Subgroups — C₂×C₂₃×#3179 #19208310

Order 5888.

2034 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#540	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3179	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#496	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#488	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#440	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×SD₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#405	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#542	—	2	4	no	—
24	C₂₃×#542	C₂²	1	8	yes	complemented
25	C₂₃×#540	—	2	4	no	—
26	C₂₃×#540	C₂²	1	8	yes	complemented
27	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#126	—	2	1	no	—
30	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
31	C₂×C₂₃×#124	—	2	1	no	—
32	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#123	—	2	1	no	—
34	C₂×C₂₃×#123	—	2	1	no	—
35	C₂×C₂₃×#123	—	2	1	no	—
36	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
37	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#121	—	2	1	no	—
39	C₂×C₂₃×#121	—	2	1	no	—
40	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
43	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
44	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×D₄×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×#501	C₂²	1	8	yes	complemented
49	C₂₃×#496	C₂²	1	8	yes	complemented
50	C₂₃×#488	C₂²	1	8	yes	complemented
51	C₂₃×#486	C₂²	1	8	yes	complemented
52	C₂₃×#469	C₂²	1	8	yes	complemented
53	C₂₃×#468	C₂²	1	8	yes	complemented
54	C₂₃×#466	C₂²	1	8	yes	complemented
55	C₂₃×#465	C₂²	1	8	yes	complemented
56	C₂₃×#442	C₂²	1	8	yes	complemented
57	C₂₃×#440	C₂²	1	8	yes	complemented
58	C₄×SD₁₆×C₂₃	C₂²	1	8	yes	complemented
59	C₄×D₈×C₂₃	C₂²	1	8	yes	complemented
60	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×#102	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	C₂₃×#405	C₂²	1	8	yes	complemented
73	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
75	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
76	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	—	2	1	no	—
78	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×D₄×C₂₃	—	2	1	no	—
80	C₂²×D₄×C₂₃	—	2	1	no	—
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	—	2	1	no	—
83	C₂²×D₄×C₂₃	—	2	1	no	—
84	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	—	2	1	no	—
89	C₂³×C₄×C₂₃	—	2	1	no	—
90	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
91	C₂×SD₁₆×C₂₃	—	2	4	no	—
92	C₂×SD₁₆×C₂₃	—	2	4	no	—
93	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
94	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
95	C₂×D₈×C₂₃	—	2	4	no	—
96	C₂×D₈×C₂₃	—	2	4	no	—
97	C₂×D₈×C₂₃	C₂³	1	4	yes	—
98	C₂×D₈×C₂₃	C₂³	1	4	yes	—
99	C₂×M₁₆×C₂₃	—	2	4	no	—
100	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
101	C₂²×C₈×C₂₃	—	2	4	no	—
102	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
104	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
107	C₂₃×C₄⋊Q₈	—	2	2	no	—
108	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
109	C₂₃×#127	—	2	2	no	—
110	C₂₃×#127	C₂³	1	4	yes	—
111	C₂₃×#126	—	2	8	no	—
112	C₂₃×#125	—	2	2	no	—
113	C₂₃×#125	C₂³	1	4	yes	—
114	C₂₃×#124	—	2	8	no	—
115	C₂₃×#124	—	2	2	no	—
116	C₂₃×#124	C₂³	1	4	yes	—
117	C₂₃×#123	—	2	8	no	—
118	C₂₃×#123	—	2	8	no	—
119	C₂₃×#123	—	2	8	no	—
120	C₂₃×C₂²⋊Q₈	—	2	2	no	—
121	C₂₃×C₂²⋊Q₈	—	2	8	no	—
122	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₂₃×#121	—	2	2	no	—
124	C₂₃×#121	—	2	2	no	—
125	C₂₃×#121	—	2	2	no	—
126	C₂₃×#121	—	2	8	no	—
127	C₂₃×#121	—	2	8	no	—
128	C₂₃×#121	C₂³	1	4	yes	—
129	C₂₃×#121	C₂³	1	4	yes	—
130	C₂₃×#121	C₂³	1	4	yes	—
131	C₄×Q₈×C₂₃	—	2	2	no	—
132	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
133	C₄×D₄×C₂₃	—	2	2	no	—
134	C₄×D₄×C₂₃	—	2	2	no	—
135	C₄×D₄×C₂₃	—	2	2	no	—
136	C₄×D₄×C₂₃	C₂³	1	4	yes	—
137	C₄×D₄×C₂₃	C₂³	1	4	yes	—
138	C₄×D₄×C₂₃	C₂³	1	4	yes	—
139	C₂₃×#117	D₄	1	4	yes	—
140	C₂₃×#117	C₂³	1	4	yes	—
141	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
142	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
143	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
144	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
145	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
149	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
155	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
156	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
162	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₂₃	—	2	1	no	—
164	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
166	C₂₃×#107	C₂³	1	4	yes	—
167	C₂₃×#107	C₂³	1	4	yes	—
168	C₂₃×#106	C₂³	1	4	yes	—
169	C₂₃×#106	C₂³	1	4	yes	—
170	C₂₃×#103	C₂³	1	4	yes	—
171	C₂₃×#103	C₂³	1	4	yes	—
172	C₂₃×#102	C₂³	1	4	yes	—
173	C₂₃×#102	C₂³	1	4	yes	—
174	C₂₃×#102	C₂³	1	4	yes	—
175	C₂₃×#102	C₂³	1	4	yes	—
176	C₂₃×#102	C₂³	1	4	yes	—
177	C₂₃×#102	C₂³	1	4	yes	—
178	C₂₃×#97	C₂³	1	4	yes	—
179	C₂₃×#97	C₂³	1	4	yes	—
180	C₄×C₈×C₂₃	C₂³	1	4	yes	—
181	C₄×C₈×C₂₃	C₂³	1	4	yes	—
182	C₂⁴×C₂₃	—	2	1	no	—
183	C₂⁴×C₂₃	—	2	1	no	—
184	C₂⁴×C₂₃	—	2	1	no	—
185	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
186	C₂×Q₈×C₂₃	—	2	1	no	—
187	C₂×Q₈×C₂₃	—	2	4	no	—
188	C₂×Q₈×C₂₃	—	2	2	no	—
189	C₂×Q₈×C₂₃	—	2	2	no	—
190	C₂×Q₈×C₂₃	—	8	2	no	—
191	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
192	C₂×D₄×C₂₃	—	2	4	no	—
193	C₂×D₄×C₂₃	—	2	4	no	—
194	C₂×D₄×C₂₃	—	2	4	no	—
195	C₂×D₄×C₂₃	—	2	1	no	—
196	C₂×D₄×C₂₃	—	2	1	no	—
197	C₂×D₄×C₂₃	—	2	1	no	—
198	C₂×D₄×C₂₃	—	2	4	no	—
199	C₂×D₄×C₂₃	—	2	4	no	—
200	C₂×D₄×C₂₃	—	2	2	no	—
201	C₂×D₄×C₂₃	—	2	2	no	—
202	C₂×D₄×C₂₃	—	2	2	no	—
203	C₂×D₄×C₂₃	—	2	2	no	—
204	C₂×D₄×C₂₃	—	2	2	no	—
205	C₂×D₄×C₂₃	—	2	2	no	—
206	C₂×D₄×C₂₃	—	8	2	no	—
207	C₂×D₄×C₂₃	—	8	2	no	—
208	C₂×D₄×C₂₃	—	8	2	no	—
209	C₂×D₄×C₂₃	—	8	2	no	—
210	C₂×D₄×C₂₃	—	8	2	no	—
211	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
212	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
213	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₂₃	—	2	2	no	—
215	C₂²×C₄×C₂₃	—	2	2	no	—
216	C₂²×C₄×C₂₃	—	2	1	no	—
217	C₂²×C₄×C₂₃	—	2	1	no	—
218	C₂²×C₄×C₂₃	—	2	1	no	—
219	C₂²×C₄×C₂₃	—	2	1	no	—
220	C₂²×C₄×C₂₃	—	2	1	no	—
221	C₂²×C₄×C₂₃	—	2	4	no	—
222	C₂²×C₄×C₂₃	—	2	4	no	—
223	C₂²×C₄×C₂₃	—	2	4	no	—
224	C₂²×C₄×C₂₃	—	8	2	no	—
225	C₂²×C₄×C₂₃	—	8	2	no	—
226	C₂²×C₄×C₂₃	—	8	2	no	—
227	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
228	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
231	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
232	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
233	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
234	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
235	SD₁₆×C₂₃	—	2	8	no	—
236	SD₁₆×C₂₃	—	2	8	no	—
237	D₈×C₂₃	—	2	8	no	—
238	D₈×C₂₃	—	2	8	no	—
239	M₁₆×C₂₃	—	2	8	no	—
240	C₂×C₈×C₂₃	—	2	2	no	—
241	C₂×C₈×C₂₃	—	2	2	no	—
242	C₂×C₈×C₂₃	—	2	8	no	—
243	C₂×C₈×C₂₃	#41	1	4	yes	—
244	C₂×C₈×C₂₃	#41	1	4	yes	—
245	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
246	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
247	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
248	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
249	C₄⋊C₄×C₂₃	—	2	4	no	—
250	C₄⋊C₄×C₂₃	—	2	4	no	—
251	C₄⋊C₄×C₂₃	—	2	4	no	—
252	C₄⋊C₄×C₂₃	—	2	4	no	—
253	C₄⋊C₄×C₂₃	—	2	4	no	—
254	C₄⋊C₄×C₂₃	—	2	1	no	—
255	C₄⋊C₄×C₂₃	—	2	1	no	—
256	C₄⋊C₄×C₂₃	—	2	1	no	—
257	C₄⋊C₄×C₂₃	—	2	1	no	—
258	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
259	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
260	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
262	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	—	2	4	no	—
266	C₂²⋊C₄×C₂₃	—	2	4	no	—
267	C₂²⋊C₄×C₂₃	—	2	4	no	—
268	C₂²⋊C₄×C₂₃	—	2	4	no	—
269	C₂²⋊C₄×C₂₃	—	2	4	no	—
270	C₂²⋊C₄×C₂₃	—	2	4	no	—
271	C₂²⋊C₄×C₂₃	—	2	4	no	—
272	C₂²⋊C₄×C₂₃	—	2	4	no	—
273	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
274	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
275	C₄²×C₂₃	—	2	4	no	—
276	C₄²×C₂₃	C₂×D₄	1	2	yes	—
277	C₄²×C₂₃	C₂×D₄	1	2	yes	—
278	C₄²×C₂₃	C₂⁴	1	2	yes	—
279	C₄²×C₂₃	C₂⁴	1	2	yes	—
280	C₂×#3179	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
281	C₂³×C₂₃	—	2	2	no	—
282	C₂³×C₂₃	—	2	2	no	—
283	C₂³×C₂₃	—	2	2	no	—
284	C₂³×C₂₃	—	2	2	no	—
285	C₂³×C₂₃	—	2	2	no	—
286	C₂³×C₂₃	—	2	2	no	—
287	C₂³×C₂₃	—	4	2	no	—
288	C₂³×C₂₃	—	4	2	no	—
289	C₂³×C₂₃	—	4	2	no	—
290	C₂³×C₂₃	—	4	2	no	—
291	C₂³×C₂₃	—	4	2	no	—
292	C₂³×C₂₃	—	4	2	no	—
293	C₂³×C₂₃	—	4	2	no	—
294	C₂³×C₂₃	—	4	2	no	—
295	C₂³×C₂₃	—	4	2	no	—
296	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
297	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₂₃	—	2	2	no	—
299	Q₈×C₂₃	—	2	2	no	—
300	Q₈×C₂₃	—	4	2	no	—
301	Q₈×C₂₃	—	8	4	no	—
302	D₄×C₂₃	—	2	2	no	—
303	D₄×C₂₃	—	2	2	no	—
304	D₄×C₂₃	—	2	2	no	—
305	D₄×C₂₃	—	2	2	no	—
306	D₄×C₂₃	—	2	2	no	—
307	D₄×C₂₃	—	2	2	no	—
308	D₄×C₂₃	—	4	2	no	—
309	D₄×C₂₃	—	4	2	no	—
310	D₄×C₂₃	—	4	2	no	—
311	D₄×C₂₃	—	8	4	no	—
312	D₄×C₂₃	—	8	4	no	—
313	D₄×C₂₃	—	8	4	no	—
314	D₄×C₂₃	—	8	4	no	—
315	D₄×C₂₃	—	8	4	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	2	2	no	—
319	C₂×C₄×C₂₃	—	2	2	no	—
320	C₂×C₄×C₂₃	—	2	2	no	—
321	C₂×C₄×C₂₃	—	2	4	no	—
322	C₂×C₄×C₂₃	—	2	2	no	—
323	C₂×C₄×C₂₃	—	2	2	no	—
324	C₂×C₄×C₂₃	—	2	2	no	—
325	C₂×C₄×C₂₃	—	2	2	no	—
326	C₂×C₄×C₂₃	—	2	2	no	—
327	C₂×C₄×C₂₃	—	2	2	no	—
328	C₂×C₄×C₂₃	—	2	2	no	—
329	C₂×C₄×C₂₃	—	4	2	no	—
330	C₂×C₄×C₂₃	—	4	2	no	—
331	C₂×C₄×C₂₃	—	4	2	no	—
332	C₂×C₄×C₂₃	—	4	2	no	—
333	C₂×C₄×C₂₃	—	4	2	no	—
334	C₂×C₄×C₂₃	—	8	4	no	—
335	C₂×C₄×C₂₃	—	8	4	no	—
336	C₂×C₄×C₂₃	—	8	4	no	—
337	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
338	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
339	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
341	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
343	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
344	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
345	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
346	C₈×C₂₃	—	2	2	no	—
347	C₈×C₂₃	—	2	2	no	—
348	C₈×C₂₃	C₂×#41	1	4	yes	—
349	C₈×C₂₃	C₂×#41	1	4	yes	—
350	C₂×#542	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂×#540	C₂×C₂₃	1	1	yes	characteristic, complemented
352	#3179	C₂×C₂₃	1	16	yes	direct product factor
353	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×#496	C₂×C₂₃	1	1	yes	characteristic, complemented
355	C₂×#488	C₂×C₂₃	1	1	yes	characteristic, complemented
356	C₂×#486	C₂×C₂₃	1	1	yes	characteristic, complemented
357	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
358	C₂×#468	C₂×C₂₃	1	1	yes	characteristic, complemented
359	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
360	C₂×#465	C₂×C₂₃	1	1	yes	characteristic, complemented
361	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
362	C₂×#440	C₂×C₂₃	1	1	yes	characteristic, complemented
363	C₂×C₄×SD₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
364	C₂×C₄×D₈	C₂×C₂₃	1	1	yes	characteristic, complemented
365	C₂×#405	C₂×C₂₃	1	1	yes	characteristic, complemented
366	C₂²×C₂₃	—	2	2	no	—
367	C₂²×C₂₃	—	2	2	no	—
368	C₂²×C₂₃	—	2	2	no	—
369	C₂²×C₂₃	—	4	4	no	—
370	C₂²×C₂₃	—	4	2	no	—
371	C₂²×C₂₃	—	4	2	no	—
372	C₂²×C₂₃	—	4	2	no	—
373	C₂²×C₂₃	—	4	2	no	—
374	C₂²×C₂₃	—	4	2	no	—
375	C₂²×C₂₃	—	4	2	no	—
376	C₂²×C₂₃	—	4	2	no	—
377	C₂²×C₂₃	—	4	2	no	—
378	C₂²×C₂₃	—	4	2	no	—
379	C₂²×C₂₃	—	8	4	no	—
380	C₂²×C₂₃	—	8	4	no	—
381	C₂²×C₂₃	—	8	4	no	—
382	C₂²×C₂₃	#532	1	2	yes	—
383	C₂²×C₂₃	#576	1	2	yes	—
384	C₂²×C₂₃	#577	1	2	yes	—
385	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
386	C₄×C₂₃	—	2	2	no	—
387	C₄×C₂₃	—	2	2	no	—
388	C₄×C₂₃	—	2	2	no	—
389	C₄×C₂₃	—	2	2	no	—
390	C₄×C₂₃	—	2	2	no	—
391	C₄×C₂₃	—	4	2	no	—
392	C₄×C₂₃	—	4	2	no	—
393	C₄×C₂₃	—	4	2	no	—
394	C₄×C₂₃	—	4	2	no	—
395	C₄×C₂₃	—	4	2	no	—
396	C₄×C₂₃	#532	1	2	yes	—
397	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
398	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
399	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
400	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
401	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
402	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
403	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
404	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
405	#542	—	2	4	no	—
406	#542	C₂²×C₂₃	1	8	yes	complemented
407	#540	—	2	4	no	—
408	#540	C₂²×C₂₃	1	8	yes	complemented
409	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#126	—	2	1	no	—
412	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#124	—	2	1	no	—
414	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
415	C₂×#123	—	2	1	no	—
416	C₂×#123	—	2	1	no	—
417	C₂×#123	—	2	1	no	—
418	C₂×C₂²⋊Q₈	—	2	1	no	—
419	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
420	C₂×#121	—	2	1	no	—
421	C₂×#121	—	2	1	no	—
422	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
424	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
425	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
430	#501	C₂²×C₂₃	1	8	yes	complemented
431	#496	C₂²×C₂₃	1	8	yes	complemented
432	#488	C₂²×C₂₃	1	8	yes	complemented
433	#486	C₂²×C₂₃	1	8	yes	complemented
434	#469	C₂²×C₂₃	1	8	yes	complemented
435	#468	C₂²×C₂₃	1	8	yes	complemented
436	#466	C₂²×C₂₃	1	8	yes	complemented
437	#465	C₂²×C₂₃	1	8	yes	complemented
438	#442	C₂²×C₂₃	1	8	yes	complemented
439	#440	C₂²×C₂₃	1	8	yes	complemented
440	C₄×SD₁₆	C₂²×C₂₃	1	8	yes	complemented
441	C₄×D₈	C₂²×C₂₃	1	8	yes	complemented
442	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
449	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
450	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
451	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
452	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
453	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
454	#405	C₂²×C₂₃	1	8	yes	complemented
455	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
456	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
457	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
458	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
459	C₂×C₂₃	—	4	2	no	—
460	C₂×C₂₃	—	8	2	no	—
461	C₂×C₂₃	—	8	2	no	—
462	C₂×C₂₃	—	8	2	no	—
463	C₂×C₂₃	#3179	1	4	yes	direct product factor
464	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
465	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
466	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
467	C₂²×Q₈	—	2	1	no	—
468	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
469	C₂²×D₄	—	2	1	no	—
470	C₂²×D₄	—	2	1	no	—
471	C₂²×D₄	—	2	1	no	—
472	C₂²×D₄	—	2	1	no	—
473	C₂²×D₄	—	2	1	no	—
474	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
476	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
477	C₂³×C₄	—	2	1	no	—
478	C₂³×C₄	—	2	1	no	—
479	C₂³×C₄	—	2	1	no	—
480	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
481	C₂×SD₁₆	—	2	4	no	—
482	C₂×SD₁₆	—	2	4	no	—
483	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
484	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
485	C₂×D₈	—	2	4	no	—
486	C₂×D₈	—	2	4	no	—
487	C₂×D₈	C₂³×C₂₃	1	4	yes	—
488	C₂×D₈	C₂³×C₂₃	1	4	yes	—
489	C₂×M₁₆	—	2	4	no	—
490	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
491	C₂²×C₈	—	2	4	no	—
492	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
493	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
494	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
495	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
496	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
497	C₄⋊Q₈	—	2	2	no	—
498	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
499	#127	—	2	2	no	—
500	#127	C₂³×C₂₃	1	4	yes	—
501	#126	—	2	8	no	—
502	#125	—	2	2	no	—
503	#125	C₂³×C₂₃	1	4	yes	—
504	#124	—	2	8	no	—
505	#124	—	2	2	no	—
506	#124	C₂³×C₂₃	1	4	yes	—
507	#123	—	2	8	no	—
508	#123	—	2	8	no	—
509	#123	—	2	8	no	—
510	C₂²⋊Q₈	—	2	2	no	—
511	C₂²⋊Q₈	—	2	8	no	—
512	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
513	#121	—	2	2	no	—
514	#121	—	2	2	no	—
515	#121	—	2	2	no	—
516	#121	—	2	8	no	—
517	#121	—	2	8	no	—
518	#121	C₂³×C₂₃	1	4	yes	—
519	#121	C₂³×C₂₃	1	4	yes	—
520	#121	C₂³×C₂₃	1	4	yes	—
521	C₄×Q₈	—	2	2	no	—
522	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
523	C₄×D₄	—	2	2	no	—
524	C₄×D₄	—	2	2	no	—
525	C₄×D₄	—	2	2	no	—
526	C₄×D₄	C₂³×C₂₃	1	4	yes	—
527	C₄×D₄	C₂³×C₂₃	1	4	yes	—
528	C₄×D₄	C₂³×C₂₃	1	4	yes	—
529	#117	D₄×C₂₃	1	4	yes	—
530	#117	C₂³×C₂₃	1	4	yes	—
531	C₂×C₄⋊C₄	—	2	1	no	—
532	C₂×C₄⋊C₄	—	2	1	no	—
533	C₂×C₄⋊C₄	—	2	1	no	—
534	C₂×C₄⋊C₄	—	2	1	no	—
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
537	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
538	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
539	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
540	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
541	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
542	C₂×C₂²⋊C₄	—	2	1	no	—
543	C₂×C₂²⋊C₄	—	2	1	no	—
544	C₂×C₂²⋊C₄	—	2	1	no	—
545	C₂×C₂²⋊C₄	—	2	1	no	—
546	C₂×C₂²⋊C₄	—	2	1	no	—
547	C₂×C₂²⋊C₄	—	2	1	no	—
548	C₂×C₂²⋊C₄	—	2	1	no	—
549	C₂×C₂²⋊C₄	—	2	1	no	—
550	C₂×C₂²⋊C₄	—	2	1	no	—
551	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
552	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
553	C₂×C₄²	—	2	1	no	—
554	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
555	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
556	#107	C₂³×C₂₃	1	4	yes	—
557	#107	C₂³×C₂₃	1	4	yes	—
558	#106	C₂³×C₂₃	1	4	yes	—
559	#106	C₂³×C₂₃	1	4	yes	—
560	#103	C₂³×C₂₃	1	4	yes	—
561	#103	C₂³×C₂₃	1	4	yes	—
562	#102	C₂³×C₂₃	1	4	yes	—
563	#102	C₂³×C₂₃	1	4	yes	—
564	#102	C₂³×C₂₃	1	4	yes	—
565	#102	C₂³×C₂₃	1	4	yes	—
566	#102	C₂³×C₂₃	1	4	yes	—
567	#102	C₂³×C₂₃	1	4	yes	—
568	#97	C₂³×C₂₃	1	4	yes	—
569	#97	C₂³×C₂₃	1	4	yes	—
570	C₄×C₈	C₂³×C₂₃	1	4	yes	—
571	C₄×C₈	C₂³×C₂₃	1	4	yes	—
572	C₂₃	C₂×#3179	1	1	yes	characteristic, direct product factor, Sylow
573	C₂⁴	—	2	1	no	—
574	C₂⁴	—	2	1	no	—
575	C₂⁴	—	2	1	no	—
576	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	4	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	—	2	2	no	—
581	C₂×Q₈	—	8	2	no	—
582	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	1	no	—
587	C₂×D₄	—	2	1	no	—
588	C₂×D₄	—	2	1	no	—
589	C₂×D₄	—	2	4	no	—
590	C₂×D₄	—	2	4	no	—
591	C₂×D₄	—	2	2	no	—
592	C₂×D₄	—	2	2	no	—
593	C₂×D₄	—	2	2	no	—
594	C₂×D₄	—	2	2	no	—
595	C₂×D₄	—	2	2	no	—
596	C₂×D₄	—	2	2	no	—
597	C₂×D₄	—	8	2	no	—
598	C₂×D₄	—	8	2	no	—
599	C₂×D₄	—	8	2	no	—
600	C₂×D₄	—	8	2	no	—
601	C₂×D₄	—	8	2	no	—
602	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
603	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
604	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
605	C₂²×C₄	—	2	2	no	—
606	C₂²×C₄	—	2	2	no	—
607	C₂²×C₄	—	2	1	no	—
608	C₂²×C₄	—	2	1	no	—
609	C₂²×C₄	—	2	1	no	—
610	C₂²×C₄	—	2	1	no	—
611	C₂²×C₄	—	2	1	no	—
612	C₂²×C₄	—	2	4	no	—
613	C₂²×C₄	—	2	4	no	—
614	C₂²×C₄	—	2	4	no	—
615	C₂²×C₄	—	8	2	no	—
616	C₂²×C₄	—	8	2	no	—
617	C₂²×C₄	—	8	2	no	—
618	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
619	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
620	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
621	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
622	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
623	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
624	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
625	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
626	SD₁₆	—	2	8	no	—
627	SD₁₆	—	2	8	no	—
628	D₈	—	2	8	no	—
629	D₈	—	2	8	no	—
630	M₁₆	—	2	8	no	—
631	C₂×C₈	—	2	2	no	—
632	C₂×C₈	—	2	2	no	—
633	C₂×C₈	—	2	8	no	—
634	C₂×C₈	#41×C₂₃	1	4	yes	—
635	C₂×C₈	#41×C₂₃	1	4	yes	—
636	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
637	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
638	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
639	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
640	C₄⋊C₄	—	2	4	no	—
641	C₄⋊C₄	—	2	4	no	—
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	2	4	no	—
644	C₄⋊C₄	—	2	4	no	—
645	C₄⋊C₄	—	2	1	no	—
646	C₄⋊C₄	—	2	1	no	—
647	C₄⋊C₄	—	2	1	no	—
648	C₄⋊C₄	—	2	1	no	—
649	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
650	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
651	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
652	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
653	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
654	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
655	C₂²⋊C₄	—	2	4	no	—
656	C₂²⋊C₄	—	2	4	no	—
657	C₂²⋊C₄	—	2	4	no	—
658	C₂²⋊C₄	—	2	4	no	—
659	C₂²⋊C₄	—	2	4	no	—
660	C₂²⋊C₄	—	2	4	no	—
661	C₂²⋊C₄	—	2	4	no	—
662	C₂²⋊C₄	—	2	4	no	—
663	C₂²⋊C₄	—	2	4	no	—
664	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
665	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
666	C₄²	—	2	4	no	—
667	C₄²	C₂×D₄×C₂₃	1	2	yes	—
668	C₄²	C₂×D₄×C₂₃	1	2	yes	—
669	C₄²	C₂⁴×C₂₃	1	2	yes	—
670	C₄²	C₂⁴×C₂₃	1	2	yes	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	2	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	2	2	no	—
675	C₂³	—	2	2	no	—
676	C₂³	—	2	2	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	4	2	no	—
682	C₂³	—	4	2	no	—
683	C₂³	—	4	2	no	—
684	C₂³	—	4	2	no	—
685	C₂³	—	4	2	no	—
686	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
687	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
688	Q₈	—	2	2	no	—
689	Q₈	—	2	2	no	—
690	Q₈	—	4	2	no	—
691	Q₈	—	8	4	no	—
692	D₄	—	2	2	no	—
693	D₄	—	2	2	no	—
694	D₄	—	2	2	no	—
695	D₄	—	2	2	no	—
696	D₄	—	2	2	no	—
697	D₄	—	2	2	no	—
698	D₄	—	4	2	no	—
699	D₄	—	4	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	8	4	no	—
702	D₄	—	8	4	no	—
703	D₄	—	8	4	no	—
704	D₄	—	8	4	no	—
705	D₄	—	8	4	no	—
706	C₂×C₄	—	2	2	no	—
707	C₂×C₄	—	2	2	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	2	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	2	no	—
716	C₂×C₄	—	2	2	no	—
717	C₂×C₄	—	2	2	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	4	2	no	—
720	C₂×C₄	—	4	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	4	2	no	—
723	C₂×C₄	—	4	2	no	—
724	C₂×C₄	—	8	4	no	—
725	C₂×C₄	—	8	4	no	—
726	C₂×C₄	—	8	4	no	—
727	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
728	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
729	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
730	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
731	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
732	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
733	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
734	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
735	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
736	C₈	—	2	2	no	—
737	C₈	—	2	2	no	—
738	C₈	C₂×#41×C₂₃	1	4	yes	—
739	C₈	C₂×#41×C₂₃	1	4	yes	—
740	C₂²	—	2	2	no	—
741	C₂²	—	2	2	no	—
742	C₂²	—	2	2	no	—
743	C₂²	—	4	4	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	2	no	—
749	C₂²	—	4	2	no	—
750	C₂²	—	4	2	no	—
751	C₂²	—	4	2	no	—
752	C₂²	—	4	2	no	—
753	C₂²	—	8	4	no	—
754	C₂²	—	8	4	no	—
755	C₂²	—	8	4	no	—
756	C₂²	C₂₃×#532	1	2	yes	—
757	C₂²	C₂₃×#576	1	2	yes	—
758	C₂²	C₂₃×#577	1	2	yes	—
759	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
760	C₄	—	2	2	no	—
761	C₄	—	2	2	no	—
762	C₄	—	2	2	no	—
763	C₄	—	2	2	no	—
764	C₄	—	2	2	no	—
765	C₄	—	4	2	no	—
766	C₄	—	4	2	no	—
767	C₄	—	4	2	no	—
768	C₄	—	4	2	no	—
769	C₄	—	4	2	no	—
770	C₄	C₂₃×#532	1	2	yes	—
771	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
772	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
773	C₂	—	4	2	no	—
774	C₂	—	8	2	no	—
775	C₂	—	8	2	no	—
776	C₂	—	8	2	no	—
777	C₂	C₂₃×#3179	1	4	yes	direct product factor
778	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
779	C₂	C₂×C₂₃×#576	1	1	yes	characteristic
780	C₂	C₂×C₂₃×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₂₃×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#542	C₂	semidirect
2. C₂×C₂₃×#540	C₂	semidirect
3. C₂₃×#3179	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#496	C₂	semidirect
6. C₂×C₂₃×#488	C₂	semidirect
7. C₂×C₂₃×#486	C₂	semidirect
8. C₂×C₂₃×#469	C₂	semidirect
9. C₂×C₂₃×#468	C₂	semidirect
10. C₂×C₂₃×#466	C₂	semidirect
11. C₂×C₂₃×#465	C₂	semidirect
12. C₂×C₂₃×#442	C₂	semidirect
13. C₂×C₂₃×#440	C₂	semidirect
14. C₂×C₄×SD₁₆×C₂₃	C₂	semidirect
15. C₂×C₄×D₈×C₂₃	C₂	semidirect
16. C₂×C₂₃×#405	C₂	semidirect
24. C₂₃×#542	C₂²	semidirect
26. C₂₃×#540	C₂²	semidirect
48. C₂₃×#501	C₂²	semidirect
49. C₂₃×#496	C₂²	semidirect
50. C₂₃×#488	C₂²	semidirect
51. C₂₃×#486	C₂²	semidirect
52. C₂₃×#469	C₂²	semidirect
53. C₂₃×#468	C₂²	semidirect
54. C₂₃×#466	C₂²	semidirect
55. C₂₃×#465	C₂²	semidirect
56. C₂₃×#442	C₂²	semidirect
57. C₂₃×#440	C₂²	semidirect
58. C₄×SD₁₆×C₂₃	C₂²	semidirect
59. C₄×D₈×C₂₃	C₂²	semidirect
72. C₂₃×#405	C₂²	semidirect
280. C₂×#3179	C₂₃	direct (N × H)
350. C₂×#542	C₂×C₂₃	semidirect
351. C₂×#540	C₂×C₂₃	semidirect
352. #3179	C₂×C₂₃	direct (N × H)
353. C₂×#501	C₂×C₂₃	semidirect
354. C₂×#496	C₂×C₂₃	semidirect
355. C₂×#488	C₂×C₂₃	semidirect
356. C₂×#486	C₂×C₂₃	semidirect
357. C₂×#469	C₂×C₂₃	semidirect
358. C₂×#468	C₂×C₂₃	semidirect
359. C₂×#466	C₂×C₂₃	semidirect
360. C₂×#465	C₂×C₂₃	semidirect
361. C₂×#442	C₂×C₂₃	semidirect
362. C₂×#440	C₂×C₂₃	semidirect
363. C₂×C₄×SD₁₆	C₂×C₂₃	semidirect
364. C₂×C₄×D₈	C₂×C₂₃	semidirect
365. C₂×#405	C₂×C₂₃	semidirect
406. #542	C₂²×C₂₃	semidirect
408. #540	C₂²×C₂₃	semidirect
430. #501	C₂²×C₂₃	semidirect
431. #496	C₂²×C₂₃	semidirect
432. #488	C₂²×C₂₃	semidirect
433. #486	C₂²×C₂₃	semidirect
434. #469	C₂²×C₂₃	semidirect
435. #468	C₂²×C₂₃	semidirect
436. #466	C₂²×C₂₃	semidirect
437. #465	C₂²×C₂₃	semidirect
438. #442	C₂²×C₂₃	semidirect
439. #440	C₂²×C₂₃	semidirect
440. C₄×SD₁₆	C₂²×C₂₃	semidirect
441. C₄×D₈	C₂²×C₂₃	semidirect
454. #405	C₂²×C₂₃	semidirect
463. C₂×C₂₃	#3179	direct (N × H)
572. C₂₃	C₂×#3179	direct (N × H)
777. C₂	C₂₃×#3179	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×#542	2
C₂×C₂₃×#540	2
C₂₃×#3179	2
C₂×C₂₃×#501	2
C₂×C₂₃×#496	2
C₂×C₂₃×#488	2
C₂×C₂₃×#486	2
C₂×C₂₃×#469	2
C₂×C₂₃×#468	2
C₂×C₂₃×#466	2
C₂×C₂₃×#465	2
C₂×C₂₃×#442	2
C₂×C₂₃×#440	2
C₂×C₄×SD₁₆×C₂₃	2
C₂×C₄×D₈×C₂₃	2
C₂×C₂₃×#405	2
C₂×#3179	23

Subgroups — C2×C23×#3179 #19208310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3179 #19208310