Subgroups — C₂×C₂₃×#3258 #19208535

Order 5888.

1818 conjugacy classes of subgroups.

The subgroup lattice has 734 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
2	C₂×C₂₃×#541	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃×#3258	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₂₃×#479	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#475	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#478	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#468	C₂	1	1	yes	maximal, characteristic
10	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#465	C₂	1	1	yes	maximal, characteristic
12	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂₃×#464	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₂₃×#462	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₂₃×#461	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
19	C₂²×SD₁₆×C₂₃	C₂²	1	1	yes	characteristic
20	C₂²×SD₁₆×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	—
25	C₂₃×#541	—	2	4	no	—
26	C₂₃×#541	C₂²	1	8	yes	complemented
27	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
29	C₂×C₂₃×#126	—	2	1	no	—
30	C₂×C₂₃×#126	—	2	1	no	—
31	C₂×C₂₃×#126	—	2	1	no	—
32	C₂×C₂₃×#125	—	2	1	no	—
33	C₂×C₂₃×#125	—	2	1	no	—
34	C₂×C₂₃×#125	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#124	—	2	1	no	—
36	C₂×C₂₃×#124	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#123	—	2	1	no	—
38	C₂×C₂₃×C₂²⋊Q₈	—	2	1	no	—
39	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
40	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
41	C₂×C₂₃×C₂²⋊Q₈	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×Q₈×C₂₃	C₂²	1	1	yes	characteristic
45	C₂×C₄×Q₈×C₂₃	C₂²	1	1	yes	characteristic
46	C₂×C₄×D₄×C₂₃	C₂²	1	1	yes	characteristic
47	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
48	C₂₃×#479	C₂²	1	8	yes	complemented
49	C₂₃×#478	C₂²	1	8	yes	complemented
50	C₂₃×#477	C₂²	1	8	yes	complemented
51	C₂₃×#475	C₂²	1	8	yes	complemented
52	C₂₃×#470	C₂²	1	8	yes	complemented
53	C₂₃×#468	C₂²	1	8	yes	—
54	C₂₃×#467	C₂²	1	8	yes	complemented
55	C₂₃×#465	C₂²	1	8	yes	—
56	C₂₃×#464	C₂²	1	8	yes	complemented
57	C₂₃×#464	C₂²	1	8	yes	complemented
58	C₂₃×#462	C₂²	1	8	yes	complemented
59	C₂₃×#461	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	C₂₃×#424	C₂²	1	8	yes	complemented
65	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×C₂₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
69	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
70	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
71	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
72	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
73	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
74	C₂×C₂₃×#103	C₂²	1	1	yes	characteristic
75	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
76	C₂×C₂₃×#102	C₂²	1	1	yes	characteristic
77	C₂²×Q₈×C₂₃	—	2	1	no	—
78	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
79	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
80	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₂₃	—	2	1	no	—
82	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
83	C₂³×C₄×C₂₃	—	2	1	no	—
84	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
85	C₂×Q₁₆×C₂₃	—	4	2	no	—
86	C₂×Q₁₆×C₂₃	—	4	2	no	—
87	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
88	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₂₃	—	4	2	no	—
90	C₂×SD₁₆×C₂₃	—	4	2	no	—
91	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
92	C₂×SD₁₆×C₂₃	C₂³	1	4	yes	—
93	C₂×M₁₆×C₂₃	—	4	2	no	—
94	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
95	C₂²×C₈×C₂₃	—	4	2	no	—
96	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
101	C₂₃×C₄⋊Q₈	—	2	2	no	—
102	C₂₃×C₄⋊Q₈	—	2	2	no	—
103	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
105	C₂₃×#126	—	2	8	no	—
106	C₂₃×#126	—	2	8	no	—
107	C₂₃×#126	—	2	8	no	—
108	C₂₃×#125	—	2	8	no	—
109	C₂₃×#125	—	2	8	no	—
110	C₂₃×#125	—	2	2	no	—
111	C₂₃×#125	C₂³	1	4	yes	—
112	C₂₃×#124	—	2	8	no	—
113	C₂₃×#124	—	2	2	no	—
114	C₂₃×#124	C₂³	1	4	yes	—
115	C₂₃×#123	—	2	8	no	—
116	C₂₃×C₂²⋊Q₈	—	2	2	no	—
117	C₂₃×C₂²⋊Q₈	—	2	2	no	—
118	C₂₃×C₂²⋊Q₈	—	2	2	no	—
119	C₂₃×C₂²⋊Q₈	—	2	8	no	—
120	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
121	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
122	C₂₃×C₂²⋊Q₈	C₂³	1	4	yes	—
123	C₂₃×#121	—	2	2	no	—
124	C₂₃×#121	C₂³	1	4	yes	—
125	C₄×Q₈×C₂₃	—	2	2	no	—
126	C₄×Q₈×C₂₃	—	2	2	no	—
127	C₄×Q₈×C₂₃	—	2	2	no	—
128	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
129	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
130	C₄×Q₈×C₂₃	C₂³	1	4	yes	—
131	C₄×D₄×C₂₃	—	2	2	no	—
132	C₄×D₄×C₂₃	C₂³	1	4	yes	—
133	C₂₃×#117	D₄	1	4	yes	—
134	C₂₃×#117	C₂³	1	4	yes	—
135	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
136	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
137	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
138	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
139	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
140	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
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	D₄	1	1	yes	characteristic
160	C₂×C₂²⋊C₄×C₂₃	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₂₃	—	2	1	no	—
162	C₂×C₄²×C₂₃	—	2	1	no	—
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×C₄⋊C₈	C₂³	1	4	yes	—
171	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
172	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
173	C₂₃×C₄⋊C₈	C₂³	1	4	yes	—
174	C₂₃×#103	C₂³	1	4	yes	—
175	C₂₃×#103	C₂³	1	4	yes	—
176	C₂₃×#103	C₂³	1	4	yes	—
177	C₂₃×#103	C₂³	1	4	yes	—
178	C₂₃×#103	C₂³	1	4	yes	—
179	C₂₃×#103	C₂³	1	4	yes	—
180	C₂₃×#102	C₂³	1	4	yes	—
181	C₂₃×#102	C₂³	1	4	yes	—
182	C₂⁴×C₂₃	—	2	1	no	—
183	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
184	C₂×Q₈×C₂₃	—	2	1	no	—
185	C₂×Q₈×C₂₃	—	2	1	no	—
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	—	2	2	no	—
191	C₂×Q₈×C₂₃	—	2	2	no	—
192	C₂×Q₈×C₂₃	—	2	2	no	—
193	C₂×Q₈×C₂₃	—	2	2	no	—
194	C₂×Q₈×C₂₃	—	8	2	no	—
195	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
196	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
197	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
198	C₂×D₄×C₂₃	—	2	4	no	—
199	C₂×D₄×C₂₃	—	2	1	no	—
200	C₂×D₄×C₂₃	—	2	2	no	—
201	C₂×D₄×C₂₃	—	2	2	no	—
202	C₂×D₄×C₂₃	—	8	2	no	—
203	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₂₃	—	2	2	no	—
205	C₂²×C₄×C₂₃	—	2	2	no	—
206	C₂²×C₄×C₂₃	—	2	1	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	—	8	2	no	—
215	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
216	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
223	Q₁₆×C₂₃	—	4	4	no	—
224	Q₁₆×C₂₃	—	4	4	no	—
225	SD₁₆×C₂₃	—	4	4	no	—
226	SD₁₆×C₂₃	—	4	4	no	—
227	M₁₆×C₂₃	—	4	4	no	—
228	C₂×C₈×C₂₃	—	2	2	no	—
229	C₂×C₈×C₂₃	—	2	2	no	—
230	C₂×C₈×C₂₃	—	2	2	no	—
231	C₂×C₈×C₂₃	—	2	2	no	—
232	C₂×C₈×C₂₃	—	4	4	no	—
233	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
234	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
235	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
236	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
237	C₄⋊C₄×C₂₃	—	2	4	no	—
238	C₄⋊C₄×C₂₃	—	2	4	no	—
239	C₄⋊C₄×C₂₃	—	2	4	no	—
240	C₄⋊C₄×C₂₃	—	2	4	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	4	no	—
246	C₄⋊C₄×C₂₃	—	2	4	no	—
247	C₄⋊C₄×C₂₃	—	2	4	no	—
248	C₄⋊C₄×C₂₃	—	2	1	no	—
249	C₄⋊C₄×C₂₃	—	2	1	no	—
250	C₄⋊C₄×C₂₃	—	2	1	no	—
251	C₄⋊C₄×C₂₃	—	2	1	no	—
252	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
253	C₄⋊C₄×C₂₃	C₂×D₄	1	4	yes	—
254	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₂₃	C₂⁴	1	2	yes	—
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	C₂×D₄	1	2	yes	—
272	C₄²×C₂₃	C₂⁴	1	2	yes	—
273	C₄²×C₂₃	C₂⁴	1	2	yes	—
274	C₂×#3258	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	4	2	no	—
280	C₂³×C₂₃	—	4	2	no	—
281	C₂³×C₂₃	—	4	2	no	—
282	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
283	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₂₃	—	2	2	no	—
285	Q₈×C₂₃	—	2	2	no	—
286	Q₈×C₂₃	—	2	2	no	—
287	Q₈×C₂₃	—	2	2	no	—
288	Q₈×C₂₃	—	2	2	no	—
289	Q₈×C₂₃	—	2	2	no	—
290	Q₈×C₂₃	—	4	2	no	—
291	Q₈×C₂₃	—	4	2	no	—
292	Q₈×C₂₃	—	4	2	no	—
293	Q₈×C₂₃	—	8	4	no	—
294	D₄×C₂₃	—	2	2	no	—
295	D₄×C₂₃	—	2	2	no	—
296	D₄×C₂₃	—	4	2	no	—
297	D₄×C₂₃	—	8	4	no	—
298	C₂×C₄×C₂₃	—	2	2	no	—
299	C₂×C₄×C₂₃	—	2	2	no	—
300	C₂×C₄×C₂₃	—	2	2	no	—
301	C₂×C₄×C₂₃	—	2	2	no	—
302	C₂×C₄×C₂₃	—	2	2	no	—
303	C₂×C₄×C₂₃	—	2	4	no	—
304	C₂×C₄×C₂₃	—	2	2	no	—
305	C₂×C₄×C₂₃	—	2	2	no	—
306	C₂×C₄×C₂₃	—	2	2	no	—
307	C₂×C₄×C₂₃	—	2	2	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	—	4	2	no	—
314	C₂×C₄×C₂₃	—	4	2	no	—
315	C₂×C₄×C₂₃	—	4	2	no	—
316	C₂×C₄×C₂₃	—	4	2	no	—
317	C₂×C₄×C₂₃	—	4	2	no	—
318	C₂×C₄×C₂₃	—	4	2	no	—
319	C₂×C₄×C₂₃	—	4	2	no	—
320	C₂×C₄×C₂₃	—	8	4	no	—
321	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
323	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
324	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
328	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
329	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
330	C₈×C₂₃	—	2	2	no	—
331	C₈×C₂₃	—	2	2	no	—
332	C₈×C₂₃	—	2	2	no	—
333	C₈×C₂₃	—	2	2	no	—
334	C₂×#542	C₂×C₂₃	1	1	yes	characteristic
335	C₂×#541	C₂×C₂₃	1	1	yes	characteristic, complemented
336	#3258	C₂×C₂₃	1	16	yes	direct product factor
337	C₂×#479	C₂×C₂₃	1	1	yes	characteristic, complemented
338	C₂×#477	C₂×C₂₃	1	1	yes	characteristic, complemented
339	C₂×#475	C₂×C₂₃	1	1	yes	characteristic, complemented
340	C₂×#478	C₂×C₂₃	1	1	yes	characteristic, complemented
341	C₂×#470	C₂×C₂₃	1	1	yes	characteristic, complemented
342	C₂×#468	C₂×C₂₃	1	1	yes	characteristic
343	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
344	C₂×#465	C₂×C₂₃	1	1	yes	characteristic
345	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
346	C₂×#464	C₂×C₂₃	1	1	yes	characteristic, complemented
347	C₂×#462	C₂×C₂₃	1	1	yes	characteristic, complemented
348	C₂×#461	C₂×C₂₃	1	1	yes	characteristic, complemented
349	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
350	C₂²×C₂₃	—	2	2	no	—
351	C₂²×C₂₃	—	2	2	no	—
352	C₂²×C₂₃	—	2	2	no	—
353	C₂²×C₂₃	—	4	4	no	—
354	C₂²×C₂₃	—	4	2	no	—
355	C₂²×C₂₃	—	4	2	no	—
356	C₂²×C₂₃	—	4	2	no	—
357	C₂²×C₂₃	—	8	4	no	—
358	C₂²×C₂₃	#537	1	2	yes	—
359	C₂²×C₂₃	#577	1	2	yes	—
360	C₂²×C₂₃	#578	1	2	yes	—
361	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
362	C₄×C₂₃	—	2	2	no	—
363	C₄×C₂₃	—	2	2	no	—
364	C₄×C₂₃	—	2	2	no	—
365	C₄×C₂₃	—	2	2	no	—
366	C₄×C₂₃	—	2	2	no	—
367	C₄×C₂₃	—	4	2	no	—
368	C₄×C₂₃	—	4	2	no	—
369	C₄×C₂₃	—	4	2	no	—
370	C₄×C₂₃	—	4	2	no	—
371	C₄×C₂₃	—	4	2	no	—
372	C₄×C₂₃	—	4	2	no	—
373	C₄×C₂₃	—	4	2	no	—
374	C₄×C₂₃	#537	1	2	yes	—
375	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
376	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
377	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
378	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
379	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
380	C₂²×SD₁₆	C₂²×C₂₃	1	1	yes	characteristic
381	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
382	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
383	#542	—	2	4	no	—
384	#542	C₂²×C₂₃	1	8	yes	—
385	#541	—	2	4	no	—
386	#541	C₂²×C₂₃	1	8	yes	complemented
387	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
388	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
389	C₂×#126	—	2	1	no	—
390	C₂×#126	—	2	1	no	—
391	C₂×#126	—	2	1	no	—
392	C₂×#125	—	2	1	no	—
393	C₂×#125	—	2	1	no	—
394	C₂×#125	C₂²×C₂₃	1	1	yes	characteristic
395	C₂×#124	—	2	1	no	—
396	C₂×#124	C₂²×C₂₃	1	1	yes	characteristic
397	C₂×#123	—	2	1	no	—
398	C₂×C₂²⋊Q₈	—	2	1	no	—
399	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
400	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
401	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
402	C₂×#121	C₂²×C₂₃	1	1	yes	characteristic
403	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
404	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
405	C₂×C₄×Q₈	C₂²×C₂₃	1	1	yes	characteristic
406	C₂×C₄×D₄	C₂²×C₂₃	1	1	yes	characteristic
407	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
408	#479	C₂²×C₂₃	1	8	yes	complemented
409	#478	C₂²×C₂₃	1	8	yes	complemented
410	#477	C₂²×C₂₃	1	8	yes	complemented
411	#475	C₂²×C₂₃	1	8	yes	complemented
412	#470	C₂²×C₂₃	1	8	yes	complemented
413	#468	C₂²×C₂₃	1	8	yes	—
414	#467	C₂²×C₂₃	1	8	yes	complemented
415	#465	C₂²×C₂₃	1	8	yes	—
416	#464	C₂²×C₂₃	1	8	yes	complemented
417	#464	C₂²×C₂₃	1	8	yes	complemented
418	#462	C₂²×C₂₃	1	8	yes	complemented
419	#461	C₂²×C₂₃	1	8	yes	complemented
420	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
421	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
422	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
423	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
424	#424	C₂²×C₂₃	1	8	yes	complemented
425	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
426	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
427	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
428	C₂×C₄⋊C₈	C₂²×C₂₃	1	1	yes	characteristic
429	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
430	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
431	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
432	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
433	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
434	C₂×#103	C₂²×C₂₃	1	1	yes	characteristic
435	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
436	C₂×#102	C₂²×C₂₃	1	1	yes	characteristic
437	C₂×C₂₃	—	4	2	no	—
438	C₂×C₂₃	—	8	2	no	—
439	C₂×C₂₃	#3258	1	4	yes	direct product factor
440	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
441	C₂×C₂₃	C₂×#577	1	1	yes	characteristic
442	C₂×C₂₃	C₂×#578	1	1	yes	characteristic
443	C₂²×Q₈	—	2	1	no	—
444	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
445	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
446	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
447	C₂²×D₄	—	2	1	no	—
448	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
449	C₂³×C₄	—	2	1	no	—
450	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
451	C₂×Q₁₆	—	4	2	no	—
452	C₂×Q₁₆	—	4	2	no	—
453	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
454	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
455	C₂×SD₁₆	—	4	2	no	—
456	C₂×SD₁₆	—	4	2	no	—
457	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
458	C₂×SD₁₆	C₂³×C₂₃	1	4	yes	—
459	C₂×M₁₆	—	4	2	no	—
460	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
461	C₂²×C₈	—	4	2	no	—
462	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
463	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
464	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
465	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
466	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	—	2	2	no	—
469	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
470	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
471	#126	—	2	8	no	—
472	#126	—	2	8	no	—
473	#126	—	2	8	no	—
474	#125	—	2	8	no	—
475	#125	—	2	8	no	—
476	#125	—	2	2	no	—
477	#125	C₂³×C₂₃	1	4	yes	—
478	#124	—	2	8	no	—
479	#124	—	2	2	no	—
480	#124	C₂³×C₂₃	1	4	yes	—
481	#123	—	2	8	no	—
482	C₂²⋊Q₈	—	2	2	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	—	2	8	no	—
486	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
487	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
488	C₂²⋊Q₈	C₂³×C₂₃	1	4	yes	—
489	#121	—	2	2	no	—
490	#121	C₂³×C₂₃	1	4	yes	—
491	C₄×Q₈	—	2	2	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	2	no	—
494	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
495	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
496	C₄×Q₈	C₂³×C₂₃	1	4	yes	—
497	C₄×D₄	—	2	2	no	—
498	C₄×D₄	C₂³×C₂₃	1	4	yes	—
499	#117	D₄×C₂₃	1	4	yes	—
500	#117	C₂³×C₂₃	1	4	yes	—
501	C₂×C₄⋊C₄	—	2	1	no	—
502	C₂×C₄⋊C₄	—	2	1	no	—
503	C₂×C₄⋊C₄	—	2	1	no	—
504	C₂×C₄⋊C₄	—	2	1	no	—
505	C₂×C₄⋊C₄	—	2	1	no	—
506	C₂×C₄⋊C₄	—	2	1	no	—
507	C₂×C₄⋊C₄	—	2	1	no	—
508	C₂×C₄⋊C₄	—	2	1	no	—
509	C₂×C₄⋊C₄	—	2	1	no	—
510	C₂×C₄⋊C₄	—	2	1	no	—
511	C₂×C₄⋊C₄	—	2	1	no	—
512	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
513	C₂×C₄⋊C₄	D₄×C₂₃	1	1	yes	characteristic
514	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
515	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
516	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
517	C₂×C₄⋊C₄	C₂³×C₂₃	1	1	yes	characteristic
518	C₂×C₂²⋊C₄	—	2	1	no	—
519	C₂×C₂²⋊C₄	—	2	1	no	—
520	C₂×C₂²⋊C₄	—	2	1	no	—
521	C₂×C₂²⋊C₄	—	2	1	no	—
522	C₂×C₂²⋊C₄	—	2	1	no	—
523	C₂×C₂²⋊C₄	—	2	1	no	—
524	C₂×C₂²⋊C₄	—	2	1	no	—
525	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	D₄×C₂₃	1	1	yes	characteristic
527	C₂×C₄²	—	2	1	no	—
528	C₂×C₄²	—	2	1	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
531	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
532	#107	C₂³×C₂₃	1	4	yes	—
533	#107	C₂³×C₂₃	1	4	yes	—
534	#106	C₂³×C₂₃	1	4	yes	—
535	#106	C₂³×C₂₃	1	4	yes	—
536	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
537	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
538	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
539	C₄⋊C₈	C₂³×C₂₃	1	4	yes	—
540	#103	C₂³×C₂₃	1	4	yes	—
541	#103	C₂³×C₂₃	1	4	yes	—
542	#103	C₂³×C₂₃	1	4	yes	—
543	#103	C₂³×C₂₃	1	4	yes	—
544	#103	C₂³×C₂₃	1	4	yes	—
545	#103	C₂³×C₂₃	1	4	yes	—
546	#102	C₂³×C₂₃	1	4	yes	—
547	#102	C₂³×C₂₃	1	4	yes	—
548	C₂₃	C₂×#3258	1	1	yes	characteristic, direct product factor, Sylow
549	C₂⁴	—	2	1	no	—
550	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	2	no	—
557	C₂×Q₈	—	2	2	no	—
558	C₂×Q₈	—	2	2	no	—
559	C₂×Q₈	—	2	2	no	—
560	C₂×Q₈	—	2	2	no	—
561	C₂×Q₈	—	8	2	no	—
562	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
563	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
564	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
565	C₂×D₄	—	2	4	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	2	no	—
568	C₂×D₄	—	2	2	no	—
569	C₂×D₄	—	8	2	no	—
570	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	1	no	—
578	C₂²×C₄	—	2	1	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	4	no	—
581	C₂²×C₄	—	8	2	no	—
582	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
583	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
584	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
585	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
586	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
587	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
588	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
589	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
590	Q₁₆	—	4	4	no	—
591	Q₁₆	—	4	4	no	—
592	SD₁₆	—	4	4	no	—
593	SD₁₆	—	4	4	no	—
594	M₁₆	—	4	4	no	—
595	C₂×C₈	—	2	2	no	—
596	C₂×C₈	—	2	2	no	—
597	C₂×C₈	—	2	2	no	—
598	C₂×C₈	—	2	2	no	—
599	C₂×C₈	—	4	4	no	—
600	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
601	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
602	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
603	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
604	C₄⋊C₄	—	2	4	no	—
605	C₄⋊C₄	—	2	4	no	—
606	C₄⋊C₄	—	2	4	no	—
607	C₄⋊C₄	—	2	4	no	—
608	C₄⋊C₄	—	2	4	no	—
609	C₄⋊C₄	—	2	4	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	4	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	—	2	1	no	—
619	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
620	C₄⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
621	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
622	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
623	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
624	C₄⋊C₄	C₂⁴×C₂₃	1	2	yes	—
625	C₂²⋊C₄	—	2	4	no	—
626	C₂²⋊C₄	—	2	4	no	—
627	C₂²⋊C₄	—	2	4	no	—
628	C₂²⋊C₄	—	2	4	no	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
633	C₂²⋊C₄	C₂×D₄×C₂₃	1	4	yes	—
634	C₄²	—	2	4	no	—
635	C₄²	—	2	4	no	—
636	C₄²	—	2	4	no	—
637	C₄²	C₂×D₄×C₂₃	1	2	yes	—
638	C₄²	C₂×D₄×C₂₃	1	2	yes	—
639	C₄²	C₂⁴×C₂₃	1	2	yes	—
640	C₄²	C₂⁴×C₂₃	1	2	yes	—
641	C₂³	—	2	2	no	—
642	C₂³	—	2	2	no	—
643	C₂³	—	2	2	no	—
644	C₂³	—	2	2	no	—
645	C₂³	—	4	2	no	—
646	C₂³	—	4	2	no	—
647	C₂³	—	4	2	no	—
648	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
649	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
650	Q₈	—	2	2	no	—
651	Q₈	—	2	2	no	—
652	Q₈	—	2	2	no	—
653	Q₈	—	2	2	no	—
654	Q₈	—	2	2	no	—
655	Q₈	—	2	2	no	—
656	Q₈	—	4	2	no	—
657	Q₈	—	4	2	no	—
658	Q₈	—	4	2	no	—
659	Q₈	—	8	4	no	—
660	D₄	—	2	2	no	—
661	D₄	—	2	2	no	—
662	D₄	—	4	2	no	—
663	D₄	—	8	4	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	2	2	no	—
668	C₂×C₄	—	2	2	no	—
669	C₂×C₄	—	2	2	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	4	no	—
672	C₂×C₄	—	2	2	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	2	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	2	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	4	2	no	—
680	C₂×C₄	—	4	2	no	—
681	C₂×C₄	—	4	2	no	—
682	C₂×C₄	—	4	2	no	—
683	C₂×C₄	—	4	2	no	—
684	C₂×C₄	—	4	2	no	—
685	C₂×C₄	—	4	2	no	—
686	C₂×C₄	—	8	4	no	—
687	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
689	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
690	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
692	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
693	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
694	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
695	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
696	C₈	—	2	2	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	2	no	—
699	C₈	—	2	2	no	—
700	C₂²	—	2	2	no	—
701	C₂²	—	2	2	no	—
702	C₂²	—	2	2	no	—
703	C₂²	—	4	4	no	—
704	C₂²	—	4	2	no	—
705	C₂²	—	4	2	no	—
706	C₂²	—	4	2	no	—
707	C₂²	—	8	4	no	—
708	C₂²	C₂₃×#537	1	2	yes	—
709	C₂²	C₂₃×#577	1	2	yes	—
710	C₂²	C₂₃×#578	1	2	yes	—
711	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
712	C₄	—	2	2	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	2	no	—
715	C₄	—	2	2	no	—
716	C₄	—	2	2	no	—
717	C₄	—	4	2	no	—
718	C₄	—	4	2	no	—
719	C₄	—	4	2	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	2	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	C₂₃×#537	1	2	yes	—
725	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
726	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
727	C₂	—	4	2	no	—
728	C₂	—	8	2	no	—
729	C₂	C₂₃×#3258	1	4	yes	direct product factor
730	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
731	C₂	C₂×C₂₃×#577	1	1	yes	characteristic
732	C₂	C₂×C₂₃×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#121	C₂²
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
2. C₂×C₂₃×#541	C₂	semidirect
3. C₂₃×#3258	C₂	direct (N × H)
4. C₂×C₂₃×#479	C₂	semidirect
5. C₂×C₂₃×#477	C₂	semidirect
6. C₂×C₂₃×#475	C₂	semidirect
7. C₂×C₂₃×#478	C₂	semidirect
8. C₂×C₂₃×#470	C₂	semidirect
10. C₂×C₂₃×#467	C₂	semidirect
12. C₂×C₂₃×#464	C₂	semidirect
13. C₂×C₂₃×#464	C₂	semidirect
14. C₂×C₂₃×#462	C₂	semidirect
15. C₂×C₂₃×#461	C₂	semidirect
16. C₂×C₂₃×#424	C₂	semidirect
26. C₂₃×#541	C₂²	semidirect
48. C₂₃×#479	C₂²	semidirect
49. C₂₃×#478	C₂²	semidirect
50. C₂₃×#477	C₂²	semidirect
51. C₂₃×#475	C₂²	semidirect
52. C₂₃×#470	C₂²	semidirect
54. C₂₃×#467	C₂²	semidirect
56. C₂₃×#464	C₂²	semidirect
57. C₂₃×#464	C₂²	semidirect
58. C₂₃×#462	C₂²	semidirect
59. C₂₃×#461	C₂²	semidirect
64. C₂₃×#424	C₂²	semidirect
274. C₂×#3258	C₂₃	direct (N × H)
335. C₂×#541	C₂×C₂₃	semidirect
336. #3258	C₂×C₂₃	direct (N × H)
337. C₂×#479	C₂×C₂₃	semidirect
338. C₂×#477	C₂×C₂₃	semidirect
339. C₂×#475	C₂×C₂₃	semidirect
340. C₂×#478	C₂×C₂₃	semidirect
341. C₂×#470	C₂×C₂₃	semidirect
343. C₂×#467	C₂×C₂₃	semidirect
345. C₂×#464	C₂×C₂₃	semidirect
346. C₂×#464	C₂×C₂₃	semidirect
347. C₂×#462	C₂×C₂₃	semidirect
348. C₂×#461	C₂×C₂₃	semidirect
349. C₂×#424	C₂×C₂₃	semidirect
386. #541	C₂²×C₂₃	semidirect
408. #479	C₂²×C₂₃	semidirect
409. #478	C₂²×C₂₃	semidirect
410. #477	C₂²×C₂₃	semidirect
411. #475	C₂²×C₂₃	semidirect
412. #470	C₂²×C₂₃	semidirect
414. #467	C₂²×C₂₃	semidirect
416. #464	C₂²×C₂₃	semidirect
417. #464	C₂²×C₂₃	semidirect
418. #462	C₂²×C₂₃	semidirect
419. #461	C₂²×C₂₃	semidirect
424. #424	C₂²×C₂₃	semidirect
439. C₂×C₂₃	#3258	direct (N × H)
548. C₂₃	C₂×#3258	direct (N × H)
729. C₂	C₂₃×#3258	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×#541	2
C₂₃×#3258	2
C₂×C₂₃×#479	2
C₂×C₂₃×#477	2
C₂×C₂₃×#475	2
C₂×C₂₃×#478	2
C₂×C₂₃×#470	2
C₂×C₂₃×#468	2
C₂×C₂₃×#467	2
C₂×C₂₃×#465	2
C₂×C₂₃×#464	2
C₂×C₂₃×#462	2
C₂×C₂₃×#461	2
C₂×C₂₃×#424	2
C₂×#3258	23

Subgroups — C2×C23×#3258 #19208535

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3258 #19208535