Subgroups — C₂×C₂₃×#3250 #19208525

Order 5888.

1962 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂₃×#529	C₂	1	2	yes	maximal, complemented
2	C₂₃×#3250	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#479	C₂	1	2	yes	maximal, complemented
4	C₂×C₂₃×#478	C₂	1	2	yes	maximal, complemented
5	C₂×C₂₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₂₃×#466	C₂	1	1	yes	maximal, characteristic
7	C₂×C₂₃×#465	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#463	C₂	1	2	yes	maximal, complemented
10	C₂²×C₂₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
13	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂₃×#529	—	2	8	no	—
17	C₂₃×#529	C₂²	1	16	yes	complemented
18	C₂×C₂₃×#126	—	2	2	no	—
19	C₂×C₂₃×#125	C₂²	1	2	yes	—
20	C₂×C₂₃×#124	C₂²	1	2	yes	—
21	C₂×C₂₃×#123	—	2	2	no	—
22	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₂×C₂₃×#121	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₂₃	—	2	2	no	—
26	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
27	C₂×C₂₃×#117	—	2	2	no	—
28	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
29	C₂₃×#479	C₂²	1	16	yes	complemented
30	C₂₃×#478	C₂²	1	16	yes	complemented
31	C₂₃×#467	C₂²	1	8	yes	complemented
32	C₂₃×#466	C₂²	1	8	yes	—
33	C₂₃×#465	C₂²	1	16	yes	complemented
34	C₂₃×#464	C₂²	1	16	yes	complemented
35	C₂₃×#463	C₂²	1	16	yes	complemented
36	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
37	C₂×C₂₃×#107	C₂²	1	1	yes	characteristic
38	C₂×C₂₃×#106	C₂²	1	2	yes	—
39	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
40	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₂₃×C₄⋊C₈	C₂²	1	8	yes	complemented
42	C₂×C₂₃×#103	C₂²	1	2	yes	—
43	C₂×C₂₃×#103	C₂²	1	2	yes	—
44	C₂×C₂₃×#102	C₂²	1	2	yes	—
45	C₂×C₂₃×#102	C₂²	1	2	yes	—
46	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
47	C₂²×D₄×C₂₃	—	2	2	no	—
48	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
49	C₂³×C₄×C₂₃	—	2	2	no	—
50	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
53	C₂×Q₁₆×C₂₃	—	4	2	no	—
54	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
55	C₂×SD₁₆×C₂₃	—	4	4	no	—
56	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
57	C₂×D₈×C₂₃	—	4	2	no	—
58	C₂×D₈×C₂₃	C₂³	1	4	yes	—
59	C₂²×C₈×C₂₃	—	4	2	no	—
60	C₂²×C₈×C₂₃	—	4	2	no	—
61	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
63	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
65	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
66	C₂₃×#126	—	2	16	no	—
67	C₂₃×#125	—	2	4	no	—
68	C₂₃×#125	C₂³	1	8	yes	—
69	C₂₃×#124	—	2	4	no	—
70	C₂₃×#124	C₂³	1	8	yes	—
71	C₂₃×#123	—	2	16	no	—
72	C₂₃×C₂²⋊Q₈	—	2	4	no	—
73	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
74	C₂₃×#121	—	2	4	no	—
75	C₂₃×#121	C₂³	1	8	yes	—
76	C₄×Q₈×C₂₃	—	2	4	no	—
77	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
78	C₄×D₄×C₂₃	—	2	16	no	—
79	C₄×D₄×C₂₃	—	2	4	no	—
80	C₄×D₄×C₂₃	C₂³	1	8	yes	—
81	C₂₃×#117	—	2	16	no	—
82	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
83	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
84	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
85	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
86	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
89	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
93	C₂×C₄²×C₂₃	—	2	2	no	—
94	C₂×C₄²×C₂₃	D₄	1	2	yes	—
95	C₂×C₄²×C₂₃	D₄	1	4	yes	—
96	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
97	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
98	C₂₃×#107	C₂³	1	4	yes	—
99	C₂₃×#107	C₂³	1	4	yes	—
100	C₂₃×#106	C₂³	1	8	yes	—
101	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
102	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
103	C₂₃×#103	C₂³	1	8	yes	—
104	C₂₃×#103	C₂³	1	8	yes	—
105	C₂₃×#102	C₂³	1	8	yes	—
106	C₂₃×#102	C₂³	1	8	yes	—
107	C₂⁴×C₂₃	—	2	2	no	—
108	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₂₃	—	2	2	no	—
110	C₂×Q₈×C₂₃	—	2	4	no	—
111	C₂×Q₈×C₂₃	—	2	4	no	—
112	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
113	C₂×D₄×C₂₃	—	2	8	no	—
114	C₂×D₄×C₂₃	—	2	2	no	—
115	C₂×D₄×C₂₃	—	2	4	no	—
116	C₂×D₄×C₂₃	—	2	4	no	—
117	C₂×D₄×C₂₃	—	4	8	no	—
118	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
119	C₂²×C₄×C₂₃	—	2	4	no	—
120	C₂²×C₄×C₂₃	—	2	2	no	—
121	C₂²×C₄×C₂₃	—	2	2	no	—
122	C₂²×C₄×C₂₃	—	2	2	no	—
123	C₂²×C₄×C₂₃	—	2	2	no	—
124	C₂²×C₄×C₂₃	—	2	2	no	—
125	C₂²×C₄×C₂₃	—	2	8	no	—
126	C₂²×C₄×C₂₃	—	4	2	no	—
127	C₂²×C₄×C₂₃	—	4	8	no	—
128	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
135	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
136	Q₁₆×C₂₃	—	4	4	no	—
137	SD₁₆×C₂₃	—	4	8	no	—
138	D₈×C₂₃	—	4	4	no	—
139	C₂×C₈×C₂₃	—	2	2	no	—
140	C₂×C₈×C₂₃	—	2	4	no	—
141	C₂×C₈×C₂₃	—	2	2	no	—
142	C₂×C₈×C₂₃	—	4	4	no	—
143	C₂×C₈×C₂₃	—	4	4	no	—
144	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
145	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
146	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
147	C₄⋊C₄×C₂₃	—	2	8	no	—
148	C₄⋊C₄×C₂₃	—	2	8	no	—
149	C₄⋊C₄×C₂₃	—	2	8	no	—
150	C₄⋊C₄×C₂₃	—	2	8	no	—
151	C₄⋊C₄×C₂₃	—	2	2	no	—
152	C₄⋊C₄×C₂₃	—	2	2	no	—
153	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
154	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
155	C₂²⋊C₄×C₂₃	—	2	8	no	—
156	C₂²⋊C₄×C₂₃	—	2	8	no	—
157	C₂²⋊C₄×C₂₃	—	2	8	no	—
158	C₂²⋊C₄×C₂₃	—	2	8	no	—
159	C₂²⋊C₄×C₂₃	—	2	8	no	—
160	C₄²×C₂₃	—	2	8	no	—
161	C₄²×C₂₃	C₂×D₄	1	8	yes	—
162	C₄²×C₂₃	C₂×D₄	1	4	yes	—
163	C₄²×C₂₃	C₂⁴	1	4	yes	—
164	C₂×#3250	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₂₃	—	2	2	no	—
166	C₂³×C₂₃	—	2	2	no	—
167	C₂³×C₂₃	—	2	4	no	—
168	C₂³×C₂₃	—	4	4	no	—
169	C₂³×C₂₃	—	4	4	no	—
170	C₂³×C₂₃	—	4	4	no	—
171	C₂³×C₂₃	#135	1	4	yes	—
172	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
173	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
174	Q₈×C₂₃	—	2	4	no	—
175	Q₈×C₂₃	—	2	4	no	—
176	Q₈×C₂₃	—	4	4	no	—
177	D₄×C₂₃	—	2	4	no	—
178	D₄×C₂₃	—	2	4	no	—
179	D₄×C₂₃	—	4	16	no	—
180	D₄×C₂₃	—	4	4	no	—
181	C₂×C₄×C₂₃	—	2	2	no	—
182	C₂×C₄×C₂₃	—	2	8	no	—
183	C₂×C₄×C₂₃	—	2	4	no	—
184	C₂×C₄×C₂₃	—	2	4	no	—
185	C₂×C₄×C₂₃	—	2	4	no	—
186	C₂×C₄×C₂₃	—	2	2	no	—
187	C₂×C₄×C₂₃	—	2	2	no	—
188	C₂×C₄×C₂₃	—	2	4	no	—
189	C₂×C₄×C₂₃	—	2	4	no	—
190	C₂×C₄×C₂₃	—	2	4	no	—
191	C₂×C₄×C₂₃	—	4	4	no	—
192	C₂×C₄×C₂₃	—	4	16	no	—
193	C₂×C₄×C₂₃	—	4	4	no	—
194	C₂×C₄×C₂₃	—	4	4	no	—
195	C₂×C₄×C₂₃	—	4	4	no	—
196	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
199	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₂₃	H(5,𝔽₂)	1	2	yes	—
201	C₂×C₄×C₂₃	2₋¹⁺⁴	1	2	yes	—
202	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
203	C₈×C₂₃	—	2	2	no	—
204	C₈×C₂₃	—	2	4	no	—
205	C₈×C₂₃	—	2	2	no	—
206	C₂×#529	C₂×C₂₃	1	2	yes	complemented
207	#3250	C₂×C₂₃	1	16	yes	direct product factor
208	C₂×#479	C₂×C₂₃	1	2	yes	complemented
209	C₂×#478	C₂×C₂₃	1	2	yes	complemented
210	C₂×#467	C₂×C₂₃	1	1	yes	characteristic, complemented
211	C₂×#466	C₂×C₂₃	1	1	yes	characteristic
212	C₂×#465	C₂×C₂₃	1	2	yes	complemented
213	C₂×#464	C₂×C₂₃	1	2	yes	complemented
214	C₂×#463	C₂×C₂₃	1	2	yes	complemented
215	C₂²×C₄⋊C₈	C₂×C₂₃	1	1	yes	characteristic, complemented
216	C₂²×C₂₃	—	2	2	no	—
217	C₂²×C₂₃	—	2	8	no	—
218	C₂²×C₂₃	—	2	2	no	—
219	C₂²×C₂₃	—	4	4	no	—
220	C₂²×C₂₃	—	4	4	no	—
221	C₂²×C₂₃	—	4	4	no	—
222	C₂²×C₂₃	—	8	8	no	—
223	C₂²×C₂₃	#537	1	2	yes	—
224	C₂²×C₂₃	C₂×#135	1	4	yes	—
225	C₂²×C₂₃	C₂×#135	1	2	yes	—
226	C₂²×C₂₃	#575	1	2	yes	—
227	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
228	C₄×C₂₃	—	2	2	no	—
229	C₄×C₂₃	—	2	4	no	—
230	C₄×C₂₃	—	2	4	no	—
231	C₄×C₂₃	—	4	4	no	—
232	C₄×C₂₃	—	4	4	no	—
233	C₄×C₂₃	—	4	4	no	—
234	C₄×C₂₃	#537	1	2	yes	—
235	C₄×C₂₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
236	C₄×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
237	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
238	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
239	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
240	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
241	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
242	#529	—	2	8	no	—
243	#529	C₂²×C₂₃	1	16	yes	complemented
244	C₂×#126	—	2	2	no	—
245	C₂×#125	C₂²×C₂₃	1	2	yes	—
246	C₂×#124	C₂²×C₂₃	1	2	yes	—
247	C₂×#123	—	2	2	no	—
248	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
249	C₂×#121	C₂²×C₂₃	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
251	C₂×C₄×D₄	—	2	2	no	—
252	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
253	C₂×#117	—	2	2	no	—
254	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
255	#479	C₂²×C₂₃	1	16	yes	complemented
256	#478	C₂²×C₂₃	1	16	yes	complemented
257	#467	C₂²×C₂₃	1	8	yes	complemented
258	#466	C₂²×C₂₃	1	8	yes	—
259	#465	C₂²×C₂₃	1	16	yes	complemented
260	#464	C₂²×C₂₃	1	16	yes	complemented
261	#463	C₂²×C₂₃	1	16	yes	complemented
262	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
263	C₂×#107	C₂²×C₂₃	1	1	yes	characteristic
264	C₂×#106	C₂²×C₂₃	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
266	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
267	C₂×C₄⋊C₈	C₂²×C₂₃	1	8	yes	complemented
268	C₂×#103	C₂²×C₂₃	1	2	yes	—
269	C₂×#103	C₂²×C₂₃	1	2	yes	—
270	C₂×#102	C₂²×C₂₃	1	2	yes	—
271	C₂×#102	C₂²×C₂₃	1	2	yes	—
272	C₂×C₂₃	—	2	4	no	—
273	C₂×C₂₃	—	8	4	no	—
274	C₂×C₂₃	#3250	1	4	yes	direct product factor
275	C₂×C₂₃	C₂×#537	1	1	yes	characteristic
276	C₂×C₂₃	C₂²×#135	1	1	yes	characteristic
277	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
279	C₂²×D₄	—	2	2	no	—
280	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
281	C₂³×C₄	—	2	2	no	—
282	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
283	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
285	C₂×Q₁₆	—	4	2	no	—
286	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
287	C₂×SD₁₆	—	4	4	no	—
288	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
289	C₂×D₈	—	4	2	no	—
290	C₂×D₈	C₂³×C₂₃	1	4	yes	—
291	C₂²×C₈	—	4	2	no	—
292	C₂²×C₈	—	4	2	no	—
293	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
295	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
297	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
298	#126	—	2	16	no	—
299	#125	—	2	4	no	—
300	#125	C₂³×C₂₃	1	8	yes	—
301	#124	—	2	4	no	—
302	#124	C₂³×C₂₃	1	8	yes	—
303	#123	—	2	16	no	—
304	C₂²⋊Q₈	—	2	4	no	—
305	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
306	#121	—	2	4	no	—
307	#121	C₂³×C₂₃	1	8	yes	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
310	C₄×D₄	—	2	16	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	C₂³×C₂₃	1	8	yes	—
313	#117	—	2	16	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	D₄×C₂₃	1	2	yes	—
327	C₂×C₄²	D₄×C₂₃	1	4	yes	—
328	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
329	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
330	#107	C₂³×C₂₃	1	4	yes	—
331	#107	C₂³×C₂₃	1	4	yes	—
332	#106	C₂³×C₂₃	1	8	yes	—
333	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
334	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
335	#103	C₂³×C₂₃	1	8	yes	—
336	#103	C₂³×C₂₃	1	8	yes	—
337	#102	C₂³×C₂₃	1	8	yes	—
338	#102	C₂³×C₂₃	1	8	yes	—
339	C₂₃	C₂×#3250	1	1	yes	characteristic, direct product factor, Sylow
340	C₂⁴	—	2	2	no	—
341	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	4	8	no	—
351	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	8	no	—
359	C₂²×C₄	—	4	2	no	—
360	C₂²×C₄	—	4	8	no	—
361	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
362	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
363	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
364	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
366	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
369	Q₁₆	—	4	4	no	—
370	SD₁₆	—	4	8	no	—
371	D₈	—	4	4	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	4	4	no	—
376	C₂×C₈	—	4	4	no	—
377	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
378	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
379	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
380	C₄⋊C₄	—	2	8	no	—
381	C₄⋊C₄	—	2	8	no	—
382	C₄⋊C₄	—	2	8	no	—
383	C₄⋊C₄	—	2	8	no	—
384	C₄⋊C₄	—	2	2	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
387	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	—	2	8	no	—
391	C₂²⋊C₄	—	2	8	no	—
392	C₂²⋊C₄	—	2	8	no	—
393	C₄²	—	2	8	no	—
394	C₄²	C₂×D₄×C₂₃	1	8	yes	—
395	C₄²	C₂×D₄×C₂₃	1	4	yes	—
396	C₄²	C₂⁴×C₂₃	1	4	yes	—
397	C₂³	—	2	2	no	—
398	C₂³	—	2	2	no	—
399	C₂³	—	2	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	—	4	4	no	—
402	C₂³	—	4	4	no	—
403	C₂³	C₂₃×#135	1	4	yes	—
404	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
405	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	4	no	—
409	D₄	—	2	4	no	—
410	D₄	—	2	4	no	—
411	D₄	—	4	16	no	—
412	D₄	—	4	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	4	4	no	—
424	C₂×C₄	—	4	16	no	—
425	C₂×C₄	—	4	4	no	—
426	C₂×C₄	—	4	4	no	—
427	C₂×C₄	—	4	4	no	—
428	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
429	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
430	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
431	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
432	C₂×C₄	C₂₃×H(5,𝔽₂)	1	2	yes	—
433	C₂×C₄	C₂₃×2₋¹⁺⁴	1	2	yes	—
434	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
435	C₈	—	2	2	no	—
436	C₈	—	2	4	no	—
437	C₈	—	2	2	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	8	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	8	8	no	—
445	C₂²	C₂₃×#537	1	2	yes	—
446	C₂²	C₂×C₂₃×#135	1	4	yes	—
447	C₂²	C₂×C₂₃×#135	1	2	yes	—
448	C₂²	C₂₃×#575	1	2	yes	—
449	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
450	C₄	—	2	2	no	—
451	C₄	—	2	4	no	—
452	C₄	—	2	4	no	—
453	C₄	—	4	4	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	C₂₃×#537	1	2	yes	—
457	C₄	C₂×C₂₃×H(5,𝔽₂)	1	1	yes	characteristic
458	C₄	C₂×C₂₃×2₋¹⁺⁴	1	1	yes	characteristic
459	C₂	—	2	4	no	—
460	C₂	—	8	4	no	—
461	C₂	C₂₃×#3250	1	4	yes	direct product factor
462	C₂	C₂×C₂₃×#537	1	1	yes	characteristic
463	C₂	C₂²×C₂₃×#135	1	1	yes	characteristic
464	C₂	C₂×C₂₃×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂²×C₄²×C₂₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₂₃×#529	C₂	semidirect
2. C₂₃×#3250	C₂	direct (N × H)
3. C₂×C₂₃×#479	C₂	semidirect
4. C₂×C₂₃×#478	C₂	semidirect
5. C₂×C₂₃×#467	C₂	semidirect
7. C₂×C₂₃×#465	C₂	semidirect
8. C₂×C₂₃×#464	C₂	semidirect
9. C₂×C₂₃×#463	C₂	semidirect
10. C₂²×C₂₃×C₄⋊C₈	C₂	semidirect
17. C₂₃×#529	C₂²	semidirect
29. C₂₃×#479	C₂²	semidirect
30. C₂₃×#478	C₂²	semidirect
31. C₂₃×#467	C₂²	semidirect
33. C₂₃×#465	C₂²	semidirect
34. C₂₃×#464	C₂²	semidirect
35. C₂₃×#463	C₂²	semidirect
41. C₂×C₂₃×C₄⋊C₈	C₂²	semidirect
164. C₂×#3250	C₂₃	direct (N × H)
206. C₂×#529	C₂×C₂₃	semidirect
207. #3250	C₂×C₂₃	direct (N × H)
208. C₂×#479	C₂×C₂₃	semidirect
209. C₂×#478	C₂×C₂₃	semidirect
210. C₂×#467	C₂×C₂₃	semidirect
212. C₂×#465	C₂×C₂₃	semidirect
213. C₂×#464	C₂×C₂₃	semidirect
214. C₂×#463	C₂×C₂₃	semidirect
215. C₂²×C₄⋊C₈	C₂×C₂₃	semidirect
243. #529	C₂²×C₂₃	semidirect
255. #479	C₂²×C₂₃	semidirect
256. #478	C₂²×C₂₃	semidirect
257. #467	C₂²×C₂₃	semidirect
259. #465	C₂²×C₂₃	semidirect
260. #464	C₂²×C₂₃	semidirect
261. #463	C₂²×C₂₃	semidirect
267. C₂×C₄⋊C₈	C₂²×C₂₃	semidirect
274. C₂×C₂₃	#3250	direct (N × H)
339. C₂₃	C₂×#3250	direct (N × H)
461. C₂	C₂₃×#3250	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×#529	2
C₂₃×#3250	2
C₂×C₂₃×#479	2
C₂×C₂₃×#478	2
C₂×C₂₃×#467	2
C₂×C₂₃×#466	2
C₂×C₂₃×#465	2
C₂×C₂₃×#464	2
C₂×C₂₃×#463	2
C₂²×C₂₃×C₄⋊C₈	2
C₂×#3250	23

Subgroups — C2×C23×#3250 #19208525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3250 #19208525