Subgroups — C₂×C₂₃×#3183 #19208316

Order 5888.

2018 conjugacy classes of subgroups.

The subgroup lattice has 480 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×#3183	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₂₃×#499	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₂₃×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₂₃×#488	C₂	1	2	yes	maximal, complemented
6	C₂×C₂₃×#470	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₂₃×#469	C₂	1	1	yes	maximal, characteristic
8	C₂×C₂₃×#468	C₂	1	2	yes	maximal, complemented
9	C₂×C₂₃×#442	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#441	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂₃×#440	C₂	1	2	yes	maximal, complemented
12	C₂×C₄×M₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×Q₁₆×C₂₃	C₂²	1	1	yes	characteristic
14	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
15	C₂²×D₈×C₂₃	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
18	C₂₃×#529	—	2	8	no	—
19	C₂₃×#529	C₂²	1	16	yes	complemented
20	C₂×C₂₃×#126	—	2	2	no	—
21	C₂×C₂₃×#125	C₂²	1	2	yes	—
22	C₂×C₂₃×#124	C₂²	1	2	yes	—
23	C₂×C₂₃×#123	—	2	2	no	—
24	C₂×C₂₃×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₂₃×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₂₃	—	2	2	no	—
28	C₂×C₄×D₄×C₂₃	C₂²	1	2	yes	—
29	C₂×C₂₃×#117	—	2	2	no	—
30	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
31	C₂₃×#499	C₂²	1	8	yes	complemented
32	C₂₃×#495	C₂²	1	8	yes	complemented
33	C₂₃×#488	C₂²	1	16	yes	complemented
34	C₂₃×#470	C₂²	1	8	yes	complemented
35	C₂₃×#469	C₂²	1	8	yes	—
36	C₂₃×#468	C₂²	1	16	yes	complemented
37	C₂₃×#442	C₂²	1	8	yes	complemented
38	C₂₃×#441	C₂²	1	8	yes	complemented
39	C₂₃×#440	C₂²	1	16	yes	complemented
40	C₂×C₂₃×#107	C₂²	1	2	yes	—
41	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
42	C₂×C₂₃×#106	C₂²	1	1	yes	characteristic
43	C₂×C₂₃×#103	C₂²	1	2	yes	—
44	C₂×C₂₃×#103	C₂²	1	2	yes	—
45	C₂×C₂₃×#102	C₂²	1	2	yes	—
46	C₂×C₂₃×#102	C₂²	1	2	yes	—
47	C₄×M₁₆×C₂₃	C₂²	1	8	yes	complemented
48	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
49	C₂×C₂₃×#97	C₂²	1	1	yes	characteristic
50	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
51	C₂×C₄×C₈×C₂₃	C₂²	1	1	yes	characteristic
52	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
53	C₂²×D₄×C₂₃	—	2	2	no	—
54	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
55	C₂³×C₄×C₂₃	—	2	2	no	—
56	C₂³×C₄×C₂₃	D₄	1	2	yes	—
57	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
58	C₂×Q₁₆×C₂₃	—	2	4	no	—
59	C₂×Q₁₆×C₂₃	C₂³	1	4	yes	—
60	C₂×SD₁₆×C₂₃	—	2	8	no	—
61	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
62	C₂×D₈×C₂₃	—	2	4	no	—
63	C₂×D₈×C₂₃	C₂³	1	4	yes	—
64	C₂×M₁₆×C₂₃	—	2	4	no	—
65	C₂×M₁₆×C₂₃	—	2	4	no	—
66	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
67	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
68	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₂₃	C₂³	1	1	yes	characteristic
72	C₂₃×#126	—	2	16	no	—
73	C₂₃×#125	—	2	4	no	—
74	C₂₃×#125	C₂³	1	8	yes	—
75	C₂₃×#124	—	2	4	no	—
76	C₂₃×#124	C₂³	1	8	yes	—
77	C₂₃×#123	—	2	16	no	—
78	C₂₃×C₂²⋊Q₈	—	2	4	no	—
79	C₂₃×C₂²⋊Q₈	C₂³	1	8	yes	—
80	C₂₃×#121	—	2	4	no	—
81	C₂₃×#121	C₂³	1	8	yes	—
82	C₄×Q₈×C₂₃	—	2	4	no	—
83	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
84	C₄×D₄×C₂₃	—	2	16	no	—
85	C₄×D₄×C₂₃	—	2	4	no	—
86	C₄×D₄×C₂₃	C₂³	1	8	yes	—
87	C₂₃×#117	—	2	16	no	—
88	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
89	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
90	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
94	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
99	C₂×C₄²×C₂₃	—	2	2	no	—
100	C₂×C₄²×C₂₃	D₄	1	2	yes	—
101	C₂×C₄²×C₂₃	D₄	1	4	yes	—
102	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
105	C₂₃×#107	C₂³	1	8	yes	—
106	C₂₃×#106	C₂³	1	4	yes	—
107	C₂₃×#106	C₂³	1	4	yes	—
108	C₂₃×#103	C₂³	1	8	yes	—
109	C₂₃×#103	C₂³	1	8	yes	—
110	C₂₃×#102	C₂³	1	8	yes	—
111	C₂₃×#102	C₂³	1	8	yes	—
112	C₂₃×#97	C₂³	1	4	yes	—
113	C₂₃×#97	C₂³	1	4	yes	—
114	C₄×C₈×C₂₃	C₂³	1	4	yes	—
115	C₄×C₈×C₂₃	C₂³	1	4	yes	—
116	C₂⁴×C₂₃	—	2	2	no	—
117	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
118	C₂×Q₈×C₂₃	—	2	2	no	—
119	C₂×Q₈×C₂₃	—	2	4	no	—
120	C₂×Q₈×C₂₃	—	2	4	no	—
121	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
122	C₂×D₄×C₂₃	—	2	8	no	—
123	C₂×D₄×C₂₃	—	2	2	no	—
124	C₂×D₄×C₂₃	—	2	4	no	—
125	C₂×D₄×C₂₃	—	2	4	no	—
126	C₂×D₄×C₂₃	—	4	8	no	—
127	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₂₃	—	2	2	no	—
129	C₂²×C₄×C₂₃	—	2	2	no	—
130	C₂²×C₄×C₂₃	—	2	2	no	—
131	C₂²×C₄×C₂₃	—	2	2	no	—
132	C₂²×C₄×C₂₃	—	2	2	no	—
133	C₂²×C₄×C₂₃	—	2	8	no	—
134	C₂²×C₄×C₂₃	—	4	4	no	—
135	C₂²×C₄×C₂₃	—	4	8	no	—
136	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
138	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₂₃	C₂×D₄	1	8	yes	—
141	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
143	Q₁₆×C₂₃	—	2	8	no	—
144	SD₁₆×C₂₃	—	2	16	no	—
145	D₈×C₂₃	—	2	8	no	—
146	M₁₆×C₂₃	—	2	8	no	—
147	M₁₆×C₂₃	—	2	8	no	—
148	C₂×C₈×C₂₃	—	2	2	no	—
149	C₂×C₈×C₂₃	—	2	2	no	—
150	C₂×C₈×C₂₃	#41	1	4	yes	—
151	C₂×C₈×C₂₃	#41	1	4	yes	—
152	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
153	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
154	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
155	C₂×C₈×C₂₃	C₂⁴	1	2	yes	—
156	C₄⋊C₄×C₂₃	—	2	8	no	—
157	C₄⋊C₄×C₂₃	—	2	8	no	—
158	C₄⋊C₄×C₂₃	—	2	8	no	—
159	C₄⋊C₄×C₂₃	—	2	8	no	—
160	C₄⋊C₄×C₂₃	—	2	2	no	—
161	C₄⋊C₄×C₂₃	—	2	2	no	—
162	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
163	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
164	C₂²⋊C₄×C₂₃	—	2	8	no	—
165	C₂²⋊C₄×C₂₃	—	2	8	no	—
166	C₂²⋊C₄×C₂₃	—	2	8	no	—
167	C₂²⋊C₄×C₂₃	—	2	8	no	—
168	C₂²⋊C₄×C₂₃	—	2	8	no	—
169	C₄²×C₂₃	—	2	8	no	—
170	C₄²×C₂₃	C₂×D₄	1	8	yes	—
171	C₄²×C₂₃	C₂×D₄	1	2	yes	—
172	C₄²×C₂₃	C₂×D₄	1	2	yes	—
173	C₄²×C₂₃	C₂⁴	1	2	yes	—
174	C₄²×C₂₃	C₂⁴	1	2	yes	—
175	C₂×#3183	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂³×C₂₃	—	2	2	no	—
177	C₂³×C₂₃	—	2	4	no	—
178	C₂³×C₂₃	—	2	4	no	—
179	C₂³×C₂₃	—	4	4	no	—
180	C₂³×C₂₃	—	4	4	no	—
181	C₂³×C₂₃	—	4	4	no	—
182	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
183	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₂₃	—	2	4	no	—
185	Q₈×C₂₃	—	2	4	no	—
186	Q₈×C₂₃	—	4	4	no	—
187	D₄×C₂₃	—	2	4	no	—
188	D₄×C₂₃	—	2	4	no	—
189	D₄×C₂₃	—	4	16	no	—
190	D₄×C₂₃	—	4	4	no	—
191	C₂×C₄×C₂₃	—	2	2	no	—
192	C₂×C₄×C₂₃	—	2	4	no	—
193	C₂×C₄×C₂₃	—	2	4	no	—
194	C₂×C₄×C₂₃	—	2	4	no	—
195	C₂×C₄×C₂₃	—	2	2	no	—
196	C₂×C₄×C₂₃	—	2	2	no	—
197	C₂×C₄×C₂₃	—	2	4	no	—
198	C₂×C₄×C₂₃	—	2	4	no	—
199	C₂×C₄×C₂₃	—	2	4	no	—
200	C₂×C₄×C₂₃	—	4	8	no	—
201	C₂×C₄×C₂₃	—	4	16	no	—
202	C₂×C₄×C₂₃	—	4	4	no	—
203	C₂×C₄×C₂₃	—	4	4	no	—
204	C₂×C₄×C₂₃	—	4	4	no	—
205	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
206	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
208	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
209	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
210	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
211	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
212	C₈×C₂₃	—	2	2	no	—
213	C₈×C₂₃	—	2	2	no	—
214	C₈×C₂₃	C₂×#41	1	4	yes	—
215	C₈×C₂₃	C₂×#41	1	4	yes	—
216	C₂×#529	C₂×C₂₃	1	2	yes	complemented
217	#3183	C₂×C₂₃	1	16	yes	direct product factor
218	C₂×#499	C₂×C₂₃	1	1	yes	characteristic, complemented
219	C₂×#495	C₂×C₂₃	1	1	yes	characteristic, complemented
220	C₂×#488	C₂×C₂₃	1	2	yes	complemented
221	C₂×#470	C₂×C₂₃	1	1	yes	characteristic, complemented
222	C₂×#469	C₂×C₂₃	1	1	yes	characteristic
223	C₂×#468	C₂×C₂₃	1	2	yes	complemented
224	C₂×#442	C₂×C₂₃	1	1	yes	characteristic, complemented
225	C₂×#441	C₂×C₂₃	1	1	yes	characteristic, complemented
226	C₂×#440	C₂×C₂₃	1	2	yes	complemented
227	C₂×C₄×M₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
228	C₂²×C₂₃	—	2	2	no	—
229	C₂²×C₂₃	—	2	4	no	—
230	C₂²×C₂₃	—	4	4	no	—
231	C₂²×C₂₃	—	4	4	no	—
232	C₂²×C₂₃	—	4	4	no	—
233	C₂²×C₂₃	—	4	4	no	—
234	C₂²×C₂₃	—	8	8	no	—
235	C₂²×C₂₃	#532	1	2	yes	—
236	C₂²×C₂₃	#575	1	4	yes	—
237	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
238	C₄×C₂₃	—	2	2	no	—
239	C₄×C₂₃	—	2	4	no	—
240	C₄×C₂₃	—	2	4	no	—
241	C₄×C₂₃	—	4	4	no	—
242	C₄×C₂₃	—	4	4	no	—
243	C₄×C₂₃	—	4	4	no	—
244	C₄×C₂₃	#532	1	2	yes	—
245	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
246	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
247	C₂²×Q₁₆	C₂²×C₂₃	1	1	yes	characteristic
248	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
249	C₂²×D₈	C₂²×C₂₃	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
252	#529	—	2	8	no	—
253	#529	C₂²×C₂₃	1	16	yes	complemented
254	C₂×#126	—	2	2	no	—
255	C₂×#125	C₂²×C₂₃	1	2	yes	—
256	C₂×#124	C₂²×C₂₃	1	2	yes	—
257	C₂×#123	—	2	2	no	—
258	C₂×C₂²⋊Q₈	C₂²×C₂₃	1	2	yes	—
259	C₂×#121	C₂²×C₂₃	1	2	yes	—
260	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
261	C₂×C₄×D₄	—	2	2	no	—
262	C₂×C₄×D₄	C₂²×C₂₃	1	2	yes	—
263	C₂×#117	—	2	2	no	—
264	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
265	#499	C₂²×C₂₃	1	8	yes	complemented
266	#495	C₂²×C₂₃	1	8	yes	complemented
267	#488	C₂²×C₂₃	1	16	yes	complemented
268	#470	C₂²×C₂₃	1	8	yes	complemented
269	#469	C₂²×C₂₃	1	8	yes	—
270	#468	C₂²×C₂₃	1	16	yes	complemented
271	#442	C₂²×C₂₃	1	8	yes	complemented
272	#441	C₂²×C₂₃	1	8	yes	complemented
273	#440	C₂²×C₂₃	1	16	yes	complemented
274	C₂×#107	C₂²×C₂₃	1	2	yes	—
275	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
276	C₂×#106	C₂²×C₂₃	1	1	yes	characteristic
277	C₂×#103	C₂²×C₂₃	1	2	yes	—
278	C₂×#103	C₂²×C₂₃	1	2	yes	—
279	C₂×#102	C₂²×C₂₃	1	2	yes	—
280	C₂×#102	C₂²×C₂₃	1	2	yes	—
281	C₄×M₁₆	C₂²×C₂₃	1	8	yes	complemented
282	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
283	C₂×#97	C₂²×C₂₃	1	1	yes	characteristic
284	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
285	C₂×C₄×C₈	C₂²×C₂₃	1	1	yes	characteristic
286	C₂×C₂₃	—	4	2	no	—
287	C₂×C₂₃	—	8	4	no	—
288	C₂×C₂₃	#3183	1	4	yes	direct product factor
289	C₂×C₂₃	C₂×#532	1	1	yes	characteristic
290	C₂×C₂₃	C₂×#575	1	2	yes	—
291	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
292	C₂²×D₄	—	2	2	no	—
293	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	D₄×C₂₃	1	2	yes	—
296	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
297	C₂×Q₁₆	—	2	4	no	—
298	C₂×Q₁₆	C₂³×C₂₃	1	4	yes	—
299	C₂×SD₁₆	—	2	8	no	—
300	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
301	C₂×D₈	—	2	4	no	—
302	C₂×D₈	C₂³×C₂₃	1	4	yes	—
303	C₂×M₁₆	—	2	4	no	—
304	C₂×M₁₆	—	2	4	no	—
305	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
306	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
307	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
310	C₂²×C₈	C₂³×C₂₃	1	1	yes	characteristic
311	#126	—	2	16	no	—
312	#125	—	2	4	no	—
313	#125	C₂³×C₂₃	1	8	yes	—
314	#124	—	2	4	no	—
315	#124	C₂³×C₂₃	1	8	yes	—
316	#123	—	2	16	no	—
317	C₂²⋊Q₈	—	2	4	no	—
318	C₂²⋊Q₈	C₂³×C₂₃	1	8	yes	—
319	#121	—	2	4	no	—
320	#121	C₂³×C₂₃	1	8	yes	—
321	C₄×Q₈	—	2	4	no	—
322	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
323	C₄×D₄	—	2	16	no	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	C₂³×C₂₃	1	8	yes	—
326	#117	—	2	16	no	—
327	C₂×C₄⋊C₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	2	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
332	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	2	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₄²	—	2	2	no	—
339	C₂×C₄²	D₄×C₂₃	1	2	yes	—
340	C₂×C₄²	D₄×C₂₃	1	4	yes	—
341	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
344	#107	C₂³×C₂₃	1	8	yes	—
345	#106	C₂³×C₂₃	1	4	yes	—
346	#106	C₂³×C₂₃	1	4	yes	—
347	#103	C₂³×C₂₃	1	8	yes	—
348	#103	C₂³×C₂₃	1	8	yes	—
349	#102	C₂³×C₂₃	1	8	yes	—
350	#102	C₂³×C₂₃	1	8	yes	—
351	#97	C₂³×C₂₃	1	4	yes	—
352	#97	C₂³×C₂₃	1	4	yes	—
353	C₄×C₈	C₂³×C₂₃	1	4	yes	—
354	C₄×C₈	C₂³×C₂₃	1	4	yes	—
355	C₂₃	C₂×#3183	1	1	yes	characteristic, direct product factor, Sylow
356	C₂⁴	—	2	2	no	—
357	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
358	C₂×Q₈	—	2	2	no	—
359	C₂×Q₈	—	2	4	no	—
360	C₂×Q₈	—	2	4	no	—
361	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	4	8	no	—
367	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	8	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	8	no	—
376	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
377	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
379	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₂₃	1	8	yes	—
381	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
382	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
383	Q₁₆	—	2	8	no	—
384	SD₁₆	—	2	16	no	—
385	D₈	—	2	8	no	—
386	M₁₆	—	2	8	no	—
387	M₁₆	—	2	8	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	#41×C₂₃	1	4	yes	—
391	C₂×C₈	#41×C₂₃	1	4	yes	—
392	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
393	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
394	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
395	C₂×C₈	C₂⁴×C₂₃	1	2	yes	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
403	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₄²	—	2	8	no	—
410	C₄²	C₂×D₄×C₂₃	1	8	yes	—
411	C₄²	C₂×D₄×C₂₃	1	2	yes	—
412	C₄²	C₂×D₄×C₂₃	1	2	yes	—
413	C₄²	C₂⁴×C₂₃	1	2	yes	—
414	C₄²	C₂⁴×C₂₃	1	2	yes	—
415	C₂³	—	2	4	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	4	no	—
418	C₂³	—	4	4	no	—
419	C₂³	—	4	4	no	—
420	C₂³	—	4	4	no	—
421	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
422	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
423	Q₈	—	2	4	no	—
424	Q₈	—	2	4	no	—
425	Q₈	—	4	4	no	—
426	D₄	—	2	4	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	16	no	—
429	D₄	—	4	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	4	8	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	—	4	4	no	—
443	C₂×C₄	—	4	4	no	—
444	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
445	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
446	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
447	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
448	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
449	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
450	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
451	C₈	—	2	2	no	—
452	C₈	—	2	2	no	—
453	C₈	C₂×#41×C₂₃	1	4	yes	—
454	C₈	C₂×#41×C₂₃	1	4	yes	—
455	C₂²	—	2	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	4	no	—
458	C₂²	—	4	4	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	4	4	no	—
461	C₂²	—	8	8	no	—
462	C₂²	C₂₃×#532	1	2	yes	—
463	C₂²	C₂₃×#575	1	4	yes	—
464	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	2	4	no	—
467	C₄	—	2	4	no	—
468	C₄	—	4	4	no	—
469	C₄	—	4	4	no	—
470	C₄	—	4	4	no	—
471	C₄	C₂₃×#532	1	2	yes	—
472	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
473	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
474	C₂	—	4	2	no	—
475	C₂	—	8	4	no	—
476	C₂	C₂₃×#3183	1	4	yes	direct product factor
477	C₂	C₂×C₂₃×#532	1	1	yes	characteristic
478	C₂	C₂×C₂₃×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂×C₂₃×#469	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×#3183	C₂	direct (N × H)
3. C₂×C₂₃×#499	C₂	semidirect
4. C₂×C₂₃×#495	C₂	semidirect
5. C₂×C₂₃×#488	C₂	semidirect
6. C₂×C₂₃×#470	C₂	semidirect
8. C₂×C₂₃×#468	C₂	semidirect
9. C₂×C₂₃×#442	C₂	semidirect
10. C₂×C₂₃×#441	C₂	semidirect
11. C₂×C₂₃×#440	C₂	semidirect
12. C₂×C₄×M₁₆×C₂₃	C₂	semidirect
19. C₂₃×#529	C₂²	semidirect
31. C₂₃×#499	C₂²	semidirect
32. C₂₃×#495	C₂²	semidirect
33. C₂₃×#488	C₂²	semidirect
34. C₂₃×#470	C₂²	semidirect
36. C₂₃×#468	C₂²	semidirect
37. C₂₃×#442	C₂²	semidirect
38. C₂₃×#441	C₂²	semidirect
39. C₂₃×#440	C₂²	semidirect
47. C₄×M₁₆×C₂₃	C₂²	semidirect
175. C₂×#3183	C₂₃	direct (N × H)
216. C₂×#529	C₂×C₂₃	semidirect
217. #3183	C₂×C₂₃	direct (N × H)
218. C₂×#499	C₂×C₂₃	semidirect
219. C₂×#495	C₂×C₂₃	semidirect
220. C₂×#488	C₂×C₂₃	semidirect
221. C₂×#470	C₂×C₂₃	semidirect
223. C₂×#468	C₂×C₂₃	semidirect
224. C₂×#442	C₂×C₂₃	semidirect
225. C₂×#441	C₂×C₂₃	semidirect
226. C₂×#440	C₂×C₂₃	semidirect
227. C₂×C₄×M₁₆	C₂×C₂₃	semidirect
253. #529	C₂²×C₂₃	semidirect
265. #499	C₂²×C₂₃	semidirect
266. #495	C₂²×C₂₃	semidirect
267. #488	C₂²×C₂₃	semidirect
268. #470	C₂²×C₂₃	semidirect
270. #468	C₂²×C₂₃	semidirect
271. #442	C₂²×C₂₃	semidirect
272. #441	C₂²×C₂₃	semidirect
273. #440	C₂²×C₂₃	semidirect
281. C₄×M₁₆	C₂²×C₂₃	semidirect
288. C₂×C₂₃	#3183	direct (N × H)
355. C₂₃	C₂×#3183	direct (N × H)
476. C₂	C₂₃×#3183	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×#3183	2
C₂×C₂₃×#499	2
C₂×C₂₃×#495	2
C₂×C₂₃×#488	2
C₂×C₂₃×#470	2
C₂×C₂₃×#469	2
C₂×C₂₃×#468	2
C₂×C₂₃×#442	2
C₂×C₂₃×#441	2
C₂×C₂₃×#440	2
C₂×C₄×M₁₆×C₂₃	2
C₂×#3183	23

Subgroups — C2×C23×#3183 #19208316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3183 #19208316