Subgroups — C₂×C₂₃×#3347 #19208865

Order 5888.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₂₃×#553	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3347	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#501	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#482	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#435	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#428	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
20	C₂₃×#555	—	2	4	no	—
21	C₂₃×#555	C₂²	1	8	yes	complemented
22	C₂₃×#553	—	2	4	no	—
23	C₂₃×#553	C₂²	1	8	yes	complemented
24	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₂×C₂₃×#126	—	2	1	no	—
26	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
27	C₂×C₂₃×#124	—	2	1	no	—
28	C₂×C₂₃×#124	—	2	1	no	—
29	C₂×C₂₃×#123	—	2	1	no	—
30	C₂×C₂₃×#121	—	2	1	no	—
31	C₂×C₂₃×#121	—	2	1	no	—
32	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
33	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
34	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#121	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₂₃	—	2	1	no	—
37	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
39	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×#117	—	2	1	no	—
41	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
45	C₂₃×#501	C₂²	1	8	yes	complemented
46	C₂₃×#482	C₂²	1	8	yes	complemented
47	C₂₃×#482	C₂²	1	8	yes	complemented
48	C₂₃×#482	C₂²	1	8	yes	complemented
49	C₂₃×#480	C₂²	1	8	yes	complemented
50	C₂₃×#478	C₂²	1	8	yes	complemented
51	C₂₃×#474	C₂²	1	8	yes	complemented
52	C₂₃×#469	C₂²	1	8	yes	complemented
53	C₂₃×#466	C₂²	1	8	yes	complemented
54	C₂₃×#442	C₂²	1	8	yes	complemented
55	C₂₃×#435	C₂²	1	8	yes	complemented
56	C₂₃×#428	C₂²	1	8	yes	complemented
57	C₂₃×#427	C₂²	1	8	yes	complemented
58	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
59	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
60	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
61	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
62	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
63	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
64	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
65	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×C₄⋊C₈	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	C₂²×Q₈×C₂₃	—	2	1	no	—
78	C₂²×D₄×C₂₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
83	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
84	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₂₃	—	2	1	no	—
86	C₂³×C₄×C₂₃	—	2	1	no	—
87	C₂³×C₄×C₂₃	—	2	1	no	—
88	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
90	C₂×D₈×C₂₃	—	2	4	no	—
91	C₂×D₈×C₂₃	C₂³	1	4	yes	—
92	C₂×M₁₆×C₂₃	—	2	4	no	—
93	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
94	C₂²×C₈×C₂₃	—	2	4	no	—
95	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
97	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
98	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
100	C₂₃×C₄⋊Q₈	—	2	2	no	—
101	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
102	C₂₃×#126	—	2	8	no	—
103	C₂₃×#125	—	2	2	no	—
104	C₂₃×#125	C₂³	1	4	yes	—
105	C₂₃×#124	—	2	8	no	—
106	C₂₃×#124	—	2	8	no	—
107	C₂₃×#123	—	2	8	no	—
108	C₂₃×#121	—	2	8	no	—
109	C₂₃×#121	—	2	8	no	—
110	C₂₃×#121	—	2	2	no	—
111	C₂₃×#121	—	2	2	no	—
112	C₂₃×#121	—	2	2	no	—
113	C₂₃×#121	—	2	2	no	—
114	C₂₃×#121	C₂³	1	4	yes	—
115	C₂₃×#121	C₂³	1	4	yes	—
116	C₂₃×#121	C₂³	1	4	yes	—
117	C₂₃×#121	C₂³	1	4	yes	—
118	C₄×D₄×C₂₃	—	2	8	no	—
119	C₄×D₄×C₂₃	—	2	2	no	—
120	C₄×D₄×C₂₃	—	2	2	no	—
121	C₄×D₄×C₂₃	D₄	1	4	yes	—
122	C₄×D₄×C₂₃	C₂³	1	4	yes	—
123	C₄×D₄×C₂₃	C₂³	1	4	yes	—
124	C₄×D₄×C₂₃	C₂³	1	4	yes	—
125	C₂₃×#117	—	2	2	no	—
126	C₂₃×#117	—	2	2	no	—
127	C₂₃×#117	—	2	2	no	—
128	C₂₃×#117	—	2	8	no	—
129	C₂₃×#117	C₂³	1	4	yes	—
130	C₂₃×#117	C₂³	1	4	yes	—
131	C₂₃×#117	C₂³	1	4	yes	—
132	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
133	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
134	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
135	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	D₄	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
139	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
140	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
143	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₂₃	C₂³	1	1	yes	characteristic
145	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
146	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
147	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
149	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
152	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
153	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
154	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
155	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
156	C₂×C₄²×C₂₃	—	2	1	no	—
157	C₂×C₄²×C₂₃	—	2	1	no	—
158	C₂×C₄²×C₂₃	—	2	1	no	—
159	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
160	C₂₃×#107	C₂³	1	4	yes	—
161	C₂₃×#107	C₂³	1	4	yes	—
162	C₂₃×#107	C₂³	1	4	yes	—
163	C₂₃×#107	C₂³	1	4	yes	—
164	C₂₃×#107	C₂³	1	4	yes	—
165	C₂₃×#106	C₂³	1	4	yes	—
166	C₂₃×#106	C₂³	1	4	yes	—
167	C₂₃×#106	C₂³	1	4	yes	—
168	C₂₃×#106	C₂³	1	4	yes	—
169	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
170	C₂₃×#102	C₂³	1	4	yes	—
171	C₂₃×#102	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×C₂²⋊C₈	C₂³	1	4	yes	—
177	C₂₃×C₂²⋊C₈	C₂³	1	4	yes	—
178	C₂₃×#97	C₂³	1	4	yes	—
179	C₂⁴×C₂₃	—	2	1	no	—
180	C₂⁴×C₂₃	—	2	1	no	—
181	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
182	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
183	C₂×Q₈×C₂₃	—	2	4	no	—
184	C₂×Q₈×C₂₃	—	8	2	no	—
185	C₂×D₄×C₂₃	—	2	4	no	—
186	C₂×D₄×C₂₃	—	2	4	no	—
187	C₂×D₄×C₂₃	—	2	4	no	—
188	C₂×D₄×C₂₃	—	2	4	no	—
189	C₂×D₄×C₂₃	—	2	1	no	—
190	C₂×D₄×C₂₃	—	2	1	no	—
191	C₂×D₄×C₂₃	—	2	2	no	—
192	C₂×D₄×C₂₃	—	2	2	no	—
193	C₂×D₄×C₂₃	—	2	2	no	—
194	C₂×D₄×C₂₃	—	2	2	no	—
195	C₂×D₄×C₂₃	—	4	2	no	—
196	C₂×D₄×C₂₃	—	4	4	no	—
197	C₂×D₄×C₂₃	—	8	2	no	—
198	C₂×D₄×C₂₃	—	8	2	no	—
199	C₂×D₄×C₂₃	—	8	2	no	—
200	C₂×D₄×C₂₃	C₂×D₄	1	4	yes	—
201	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
202	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₂₃	—	2	2	no	—
204	C₂²×C₄×C₂₃	—	2	2	no	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	2	no	—
207	C₂²×C₄×C₂₃	—	2	1	no	—
208	C₂²×C₄×C₂₃	—	2	1	no	—
209	C₂²×C₄×C₂₃	—	2	1	no	—
210	C₂²×C₄×C₂₃	—	2	1	no	—
211	C₂²×C₄×C₂₃	—	2	1	no	—
212	C₂²×C₄×C₂₃	—	2	1	no	—
213	C₂²×C₄×C₂₃	—	2	4	no	—
214	C₂²×C₄×C₂₃	—	2	4	no	—
215	C₂²×C₄×C₂₃	—	2	4	no	—
216	C₂²×C₄×C₂₃	—	4	4	no	—
217	C₂²×C₄×C₂₃	—	8	2	no	—
218	C₂²×C₄×C₂₃	—	8	2	no	—
219	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
220	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
226	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
227	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
228	D₈×C₂₃	—	2	8	no	—
229	M₁₆×C₂₃	—	2	8	no	—
230	C₂×C₈×C₂₃	—	2	2	no	—
231	C₂×C₈×C₂₃	—	2	2	no	—
232	C₂×C₈×C₂₃	—	2	2	no	—
233	C₂×C₈×C₂₃	—	2	8	no	—
234	C₂×C₈×C₂₃	#41	1	4	yes	—
235	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
237	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
238	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₂₃	—	2	1	no	—
240	C₄⋊C₄×C₂₃	—	2	1	no	—
241	C₄⋊C₄×C₂₃	—	2	4	no	—
242	C₄⋊C₄×C₂₃	—	2	4	no	—
243	C₄⋊C₄×C₂₃	—	2	4	no	—
244	C₄⋊C₄×C₂₃	—	2	4	no	—
245	C₄⋊C₄×C₂₃	—	2	1	no	—
246	C₄⋊C₄×C₂₃	—	2	1	no	—
247	C₄⋊C₄×C₂₃	—	2	1	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
250	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
252	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₂₃	—	2	4	no	—
257	C₂²⋊C₄×C₂₃	—	2	4	no	—
258	C₂²⋊C₄×C₂₃	—	2	4	no	—
259	C₂²⋊C₄×C₂₃	—	2	4	no	—
260	C₂²⋊C₄×C₂₃	—	2	4	no	—
261	C₂²⋊C₄×C₂₃	—	2	4	no	—
262	C₂²⋊C₄×C₂₃	—	2	4	no	—
263	C₂²⋊C₄×C₂₃	—	2	4	no	—
264	C₂²⋊C₄×C₂₃	—	2	4	no	—
265	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
266	C₂²⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
267	C₄²×C₂₃	—	2	4	no	—
268	C₄²×C₂₃	—	2	4	no	—
269	C₄²×C₂₃	—	2	4	no	—
270	C₄²×C₂₃	C₂×D₄	1	2	yes	—
271	C₄²×C₂₃	C₂⁴	1	2	yes	—
272	C₂×#3347	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
273	C₂³×C₂₃	—	2	2	no	—
274	C₂³×C₂₃	—	2	2	no	—
275	C₂³×C₂₃	—	2	2	no	—
276	C₂³×C₂₃	—	2	2	no	—
277	C₂³×C₂₃	—	2	2	no	—
278	C₂³×C₂₃	—	2	2	no	—
279	C₂³×C₂₃	—	2	2	no	—
280	C₂³×C₂₃	—	2	2	no	—
281	C₂³×C₂₃	—	4	2	no	—
282	C₂³×C₂₃	—	4	2	no	—
283	C₂³×C₂₃	—	4	2	no	—
284	C₂³×C₂₃	—	4	2	no	—
285	C₂³×C₂₃	—	4	2	no	—
286	C₂³×C₂₃	—	4	2	no	—
287	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
288	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
289	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
290	Q₈×C₂₃	—	8	4	no	—
291	D₄×C₂₃	—	2	2	no	—
292	D₄×C₂₃	—	2	2	no	—
293	D₄×C₂₃	—	2	2	no	—
294	D₄×C₂₃	—	2	2	no	—
295	D₄×C₂₃	—	4	4	no	—
296	D₄×C₂₃	—	4	8	no	—
297	D₄×C₂₃	—	4	2	no	—
298	D₄×C₂₃	—	4	2	no	—
299	D₄×C₂₃	—	8	4	no	—
300	D₄×C₂₃	—	8	4	no	—
301	D₄×C₂₃	—	8	4	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	2	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	4	no	—
307	C₂×C₄×C₂₃	—	2	4	no	—
308	C₂×C₄×C₂₃	—	2	2	no	—
309	C₂×C₄×C₂₃	—	2	2	no	—
310	C₂×C₄×C₂₃	—	2	2	no	—
311	C₂×C₄×C₂₃	—	2	2	no	—
312	C₂×C₄×C₂₃	—	2	2	no	—
313	C₂×C₄×C₂₃	—	2	2	no	—
314	C₂×C₄×C₂₃	—	2	2	no	—
315	C₂×C₄×C₂₃	—	2	2	no	—
316	C₂×C₄×C₂₃	—	2	2	no	—
317	C₂×C₄×C₂₃	—	2	2	no	—
318	C₂×C₄×C₂₃	—	4	8	no	—
319	C₂×C₄×C₂₃	—	4	2	no	—
320	C₂×C₄×C₂₃	—	4	2	no	—
321	C₂×C₄×C₂₃	—	4	2	no	—
322	C₂×C₄×C₂₃	—	4	2	no	—
323	C₂×C₄×C₂₃	—	4	2	no	—
324	C₂×C₄×C₂₃	—	4	2	no	—
325	C₂×C₄×C₂₃	—	8	4	no	—
326	C₂×C₄×C₂₃	—	8	4	no	—
327	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
328	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
329	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
330	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
331	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
333	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
334	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
335	C₈×C₂₃	—	2	2	no	—
336	C₈×C₂₃	—	2	2	no	—
337	C₈×C₂₃	—	2	2	no	—
338	C₈×C₂₃	C₂×#41	1	4	yes	—
339	C₂×#555	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#553	C₂×C₂₃	1	1	yes	characteristic, complemented
341	#3347	C₂×C₂₃	1	16	yes	direct product factor
342	C₂×#501	C₂×C₂₃	1	1	yes	characteristic, complemented
343	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
345	C₂×#482	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#480	C₂×C₂₃	1	1	yes	characteristic, complemented
347	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
348	C₂×#474	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×#469	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂×#466	C₂×C₂₃	1	1	yes	characteristic, complemented
351	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
352	C₂×#435	C₂×C₂₃	1	1	yes	characteristic, complemented
353	C₂×#428	C₂×C₂₃	1	1	yes	characteristic, complemented
354	C₂×#427	C₂×C₂₃	1	1	yes	characteristic, complemented
355	C₂²×C₂₃	—	2	2	no	—
356	C₂²×C₂₃	—	2	2	no	—
357	C₂²×C₂₃	—	2	2	no	—
358	C₂²×C₂₃	—	2	2	no	—
359	C₂²×C₂₃	—	2	2	no	—
360	C₂²×C₂₃	—	2	2	no	—
361	C₂²×C₂₃	—	4	4	no	—
362	C₂²×C₂₃	—	4	4	no	—
363	C₂²×C₂₃	—	4	2	no	—
364	C₂²×C₂₃	—	4	2	no	—
365	C₂²×C₂₃	—	4	2	no	—
366	C₂²×C₂₃	—	4	2	no	—
367	C₂²×C₂₃	—	4	2	no	—
368	C₂²×C₂₃	—	4	2	no	—
369	C₂²×C₂₃	—	8	4	no	—
370	C₂²×C₂₃	—	8	4	no	—
371	C₂²×C₂₃	#547	1	2	yes	—
372	C₂²×C₂₃	#575	1	2	yes	—
373	C₂²×C₂₃	#576	1	2	yes	—
374	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
375	C₄×C₂₃	—	2	2	no	—
376	C₄×C₂₃	—	2	2	no	—
377	C₄×C₂₃	—	2	2	no	—
378	C₄×C₂₃	—	2	2	no	—
379	C₄×C₂₃	—	4	2	no	—
380	C₄×C₂₃	—	4	2	no	—
381	C₄×C₂₃	—	4	2	no	—
382	C₄×C₂₃	—	4	2	no	—
383	C₄×C₂₃	—	4	2	no	—
384	C₄×C₂₃	—	4	2	no	—
385	C₄×C₂₃	#547	1	2	yes	—
386	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
387	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
388	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
389	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
390	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
391	#555	—	2	4	no	—
392	#555	C₂²×C₂₃	1	8	yes	complemented
393	#553	—	2	4	no	—
394	#553	C₂²×C₂₃	1	8	yes	complemented
395	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
396	C₂×#126	—	2	1	no	—
397	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
398	C₂×#124	—	2	1	no	—
399	C₂×#124	—	2	1	no	—
400	C₂×#123	—	2	1	no	—
401	C₂×#121	—	2	1	no	—
402	C₂×#121	—	2	1	no	—
403	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×C₄×D₄	—	2	1	no	—
408	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
409	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
410	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
411	C₂×#117	—	2	1	no	—
412	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
413	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
414	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
415	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
416	#501	C₂²×C₂₃	1	8	yes	complemented
417	#482	C₂²×C₂₃	1	8	yes	complemented
418	#482	C₂²×C₂₃	1	8	yes	complemented
419	#482	C₂²×C₂₃	1	8	yes	complemented
420	#480	C₂²×C₂₃	1	8	yes	complemented
421	#478	C₂²×C₂₃	1	8	yes	complemented
422	#474	C₂²×C₂₃	1	8	yes	complemented
423	#469	C₂²×C₂₃	1	8	yes	complemented
424	#466	C₂²×C₂₃	1	8	yes	complemented
425	#442	C₂²×C₂₃	1	8	yes	complemented
426	#435	C₂²×C₂₃	1	8	yes	complemented
427	#428	C₂²×C₂₃	1	8	yes	complemented
428	#427	C₂²×C₂₃	1	8	yes	complemented
429	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
438	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
439	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
440	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
441	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
442	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
443	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
444	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
445	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
446	C₂×C₂²⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
447	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
448	C₂×C₂₃	—	4	2	no	—
449	C₂×C₂₃	—	4	2	no	—
450	C₂×C₂₃	—	8	2	no	—
451	C₂×C₂₃	—	8	2	no	—
452	C₂×C₂₃	#3347	1	4	yes	direct product factor
453	C₂×C₂₃	C₂×#547	1	1	yes	characteristic
454	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
455	C₂×C₂₃	C₂×#576	1	1	yes	characteristic
456	C₂²×Q₈	—	2	1	no	—
457	C₂²×D₄	—	2	1	no	—
458	C₂²×D₄	—	2	1	no	—
459	C₂²×D₄	—	2	1	no	—
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	D₄×C₂₃	1	1	yes	characteristic
462	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	1	no	—
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
468	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
469	C₂×D₈	—	2	4	no	—
470	C₂×D₈	C₂³×C₂₃	1	4	yes	—
471	C₂×M₁₆	—	2	4	no	—
472	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
473	C₂²×C₈	—	2	4	no	—
474	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
475	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
476	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
477	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
479	C₄⋊Q₈	—	2	2	no	—
480	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
481	#126	—	2	8	no	—
482	#125	—	2	2	no	—
483	#125	C₂³×C₂₃	1	4	yes	—
484	#124	—	2	8	no	—
485	#124	—	2	8	no	—
486	#123	—	2	8	no	—
487	#121	—	2	8	no	—
488	#121	—	2	8	no	—
489	#121	—	2	2	no	—
490	#121	—	2	2	no	—
491	#121	—	2	2	no	—
492	#121	—	2	2	no	—
493	#121	C₂³×C₂₃	1	4	yes	—
494	#121	C₂³×C₂₃	1	4	yes	—
495	#121	C₂³×C₂₃	1	4	yes	—
496	#121	C₂³×C₂₃	1	4	yes	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	2	no	—
499	C₄×D₄	—	2	2	no	—
500	C₄×D₄	D₄×C₂₃	1	4	yes	—
501	C₄×D₄	C₂³×C₂₃	1	4	yes	—
502	C₄×D₄	C₂³×C₂₃	1	4	yes	—
503	C₄×D₄	C₂³×C₂₃	1	4	yes	—
504	#117	—	2	2	no	—
505	#117	—	2	2	no	—
506	#117	—	2	2	no	—
507	#117	—	2	8	no	—
508	#117	C₂³×C₂₃	1	4	yes	—
509	#117	C₂³×C₂₃	1	4	yes	—
510	#117	C₂³×C₂₃	1	4	yes	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	—	2	2	no	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
519	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
520	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
521	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
523	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	—	2	1	no	—
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	1	no	—
529	C₂×C₂²⋊C₄	—	2	1	no	—
530	C₂×C₂²⋊C₄	—	2	1	no	—
531	C₂×C₂²⋊C₄	—	2	1	no	—
532	C₂×C₂²⋊C₄	—	2	1	no	—
533	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
534	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
535	C₂×C₄²	—	2	1	no	—
536	C₂×C₄²	—	2	1	no	—
537	C₂×C₄²	—	2	1	no	—
538	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
539	#107	C₂³×C₂₃	1	4	yes	—
540	#107	C₂³×C₂₃	1	4	yes	—
541	#107	C₂³×C₂₃	1	4	yes	—
542	#107	C₂³×C₂₃	1	4	yes	—
543	#107	C₂³×C₂₃	1	4	yes	—
544	#106	C₂³×C₂₃	1	4	yes	—
545	#106	C₂³×C₂₃	1	4	yes	—
546	#106	C₂³×C₂₃	1	4	yes	—
547	#106	C₂³×C₂₃	1	4	yes	—
548	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
549	#102	C₂³×C₂₃	1	4	yes	—
550	#102	C₂³×C₂₃	1	4	yes	—
551	#102	C₂³×C₂₃	1	4	yes	—
552	#102	C₂³×C₂₃	1	4	yes	—
553	#102	C₂³×C₂₃	1	4	yes	—
554	#102	C₂³×C₂₃	1	4	yes	—
555	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
556	C₂²⋊C₈	C₂³×C₂₃	1	4	yes	—
557	#97	C₂³×C₂₃	1	4	yes	—
558	C₂₃	C₂×#3347	1	1	yes	characteristic, direct product factor, Sylow
559	C₂⁴	—	2	1	no	—
560	C₂⁴	—	2	1	no	—
561	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
562	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
563	C₂×Q₈	—	2	4	no	—
564	C₂×Q₈	—	8	2	no	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	4	no	—
567	C₂×D₄	—	2	4	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	2	2	no	—
572	C₂×D₄	—	2	2	no	—
573	C₂×D₄	—	2	2	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	4	no	—
577	C₂×D₄	—	8	2	no	—
578	C₂×D₄	—	8	2	no	—
579	C₂×D₄	—	8	2	no	—
580	C₂×D₄	C₂×D₄×C₂₃	1	4	yes	—
581	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
582	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	1	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	1	no	—
592	C₂²×C₄	—	2	1	no	—
593	C₂²×C₄	—	2	4	no	—
594	C₂²×C₄	—	2	4	no	—
595	C₂²×C₄	—	2	4	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	8	2	no	—
598	C₂²×C₄	—	8	2	no	—
599	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
604	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
605	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
606	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
607	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
608	D₈	—	2	8	no	—
609	M₁₆	—	2	8	no	—
610	C₂×C₈	—	2	2	no	—
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	2	no	—
613	C₂×C₈	—	2	8	no	—
614	C₂×C₈	#41×C₂₃	1	4	yes	—
615	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
616	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
617	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
618	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	1	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	—	2	4	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	1	no	—
627	C₄⋊C₄	—	2	1	no	—
628	C₄⋊C₄	—	2	1	no	—
629	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
630	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
633	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
634	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	4	no	—
645	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
646	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	4	no	—
649	C₄²	—	2	4	no	—
650	C₄²	C₂×D₄×C₂₃	1	2	yes	—
651	C₄²	C₂⁴×C₂₃	1	2	yes	—
652	C₂³	—	2	2	no	—
653	C₂³	—	2	2	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	2	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	4	2	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	4	2	no	—
663	C₂³	—	4	2	no	—
664	C₂³	—	4	2	no	—
665	C₂³	—	4	2	no	—
666	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
667	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
668	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
669	Q₈	—	8	4	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	—	2	2	no	—
673	D₄	—	2	2	no	—
674	D₄	—	4	4	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	2	no	—
677	D₄	—	4	2	no	—
678	D₄	—	8	4	no	—
679	D₄	—	8	4	no	—
680	D₄	—	8	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	4	no	—
686	C₂×C₄	—	2	4	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	2	no	—
693	C₂×C₄	—	2	2	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	2	no	—
696	C₂×C₄	—	2	2	no	—
697	C₂×C₄	—	4	8	no	—
698	C₂×C₄	—	4	2	no	—
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	4	2	no	—
701	C₂×C₄	—	4	2	no	—
702	C₂×C₄	—	4	2	no	—
703	C₂×C₄	—	4	2	no	—
704	C₂×C₄	—	8	4	no	—
705	C₂×C₄	—	8	4	no	—
706	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
707	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
708	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
709	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
710	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
711	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
712	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
713	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
714	C₈	—	2	2	no	—
715	C₈	—	2	2	no	—
716	C₈	—	2	2	no	—
717	C₈	C₂×#41×C₂₃	1	4	yes	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	2	no	—
722	C₂²	—	2	2	no	—
723	C₂²	—	2	2	no	—
724	C₂²	—	4	4	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	4	2	no	—
729	C₂²	—	4	2	no	—
730	C₂²	—	4	2	no	—
731	C₂²	—	4	2	no	—
732	C₂²	—	8	4	no	—
733	C₂²	—	8	4	no	—
734	C₂²	C₂₃×#547	1	2	yes	—
735	C₂²	C₂₃×#575	1	2	yes	—
736	C₂²	C₂₃×#576	1	2	yes	—
737	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	2	2	no	—
742	C₄	—	4	2	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	2	no	—
745	C₄	—	4	2	no	—
746	C₄	—	4	2	no	—
747	C₄	—	4	2	no	—
748	C₄	C₂₃×#547	1	2	yes	—
749	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
750	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
751	C₂	—	4	2	no	—
752	C₂	—	4	2	no	—
753	C₂	—	8	2	no	—
754	C₂	—	8	2	no	—
755	C₂	C₂₃×#3347	1	4	yes	direct product factor
756	C₂	C₂×C₂₃×#547	1	1	yes	characteristic
757	C₂	C₂×C₂₃×#575	1	1	yes	characteristic
758	C₂	C₂×C₂₃×#576	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×C₄×D₄×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#555	C₂	semidirect
2. C₂×C₂₃×#553	C₂	semidirect
3. C₂₃×#3347	C₂	direct (N × H)
4. C₂×C₂₃×#501	C₂	semidirect
5. C₂×C₂₃×#482	C₂	semidirect
6. C₂×C₂₃×#482	C₂	semidirect
7. C₂×C₂₃×#482	C₂	semidirect
8. C₂×C₂₃×#480	C₂	semidirect
9. C₂×C₂₃×#478	C₂	semidirect
10. C₂×C₂₃×#474	C₂	semidirect
11. C₂×C₂₃×#469	C₂	semidirect
12. C₂×C₂₃×#466	C₂	semidirect
13. C₂×C₂₃×#442	C₂	semidirect
14. C₂×C₂₃×#435	C₂	semidirect
15. C₂×C₂₃×#428	C₂	semidirect
16. C₂×C₂₃×#427	C₂	semidirect
21. C₂₃×#555	C₂²	semidirect
23. C₂₃×#553	C₂²	semidirect
45. C₂₃×#501	C₂²	semidirect
46. C₂₃×#482	C₂²	semidirect
47. C₂₃×#482	C₂²	semidirect
48. C₂₃×#482	C₂²	semidirect
49. C₂₃×#480	C₂²	semidirect
50. C₂₃×#478	C₂²	semidirect
51. C₂₃×#474	C₂²	semidirect
52. C₂₃×#469	C₂²	semidirect
53. C₂₃×#466	C₂²	semidirect
54. C₂₃×#442	C₂²	semidirect
55. C₂₃×#435	C₂²	semidirect
56. C₂₃×#428	C₂²	semidirect
57. C₂₃×#427	C₂²	semidirect
272. C₂×#3347	C₂₃	direct (N × H)
339. C₂×#555	C₂×C₂₃	semidirect
340. C₂×#553	C₂×C₂₃	semidirect
341. #3347	C₂×C₂₃	direct (N × H)
342. C₂×#501	C₂×C₂₃	semidirect
343. C₂×#482	C₂×C₂₃	semidirect
344. C₂×#482	C₂×C₂₃	semidirect
345. C₂×#482	C₂×C₂₃	semidirect
346. C₂×#480	C₂×C₂₃	semidirect
347. C₂×#478	C₂×C₂₃	semidirect
348. C₂×#474	C₂×C₂₃	semidirect
349. C₂×#469	C₂×C₂₃	semidirect
350. C₂×#466	C₂×C₂₃	semidirect
351. C₂×#442	C₂×C₂₃	semidirect
352. C₂×#435	C₂×C₂₃	semidirect
353. C₂×#428	C₂×C₂₃	semidirect
354. C₂×#427	C₂×C₂₃	semidirect
392. #555	C₂²×C₂₃	semidirect
394. #553	C₂²×C₂₃	semidirect
416. #501	C₂²×C₂₃	semidirect
417. #482	C₂²×C₂₃	semidirect
418. #482	C₂²×C₂₃	semidirect
419. #482	C₂²×C₂₃	semidirect
420. #480	C₂²×C₂₃	semidirect
421. #478	C₂²×C₂₃	semidirect
422. #474	C₂²×C₂₃	semidirect
423. #469	C₂²×C₂₃	semidirect
424. #466	C₂²×C₂₃	semidirect
425. #442	C₂²×C₂₃	semidirect
426. #435	C₂²×C₂₃	semidirect
427. #428	C₂²×C₂₃	semidirect
428. #427	C₂²×C₂₃	semidirect
452. C₂×C₂₃	#3347	direct (N × H)
558. C₂₃	C₂×#3347	direct (N × H)
755. C₂	C₂₃×#3347	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×#555	2
C₂×C₂₃×#553	2
C₂₃×#3347	2
C₂×C₂₃×#501	2
C₂×C₂₃×#482	2
C₂×C₂₃×#480	2
C₂×C₂₃×#478	2
C₂×C₂₃×#474	2
C₂×C₂₃×#469	2
C₂×C₂₃×#466	2
C₂×C₂₃×#442	2
C₂×C₂₃×#435	2
C₂×C₂₃×#428	2
C₂×C₂₃×#427	2
C₂×#3347	23

Subgroups — C2×C23×#3347 #19208865

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3347 #19208865