Subgroups — C₂₃×#60367 #19207993

Order 5888.

5070 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#575	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂₃×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3449	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3012	C₂	1	8	yes	maximal, complemented
6	C₂₃×#3009	C₂	1	4	yes	maximal, complemented
7	C₂₃×#3008	C₂	1	4	yes	maximal, complemented
8	C₂₃×#3005	C₂	1	4	yes	maximal, complemented
9	C₂₃×#3003	C₂	1	4	yes	maximal, complemented
10	C₂₃×#2896	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#418	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂₃×#2879	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×H(5,𝔽₂)	—	2	2	no	—
14	C₂×C₂₃×H(5,𝔽₂)	—	2	2	no	—
15	C₂×C₂₃×H(5,𝔽₂)	—	2	8	no	—
16	C₂×C₂₃×H(5,𝔽₂)	—	2	8	no	—
17	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	4	yes	—
18	C₂×C₂₃×H(5,𝔽₂)	C₂²	1	4	yes	complemented
19	C₂²×#41×C₂₃	—	2	1	no	—
20	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₂₃	C₂²	1	2	yes	complemented
23	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic, complemented
24	C₂³×D₄×C₂₃	—	2	1	no	—
25	C₂³×D₄×C₂₃	—	2	2	no	—
26	C₂³×D₄×C₂₃	C₂²	1	1	yes	characteristic
27	C₂³×D₄×C₂₃	C₂²	1	2	yes	complemented
28	C₂₃×#575	—	2	8	no	—
29	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
30	C₂×C₂₃×#137	C₂²	1	2	yes	complemented
31	C₂×C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
32	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
33	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
34	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	4	yes	complemented
35	C₂×C₂₃×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
36	C₂×C₂₃×#135	C₂²	1	4	yes	complemented
37	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	complemented
38	C₂²×D₈×C₂₃	C₂²	1	2	yes	complemented
39	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
40	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic, complemented
41	C₂₃×#537	C₂²	1	4	yes	complemented
42	C₂₃×#536	—	2	1	no	—
43	C₂₃×#536	C₂²	1	2	yes	complemented
44	C₂₃×#535	—	2	1	no	—
45	C₂₃×#535	C₂²	1	2	yes	complemented
46	C₂₃×#534	—	2	2	no	—
47	C₂₃×#532	—	2	2	no	—
48	C₂₃×#525	—	2	2	no	—
49	C₂₃×#525	C₂²	1	4	yes	complemented
50	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic, complemented
51	C₂₃×#452	C₂²	1	16	yes	complemented
52	C₂₃×#450	C₂²	1	16	yes	complemented
53	C₂₃×#449	C₂²	1	16	yes	complemented
54	C₂₃×#447	C₂²	1	16	yes	complemented
55	C₂₃×#419	C₂²	1	2	yes	complemented
56	C₂₃×#418	C₂²	1	2	yes	complemented
57	C₂₃×#418	C₂²	1	4	yes	complemented
58	C₂₃×#418	C₂²	1	4	yes	complemented
59	C₂₃×#417	C₂²	1	4	yes	complemented
60	C₂₃×#416	C₂²	1	4	yes	complemented
61	C₂×C₂₃×#102	C₂²	1	4	yes	complemented
62	C₂₃×#408	C₂²	1	4	yes	complemented
63	C₂₃×#408	C₂²	1	4	yes	complemented
64	C₂₃×#407	C₂²	1	4	yes	complemented
65	C₂⁵×C₂₃	—	2	1	no	—
66	C₂⁵×C₂₃	—	2	2	no	—
67	C₂₃×H(5,𝔽₂)	—	2	32	no	—
68	C₂₃×H(5,𝔽₂)	—	2	32	no	—
69	C₂₃×H(5,𝔽₂)	—	2	16	no	—
70	C₂₃×H(5,𝔽₂)	—	2	16	no	—
71	C₂₃×H(5,𝔽₂)	—	2	16	no	—
72	C₂₃×H(5,𝔽₂)	—	2	16	no	—
73	C₂×#41×C₂₃	—	2	16	no	—
74	C₂×#41×C₂₃	—	2	4	no	—
75	C₂×#41×C₂₃	—	2	4	no	—
76	C₂×#41×C₂₃	—	2	8	no	—
77	C₂×#41×C₂₃	—	2	8	no	—
78	C₂×#41×C₂₃	—	2	4	no	—
79	C₂×#41×C₂₃	—	2	1	no	—
80	C₂×#41×C₂₃	—	2	1	no	—
81	C₂×#41×C₂₃	—	2	4	no	—
82	C₂×#41×C₂₃	—	2	4	no	—
83	C₂×#41×C₂₃	—	2	4	no	—
84	C₂×#41×C₂₃	—	2	1	no	—
85	C₂×#41×C₂₃	—	2	1	no	—
86	C₂×#41×C₂₃	—	2	4	no	—
87	C₂×#41×C₂₃	—	2	4	no	—
88	C₂×#41×C₂₃	D₄	1	2	yes	—
89	C₂×#41×C₂₃	D₄	1	2	yes	—
90	C₂×#41×C₂₃	D₄	1	8	yes	complemented
91	C₂×#41×C₂₃	C₂³	1	2	yes	—
92	C₂×#41×C₂₃	C₂³	1	8	yes	—
93	C₂×#41×C₂₃	C₂³	1	2	yes	—
94	C₂×#41×C₂₃	C₂³	1	2	yes	—
95	C₂×#41×C₂₃	C₂³	1	2	yes	—
96	C₂×#41×C₂₃	C₂³	1	2	yes	—
97	C₂×#41×C₂₃	C₂³	1	2	yes	complemented
98	C₂²×Q₈×C₂₃	D₄	1	1	yes	characteristic
99	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic, complemented
101	C₂²×D₄×C₂₃	—	2	32	no	—
102	C₂²×D₄×C₂₃	—	2	16	no	—
103	C₂²×D₄×C₂₃	—	2	1	no	—
104	C₂²×D₄×C₂₃	—	2	2	no	—
105	C₂²×D₄×C₂₃	—	2	8	no	—
106	C₂²×D₄×C₂₃	—	2	4	no	—
107	C₂²×D₄×C₂₃	—	2	8	no	—
108	C₂²×D₄×C₂₃	—	2	4	no	—
109	C₂²×D₄×C₂₃	—	2	8	no	—
110	C₂²×D₄×C₂₃	—	2	8	no	—
111	C₂²×D₄×C₂₃	—	2	1	no	—
112	C₂²×D₄×C₂₃	—	2	1	no	—
113	C₂²×D₄×C₂₃	—	2	2	no	—
114	C₂²×D₄×C₂₃	—	2	1	no	—
115	C₂²×D₄×C₂₃	—	2	1	no	—
116	C₂²×D₄×C₂₃	—	2	4	no	—
117	C₂²×D₄×C₂₃	—	2	4	no	—
118	C₂²×D₄×C₂₃	D₄	1	2	yes	—
119	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
120	C₂²×D₄×C₂₃	D₄	1	8	yes	complemented
121	C₂²×D₄×C₂₃	C₂³	1	8	yes	—
122	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
123	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
124	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
125	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
126	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic, complemented
127	C₂³×C₄×C₂₃	—	2	1	no	—
128	C₂³×C₄×C₂₃	—	2	2	no	—
129	C₂³×C₄×C₂₃	—	2	1	no	—
130	C₂³×C₄×C₂₃	C₂³	1	2	yes	—
131	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
132	C₂₃×#137	—	2	8	no	—
133	C₂₃×#137	—	2	8	no	—
134	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
135	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
136	C₂₃×AGL(1,ℤ/8)	—	2	16	no	—
137	C₂₃×AGL(1,ℤ/8)	—	2	8	no	—
138	C₂₃×#135	—	2	16	no	—
139	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	complemented
140	C₂×SD₁₆×C₂₃	—	2	8	no	—
141	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	complemented
142	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
143	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	complemented
144	C₂×D₈×C₂₃	—	2	8	no	—
145	C₂×D₈×C₂₃	C₂³	1	8	yes	complemented
146	C₂×D₈×C₂₃	C₂³	1	4	yes	complemented
147	C₂×M₁₆×C₂₃	—	2	4	no	—
148	C₂×M₁₆×C₂₃	—	2	4	no	—
149	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
150	C₂×M₁₆×C₂₃	C₂³	1	2	yes	—
151	C₂×M₁₆×C₂₃	C₂³	1	2	yes	complemented
152	C₂×M₁₆×C₂₃	C₂³	1	2	yes	complemented
153	C₂²×C₈×C₂₃	C₂³	1	2	yes	complemented
154	C₂²×C₈×C₂₃	C₂³	1	2	yes	complemented
155	C₂₃×C₄⋊Q₈	—	2	2	no	—
156	C₂₃×#127	—	2	2	no	—
157	C₂₃×#124	—	2	2	no	—
158	C₂₃×#124	—	2	2	no	—
159	C₂₃×#123	—	2	4	no	—
160	C₂₃×#123	—	2	4	no	—
161	C₂₃×C₂²⋊Q₈	—	2	4	no	—
162	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	complemented
163	C₂₃×#121	—	2	4	no	—
164	C₂₃×#121	—	2	8	no	—
165	C₂₃×#121	C₂³	1	8	yes	complemented
166	C₂₃×#120	—	2	4	no	—
167	C₂₃×#120	—	2	4	no	—
168	C₄×D₄×C₂₃	—	2	8	no	—
169	C₂₃×#117	—	2	1	no	—
170	C₂₃×#117	—	2	1	no	—
171	C₂₃×#117	C₂³	1	2	yes	—
172	C₂₃×#117	C₂³	1	2	yes	complemented
173	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	complemented
174	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
175	C₂×C₄²×C₂₃	—	2	1	no	—
176	C₂₃×#103	C₂³	1	8	yes	complemented
177	C₂₃×#102	C₂³	1	16	yes	complemented
178	C₂₃×#102	C₂³	1	8	yes	complemented
179	C₂₃×C₂²⋊C₈	C₂³	1	16	yes	complemented
180	C₂⁴×C₂₃	—	2	16	no	—
181	C₂⁴×C₂₃	—	2	1	no	—
182	C₂⁴×C₂₃	—	2	2	no	—
183	C₂⁴×C₂₃	—	2	8	no	—
184	C₂⁴×C₂₃	—	2	8	no	—
185	C₂⁴×C₂₃	—	2	2	no	—
186	C₂⁴×C₂₃	—	2	2	no	—
187	C₂⁴×C₂₃	—	2	1	no	—
188	C₂⁴×C₂₃	—	8	4	no	—
189	C₂⁴×C₂₃	—	8	8	no	—
190	C₂⁴×C₂₃	C₂×D₄	1	2	yes	—
191	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
192	#41×C₂₃	—	2	32	no	—
193	#41×C₂₃	—	2	32	no	—
194	#41×C₂₃	—	2	32	no	—
195	#41×C₂₃	—	2	16	no	—
196	#41×C₂₃	—	2	16	no	—
197	#41×C₂₃	—	2	8	no	—
198	#41×C₂₃	—	2	8	no	—
199	#41×C₂₃	—	2	8	no	—
200	#41×C₂₃	—	2	8	no	—
201	#41×C₂₃	—	2	4	no	—
202	#41×C₂₃	—	2	4	no	—
203	#41×C₂₃	—	2	4	no	—
204	#41×C₂₃	—	2	4	no	—
205	#41×C₂₃	—	2	4	no	—
206	#41×C₂₃	—	2	4	no	—
207	#41×C₂₃	—	2	4	no	—
208	#41×C₂₃	—	2	4	no	—
209	#41×C₂₃	—	2	4	no	—
210	#41×C₂₃	—	2	4	no	—
211	#41×C₂₃	—	4	4	no	—
212	#41×C₂₃	—	4	4	no	—
213	#41×C₂₃	C₂×D₄	1	8	yes	—
214	#41×C₂₃	C₂×D₄	1	8	yes	—
215	C₂×Q₈×C₂₃	—	2	4	no	—
216	C₂×Q₈×C₂₃	—	2	2	no	—
217	C₂×Q₈×C₂₃	—	2	1	no	—
218	C₂×Q₈×C₂₃	—	2	1	no	—
219	C₂×Q₈×C₂₃	—	2	2	no	—
220	C₂×Q₈×C₂₃	—	2	2	no	—
221	C₂×Q₈×C₂₃	C₂×D₄	1	4	yes	—
222	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
223	C₂×Q₈×C₂₃	C₂×D₄	1	2	yes	—
224	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
225	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
226	C₂×D₄×C₂₃	—	2	16	no	—
227	C₂×D₄×C₂₃	—	2	16	no	—
228	C₂×D₄×C₂₃	—	2	64	no	—
229	C₂×D₄×C₂₃	—	2	64	no	—
230	C₂×D₄×C₂₃	—	2	32	no	—
231	C₂×D₄×C₂₃	—	2	32	no	—
232	C₂×D₄×C₂₃	—	2	32	no	—
233	C₂×D₄×C₂₃	—	2	8	no	—
234	C₂×D₄×C₂₃	—	2	8	no	—
235	C₂×D₄×C₂₃	—	2	8	no	—
236	C₂×D₄×C₂₃	—	2	2	no	—
237	C₂×D₄×C₂₃	—	2	2	no	—
238	C₂×D₄×C₂₃	—	2	16	no	—
239	C₂×D₄×C₂₃	—	2	16	no	—
240	C₂×D₄×C₂₃	—	2	2	no	—
241	C₂×D₄×C₂₃	—	2	2	no	—
242	C₂×D₄×C₂₃	—	2	8	no	—
243	C₂×D₄×C₂₃	—	2	4	no	—
244	C₂×D₄×C₂₃	—	2	8	no	—
245	C₂×D₄×C₂₃	—	2	8	no	—
246	C₂×D₄×C₂₃	—	2	8	no	—
247	C₂×D₄×C₂₃	—	2	8	no	—
248	C₂×D₄×C₂₃	—	2	2	no	—
249	C₂×D₄×C₂₃	—	2	1	no	—
250	C₂×D₄×C₂₃	—	2	2	no	—
251	C₂×D₄×C₂₃	—	2	2	no	—
252	C₂×D₄×C₂₃	—	2	4	no	—
253	C₂×D₄×C₂₃	—	2	2	no	—
254	C₂×D₄×C₂₃	—	2	4	no	—
255	C₂×D₄×C₂₃	—	2	4	no	—
256	C₂×D₄×C₂₃	—	2	2	no	—
257	C₂×D₄×C₂₃	—	2	2	no	—
258	C₂×D₄×C₂₃	—	2	1	no	—
259	C₂×D₄×C₂₃	—	4	4	no	—
260	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
261	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
262	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
263	C₂×D₄×C₂₃	C₂×D₄	1	2	yes	—
264	C₂×D₄×C₂₃	C₂×D₄	1	8	yes	—
265	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
266	C₂×D₄×C₂₃	C₂×D₄	1	8	yes	—
267	C₂×D₄×C₂₃	C₂×D₄	1	8	yes	—
268	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
269	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
270	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
271	C₂²×C₄×C₂₃	—	2	16	no	—
272	C₂²×C₄×C₂₃	—	2	1	no	—
273	C₂²×C₄×C₂₃	—	2	8	no	—
274	C₂²×C₄×C₂₃	—	2	8	no	—
275	C₂²×C₄×C₂₃	—	2	2	no	—
276	C₂²×C₄×C₂₃	—	2	2	no	—
277	C₂²×C₄×C₂₃	—	2	4	no	—
278	C₂²×C₄×C₂₃	—	2	4	no	—
279	C₂²×C₄×C₂₃	—	2	1	no	—
280	C₂²×C₄×C₂₃	—	2	2	no	—
281	C₂²×C₄×C₂₃	—	2	2	no	—
282	C₂²×C₄×C₂₃	—	2	2	no	—
283	C₂²×C₄×C₂₃	—	4	4	no	—
284	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
285	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
286	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
290	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
291	C₂²×C₄×C₂₃	C₂⁴	1	4	yes	—
292	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
293	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
294	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
295	Q₁₆×C₂₃	—	2	8	no	—
296	SD₁₆×C₂₃	—	2	8	no	—
297	SD₁₆×C₂₃	—	2	16	no	—
298	SD₁₆×C₂₃	—	2	8	no	—
299	D₈×C₂₃	—	2	16	no	—
300	D₈×C₂₃	—	2	8	no	—
301	M₁₆×C₂₃	—	2	4	no	—
302	M₁₆×C₂₃	—	2	4	no	—
303	M₁₆×C₂₃	—	2	4	no	—
304	M₁₆×C₂₃	—	2	4	no	—
305	C₂×C₈×C₂₃	—	2	4	no	—
306	C₂×C₈×C₂₃	—	2	4	no	—
307	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
308	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
309	C₄⋊C₄×C₂₃	—	2	2	no	—
310	C₄⋊C₄×C₂₃	—	2	8	no	—
311	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
312	C₂²⋊C₄×C₂₃	—	2	2	no	—
313	C₂²⋊C₄×C₂₃	—	2	2	no	—
314	C₂²⋊C₄×C₂₃	—	2	8	no	—
315	C₂²⋊C₄×C₂₃	—	2	8	no	—
316	C₄²×C₂₃	—	2	2	no	—
317	C₄²×C₂₃	—	2	2	no	—
318	#60367	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂³×C₂₃	—	2	32	no	—
320	C₂³×C₂₃	—	2	4	no	—
321	C₂³×C₂₃	—	2	8	no	—
322	C₂³×C₂₃	—	2	4	no	—
323	C₂³×C₂₃	—	2	4	no	—
324	C₂³×C₂₃	—	2	2	no	—
325	C₂³×C₂₃	—	2	8	no	—
326	C₂³×C₂₃	—	2	8	no	—
327	C₂³×C₂₃	—	2	2	no	—
328	C₂³×C₂₃	—	4	2	no	—
329	C₂³×C₂₃	—	4	4	no	—
330	C₂³×C₂₃	—	4	4	no	—
331	C₂³×C₂₃	—	4	8	no	—
332	C₂³×C₂₃	—	4	2	no	—
333	C₂³×C₂₃	—	8	2	no	—
334	C₂³×C₂₃	—	8	4	no	—
335	C₂³×C₂₃	—	8	4	no	—
336	C₂³×C₂₃	—	8	16	no	—
337	C₂³×C₂₃	—	8	16	no	—
338	C₂³×C₂₃	—	8	32	no	—
339	C₂³×C₂₃	#120	1	4	yes	—
340	C₂³×C₂₃	C₂²×D₄	1	4	yes	—
341	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
342	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
344	Q₈×C₂₃	—	2	4	no	—
345	Q₈×C₂₃	—	2	4	no	—
346	Q₈×C₂₃	—	2	4	no	—
347	Q₈×C₂₃	—	2	2	no	—
348	Q₈×C₂₃	—	2	2	no	—
349	Q₈×C₂₃	—	2	2	no	—
350	Q₈×C₂₃	—	4	2	no	—
351	Q₈×C₂₃	C₂²×D₄	1	4	yes	—
352	D₄×C₂₃	—	2	32	no	—
353	D₄×C₂₃	—	2	32	no	—
354	D₄×C₂₃	—	2	8	no	—
355	D₄×C₂₃	—	2	8	no	—
356	D₄×C₂₃	—	2	8	no	—
357	D₄×C₂₃	—	2	8	no	—
358	D₄×C₂₃	—	2	4	no	—
359	D₄×C₂₃	—	2	4	no	—
360	D₄×C₂₃	—	2	8	no	—
361	D₄×C₂₃	—	2	8	no	—
362	D₄×C₂₃	—	2	4	no	—
363	D₄×C₂₃	—	2	8	no	—
364	D₄×C₂₃	—	2	4	no	—
365	D₄×C₂₃	—	2	2	no	—
366	D₄×C₂₃	—	2	2	no	—
367	D₄×C₂₃	—	2	2	no	—
368	D₄×C₂₃	—	4	4	no	—
369	D₄×C₂₃	—	4	4	no	—
370	D₄×C₂₃	—	4	2	no	—
371	D₄×C₂₃	—	8	8	no	—
372	D₄×C₂₃	C₂²×D₄	1	4	yes	—
373	D₄×C₂₃	C₂²×D₄	1	8	yes	—
374	C₂×C₄×C₂₃	—	2	32	no	—
375	C₂×C₄×C₂₃	—	2	4	no	—
376	C₂×C₄×C₂₃	—	2	4	no	—
377	C₂×C₄×C₂₃	—	2	2	no	—
378	C₂×C₄×C₂₃	—	2	8	no	—
379	C₂×C₄×C₂₃	—	2	8	no	—
380	C₂×C₄×C₂₃	—	2	8	no	—
381	C₂×C₄×C₂₃	—	2	4	no	—
382	C₂×C₄×C₂₃	—	2	4	no	—
383	C₂×C₄×C₂₃	—	2	4	no	—
384	C₂×C₄×C₂₃	—	2	2	no	—
385	C₂×C₄×C₂₃	—	4	2	no	—
386	C₂×C₄×C₂₃	—	4	4	no	—
387	C₂×C₄×C₂₃	—	4	4	no	—
388	C₂×C₄×C₂₃	—	8	2	no	—
389	C₂×C₄×C₂₃	#120	1	4	yes	—
390	C₂×C₄×C₂₃	#120	1	4	yes	—
391	C₂×C₄×C₂₃	#120	1	4	yes	—
392	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
393	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
395	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
396	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
398	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
399	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
400	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
401	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
402	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
403	C₈×C₂₃	—	2	4	no	—
404	C₈×C₂₃	—	2	4	no	—
405	C₂²×H(5,𝔽₂)	C₂×C₂₃	1	1	yes	characteristic, complemented
406	C₂×#575	C₂×C₂₃	1	1	yes	characteristic, complemented
407	C₂²×AGL(1,ℤ/8)	C₂×C₂₃	1	1	yes	characteristic, complemented
408	#3449	C₂×C₂₃	1	1	yes	characteristic, complemented
409	#3012	C₂×C₂₃	1	8	yes	complemented
410	#3009	C₂×C₂₃	1	4	yes	complemented
411	#3008	C₂×C₂₃	1	4	yes	complemented
412	#3005	C₂×C₂₃	1	4	yes	complemented
413	#3003	C₂×C₂₃	1	4	yes	complemented
414	#2896	C₂×C₂₃	1	1	yes	characteristic, complemented
415	C₂×#418	C₂×C₂₃	1	1	yes	characteristic, complemented
416	#2879	C₂×C₂₃	1	1	yes	characteristic, complemented
417	C₂²×C₂₃	—	2	2	no	—
418	C₂²×C₂₃	—	2	2	no	—
419	C₂²×C₂₃	—	2	2	no	—
420	C₂²×C₂₃	—	2	8	no	—
421	C₂²×C₂₃	—	2	4	no	—
422	C₂²×C₂₃	—	2	8	no	—
423	C₂²×C₂₃	—	2	4	no	—
424	C₂²×C₂₃	—	4	4	no	—
425	C₂²×C₂₃	—	4	8	no	—
426	C₂²×C₂₃	—	4	16	no	—
427	C₂²×C₂₃	—	4	8	no	—
428	C₂²×C₂₃	—	4	8	no	—
429	C₂²×C₂₃	—	4	4	no	—
430	C₂²×C₂₃	—	4	4	no	—
431	C₂²×C₂₃	—	4	2	no	—
432	C₂²×C₂₃	—	8	8	no	—
433	C₂²×C₂₃	—	8	8	no	—
434	C₂²×C₂₃	—	8	4	no	—
435	C₂²×C₂₃	—	8	32	no	—
436	C₂²×C₂₃	C₂×#120	1	2	yes	—
437	C₂²×C₂₃	C₂×#120	1	2	yes	—
438	C₂²×C₂₃	C₂×#120	1	2	yes	—
439	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
440	C₄×C₂₃	—	2	4	no	—
441	C₄×C₂₃	—	2	4	no	—
442	C₄×C₂₃	—	4	4	no	—
443	C₄×C₂₃	—	4	2	no	—
444	C₄×C₂₃	C₂×#120	1	2	yes	—
445	C₄×C₂₃	C₂×#120	1	2	yes	—
446	C₄×C₂₃	C₂×#120	1	2	yes	—
447	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
448	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
449	C₂×H(5,𝔽₂)	—	2	2	no	—
450	C₂×H(5,𝔽₂)	—	2	2	no	—
451	C₂×H(5,𝔽₂)	—	2	8	no	—
452	C₂×H(5,𝔽₂)	—	2	8	no	—
453	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	4	yes	—
454	C₂×H(5,𝔽₂)	C₂²×C₂₃	1	4	yes	complemented
455	C₂²×#41	—	2	1	no	—
456	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
457	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
458	C₂²×#41	C₂²×C₂₃	1	2	yes	complemented
459	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic, complemented
460	C₂³×D₄	—	2	1	no	—
461	C₂³×D₄	—	2	2	no	—
462	C₂³×D₄	C₂²×C₂₃	1	1	yes	characteristic
463	C₂³×D₄	C₂²×C₂₃	1	2	yes	complemented
464	#575	—	2	8	no	—
465	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
466	C₂×#137	C₂²×C₂₃	1	2	yes	complemented
467	C₂×AGL(1,ℤ/8)	—	2	8	no	—
468	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
469	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
470	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	4	yes	complemented
471	C₂×AGL(1,ℤ/8)	C₂²×C₂₃	1	2	yes	complemented
472	C₂×#135	C₂²×C₂₃	1	4	yes	complemented
473	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	complemented
474	C₂²×D₈	C₂²×C₂₃	1	2	yes	complemented
475	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
476	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic, complemented
477	#537	C₂²×C₂₃	1	4	yes	complemented
478	#536	—	2	1	no	—
479	#536	C₂²×C₂₃	1	2	yes	complemented
480	#535	—	2	1	no	—
481	#535	C₂²×C₂₃	1	2	yes	complemented
482	#534	—	2	2	no	—
483	#532	—	2	2	no	—
484	#525	—	2	2	no	—
485	#525	C₂²×C₂₃	1	4	yes	complemented
486	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic, complemented
487	#452	C₂²×C₂₃	1	16	yes	complemented
488	#450	C₂²×C₂₃	1	16	yes	complemented
489	#449	C₂²×C₂₃	1	16	yes	complemented
490	#447	C₂²×C₂₃	1	16	yes	complemented
491	#419	C₂²×C₂₃	1	2	yes	complemented
492	#418	C₂²×C₂₃	1	4	yes	complemented
493	#418	C₂²×C₂₃	1	2	yes	complemented
494	#418	C₂²×C₂₃	1	4	yes	complemented
495	#417	C₂²×C₂₃	1	4	yes	complemented
496	#416	C₂²×C₂₃	1	4	yes	complemented
497	C₂×#102	C₂²×C₂₃	1	4	yes	complemented
498	#408	C₂²×C₂₃	1	4	yes	complemented
499	#408	C₂²×C₂₃	1	4	yes	complemented
500	#407	C₂²×C₂₃	1	4	yes	complemented
501	C₂×C₂₃	—	2	2	no	—
502	C₂×C₂₃	—	2	2	no	—
503	C₂×C₂₃	—	2	2	no	—
504	C₂×C₂₃	—	4	4	no	—
505	C₂×C₂₃	—	4	8	no	—
506	C₂×C₂₃	—	4	4	no	—
507	C₂×C₂₃	—	8	2	no	—
508	C₂×C₂₃	C₂²×#120	1	1	yes	characteristic
509	C₂×C₂₃	#3585	1	2	yes	—
510	C₂⁵	—	2	1	no	—
511	C₂⁵	—	2	2	no	—
512	H(5,𝔽₂)	—	2	32	no	—
513	H(5,𝔽₂)	—	2	32	no	—
514	H(5,𝔽₂)	—	2	16	no	—
515	H(5,𝔽₂)	—	2	16	no	—
516	H(5,𝔽₂)	—	2	16	no	—
517	H(5,𝔽₂)	—	2	16	no	—
518	C₂×#41	—	2	16	no	—
519	C₂×#41	—	2	4	no	—
520	C₂×#41	—	2	4	no	—
521	C₂×#41	—	2	8	no	—
522	C₂×#41	—	2	8	no	—
523	C₂×#41	—	2	4	no	—
524	C₂×#41	—	2	1	no	—
525	C₂×#41	—	2	1	no	—
526	C₂×#41	—	2	4	no	—
527	C₂×#41	—	2	4	no	—
528	C₂×#41	—	2	4	no	—
529	C₂×#41	—	2	1	no	—
530	C₂×#41	—	2	1	no	—
531	C₂×#41	—	2	4	no	—
532	C₂×#41	—	2	4	no	—
533	C₂×#41	D₄×C₂₃	1	2	yes	—
534	C₂×#41	D₄×C₂₃	1	2	yes	—
535	C₂×#41	D₄×C₂₃	1	8	yes	complemented
536	C₂×#41	C₂³×C₂₃	1	2	yes	—
537	C₂×#41	C₂³×C₂₃	1	8	yes	—
538	C₂×#41	C₂³×C₂₃	1	2	yes	—
539	C₂×#41	C₂³×C₂₃	1	2	yes	—
540	C₂×#41	C₂³×C₂₃	1	2	yes	—
541	C₂×#41	C₂³×C₂₃	1	2	yes	—
542	C₂×#41	C₂³×C₂₃	1	2	yes	complemented
543	C₂²×Q₈	D₄×C₂₃	1	1	yes	characteristic
544	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
545	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic, complemented
546	C₂²×D₄	—	2	32	no	—
547	C₂²×D₄	—	2	16	no	—
548	C₂²×D₄	—	2	1	no	—
549	C₂²×D₄	—	2	2	no	—
550	C₂²×D₄	—	2	8	no	—
551	C₂²×D₄	—	2	4	no	—
552	C₂²×D₄	—	2	8	no	—
553	C₂²×D₄	—	2	4	no	—
554	C₂²×D₄	—	2	8	no	—
555	C₂²×D₄	—	2	8	no	—
556	C₂²×D₄	—	2	1	no	—
557	C₂²×D₄	—	2	1	no	—
558	C₂²×D₄	—	2	2	no	—
559	C₂²×D₄	—	2	1	no	—
560	C₂²×D₄	—	2	1	no	—
561	C₂²×D₄	—	2	4	no	—
562	C₂²×D₄	—	2	4	no	—
563	C₂²×D₄	D₄×C₂₃	1	2	yes	—
564	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
565	C₂²×D₄	D₄×C₂₃	1	8	yes	complemented
566	C₂²×D₄	C₂³×C₂₃	1	8	yes	—
567	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
568	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
569	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
570	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
571	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic, complemented
572	C₂³×C₄	—	2	1	no	—
573	C₂³×C₄	—	2	2	no	—
574	C₂³×C₄	—	2	1	no	—
575	C₂³×C₄	C₂³×C₂₃	1	2	yes	—
576	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
577	#137	—	2	8	no	—
578	#137	—	2	8	no	—
579	AGL(1,ℤ/8)	—	2	8	no	—
580	AGL(1,ℤ/8)	—	2	16	no	—
581	AGL(1,ℤ/8)	—	2	16	no	—
582	AGL(1,ℤ/8)	—	2	8	no	—
583	#135	—	2	16	no	—
584	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	complemented
585	C₂×SD₁₆	—	2	8	no	—
586	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	complemented
587	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
588	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	complemented
589	C₂×D₈	—	2	8	no	—
590	C₂×D₈	C₂³×C₂₃	1	8	yes	complemented
591	C₂×D₈	C₂³×C₂₃	1	4	yes	complemented
592	C₂×M₁₆	—	2	4	no	—
593	C₂×M₁₆	—	2	4	no	—
594	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
595	C₂×M₁₆	C₂³×C₂₃	1	2	yes	—
596	C₂×M₁₆	C₂³×C₂₃	1	2	yes	complemented
597	C₂×M₁₆	C₂³×C₂₃	1	2	yes	complemented
598	C₂²×C₈	C₂³×C₂₃	1	2	yes	complemented
599	C₂²×C₈	C₂³×C₂₃	1	2	yes	complemented
600	C₄⋊Q₈	—	2	2	no	—
601	#127	—	2	2	no	—
602	#124	—	2	2	no	—
603	#124	—	2	2	no	—
604	#123	—	2	4	no	—
605	#123	—	2	4	no	—
606	C₂²⋊Q₈	—	2	4	no	—
607	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	complemented
608	#121	—	2	4	no	—
609	#121	—	2	8	no	—
610	#121	C₂³×C₂₃	1	8	yes	complemented
611	#120	—	2	4	no	—
612	#120	—	2	4	no	—
613	C₄×D₄	—	2	8	no	—
614	#117	—	2	1	no	—
615	#117	—	2	1	no	—
616	#117	C₂³×C₂₃	1	2	yes	—
617	#117	C₂³×C₂₃	1	2	yes	complemented
618	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	complemented
619	C₂×C₂²⋊C₄	—	2	1	no	—
620	C₂×C₄²	—	2	1	no	—
621	#103	C₂³×C₂₃	1	8	yes	complemented
622	#102	C₂³×C₂₃	1	16	yes	complemented
623	#102	C₂³×C₂₃	1	8	yes	complemented
624	C₂²⋊C₈	C₂³×C₂₃	1	16	yes	complemented
625	C₂₃	#60367	1	1	yes	characteristic, direct product factor, Sylow
626	C₂⁴	—	2	16	no	—
627	C₂⁴	—	2	1	no	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	8	no	—
630	C₂⁴	—	2	8	no	—
631	C₂⁴	—	2	2	no	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	1	no	—
634	C₂⁴	—	8	4	no	—
635	C₂⁴	—	8	8	no	—
636	C₂⁴	C₂×D₄×C₂₃	1	2	yes	—
637	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
638	#41	—	2	32	no	—
639	#41	—	2	32	no	—
640	#41	—	2	32	no	—
641	#41	—	2	16	no	—
642	#41	—	2	16	no	—
643	#41	—	2	8	no	—
644	#41	—	2	8	no	—
645	#41	—	2	8	no	—
646	#41	—	2	8	no	—
647	#41	—	2	4	no	—
648	#41	—	2	4	no	—
649	#41	—	2	4	no	—
650	#41	—	2	4	no	—
651	#41	—	2	4	no	—
652	#41	—	2	4	no	—
653	#41	—	2	4	no	—
654	#41	—	2	4	no	—
655	#41	—	2	4	no	—
656	#41	—	2	4	no	—
657	#41	—	4	4	no	—
658	#41	—	4	4	no	—
659	#41	C₂×D₄×C₂₃	1	8	yes	—
660	#41	C₂×D₄×C₂₃	1	8	yes	—
661	C₂×Q₈	—	2	4	no	—
662	C₂×Q₈	—	2	1	no	—
663	C₂×Q₈	—	2	2	no	—
664	C₂×Q₈	—	2	1	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	C₂×D₄×C₂₃	1	4	yes	—
668	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
669	C₂×Q₈	C₂×D₄×C₂₃	1	2	yes	—
670	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
671	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
672	C₂×D₄	—	2	16	no	—
673	C₂×D₄	—	2	16	no	—
674	C₂×D₄	—	2	64	no	—
675	C₂×D₄	—	2	64	no	—
676	C₂×D₄	—	2	32	no	—
677	C₂×D₄	—	2	32	no	—
678	C₂×D₄	—	2	32	no	—
679	C₂×D₄	—	2	8	no	—
680	C₂×D₄	—	2	8	no	—
681	C₂×D₄	—	2	8	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	16	no	—
685	C₂×D₄	—	2	16	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	2	no	—
688	C₂×D₄	—	2	8	no	—
689	C₂×D₄	—	2	4	no	—
690	C₂×D₄	—	2	8	no	—
691	C₂×D₄	—	2	8	no	—
692	C₂×D₄	—	2	8	no	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	2	4	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	2	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	2	no	—
699	C₂×D₄	—	2	2	no	—
700	C₂×D₄	—	2	4	no	—
701	C₂×D₄	—	2	4	no	—
702	C₂×D₄	—	2	2	no	—
703	C₂×D₄	—	2	2	no	—
704	C₂×D₄	—	2	1	no	—
705	C₂×D₄	—	4	4	no	—
706	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
707	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
708	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
709	C₂×D₄	C₂×D₄×C₂₃	1	2	yes	—
710	C₂×D₄	C₂×D₄×C₂₃	1	8	yes	—
711	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
712	C₂×D₄	C₂×D₄×C₂₃	1	8	yes	—
713	C₂×D₄	C₂×D₄×C₂₃	1	8	yes	—
714	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
715	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
716	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
717	C₂²×C₄	—	2	16	no	—
718	C₂²×C₄	—	2	1	no	—
719	C₂²×C₄	—	2	8	no	—
720	C₂²×C₄	—	2	8	no	—
721	C₂²×C₄	—	2	2	no	—
722	C₂²×C₄	—	2	2	no	—
723	C₂²×C₄	—	2	4	no	—
724	C₂²×C₄	—	2	4	no	—
725	C₂²×C₄	—	2	1	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	2	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	4	4	no	—
730	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
731	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
732	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
733	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
734	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
735	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
736	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
737	C₂²×C₄	C₂⁴×C₂₃	1	4	yes	—
738	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
739	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
740	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
741	Q₁₆	—	2	8	no	—
742	SD₁₆	—	2	8	no	—
743	SD₁₆	—	2	16	no	—
744	SD₁₆	—	2	8	no	—
745	D₈	—	2	16	no	—
746	D₈	—	2	8	no	—
747	M₁₆	—	2	4	no	—
748	M₁₆	—	2	4	no	—
749	M₁₆	—	2	4	no	—
750	M₁₆	—	2	4	no	—
751	C₂×C₈	—	2	4	no	—
752	C₂×C₈	—	2	4	no	—
753	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
754	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	—	2	8	no	—
757	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	8	no	—
761	C₂²⋊C₄	—	2	8	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	2	no	—
764	C₂³	—	2	32	no	—
765	C₂³	—	2	4	no	—
766	C₂³	—	2	2	no	—
767	C₂³	—	2	4	no	—
768	C₂³	—	2	8	no	—
769	C₂³	—	2	4	no	—
770	C₂³	—	2	8	no	—
771	C₂³	—	2	8	no	—
772	C₂³	—	2	2	no	—
773	C₂³	—	4	2	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	8	no	—
777	C₂³	—	4	2	no	—
778	C₂³	—	8	4	no	—
779	C₂³	—	8	4	no	—
780	C₂³	—	8	16	no	—
781	C₂³	—	8	2	no	—
782	C₂³	—	8	16	no	—
783	C₂³	—	8	32	no	—
784	C₂³	C₂₃×#120	1	4	yes	—
785	C₂³	C₂²×D₄×C₂₃	1	4	yes	—
786	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
787	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
788	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
789	Q₈	—	2	2	no	—
790	Q₈	—	2	4	no	—
791	Q₈	—	2	4	no	—
792	Q₈	—	2	4	no	—
793	Q₈	—	2	2	no	—
794	Q₈	—	2	2	no	—
795	Q₈	—	4	2	no	—
796	Q₈	C₂²×D₄×C₂₃	1	4	yes	—
797	D₄	—	2	32	no	—
798	D₄	—	2	32	no	—
799	D₄	—	2	8	no	—
800	D₄	—	2	8	no	—
801	D₄	—	2	8	no	—
802	D₄	—	2	8	no	—
803	D₄	—	2	4	no	—
804	D₄	—	2	2	no	—
805	D₄	—	2	2	no	—
806	D₄	—	2	2	no	—
807	D₄	—	2	4	no	—
808	D₄	—	2	4	no	—
809	D₄	—	2	8	no	—
810	D₄	—	2	8	no	—
811	D₄	—	2	4	no	—
812	D₄	—	2	8	no	—
813	D₄	—	4	4	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	2	no	—
816	D₄	—	8	8	no	—
817	D₄	C₂²×D₄×C₂₃	1	4	yes	—
818	D₄	C₂²×D₄×C₂₃	1	8	yes	—
819	C₂×C₄	—	2	32	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	4	no	—
822	C₂×C₄	—	2	4	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	no	—
825	C₂×C₄	—	2	8	no	—
826	C₂×C₄	—	2	8	no	—
827	C₂×C₄	—	2	8	no	—
828	C₂×C₄	—	2	4	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	4	2	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	8	2	no	—
834	C₂×C₄	C₂₃×#120	1	4	yes	—
835	C₂×C₄	C₂₃×#120	1	4	yes	—
836	C₂×C₄	C₂₃×#120	1	4	yes	—
837	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
838	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
839	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
840	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
841	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
842	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
843	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
844	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
845	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
846	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
847	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
848	C₈	—	2	4	no	—
849	C₈	—	2	4	no	—
850	C₂²	—	2	2	no	—
851	C₂²	—	2	2	no	—
852	C₂²	—	2	2	no	—
853	C₂²	—	2	4	no	—
854	C₂²	—	2	8	no	—
855	C₂²	—	2	4	no	—
856	C₂²	—	2	8	no	—
857	C₂²	—	4	4	no	—
858	C₂²	—	4	8	no	—
859	C₂²	—	4	16	no	—
860	C₂²	—	4	8	no	—
861	C₂²	—	4	8	no	—
862	C₂²	—	4	4	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	4	no	—
865	C₂²	—	8	8	no	—
866	C₂²	—	8	8	no	—
867	C₂²	—	8	4	no	—
868	C₂²	—	8	32	no	—
869	C₂²	C₂×C₂₃×#120	1	2	yes	—
870	C₂²	C₂×C₂₃×#120	1	2	yes	—
871	C₂²	C₂×C₂₃×#120	1	2	yes	—
872	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
873	C₄	—	2	4	no	—
874	C₄	—	2	4	no	—
875	C₄	—	4	2	no	—
876	C₄	—	4	4	no	—
877	C₄	C₂×C₂₃×#120	1	2	yes	—
878	C₄	C₂×C₂₃×#120	1	2	yes	—
879	C₄	C₂×C₂₃×#120	1	2	yes	—
880	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
881	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
882	C₂	—	2	2	no	—
883	C₂	—	2	2	no	—
884	C₂	—	2	2	no	—
885	C₂	—	4	4	no	—
886	C₂	—	4	8	no	—
887	C₂	—	4	4	no	—
888	C₂	—	8	2	no	—
889	C₂	C₂²×C₂₃×#120	1	1	yes	characteristic
890	C₂	C₂₃×#3585	1	2	yes	—

	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 ◁ C₂²×#41×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₂₃×H(5,𝔽₂)	C₂	semidirect
2. C₂×C₂₃×#575	C₂	semidirect
3. C₂²×C₂₃×AGL(1,ℤ/8)	C₂	semidirect
4. C₂₃×#3449	C₂	semidirect
5. C₂₃×#3012	C₂	semidirect
6. C₂₃×#3009	C₂	semidirect
7. C₂₃×#3008	C₂	semidirect
8. C₂₃×#3005	C₂	semidirect
9. C₂₃×#3003	C₂	semidirect
10. C₂₃×#2896	C₂	semidirect
11. C₂×C₂₃×#418	C₂	semidirect
12. C₂₃×#2879	C₂	semidirect
18. C₂×C₂₃×H(5,𝔽₂)	C₂²	semidirect
22. C₂²×#41×C₂₃	C₂²	semidirect
23. C₂²×#41×C₂₃	C₂²	semidirect
27. C₂³×D₄×C₂₃	C₂²	semidirect
29. C₂×C₂₃×#137	C₂²	semidirect
30. C₂×C₂₃×#137	C₂²	semidirect
32. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
33. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
34. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
35. C₂×C₂₃×AGL(1,ℤ/8)	C₂²	semidirect
36. C₂×C₂₃×#135	C₂²	semidirect
37. C₂²×SD₁₆×C₂₃	C₂²	semidirect
38. C₂²×D₈×C₂₃	C₂²	semidirect
39. C₂²×M₁₆×C₂₃	C₂²	semidirect
40. C₂²×M₁₆×C₂₃	C₂²	semidirect
41. C₂₃×#537	C₂²	semidirect
43. C₂₃×#536	C₂²	semidirect
45. C₂₃×#535	C₂²	semidirect
49. C₂₃×#525	C₂²	semidirect
50. C₂×C₂₃×#117	C₂²	semidirect
51. C₂₃×#452	C₂²	semidirect
52. C₂₃×#450	C₂²	semidirect
53. C₂₃×#449	C₂²	semidirect
54. C₂₃×#447	C₂²	semidirect
55. C₂₃×#419	C₂²	semidirect
56. C₂₃×#418	C₂²	semidirect
57. C₂₃×#418	C₂²	semidirect
58. C₂₃×#418	C₂²	semidirect
59. C₂₃×#417	C₂²	semidirect
60. C₂₃×#416	C₂²	semidirect
61. C₂×C₂₃×#102	C₂²	semidirect
62. C₂₃×#408	C₂²	semidirect
63. C₂₃×#408	C₂²	semidirect
64. C₂₃×#407	C₂²	semidirect
90. C₂×#41×C₂₃	D₄	semidirect
97. C₂×#41×C₂₃	C₂³	semidirect
100. C₂²×Q₈×C₂₃	C₂³	semidirect
120. C₂²×D₄×C₂₃	D₄	semidirect
126. C₂²×D₄×C₂₃	C₂³	semidirect
139. C₂×Q₁₆×C₂₃	C₂³	semidirect
141. C₂×SD₁₆×C₂₃	C₂³	semidirect
142. C₂×SD₁₆×C₂₃	C₂³	semidirect
143. C₂×SD₁₆×C₂₃	C₂³	semidirect
145. C₂×D₈×C₂₃	C₂³	semidirect
146. C₂×D₈×C₂₃	C₂³	semidirect
151. C₂×M₁₆×C₂₃	C₂³	semidirect
152. C₂×M₁₆×C₂₃	C₂³	semidirect
153. C₂²×C₈×C₂₃	C₂³	semidirect
154. C₂²×C₈×C₂₃	C₂³	semidirect
162. C₂₃×C₂²⋊Q₈	C₂³	semidirect
165. C₂₃×#121	C₂³	semidirect
172. C₂₃×#117	C₂³	semidirect
173. C₂×C₄⋊C₄×C₂₃	C₂³	semidirect
176. C₂₃×#103	C₂³	semidirect
177. C₂₃×#102	C₂³	semidirect
178. C₂₃×#102	C₂³	semidirect
179. C₂₃×C₂²⋊C₈	C₂³	semidirect
318. #60367	C₂₃	direct (N × H)
405. C₂²×H(5,𝔽₂)	C₂×C₂₃	semidirect
406. C₂×#575	C₂×C₂₃	semidirect
407. C₂²×AGL(1,ℤ/8)	C₂×C₂₃	semidirect
408. #3449	C₂×C₂₃	semidirect
409. #3012	C₂×C₂₃	semidirect
410. #3009	C₂×C₂₃	semidirect
411. #3008	C₂×C₂₃	semidirect
412. #3005	C₂×C₂₃	semidirect
413. #3003	C₂×C₂₃	semidirect
414. #2896	C₂×C₂₃	semidirect
415. C₂×#418	C₂×C₂₃	semidirect
416. #2879	C₂×C₂₃	semidirect
454. C₂×H(5,𝔽₂)	C₂²×C₂₃	semidirect
458. C₂²×#41	C₂²×C₂₃	semidirect
459. C₂²×#41	C₂²×C₂₃	semidirect
463. C₂³×D₄	C₂²×C₂₃	semidirect
465. C₂×#137	C₂²×C₂₃	semidirect
466. C₂×#137	C₂²×C₂₃	semidirect
468. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
469. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
470. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
471. C₂×AGL(1,ℤ/8)	C₂²×C₂₃	semidirect
472. C₂×#135	C₂²×C₂₃	semidirect
473. C₂²×SD₁₆	C₂²×C₂₃	semidirect
474. C₂²×D₈	C₂²×C₂₃	semidirect
475. C₂²×M₁₆	C₂²×C₂₃	semidirect
476. C₂²×M₁₆	C₂²×C₂₃	semidirect
477. #537	C₂²×C₂₃	semidirect
479. #536	C₂²×C₂₃	semidirect
481. #535	C₂²×C₂₃	semidirect
485. #525	C₂²×C₂₃	semidirect
486. C₂×#117	C₂²×C₂₃	semidirect
487. #452	C₂²×C₂₃	semidirect
488. #450	C₂²×C₂₃	semidirect
489. #449	C₂²×C₂₃	semidirect
490. #447	C₂²×C₂₃	semidirect
491. #419	C₂²×C₂₃	semidirect
492. #418	C₂²×C₂₃	semidirect
493. #418	C₂²×C₂₃	semidirect
494. #418	C₂²×C₂₃	semidirect
495. #417	C₂²×C₂₃	semidirect
496. #416	C₂²×C₂₃	semidirect
497. C₂×#102	C₂²×C₂₃	semidirect
498. #408	C₂²×C₂₃	semidirect
499. #408	C₂²×C₂₃	semidirect
500. #407	C₂²×C₂₃	semidirect
535. C₂×#41	D₄×C₂₃	semidirect
542. C₂×#41	C₂³×C₂₃	semidirect
545. C₂²×Q₈	C₂³×C₂₃	semidirect
565. C₂²×D₄	D₄×C₂₃	semidirect
571. C₂²×D₄	C₂³×C₂₃	semidirect
584. C₂×Q₁₆	C₂³×C₂₃	semidirect
586. C₂×SD₁₆	C₂³×C₂₃	semidirect
587. C₂×SD₁₆	C₂³×C₂₃	semidirect
588. C₂×SD₁₆	C₂³×C₂₃	semidirect
590. C₂×D₈	C₂³×C₂₃	semidirect
591. C₂×D₈	C₂³×C₂₃	semidirect
596. C₂×M₁₆	C₂³×C₂₃	semidirect
597. C₂×M₁₆	C₂³×C₂₃	semidirect
598. C₂²×C₈	C₂³×C₂₃	semidirect
599. C₂²×C₈	C₂³×C₂₃	semidirect
607. C₂²⋊Q₈	C₂³×C₂₃	semidirect
610. #121	C₂³×C₂₃	semidirect
617. #117	C₂³×C₂₃	semidirect
618. C₂×C₄⋊C₄	C₂³×C₂₃	semidirect
621. #103	C₂³×C₂₃	semidirect
622. #102	C₂³×C₂₃	semidirect
623. #102	C₂³×C₂₃	semidirect
624. C₂²⋊C₈	C₂³×C₂₃	semidirect
625. C₂₃	#60367	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₂₃×H(5,𝔽₂)	2
C₂×C₂₃×#575	2
C₂²×C₂₃×AGL(1,ℤ/8)	2
C₂₃×#3449	2
C₂₃×#3012	2
C₂₃×#3009	2
C₂₃×#3008	2
C₂₃×#3005	2
C₂₃×#3003	2
C₂₃×#2896	2
C₂×C₂₃×#418	2
C₂₃×#2879	2
#60367	23

Subgroups — C23×#60367 #19207993

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₃×#60367 #19207993