C₄⋊C₄×C₂₃	—	2	1	no	—
279	C₄⋊C₄×C₂₃	—	2	2	no	—
280	C₄⋊C₄×C₂₃	—	2	2	no	—
281	C₄⋊C₄×C₂₃	—	2	2	no	—
282	C₄⋊C₄×C₂₃	—	2	2	no	—
283	C₄⋊C₄×C₂₃	—	2	1	no	—
284	C₄⋊C₄×C₂₃	—	2	1	no	—
285	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
286	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
287	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
288	C₄⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
289	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
290	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
291	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
293	C₂²⋊C₄×C₂₃	—	2	4	no	—
294	C₂²⋊C₄×C₂₃	—	2	2	no	—
295	C₂²⋊C₄×C₂₃	—	2	2	no	—
296	C₂²⋊C₄×C₂₃	—	2	2	no	—
297	C₂²⋊C₄×C₂₃	—	2	2	no	—
298	C₂²⋊C₄×C₂₃	—	2	2	no	—
299	C₂²⋊C₄×C₂₃	—	2	4	no	—
300	C₂²⋊C₄×C₂₃	—	2	4	no	—
301	C₂²⋊C₄×C₂₃	—	2	4	no	—
302	C₂²⋊C₄×C₂₃	—	2	2	no	—
303	C₂²⋊C₄×C₂₃	—	2	2	no	—
304	C₂²⋊C₄×C₂₃	—	2	2	no	—
305	C₂²⋊C₄×C₂₃	—	2	2	no	—
306	C₂²⋊C₄×C₂₃	—	2	2	no	—
307	C₂²⋊C₄×C₂₃	—	2	2	no	—
308	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
309	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
310	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
311	C₂²⋊C₄×C₂₃	C₂×D₄	1	2	yes	—
312	C₄²×C₂₃	—	2	2	no	—
313	C₄²×C₂₃	—	2	2	no	—
314	C₄²×C₂₃	—	2	2	no	—
315	C₄²×C₂₃	—	2	2	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	C₂×D₄	1	2	yes	—
318	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₂₃	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
321	C₄²×C₂₃	C₂⁴	1	2	yes	—
322	C₄²×C₂₃	C₂⁴	1	1	yes	characteristic
323	#60919	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
324	C₂³×C₂₃	—	2	2	no	—
325	C₂³×C₂₃	—	2	2	no	—
326	C₂³×C₂₃	—	2	2	no	—
327	C₂³×C₂₃	—	4	1	no	—
328	C₂³×C₂₃	—	4	1	no	—
329	C₂³×C₂₃	—	4	2	no	—
330	C₂³×C₂₃	—	4	2	no	—
331	C₂³×C₂₃	—	4	2	no	—
332	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
333	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
334	Q₈×C₂₃	—	2	2	no	—
335	Q₈×C₂₃	—	2	2	no	—
336	Q₈×C₂₃	—	2	2	no	—
337	Q₈×C₂₃	—	2	2	no	—
338	Q₈×C₂₃	—	4	2	no	—
339	Q₈×C₂₃	—	8	1	no	—
340	Q₈×C₂₃	—	8	1	no	—
341	Q₈×C₂₃	—	8	4	no	—
342	D₄×C₂₃	—	2	2	no	—
343	D₄×C₂₃	—	2	2	no	—
344	D₄×C₂₃	—	2	2	no	—
345	D₄×C₂₃	—	2	2	no	—
346	D₄×C₂₃	—	4	4	no	—
347	D₄×C₂₃	—	4	2	no	—
348	D₄×C₂₃	—	8	1	no	—
349	D₄×C₂₃	—	8	1	no	—
350	D₄×C₂₃	—	8	2	no	—
351	D₄×C₂₃	—	8	2	no	—
352	D₄×C₂₃	—	8	4	no	—
353	C₂×C₄×C₂₃	—	2	2	no	—
354	C₂×C₄×C₂₃	—	2	4	no	—
355	C₂×C₄×C₂₃	—	2	2	no	—
356	C₂×C₄×C₂₃	—	2	2	no	—
357	C₂×C₄×C₂₃	—	2	2	no	—
358	C₂×C₄×C₂₃	—	2	2	no	—
359	C₂×C₄×C₂₃	—	2	2	no	—
360	C₂×C₄×C₂₃	—	2	2	no	—
361	C₂×C₄×C₂₃	—	2	2	no	—
362	C₂×C₄×C₂₃	—	2	2	no	—
363	C₂×C₄×C₂₃	—	4	1	no	—
364	C₂×C₄×C₂₃	—	4	1	no	—
365	C₂×C₄×C₂₃	—	4	1	no	—
366	C₂×C₄×C₂₃	—	4	1	no	—
367	C₂×C₄×C₂₃	—	4	2	no	—
368	C₂×C₄×C₂₃	—	4	2	no	—
369	C₂×C₄×C₂₃	—	4	2	no	—
370	C₂×C₄×C₂₃	—	4	4	no	—
371	C₂×C₄×C₂₃	—	8	2	no	—
372	C₂×C₄×C₂₃	—	8	2	no	—
373	C₂×C₄×C₂₃	—	8	2	no	—
374	C₂×C₄×C₂₃	—	8	2	no	—
375	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
376	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
377	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
380	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
381	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
382	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
383	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
384	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
385	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
386	C₈×C₂₃	—	2	4	no	—
387	C₈×C₂₃	—	2	4	no	—
388	#3455	C₂×C₂₃	1	1	yes	characteristic, complemented
389	C₂×#542	C₂×C₂₃	1	1	yes	characteristic, complemented
390	#3263	C₂×C₂₃	1	4	yes	complemented
391	#3262	C₂×C₂₃	1	4	yes	complemented
392	#3258	C₂×C₂₃	1	4	yes	complemented
393	#3257	C₂×C₂₃	1	4	yes	complemented
394	#3079	C₂×C₂₃	1	2	yes	complemented
395	#3078	C₂×C₂₃	1	1	yes	characteristic, complemented
396	#3077	C₂×C₂₃	1	1	yes	characteristic, complemented
397	#3056	C₂×C₂₃	1	2	yes	complemented
398	#3055	C₂×C₂₃	1	2	yes	complemented
399	#3040	C₂×C₂₃	1	2	yes	complemented
400	#3037	C₂×C₂₃	1	1	yes	characteristic, complemented
401	#3036	C₂×C₂₃	1	1	yes	characteristic, complemented
402	#2905	C₂×C₂₃	1	1	yes	characteristic, complemented
403	C₂²×C₂₃	—	2	1	no	—
404	C₂²×C₂₃	—	2	1	no	—
405	C₂²×C₂₃	—	2	2	no	—
406	C₂²×C₂₃	—	2	2	no	—
407	C₂²×C₂₃	—	2	2	no	—
408	C₂²×C₂₃	—	4	2	no	—
409	C₂²×C₂₃	—	4	2	no	—
410	C₂²×C₂₃	—	4	2	no	—
411	C₂²×C₂₃	—	4	2	no	—
412	C₂²×C₂₃	—	4	2	no	—
413	C₂²×C₂₃	—	4	2	no	—
414	C₂²×C₂₃	—	8	2	no	—
415	C₂²×C₂₃	—	8	4	no	—
416	C₂²×C₂₃	#537	1	2	yes	—
417	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
418	C₄×C₂₃	—	2	1	no	—
419	C₄×C₂₃	—	2	1	no	—
420	C₄×C₂₃	—	2	2	no	—
421	C₄×C₂₃	—	2	2	no	—
422	C₄×C₂₃	—	2	1	no	—
423	C₄×C₂₃	—	2	1	no	—
424	C₄×C₂₃	—	2	2	no	—
425	C₄×C₂₃	—	4	2	no	—
426	C₄×C₂₃	—	4	2	no	—
427	C₄×C₂₃	—	4	2	no	—
428	C₄×C₂₃	—	4	2	no	—
429	C₄×C₂₃	—	4	2	no	—
430	C₄×C₂₃	—	4	2	no	—
431	C₄×C₂₃	#537	1	2	yes	—
432	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
433	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
434	C₂×#137	C₂²×C₂₃	1	2	yes	—
435	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	—
436	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
437	#542	—	2	2	no	—
438	#542	—	2	2	no	—
439	#542	C₂²×C₂₃	1	4	yes	—
440	#542	C₂²×C₂₃	1	4	yes	—
441	#542	C₂²×C₂₃	1	2	yes	complemented
442	#542	C₂²×C₂₃	1	2	yes	complemented
443	#541	C₂²×C₂₃	1	2	yes	complemented
444	#540	C₂²×C₂₃	1	2	yes	complemented
445	#539	—	2	1	no	—
446	#539	—	2	1	no	—
447	#538	—	2	1	no	—
448	#538	—	2	1	no	—
449	#533	C₂²×C₂₃	1	1	yes	characteristic
450	#532	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
452	#529	—	2	2	no	—
453	#529	—	2	2	no	—
454	C₂×#126	—	2	1	no	—
455	C₂×#124	—	2	1	no	—
456	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
457	#525	C₂²×C₂₃	1	2	yes	—
458	C₂×#123	—	2	1	no	—
459	C₂×C₂²⋊Q₈	—	2	1	no	—
460	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
461	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
462	C₄×#41	C₂²×C₂₃	1	2	yes	—
463	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
466	#479	C₂²×C₂₃	1	4	yes	complemented
467	#478	C₂²×C₂₃	1	4	yes	complemented
468	#477	C₂²×C₂₃	1	2	yes	complemented
469	#477	C₂²×C₂₃	1	4	yes	complemented
470	#476	C₂²×C₂₃	1	2	yes	complemented
471	#476	C₂²×C₂₃	1	4	yes	complemented
472	#475	C₂²×C₂₃	1	2	yes	complemented
473	#475	C₂²×C₂₃	1	4	yes	complemented
474	#474	C₂²×C₂₃	1	2	yes	complemented
475	#474	C₂²×C₂₃	1	4	yes	complemented
476	#470	C₂²×C₂₃	1	4	yes	complemented
477	#469	C₂²×C₂₃	1	4	yes	—
478	#468	C₂²×C₂₃	1	4	yes	—
479	#468	C₂²×C₂₃	1	4	yes	complemented
480	#467	C₂²×C₂₃	1	4	yes	complemented
481	#466	C₂²×C₂₃	1	4	yes	—
482	#465	C₂²×C₂₃	1	4	yes	—
483	#465	C₂²×C₂₃	1	4	yes	complemented
484	#464	C₂²×C₂₃	1	4	yes	complemented
485	#464	C₂²×C₂₃	1	4	yes	complemented
486	#464	C₂²×C₂₃	1	4	yes	complemented
487	#463	C₂²×C₂₃	1	4	yes	complemented
488	#463	C₂²×C₂₃	1	4	yes	complemented
489	#463	C₂²×C₂₃	1	4	yes	complemented
490	#462	C₂²×C₂₃	1	2	yes	complemented
491	#461	C₂²×C₂₃	1	2	yes	complemented
492	#460	C₂²×C₂₃	1	2	yes	complemented
493	#459	C₂²×C₂₃	1	2	yes	complemented
494	#428	C₂²×C₂₃	1	2	yes	—
495	#428	C₂²×C₂₃	1	2	yes	—
496	#424	C₂²×C₂₃	1	4	yes	complemented
497	#424	C₂²×C₂₃	1	4	yes	complemented
498	#423	C₂²×C₂₃	1	1	yes	characteristic
499	#423	C₂²×C₂₃	1	1	yes	characteristic
500	#423	C₂²×C₂₃	1	2	yes	—
501	#419	C₂²×C₂₃	1	2	yes	—
502	#418	C₂²×C₂₃	1	2	yes	—
503	#417	C₂²×C₂₃	1	2	yes	—
504	#417	C₂²×C₂₃	1	2	yes	—
505	C₂×C₂₃	—	2	2	no	—
506	C₂×C₂₃	—	4	2	no	—
507	C₂×C₂₃	—	8	2	no	—
508	C₂×C₂₃	—	8	2	no	—
509	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
510	C₂×C₂₃	#3585	1	1	yes	characteristic
511	C₂×C₂₃	#3586	1	1	yes	characteristic
512	C₂×#41	C₂³×C₂₃	1	2	yes	—
513	C₂²×Q₈	—	2	1	no	—
514	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
519	#137	—	4	4	no	—
520	AGL(1,ℤ/8)	—	4	4	no	—
521	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
522	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
523	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
524	C₂×D₈	C₂³×C₂₃	1	4	yes	—
525	C₂×M₁₆	—	4	4	no	—
526	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
527	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
528	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
529	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
530	C₄⋊Q₈	—	2	2	no	—
531	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
532	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
533	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
534	C₄⋊Q₈	C₂³×C₂₃	1	1	yes	characteristic
535	#127	C₂³×C₂₃	1	1	yes	characteristic
536	#126	—	2	4	no	—
537	#126	—	2	4	no	—
538	#126	—	2	2	no	—
539	#126	—	2	2	no	—
540	#126	—	2	2	no	—
541	#126	—	2	2	no	—
542	#125	—	2	2	no	—
543	#125	—	2	2	no	—
544	#125	C₂³×C₂₃	1	2	yes	—
545	#124	—	2	4	no	—
546	#124	—	2	4	no	—
547	#124	—	2	2	no	—
548	#124	—	2	2	no	—
549	#124	—	2	2	no	—
550	#124	C₂³×C₂₃	1	4	yes	—
551	#124	C₂³×C₂₃	1	2	yes	—
552	#123	—	2	2	no	—
553	#123	—	2	2	no	—
554	#123	—	2	2	no	—
555	#123	—	2	4	no	—
556	#123	—	2	4	no	—
557	#123	—	2	2	no	—
558	#123	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	—	2	1	no	—
561	C₂²⋊Q₈	—	2	1	no	—
562	C₂²⋊Q₈	—	2	4	no	—
563	C₂²⋊Q₈	—	2	4	no	—
564	C₂²⋊Q₈	—	2	2	no	—
565	C₂²⋊Q₈	—	2	2	no	—
566	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
567	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
568	C₂²⋊Q₈	C₂³×C₂₃	1	2	yes	—
569	#121	—	2	2	no	—
570	#121	—	2	1	no	—
571	#121	—	2	1	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	C₂³×C₂₃	1	4	yes	—
575	#121	C₂³×C₂₃	1	2	yes	—
576	#121	C₂³×C₂₃	1	2	yes	—
577	#120	—	2	2	no	—
578	C₄×Q₈	—	2	1	no	—
579	C₄×Q₈	—	2	1	no	—
580	C₄×Q₈	—	2	1	no	—
581	C₄×Q₈	—	2	1	no	—
582	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
583	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
584	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
585	C₄×Q₈	C₂³×C₂₃	1	2	yes	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	2	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	1	no	—
591	C₄×D₄	—	2	1	no	—
592	C₄×D₄	—	2	1	no	—
593	C₄×D₄	—	2	1	no	—
594	C₄×D₄	C₂³×C₂₃	1	2	yes	—
595	C₄×D₄	C₂³×C₂₃	1	2	yes	—
596	C₄×D₄	C₂³×C₂₃	1	2	yes	—
597	C₄×D₄	C₂³×C₂₃	1	2	yes	—
598	#117	—	2	2	no	—
599	#117	D₄×C₂₃	1	2	yes	—
600	#117	D₄×C₂₃	1	2	yes	—
601	#117	C₂³×C₂₃	1	2	yes	—
602	#117	C₂³×C₂₃	1	2	yes	—
603	#117	C₂³×C₂₃	1	2	yes	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	1	no	—
606	C₂×C₄⋊C₄	—	2	1	no	—
607	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
608	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
609	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
611	C₂×C₂²⋊C₄	—	2	1	no	—
612	C₂×C₂²⋊C₄	—	2	1	no	—
613	C₂×C₂²⋊C₄	—	2	1	no	—
614	C₂×C₂²⋊C₄	—	2	1	no	—
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
617	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
618	C₂×C₄²	—	2	1	no	—
619	C₂×C₄²	—	2	2	no	—
620	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
621	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
622	#107	C₂³×C₂₃	1	4	yes	—
623	#107	C₂³×C₂₃	1	4	yes	—
624	#106	C₂³×C₂₃	1	4	yes	—
625	#106	C₂³×C₂₃	1	4	yes	—
626	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
627	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
628	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
629	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
630	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
631	C₄⋊C₈	C₂³×C₂₃	1	2	yes	—
632	#103	C₂³×C₂₃	1	4	yes	—
633	#103	C₂³×C₂₃	1	4	yes	—
634	#103	C₂³×C₂₃	1	4	yes	—
635	#103	C₂³×C₂₃	1	4	yes	—
636	#102	C₂³×C₂₃	1	4	yes	—
637	#102	C₂³×C₂₃	1	4	yes	—
638	#102	C₂³×C₂₃	1	4	yes	—
639	#102	C₂³×C₂₃	1	4	yes	—
640	C₂₃	#60919	1	1	yes	characteristic, direct product factor, Sylow
641	C₂⁴	—	2	1	no	—
642	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
643	#41	—	2	4	no	—
644	#41	—	2	4	no	—
645	C₂×Q₈	—	2	1	no	—
646	C₂×Q₈	—	2	1	no	—
647	C₂×Q₈	—	2	1	no	—
648	C₂×Q₈	—	2	4	no	—
649	C₂×Q₈	—	2	2	no	—
650	C₂×Q₈	—	2	2	no	—
651	C₂×Q₈	—	8	2	no	—
652	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
653	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
654	C₂×D₄	—	2	2	no	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	2	no	—
657	C₂×D₄	—	2	4	no	—
658	C₂×D₄	—	2	1	no	—
659	C₂×D₄	—	2	1	no	—
660	C₂×D₄	—	2	1	no	—
661	C₂×D₄	—	2	2	no	—
662	C₂×D₄	—	2	2	no	—
663	C₂×D₄	—	8	2	no	—
664	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
665	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	1	no	—
669	C₂²×C₄	—	2	1	no	—
670	C₂²×C₄	—	2	1	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	8	2	no	—
677	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
678	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
679	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
680	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
681	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
682	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
683	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
685	Q₁₆	—	4	4	no	—
686	SD₁₆	—	4	4	no	—
687	SD₁₆	—	4	4	no	—
688	D₈	—	4	4	no	—
689	M₁₆	—	2	4	no	—
690	M₁₆	—	2	4	no	—
691	M₁₆	—	4	4	no	—
692	C₂×C₈	—	4	4	no	—
693	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
694	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
695	C₄⋊C₄	—	2	2	no	—
696	C₄⋊C₄	—	2	2	no	—
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	1	no	—
700	C₄⋊C₄	—	2	1	no	—
701	C₄⋊C₄	—	2	2	no	—
702	C₄⋊C₄	—	2	2	no	—
703	C₄⋊C₄	—	2	1	no	—
704	C₄⋊C₄	—	2	1	no	—
705	C₄⋊C₄	—	2	2	no	—
706	C₄⋊C₄	—	2	2	no	—
707	C₄⋊C₄	—	2	2	no	—
708	C₄⋊C₄	—	2	2	no	—
709	C₄⋊C₄	—	2	1	no	—
710	C₄⋊C₄	—	2	1	no	—
711	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
712	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
713	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
714	C₄⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
715	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
716	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
717	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
718	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	2	no	—
721	C₂²⋊C₄	—	2	2	no	—
722	C₂²⋊C₄	—	2	2	no	—
723	C₂²⋊C₄	—	2	2	no	—
724	C₂²⋊C₄	—	2	2	no	—
725	C₂²⋊C₄	—	2	4	no	—
726	C₂²⋊C₄	—	2	4	no	—
727	C₂²⋊C₄	—	2	4	no	—
728	C₂²⋊C₄	—	2	2	no	—
729	C₂²⋊C₄	—	2	2	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	2	no	—
732	C₂²⋊C₄	—	2	2	no	—
733	C₂²⋊C₄	—	2	2	no	—
734	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
735	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
736	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
737	C₂²⋊C₄	C₂×D₄×C₂₃	1	2	yes	—
738	C₄²	—	2	2	no	—
739	C₄²	—	2	2	no	—
740	C₄²	—	2	2	no	—
741	C₄²	—	2	2	no	—
742	C₄²	—	2	2	no	—
743	C₄²	C₂×D₄×C₂₃	1	2	yes	—
744	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
745	C₄²	C₂×D₄×C₂₃	1	1	yes	characteristic
746	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
747	C₄²	C₂⁴×C₂₃	1	2	yes	—
748	C₄²	C₂⁴×C₂₃	1	1	yes	characteristic
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	4	1	no	—
753	C₂³	—	4	1	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	2	no	—
756	C₂³	—	4	2	no	—
757	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
758	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
759	Q₈	—	2	2	no	—
760	Q₈	—	2	2	no	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	2	no	—
763	Q₈	—	4	2	no	—
764	Q₈	—	8	4	no	—
765	Q₈	—	8	1	no	—
766	Q₈	—	8	1	no	—
767	D₄	—	2	2	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	2	no	—
770	D₄	—	2	2	no	—
771	D₄	—	4	4	no	—
772	D₄	—	4	2	no	—
773	D₄	—	8	1	no	—
774	D₄	—	8	1	no	—
775	D₄	—	8	4	no	—
776	D₄	—	8	2	no	—
777	D₄	—	8	2	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	4	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	no	—
786	C₂×C₄	—	2	2	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	4	1	no	—
789	C₂×C₄	—	4	1	no	—
790	C₂×C₄	—	4	1	no	—
791	C₂×C₄	—	4	1	no	—
792	C₂×C₄	—	4	2	no	—
793	C₂×C₄	—	4	2	no	—
794	C₂×C₄	—	4	2	no	—
795	C₂×C₄	—	4	4	no	—
796	C₂×C₄	—	8	2	no	—
797	C₂×C₄	—	8	2	no	—
798	C₂×C₄	—	8	2	no	—
799	C₂×C₄	—	8	2	no	—
800	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
801	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
802	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
803	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
804	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
806	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
808	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
809	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
810	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
811	C₈	—	2	4	no	—
812	C₈	—	2	4	no	—
813	C₂²	—	2	1	no	—
814	C₂²	—	2	1	no	—
815	C₂²	—	2	2	no	—
816	C₂²	—	2	2	no	—
817	C₂²	—	2	2	no	—
818	C₂²	—	4	2	no	—
819	C₂²	—	4	2	no	—
820	C₂²	—	4	2	no	—
821	C₂²	—	4	2	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	8	2	no	—
825	C₂²	—	8	4	no	—
826	C₂²	C₂₃×#537	1	2	yes	—
827	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
828	C₄	—	2	2	no	—
829	C₄	—	2	1	no	—
830	C₄	—	2	1	no	—
831	C₄	—	2	2	no	—
832	C₄	—	2	2	no	—
833	C₄	—	2	1	no	—
834	C₄	—	2	1	no	—
835	C₄	—	4	2	no	—
836	C₄	—	4	2	no	—
837	C₄	—	4	2	no	—
838	C₄	—	4	2	no	—
839	C₄	—	4	2	no	—
840	C₄	—	4	2	no	—
841	C₄	C₂₃×#537	1	2	yes	—
842	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
843	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
844	C₂	—	2	2	no	—
845	C₂	—	4	2	no	—
846	C₂	—	8	2	no	—
847	C₂	—	8	2	no	—
848	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
849	C₂	C₂₃×#3585	1	1	yes	characteristic
850	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 ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂₃×#3455	C₂	semidirect
2. C₂×C₂₃×#542	C₂	semidirect
3. C₂₃×#3263	C₂	semidirect
4. C₂₃×#3262	C₂	semidirect
5. C₂₃×#3258	C₂	semidirect
6. C₂₃×#3257	C₂	semidirect
7. C₂₃×#3079	C₂	semidirect
8. C₂₃×#3078	C₂	semidirect
9. C₂₃×#3077	C₂	semidirect
10. C₂₃×#3056	C₂	semidirect
11. C₂₃×#3055	C₂	semidirect
12. C₂₃×#3040	C₂	semidirect
13. C₂₃×#3037	C₂	semidirect
14. C₂₃×#3036	C₂	semidirect
15. C₂₃×#2905	C₂	semidirect
23. C₂₃×#542	C₂²	semidirect
24. C₂₃×#542	C₂²	semidirect
25. C₂₃×#541	C₂²	semidirect
26. C₂₃×#540	C₂²	semidirect
48. C₂₃×#479	C₂²	semidirect
49. C₂₃×#478	C₂²	semidirect
50. C₂₃×#477	C₂²	semidirect
51. C₂₃×#477	C₂²	semidirect
52. C₂₃×#476	C₂²	semidirect
53. C₂₃×#476	C₂²	semidirect
54. C₂₃×#475	C₂²	semidirect
55. C₂₃×#475	C₂²	semidirect
56. C₂₃×#474	C₂²	semidirect
57. C₂₃×#474	C₂²	semidirect
58. C₂₃×#470	C₂²	semidirect
61. C₂₃×#468	C₂²	semidirect
62. C₂₃×#467	C₂²	semidirect
65. C₂₃×#465	C₂²	semidirect
66. C₂₃×#464	C₂²	semidirect
67. C₂₃×#464	C₂²	semidirect
68. C₂₃×#464	C₂²	semidirect
69. C₂₃×#463	C₂²	semidirect
70. C₂₃×#463	C₂²	semidirect
71. C₂₃×#463	C₂²	semidirect
72. C₂₃×#462	C₂²	semidirect
73. C₂₃×#461	C₂²	semidirect
74. C₂₃×#460	C₂²	semidirect
75. C₂₃×#459	C₂²	semidirect
78. C₂₃×#424	C₂²	semidirect
79. C₂₃×#424	C₂²	semidirect
323. #60919	C₂₃	direct (N × H)
388. #3455	C₂×C₂₃	semidirect
389. C₂×#542	C₂×C₂₃	semidirect
390. #3263	C₂×C₂₃	semidirect
391. #3262	C₂×C₂₃	semidirect
392. #3258	C₂×C₂₃	semidirect
393. #3257	C₂×C₂₃	semidirect
394. #3079	C₂×C₂₃	semidirect
395. #3078	C₂×C₂₃	semidirect
396. #3077	C₂×C₂₃	semidirect
397. #3056	C₂×C₂₃	semidirect
398. #3055	C₂×C₂₃	semidirect
399. #3040	C₂×C₂₃	semidirect
400. #3037	C₂×C₂₃	semidirect
401. #3036	C₂×C₂₃	semidirect
402. #2905	C₂×C₂₃	semidirect
441. #542	C₂²×C₂₃	semidirect
442. #542	C₂²×C₂₃	semidirect
443. #541	C₂²×C₂₃	semidirect
444. #540	C₂²×C₂₃	semidirect
466. #479	C₂²×C₂₃	semidirect
467. #478	C₂²×C₂₃	semidirect
468. #477	C₂²×C₂₃	semidirect
469. #477	C₂²×C₂₃	semidirect
470. #476	C₂²×C₂₃	semidirect
471. #476	C₂²×C₂₃	semidirect
472. #475	C₂²×C₂₃	semidirect
473. #475	C₂²×C₂₃	semidirect
474. #474	C₂²×C₂₃	semidirect
475. #474	C₂²×C₂₃	semidirect
476. #470	C₂²×C₂₃	semidirect
479. #468	C₂²×C₂₃	semidirect
480. #467	C₂²×C₂₃	semidirect
483. #465	C₂²×C₂₃	semidirect
484. #464	C₂²×C₂₃	semidirect
485. #464	C₂²×C₂₃	semidirect
486. #464	C₂²×C₂₃	semidirect
487. #463	C₂²×C₂₃	semidirect
488. #463	C₂²×C₂₃	semidirect
489. #463	C₂²×C₂₃	semidirect
490. #462	C₂²×C₂₃	semidirect
491. #461	C₂²×C₂₃	semidirect
492. #460	C₂²×C₂₃	semidirect
493. #459	C₂²×C₂₃	semidirect
496. #424	C₂²×C₂₃	semidirect
497. #424	C₂²×C₂₃	semidirect
640. C₂₃	#60919	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×#3455	2
C₂×C₂₃×#542	2
C₂₃×#3263	2
C₂₃×#3262	2
C₂₃×#3258	2
C₂₃×#3257	2
C₂₃×#3079	2
C₂₃×#3078	2
C₂₃×#3077	2
C₂₃×#3056	2
C₂₃×#3055	2
C₂₃×#3040	2
C₂₃×#3037	2
C₂₃×#3036	2
C₂₃×#2905	2
#60919	23

Subgroups — C23×#60919 #19208545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60919 #19208545