Subgroups — C₂×C₂₃×#3317 #19208764

Order 5888.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#550	C₂	1	1	yes	maximal, characteristic
3	C₂₃×#3317	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#490	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#481	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#460	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#452	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#417	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
24	C₂₃×#552	—	2	4	no	—
25	C₂₃×#552	C₂²	1	8	yes	complemented
26	C₂₃×#550	—	2	4	no	—
27	C₂₃×#550	C₂²	1	8	yes	—
28	C₂×C₂₃×#127	—	2	1	no	—
29	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
30	C₂×C₂₃×#126	—	2	1	no	—
31	C₂×C₂₃×#125	—	2	1	no	—
32	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₂₃×#121	—	2	1	no	—
37	C₂×C₂₃×#121	—	2	1	no	—
38	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
39	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
40	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×D₄×C₂₃	—	2	1	no	—
43	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₂₃×#117	—	2	1	no	—
45	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
46	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂₃×#490	C₂²	1	8	yes	complemented
48	C₂₃×#482	C₂²	1	8	yes	complemented
49	C₂₃×#481	C₂²	1	8	yes	complemented
50	C₂₃×#479	C₂²	1	8	yes	complemented
51	C₂₃×#468	C₂²	1	8	yes	complemented
52	C₂₃×#465	C₂²	1	8	yes	complemented
53	C₂₃×#460	C₂²	1	8	yes	complemented
54	C₂₃×#452	C₂²	1	8	yes	complemented
55	C₂₃×#452	C₂²	1	8	yes	complemented
56	C₂₃×#441	C₂²	1	8	yes	complemented
57	C₂₃×#435	C₂²	1	8	yes	complemented
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₂₃×#417	C₂²	1	8	yes	complemented
63	C₂₃×#416	C₂²	1	8	yes	complemented
64	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
71	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
77	C₂×#41×C₂₃	—	2	2	no	—
78	C₂×#41×C₂₃	—	2	2	no	—
79	C₂×#41×C₂₃	—	2	4	no	—
80	C₂×#41×C₂₃	—	2	4	no	—
81	C₂×#41×C₂₃	—	4	2	no	—
82	C₂×#41×C₂₃	—	4	2	no	—
83	C₂×#41×C₂₃	C₂³	1	4	yes	—
84	C₂×#41×C₂₃	C₂³	1	4	yes	—
85	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
87	C₂²×D₄×C₂₃	—	2	1	no	—
88	C₂²×D₄×C₂₃	—	2	1	no	—
89	C₂²×D₄×C₂₃	—	2	1	no	—
90	C₂²×D₄×C₂₃	—	2	1	no	—
91	C₂²×D₄×C₂₃	—	2	1	no	—
92	C₂²×D₄×C₂₃	—	2	1	no	—
93	C₂²×D₄×C₂₃	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
95	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₂₃	—	2	1	no	—
97	C₂³×C₄×C₂₃	—	2	1	no	—
98	C₂³×C₄×C₂₃	—	2	1	no	—
99	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
101	C₂×Q₁₆×C₂₃	—	2	4	no	—
102	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
103	C₂×SD₁₆×C₂₃	—	4	2	no	—
104	C₂×SD₁₆×C₂₃	—	4	2	no	—
105	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
106	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
107	C₂×M₁₆×C₂₃	—	4	2	no	—
108	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
109	C₂²×C₈×C₂₃	—	4	2	no	—
110	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
111	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
115	C₂₃×#127	—	2	8	no	—
116	C₂₃×#127	—	2	2	no	—
117	C₂₃×#127	C₂³	1	4	yes	—
118	C₂₃×#126	—	2	8	no	—
119	C₂₃×#125	—	2	8	no	—
120	C₂₃×#125	—	2	2	no	—
121	C₂₃×#125	C₂³	1	4	yes	—
122	C₂₃×#123	—	2	8	no	—
123	C₂₃×C₂²⋊Q₈	—	2	2	no	—
124	C₂₃×C₂²⋊Q₈	—	2	2	no	—
125	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
126	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
127	C₂₃×#121	—	2	2	no	—
128	C₂₃×#121	—	2	2	no	—
129	C₂₃×#121	—	2	8	no	—
130	C₂₃×#121	—	2	8	no	—
131	C₂₃×#121	C₂³	1	4	yes	—
132	C₂₃×#121	C₂³	1	4	yes	—
133	C₄×Q₈×C₂₃	—	2	2	no	—
134	C₄×Q₈×C₂₃	—	2	2	no	—
135	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
136	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
137	C₄×D₄×C₂₃	—	2	8	no	—
138	C₄×D₄×C₂₃	D₄	1	4	yes	—
139	C₄×D₄×C₂₃	C₂³	1	4	yes	—
140	C₂₃×#117	—	2	2	no	—
141	C₂₃×#117	—	2	8	no	—
142	C₂₃×#117	C₂³	1	4	yes	—
143	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
153	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
154	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
155	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
156	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
157	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
158	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
159	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
160	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
161	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
162	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
163	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₂₃	—	2	1	no	—
165	C₂×C₄²×C₂₃	—	2	1	no	—
166	C₂×C₄²×C₂₃	—	2	1	no	—
167	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
168	C₂₃×#107	C₂³	1	4	yes	—
169	C₂₃×#106	C₂³	1	4	yes	—
170	C₂₃×#106	C₂³	1	4	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₂₃×#103	C₂³	1	4	yes	—
173	C₂₃×#103	C₂³	1	4	yes	—
174	C₂₃×#103	C₂³	1	4	yes	—
175	C₂₃×#103	C₂³	1	4	yes	—
176	C₂₃×#102	C₂³	1	4	yes	—
177	C₂₃×#102	C₂³	1	4	yes	—
178	C₂₃×#102	C₂³	1	4	yes	—
179	C₂₃×#102	C₂³	1	4	yes	—
180	C₂₃×#102	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	4	yes	—
182	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
183	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
184	C₂₃×#97	C₂³	1	4	yes	—
185	C₂⁴×C₂₃	—	2	1	no	—
186	C₂⁴×C₂₃	—	2	1	no	—
187	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
188	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
189	#41×C₂₃	—	2	8	no	—
190	#41×C₂₃	—	2	8	no	—
191	#41×C₂₃	—	4	4	no	—
192	#41×C₂₃	—	4	4	no	—
193	#41×C₂₃	—	4	8	no	—
194	#41×C₂₃	—	4	8	no	—
195	C₂×Q₈×C₂₃	—	2	1	no	—
196	C₂×Q₈×C₂₃	—	2	1	no	—
197	C₂×Q₈×C₂₃	—	2	2	no	—
198	C₂×Q₈×C₂₃	—	2	2	no	—
199	C₂×Q₈×C₂₃	—	2	2	no	—
200	C₂×Q₈×C₂₃	#41	1	4	yes	—
201	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
202	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
203	C₂×D₄×C₂₃	—	2	4	no	—
204	C₂×D₄×C₂₃	—	2	4	no	—
205	C₂×D₄×C₂₃	—	2	4	no	—
206	C₂×D₄×C₂₃	—	2	4	no	—
207	C₂×D₄×C₂₃	—	2	4	no	—
208	C₂×D₄×C₂₃	—	2	1	no	—
209	C₂×D₄×C₂₃	—	2	1	no	—
210	C₂×D₄×C₂₃	—	2	4	no	—
211	C₂×D₄×C₂₃	—	2	2	no	—
212	C₂×D₄×C₂₃	—	2	2	no	—
213	C₂×D₄×C₂₃	—	2	2	no	—
214	C₂×D₄×C₂₃	—	2	2	no	—
215	C₂×D₄×C₂₃	—	4	2	no	—
216	C₂×D₄×C₂₃	—	4	4	no	—
217	C₂×D₄×C₂₃	—	4	4	no	—
218	C₂×D₄×C₂₃	—	4	4	no	—
219	C₂×D₄×C₂₃	—	8	2	no	—
220	C₂×D₄×C₂₃	—	8	2	no	—
221	C₂×D₄×C₂₃	—	8	2	no	—
222	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
223	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
224	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
225	C₂²×C₄×C₂₃	—	2	1	no	—
226	C₂²×C₄×C₂₃	—	2	2	no	—
227	C₂²×C₄×C₂₃	—	2	2	no	—
228	C₂²×C₄×C₂₃	—	2	2	no	—
229	C₂²×C₄×C₂₃	—	2	2	no	—
230	C₂²×C₄×C₂₃	—	2	4	no	—
231	C₂²×C₄×C₂₃	—	2	1	no	—
232	C₂²×C₄×C₂₃	—	2	1	no	—
233	C₂²×C₄×C₂₃	—	2	1	no	—
234	C₂²×C₄×C₂₃	—	2	1	no	—
235	C₂²×C₄×C₂₃	—	2	1	no	—
236	C₂²×C₄×C₂₃	—	2	4	no	—
237	C₂²×C₄×C₂₃	—	2	4	no	—
238	C₂²×C₄×C₂₃	—	4	4	no	—
239	C₂²×C₄×C₂₃	—	4	4	no	—
240	C₂²×C₄×C₂₃	—	4	4	no	—
241	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
245	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
246	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
247	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
250	Q₁₆×C₂₃	—	2	8	no	—
251	SD₁₆×C₂₃	—	4	4	no	—
252	SD₁₆×C₂₃	—	4	4	no	—
253	M₁₆×C₂₃	—	4	4	no	—
254	C₂×C₈×C₂₃	—	2	2	no	—
255	C₂×C₈×C₂₃	—	2	2	no	—
256	C₂×C₈×C₂₃	—	2	2	no	—
257	C₂×C₈×C₂₃	—	2	2	no	—
258	C₂×C₈×C₂₃	—	4	4	no	—
259	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
260	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
261	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
262	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₂₃	—	2	1	no	—
264	C₄⋊C₄×C₂₃	—	2	1	no	—
265	C₄⋊C₄×C₂₃	—	2	4	no	—
266	C₄⋊C₄×C₂₃	—	2	4	no	—
267	C₄⋊C₄×C₂₃	—	2	4	no	—
268	C₄⋊C₄×C₂₃	—	2	4	no	—
269	C₄⋊C₄×C₂₃	—	2	4	no	—
270	C₄⋊C₄×C₂₃	—	2	4	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	C₂×D₄	1	4	yes	—
275	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
276	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
277	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
278	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
279	C₂²⋊C₄×C₂₃	—	2	4	no	—
280	C₂²⋊C₄×C₂₃	—	2	4	no	—
281	C₂²⋊C₄×C₂₃	—	2	4	no	—
282	C₂²⋊C₄×C₂₃	—	2	4	no	—
283	C₂²⋊C₄×C₂₃	—	2	4	no	—
284	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
285	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
286	C₄²×C₂₃	—	2	4	no	—
287	C₄²×C₂₃	—	2	4	no	—
288	C₄²×C₂₃	—	2	4	no	—
289	C₄²×C₂₃	C₂×D₄	1	2	yes	—
290	C₄²×C₂₃	C₂⁴	1	2	yes	—
291	C₂×#3317	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
292	C₂³×C₂₃	—	2	2	no	—
293	C₂³×C₂₃	—	2	2	no	—
294	C₂³×C₂₃	—	2	2	no	—
295	C₂³×C₂₃	—	2	2	no	—
296	C₂³×C₂₃	—	2	2	no	—
297	C₂³×C₂₃	—	2	2	no	—
298	C₂³×C₂₃	—	2	2	no	—
299	C₂³×C₂₃	—	2	2	no	—
300	C₂³×C₂₃	—	4	2	no	—
301	C₂³×C₂₃	—	4	2	no	—
302	C₂³×C₂₃	—	4	2	no	—
303	C₂³×C₂₃	—	4	2	no	—
304	C₂³×C₂₃	—	4	2	no	—
305	C₂³×C₂₃	—	4	2	no	—
306	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
307	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
308	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
309	Q₈×C₂₃	—	2	4	no	—
310	Q₈×C₂₃	—	2	2	no	—
311	Q₈×C₂₃	—	2	2	no	—
312	Q₈×C₂₃	—	2	2	no	—
313	Q₈×C₂₃	—	4	2	no	—
314	Q₈×C₂₃	C₂×#41	1	4	yes	—
315	D₄×C₂₃	—	2	2	no	—
316	D₄×C₂₃	—	2	2	no	—
317	D₄×C₂₃	—	2	2	no	—
318	D₄×C₂₃	—	2	2	no	—
319	D₄×C₂₃	—	4	4	no	—
320	D₄×C₂₃	—	4	8	no	—
321	D₄×C₂₃	—	4	8	no	—
322	D₄×C₂₃	—	4	8	no	—
323	D₄×C₂₃	—	4	2	no	—
324	D₄×C₂₃	—	4	2	no	—
325	D₄×C₂₃	—	8	4	no	—
326	D₄×C₂₃	—	8	4	no	—
327	D₄×C₂₃	—	8	4	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	2	2	no	—
330	C₂×C₄×C₂₃	—	2	4	no	—
331	C₂×C₄×C₂₃	—	2	2	no	—
332	C₂×C₄×C₂₃	—	2	2	no	—
333	C₂×C₄×C₂₃	—	2	2	no	—
334	C₂×C₄×C₂₃	—	2	4	no	—
335	C₂×C₄×C₂₃	—	2	4	no	—
336	C₂×C₄×C₂₃	—	2	2	no	—
337	C₂×C₄×C₂₃	—	2	2	no	—
338	C₂×C₄×C₂₃	—	2	2	no	—
339	C₂×C₄×C₂₃	—	2	2	no	—
340	C₂×C₄×C₂₃	—	2	2	no	—
341	C₂×C₄×C₂₃	—	2	2	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	—	4	8	no	—
346	C₂×C₄×C₂₃	—	4	8	no	—
347	C₂×C₄×C₂₃	—	4	8	no	—
348	C₂×C₄×C₂₃	—	4	2	no	—
349	C₂×C₄×C₂₃	—	4	2	no	—
350	C₂×C₄×C₂₃	—	4	2	no	—
351	C₂×C₄×C₂₃	—	4	2	no	—
352	C₂×C₄×C₂₃	—	4	2	no	—
353	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
354	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
355	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
356	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
357	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
358	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
359	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
360	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
361	C₈×C₂₃	—	2	2	no	—
362	C₈×C₂₃	—	2	2	no	—
363	C₈×C₂₃	—	2	2	no	—
364	C₈×C₂₃	—	2	2	no	—
365	C₂×#552	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂×#550	C₂×C₂₃	1	1	yes	characteristic
367	#3317	C₂×C₂₃	1	16	yes	direct product factor
368	C₂×#490	C₂×C₂₃	1	1	yes	characteristic, complemented
369	C₂×#481	C₂×C₂₃	1	1	yes	characteristic, complemented
370	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
371	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
372	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
373	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
374	C₂×#460	C₂×C₂₃	1	1	yes	characteristic, complemented
375	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
376	C₂×#452	C₂×C₂₃	1	1	yes	characteristic, complemented
377	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
378	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
379	C₂×#417	C₂×C₂₃	1	1	yes	characteristic, complemented
380	C₂×#416	C₂×C₂₃	1	1	yes	characteristic, complemented
381	C₂²×C₂₃	—	2	2	no	—
382	C₂²×C₂₃	—	2	2	no	—
383	C₂²×C₂₃	—	2	2	no	—
384	C₂²×C₂₃	—	2	2	no	—
385	C₂²×C₂₃	—	2	2	no	—
386	C₂²×C₂₃	—	2	2	no	—
387	C₂²×C₂₃	—	4	4	no	—
388	C₂²×C₂₃	—	4	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	—	8	4	no	—
396	C₂²×C₂₃	—	8	4	no	—
397	C₂²×C₂₃	#546	1	2	yes	—
398	C₂²×C₂₃	#575	1	2	yes	—
399	C₂²×C₂₃	#577	1	2	yes	—
400	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
401	C₄×C₂₃	—	2	2	no	—
402	C₄×C₂₃	—	2	2	no	—
403	C₄×C₂₃	—	2	4	no	—
404	C₄×C₂₃	—	2	2	no	—
405	C₄×C₂₃	—	2	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	—	4	2	no	—
411	C₄×C₂₃	#546	1	2	yes	—
412	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
413	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
415	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
416	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
417	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
418	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
419	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
420	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
421	#552	—	2	4	no	—
422	#552	C₂²×C₂₃	1	8	yes	complemented
423	#550	—	2	4	no	—
424	#550	C₂²×C₂₃	1	8	yes	—
425	C₂×#127	—	2	1	no	—
426	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×#126	—	2	1	no	—
428	C₂×#125	—	2	1	no	—
429	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#123	—	2	1	no	—
431	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#121	—	2	1	no	—
434	C₂×#121	—	2	1	no	—
435	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×C₄×D₄	—	2	1	no	—
440	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#117	—	2	1	no	—
442	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
443	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
444	#490	C₂²×C₂₃	1	8	yes	complemented
445	#482	C₂²×C₂₃	1	8	yes	complemented
446	#481	C₂²×C₂₃	1	8	yes	complemented
447	#479	C₂²×C₂₃	1	8	yes	complemented
448	#468	C₂²×C₂₃	1	8	yes	complemented
449	#465	C₂²×C₂₃	1	8	yes	complemented
450	#460	C₂²×C₂₃	1	8	yes	complemented
451	#452	C₂²×C₂₃	1	8	yes	complemented
452	#452	C₂²×C₂₃	1	8	yes	complemented
453	#441	C₂²×C₂₃	1	8	yes	complemented
454	#435	C₂²×C₂₃	1	8	yes	complemented
455	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
459	#417	C₂²×C₂₃	1	8	yes	complemented
460	#416	C₂²×C₂₃	1	8	yes	complemented
461	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
462	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
463	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
464	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
465	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
466	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
467	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
468	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
469	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
470	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
471	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
472	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
473	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
474	C₂×C₂₃	—	4	2	no	—
475	C₂×C₂₃	—	4	2	no	—
476	C₂×C₂₃	—	8	2	no	—
477	C₂×C₂₃	—	8	2	no	—
478	C₂×C₂₃	#3317	1	4	yes	direct product factor
479	C₂×C₂₃	C₂×#546	1	1	yes	characteristic
480	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
481	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
482	C₂×#41	—	2	2	no	—
483	C₂×#41	—	2	2	no	—
484	C₂×#41	—	2	4	no	—
485	C₂×#41	—	2	4	no	—
486	C₂×#41	—	4	2	no	—
487	C₂×#41	—	4	2	no	—
488	C₂×#41	C₂³×C₂₃	1	4	yes	—
489	C₂×#41	C₂³×C₂₃	1	4	yes	—
490	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
491	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
492	C₂²×D₄	—	2	1	no	—
493	C₂²×D₄	—	2	1	no	—
494	C₂²×D₄	—	2	1	no	—
495	C₂²×D₄	—	2	1	no	—
496	C₂²×D₄	—	2	1	no	—
497	C₂²×D₄	—	2	1	no	—
498	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
500	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
505	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
506	C₂×Q₁₆	—	2	4	no	—
507	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
508	C₂×SD₁₆	—	4	2	no	—
509	C₂×SD₁₆	—	4	2	no	—
510	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
511	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
512	C₂×M₁₆	—	4	2	no	—
513	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
514	C₂²×C₈	—	4	2	no	—
515	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
516	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
517	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
518	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
519	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
520	#127	—	2	8	no	—
521	#127	—	2	2	no	—
522	#127	C₂³×C₂₃	1	4	yes	—
523	#126	—	2	8	no	—
524	#125	—	2	8	no	—
525	#125	—	2	2	no	—
526	#125	C₂³×C₂₃	1	4	yes	—
527	#123	—	2	8	no	—
528	C₂²⋊Q₈	—	2	2	no	—
529	C₂²⋊Q₈	—	2	2	no	—
530	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
531	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
532	#121	—	2	2	no	—
533	#121	—	2	2	no	—
534	#121	—	2	8	no	—
535	#121	—	2	8	no	—
536	#121	C₂³×C₂₃	1	4	yes	—
537	#121	C₂³×C₂₃	1	4	yes	—
538	C₄×Q₈	—	2	2	no	—
539	C₄×Q₈	—	2	2	no	—
540	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
541	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
542	C₄×D₄	—	2	8	no	—
543	C₄×D₄	D₄×C₂₃	1	4	yes	—
544	C₄×D₄	C₂³×C₂₃	1	4	yes	—
545	#117	—	2	2	no	—
546	#117	—	2	8	no	—
547	#117	C₂³×C₂₃	1	4	yes	—
548	C₂×C₄⋊C₄	—	2	1	no	—
549	C₂×C₄⋊C₄	—	2	2	no	—
550	C₂×C₄⋊C₄	—	2	1	no	—
551	C₂×C₄⋊C₄	—	2	1	no	—
552	C₂×C₄⋊C₄	—	2	1	no	—
553	C₂×C₄⋊C₄	—	2	1	no	—
554	C₂×C₄⋊C₄	—	2	1	no	—
555	C₂×C₄⋊C₄	—	2	1	no	—
556	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
557	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
558	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
559	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
560	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
561	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
562	C₂×C₂²⋊C₄	—	2	1	no	—
563	C₂×C₂²⋊C₄	—	2	1	no	—
564	C₂×C₂²⋊C₄	—	2	1	no	—
565	C₂×C₂²⋊C₄	—	2	1	no	—
566	C₂×C₂²⋊C₄	—	2	1	no	—
567	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
568	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
569	C₂×C₄²	—	2	1	no	—
570	C₂×C₄²	—	2	1	no	—
571	C₂×C₄²	—	2	1	no	—
572	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
573	#107	C₂³×C₂₃	1	4	yes	—
574	#106	C₂³×C₂₃	1	4	yes	—
575	#106	C₂³×C₂₃	1	4	yes	—
576	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
577	#103	C₂³×C₂₃	1	4	yes	—
578	#103	C₂³×C₂₃	1	4	yes	—
579	#103	C₂³×C₂₃	1	4	yes	—
580	#103	C₂³×C₂₃	1	4	yes	—
581	#102	C₂³×C₂₃	1	4	yes	—
582	#102	C₂³×C₂₃	1	4	yes	—
583	#102	C₂³×C₂₃	1	4	yes	—
584	#102	C₂³×C₂₃	1	4	yes	—
585	#102	C₂³×C₂₃	1	4	yes	—
586	#102	C₂³×C₂₃	1	4	yes	—
587	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
588	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
589	#97	C₂³×C₂₃	1	4	yes	—
590	C₂₃	C₂×#3317	1	1	yes	characteristic, direct product factor, Sylow
591	C₂⁴	—	2	1	no	—
592	C₂⁴	—	2	1	no	—
593	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
594	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
595	#41	—	2	8	no	—
596	#41	—	2	8	no	—
597	#41	—	4	4	no	—
598	#41	—	4	4	no	—
599	#41	—	4	8	no	—
600	#41	—	4	8	no	—
601	C₂×Q₈	—	2	1	no	—
602	C₂×Q₈	—	2	1	no	—
603	C₂×Q₈	—	2	2	no	—
604	C₂×Q₈	—	2	2	no	—
605	C₂×Q₈	—	2	2	no	—
606	C₂×Q₈	#41×C₂₃	1	4	yes	—
607	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
608	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
609	C₂×D₄	—	2	4	no	—
610	C₂×D₄	—	2	4	no	—
611	C₂×D₄	—	2	4	no	—
612	C₂×D₄	—	2	4	no	—
613	C₂×D₄	—	2	4	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	2	4	no	—
617	C₂×D₄	—	2	2	no	—
618	C₂×D₄	—	2	2	no	—
619	C₂×D₄	—	2	2	no	—
620	C₂×D₄	—	2	2	no	—
621	C₂×D₄	—	4	2	no	—
622	C₂×D₄	—	4	4	no	—
623	C₂×D₄	—	4	4	no	—
624	C₂×D₄	—	4	4	no	—
625	C₂×D₄	—	8	2	no	—
626	C₂×D₄	—	8	2	no	—
627	C₂×D₄	—	8	2	no	—
628	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
629	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
630	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
631	C₂²×C₄	—	2	1	no	—
632	C₂²×C₄	—	2	2	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	1	no	—
637	C₂²×C₄	—	2	1	no	—
638	C₂²×C₄	—	2	1	no	—
639	C₂²×C₄	—	2	1	no	—
640	C₂²×C₄	—	2	1	no	—
641	C₂²×C₄	—	2	4	no	—
642	C₂²×C₄	—	2	4	no	—
643	C₂²×C₄	—	2	4	no	—
644	C₂²×C₄	—	4	4	no	—
645	C₂²×C₄	—	4	4	no	—
646	C₂²×C₄	—	4	4	no	—
647	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
648	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
649	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
650	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
651	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
652	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
653	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
654	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
655	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
656	Q₁₆	—	2	8	no	—
657	SD₁₆	—	4	4	no	—
658	SD₁₆	—	4	4	no	—
659	M₁₆	—	4	4	no	—
660	C₂×C₈	—	2	2	no	—
661	C₂×C₈	—	2	2	no	—
662	C₂×C₈	—	2	2	no	—
663	C₂×C₈	—	2	2	no	—
664	C₂×C₈	—	4	4	no	—
665	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
666	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
667	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
668	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
669	C₄⋊C₄	—	2	1	no	—
670	C₄⋊C₄	—	2	1	no	—
671	C₄⋊C₄	—	2	4	no	—
672	C₄⋊C₄	—	2	4	no	—
673	C₄⋊C₄	—	2	4	no	—
674	C₄⋊C₄	—	2	4	no	—
675	C₄⋊C₄	—	2	4	no	—
676	C₄⋊C₄	—	2	4	no	—
677	C₄⋊C₄	—	2	4	no	—
678	C₄⋊C₄	—	2	1	no	—
679	C₄⋊C₄	—	2	1	no	—
680	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
681	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
682	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
683	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
684	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
685	C₂²⋊C₄	—	2	4	no	—
686	C₂²⋊C₄	—	2	4	no	—
687	C₂²⋊C₄	—	2	4	no	—
688	C₂²⋊C₄	—	2	4	no	—
689	C₂²⋊C₄	—	2	4	no	—
690	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
691	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
692	C₄²	—	2	4	no	—
693	C₄²	—	2	4	no	—
694	C₄²	—	2	4	no	—
695	C₄²	C₂×D₄×C₂₃	1	2	yes	—
696	C₄²	C₂⁴×C₂₃	1	2	yes	—
697	C₂³	—	2	2	no	—
698	C₂³	—	2	2	no	—
699	C₂³	—	2	2	no	—
700	C₂³	—	2	2	no	—
701	C₂³	—	2	2	no	—
702	C₂³	—	2	2	no	—
703	C₂³	—	2	2	no	—
704	C₂³	—	2	2	no	—
705	C₂³	—	4	2	no	—
706	C₂³	—	4	2	no	—
707	C₂³	—	4	2	no	—
708	C₂³	—	4	2	no	—
709	C₂³	—	4	2	no	—
710	C₂³	—	4	2	no	—
711	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
712	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
713	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
714	Q₈	—	2	2	no	—
715	Q₈	—	2	4	no	—
716	Q₈	—	2	2	no	—
717	Q₈	—	2	2	no	—
718	Q₈	—	4	2	no	—
719	Q₈	C₂×#41×C₂₃	1	4	yes	—
720	D₄	—	2	2	no	—
721	D₄	—	2	2	no	—
722	D₄	—	2	2	no	—
723	D₄	—	2	2	no	—
724	D₄	—	4	4	no	—
725	D₄	—	4	8	no	—
726	D₄	—	4	8	no	—
727	D₄	—	4	8	no	—
728	D₄	—	4	2	no	—
729	D₄	—	4	2	no	—
730	D₄	—	8	4	no	—
731	D₄	—	8	4	no	—
732	D₄	—	8	4	no	—
733	C₂×C₄	—	2	2	no	—
734	C₂×C₄	—	2	2	no	—
735	C₂×C₄	—	2	2	no	—
736	C₂×C₄	—	2	2	no	—
737	C₂×C₄	—	2	2	no	—
738	C₂×C₄	—	2	4	no	—
739	C₂×C₄	—	2	2	no	—
740	C₂×C₄	—	2	2	no	—
741	C₂×C₄	—	2	2	no	—
742	C₂×C₄	—	2	2	no	—
743	C₂×C₄	—	2	4	no	—
744	C₂×C₄	—	2	4	no	—
745	C₂×C₄	—	2	2	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	—	4	8	no	—
751	C₂×C₄	—	4	8	no	—
752	C₂×C₄	—	4	8	no	—
753	C₂×C₄	—	4	2	no	—
754	C₂×C₄	—	4	2	no	—
755	C₂×C₄	—	4	2	no	—
756	C₂×C₄	—	4	2	no	—
757	C₂×C₄	—	4	2	no	—
758	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
759	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
760	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
761	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
762	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
763	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
764	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
765	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
766	C₈	—	2	2	no	—
767	C₈	—	2	2	no	—
768	C₈	—	2	2	no	—
769	C₈	—	2	2	no	—
770	C₂²	—	2	2	no	—
771	C₂²	—	2	2	no	—
772	C₂²	—	2	2	no	—
773	C₂²	—	2	2	no	—
774	C₂²	—	2	2	no	—
775	C₂²	—	2	2	no	—
776	C₂²	—	4	4	no	—
777	C₂²	—	4	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	—	8	4	no	—
785	C₂²	—	8	4	no	—
786	C₂²	C₂₃×#546	1	2	yes	—
787	C₂²	C₂₃×#575	1	2	yes	—
788	C₂²	C₂₃×#577	1	2	yes	—
789	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
790	C₄	—	2	2	no	—
791	C₄	—	2	2	no	—
792	C₄	—	2	4	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	4	2	no	—
796	C₄	—	4	2	no	—
797	C₄	—	4	2	no	—
798	C₄	—	4	2	no	—
799	C₄	—	4	2	no	—
800	C₄	C₂₃×#546	1	2	yes	—
801	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
802	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
803	C₂	—	4	2	no	—
804	C₂	—	4	2	no	—
805	C₂	—	8	2	no	—
806	C₂	—	8	2	no	—
807	C₂	C₂₃×#3317	1	4	yes	direct product factor
808	C₂	C₂×C₂₃×#546	1	1	yes	characteristic
809	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
810	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#550	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#552	C₂	semidirect
3. C₂₃×#3317	C₂	direct (N × H)
4. C₂×C₂₃×#490	C₂	semidirect
5. C₂×C₂₃×#481	C₂	semidirect
6. C₂×C₂₃×#482	C₂	semidirect
7. C₂×C₂₃×#479	C₂	semidirect
8. C₂×C₂₃×#468	C₂	semidirect
9. C₂×C₂₃×#465	C₂	semidirect
10. C₂×C₂₃×#460	C₂	semidirect
11. C₂×C₂₃×#452	C₂	semidirect
12. C₂×C₂₃×#452	C₂	semidirect
13. C₂×C₂₃×#441	C₂	semidirect
14. C₂×C₂₃×#435	C₂	semidirect
15. C₂×C₂₃×#417	C₂	semidirect
16. C₂×C₂₃×#416	C₂	semidirect
25. C₂₃×#552	C₂²	semidirect
47. C₂₃×#490	C₂²	semidirect
48. C₂₃×#482	C₂²	semidirect
49. C₂₃×#481	C₂²	semidirect
50. C₂₃×#479	C₂²	semidirect
51. C₂₃×#468	C₂²	semidirect
52. C₂₃×#465	C₂²	semidirect
53. C₂₃×#460	C₂²	semidirect
54. C₂₃×#452	C₂²	semidirect
55. C₂₃×#452	C₂²	semidirect
56. C₂₃×#441	C₂²	semidirect
57. C₂₃×#435	C₂²	semidirect
62. C₂₃×#417	C₂²	semidirect
63. C₂₃×#416	C₂²	semidirect
291. C₂×#3317	C₂₃	direct (N × H)
365. C₂×#552	C₂×C₂₃	semidirect
367. #3317	C₂×C₂₃	direct (N × H)
368. C₂×#490	C₂×C₂₃	semidirect
369. C₂×#481	C₂×C₂₃	semidirect
370. C₂×#482	C₂×C₂₃	semidirect
371. C₂×#479	C₂×C₂₃	semidirect
372. C₂×#468	C₂×C₂₃	semidirect
373. C₂×#465	C₂×C₂₃	semidirect
374. C₂×#460	C₂×C₂₃	semidirect
375. C₂×#452	C₂×C₂₃	semidirect
376. C₂×#452	C₂×C₂₃	semidirect
377. C₂×#441	C₂×C₂₃	semidirect
378. C₂×#435	C₂×C₂₃	semidirect
379. C₂×#417	C₂×C₂₃	semidirect
380. C₂×#416	C₂×C₂₃	semidirect
422. #552	C₂²×C₂₃	semidirect
444. #490	C₂²×C₂₃	semidirect
445. #482	C₂²×C₂₃	semidirect
446. #481	C₂²×C₂₃	semidirect
447. #479	C₂²×C₂₃	semidirect
448. #468	C₂²×C₂₃	semidirect
449. #465	C₂²×C₂₃	semidirect
450. #460	C₂²×C₂₃	semidirect
451. #452	C₂²×C₂₃	semidirect
452. #452	C₂²×C₂₃	semidirect
453. #441	C₂²×C₂₃	semidirect
454. #435	C₂²×C₂₃	semidirect
459. #417	C₂²×C₂₃	semidirect
460. #416	C₂²×C₂₃	semidirect
478. C₂×C₂₃	#3317	direct (N × H)
590. C₂₃	C₂×#3317	direct (N × H)
807. C₂	C₂₃×#3317	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₂₃×#552	2
C₂×C₂₃×#550	2
C₂₃×#3317	2
C₂×C₂₃×#490	2
C₂×C₂₃×#481	2
C₂×C₂₃×#482	2
C₂×C₂₃×#479	2
C₂×C₂₃×#468	2
C₂×C₂₃×#465	2
C₂×C₂₃×#460	2
C₂×C₂₃×#452	2
C₂×C₂₃×#441	2
C₂×C₂₃×#435	2
C₂×C₂₃×#417	2
C₂×C₂₃×#416	2
C₂×#3317	23

Subgroups — C2×C23×#3317 #19208764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3317 #19208764