Subgroups — C₂×C₂₃×#3044 #19208045

Order 5888.

2666 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂₃×#137	C₂	1	1	yes	maximal, characteristic
2	C₂³×Q₁₆×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₂₃×#536	C₂	1	1	yes	maximal, characteristic
4	C₂×C₂₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂₃×#3044	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₂₃×#464	C₂	1	4	yes	maximal, complemented
7	C₂×C₂₃×#462	C₂	1	4	yes	maximal, complemented
8	C₂×C₂₃×#424	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#419	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₂₃×#416	C₂	1	1	yes	maximal, characteristic
11	C₂²×#41×C₂₃	C₂²	1	1	yes	characteristic
12	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
13	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₂₃×#137	—	2	8	no	—
15	C₂×C₂₃×#137	C₂²	1	8	yes	—
16	C₂²×Q₁₆×C₂₃	—	2	8	no	—
17	C₂²×Q₁₆×C₂₃	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	—
19	C₂²×Q₁₆×C₂₃	C₂²	1	8	yes	complemented
20	C₂²×SD₁₆×C₂₃	C₂²	1	2	yes	—
21	C₂²×M₁₆×C₂₃	C₂²	1	1	yes	characteristic
22	C₂³×C₈×C₂₃	C₂²	1	1	yes	characteristic
23	C₂₃×#536	—	2	4	no	—
24	C₂₃×#536	C₂²	1	8	yes	—
25	C₂×C₂₃×C₄⋊Q₈	C₂²	1	2	yes	—
26	C₂×C₂₃×#124	C₂²	1	2	yes	—
27	C₂×C₂₃×#123	—	2	2	no	—
28	C₂×C₂₃×C₂²⋊Q₈	—	2	2	no	—
29	C₂₃×#519	—	2	4	no	—
30	C₂₃×#519	C₂²	1	8	yes	complemented
31	C₂×C₄×Q₈×C₂₃	—	2	2	no	—
32	C₂×C₄×Q₈×C₂₃	C₂²	1	4	yes	—
33	C₂×C₂₃×#117	—	2	2	no	—
34	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
35	C₂×C₂₃×#117	C₂²	1	1	yes	characteristic
36	C₂₃×#464	C₂²	1	32	yes	complemented
37	C₂₃×#462	C₂²	1	32	yes	complemented
38	C₂₃×#424	C₂²	1	8	yes	complemented
39	C₂×C₂₃×C₄⋊C₈	C₂²	1	4	yes	—
40	C₂₃×#419	C₂²	1	8	yes	complemented
41	C₂₃×#416	C₂²	1	8	yes	—
42	C₂×C₂₃×#103	C₂²	1	2	yes	—
43	C₂×C₂₃×#103	C₂²	1	4	yes	—
44	C₂×C₂₃×#102	C₂²	1	2	yes	—
45	C₂×#41×C₂₃	—	2	2	no	—
46	C₂×#41×C₂₃	—	2	4	no	—
47	C₂×#41×C₂₃	—	2	4	no	—
48	C₂×#41×C₂₃	C₂³	1	4	yes	—
49	C₂²×Q₈×C₂₃	—	2	1	no	—
50	C₂²×Q₈×C₂₃	—	2	2	no	—
51	C₂²×Q₈×C₂₃	—	2	1	no	—
52	C₂²×Q₈×C₂₃	—	2	2	no	—
53	C₂²×Q₈×C₂₃	—	2	4	no	—
54	C₂²×Q₈×C₂₃	—	2	4	no	—
55	C₂²×Q₈×C₂₃	—	2	4	no	—
56	C₂²×Q₈×C₂₃	D₄	1	8	yes	—
57	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
58	C₂²×Q₈×C₂₃	C₂³	1	1	yes	characteristic
59	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
60	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
61	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
62	C₂²×D₄×C₂₃	—	2	1	no	—
63	C₂²×D₄×C₂₃	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₂₃	—	2	1	no	—
65	C₂³×C₄×C₂₃	—	2	1	no	—
66	C₂³×C₄×C₂₃	—	2	1	no	—
67	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
68	C₂₃×#137	—	2	32	no	—
69	C₂×Q₁₆×C₂₃	—	2	16	no	—
70	C₂×Q₁₆×C₂₃	—	2	32	no	—
71	C₂×Q₁₆×C₂₃	—	2	8	no	—
72	C₂×Q₁₆×C₂₃	C₂³	1	16	yes	—
73	C₂×Q₁₆×C₂₃	C₂³	1	8	yes	—
74	C₂×SD₁₆×C₂₃	—	2	8	no	—
75	C₂×SD₁₆×C₂₃	C₂³	1	8	yes	—
76	C₂×M₁₆×C₂₃	—	2	4	no	—
77	C₂×M₁₆×C₂₃	C₂³	1	4	yes	—
78	C₂²×C₈×C₂₃	—	2	4	no	—
79	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
80	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
81	C₂²×C₈×C₂₃	C₂³	1	2	yes	—
82	C₂₃×C₄⋊Q₈	—	2	4	no	—
83	C₂₃×C₄⋊Q₈	C₂³	1	8	yes	—
84	C₂₃×#124	—	2	4	no	—
85	C₂₃×#124	C₂³	1	8	yes	—
86	C₂₃×#123	—	2	16	no	—
87	C₂₃×C₂²⋊Q₈	—	2	16	no	—
88	C₄×Q₈×C₂₃	—	2	16	no	—
89	C₄×Q₈×C₂₃	—	2	8	no	—
90	C₄×Q₈×C₂₃	C₂³	1	16	yes	—
91	C₂₃×#117	—	2	2	no	—
92	C₂₃×#117	—	2	16	no	—
93	C₂₃×#117	D₄	1	4	yes	—
94	C₂₃×#117	C₂³	1	4	yes	—
95	C₂₃×#117	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
97	C₂×C₄⋊C₄×C₂₃	—	2	4	no	—
98	C₂×C₄⋊C₄×C₂₃	D₄	1	2	yes	—
99	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
100	C₂×C₂²⋊C₄×C₂₃	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₂₃	—	2	4	no	—
102	C₂×C₂²⋊C₄×C₂₃	D₄	1	2	yes	—
103	C₂×C₄²×C₂₃	—	2	4	no	—
104	C₂×C₄²×C₂₃	—	2	1	no	—
105	C₂×C₄²×C₂₃	C₂³	1	2	yes	—
106	C₂₃×C₄⋊C₈	C₂³	1	16	yes	—
107	C₂₃×#103	C₂³	1	8	yes	—
108	C₂₃×#103	C₂³	1	16	yes	—
109	C₂₃×#102	C₂³	1	8	yes	—
110	C₂⁴×C₂₃	—	2	1	no	—
111	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
112	#41×C₂₃	—	2	8	no	—
113	#41×C₂₃	—	2	8	no	—
114	#41×C₂₃	—	4	8	no	—
115	C₂×Q₈×C₂₃	—	2	8	no	—
116	C₂×Q₈×C₂₃	—	2	16	no	—
117	C₂×Q₈×C₂₃	—	2	4	no	—
118	C₂×Q₈×C₂₃	—	2	2	no	—
119	C₂×Q₈×C₂₃	—	2	4	no	—
120	C₂×Q₈×C₂₃	—	2	2	no	—
121	C₂×Q₈×C₂₃	—	2	1	no	—
122	C₂×Q₈×C₂₃	—	2	4	no	—
123	C₂×Q₈×C₂₃	—	2	8	no	—
124	C₂×Q₈×C₂₃	—	2	4	no	—
125	C₂×Q₈×C₂₃	—	2	8	no	—
126	C₂×Q₈×C₂₃	—	2	2	no	—
127	C₂×Q₈×C₂₃	—	2	4	no	—
128	C₂×Q₈×C₂₃	—	2	8	no	—
129	C₂×Q₈×C₂₃	—	2	2	no	—
130	C₂×Q₈×C₂₃	—	4	4	no	—
131	C₂×Q₈×C₂₃	—	4	8	no	—
132	C₂×Q₈×C₂₃	C₂×D₄	1	8	yes	—
133	C₂×Q₈×C₂₃	C₂×D₄	1	16	yes	—
134	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
135	C₂×Q₈×C₂₃	C₂⁴	1	2	yes	—
136	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
137	C₂×D₄×C₂₃	—	2	4	no	—
138	C₂×D₄×C₂₃	—	2	2	no	—
139	C₂×D₄×C₂₃	—	2	1	no	—
140	C₂×D₄×C₂₃	—	2	2	no	—
141	C₂×D₄×C₂₃	—	4	4	no	—
142	C₂×D₄×C₂₃	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₂₃	—	2	8	no	—
144	C₂²×C₄×C₂₃	—	2	4	no	—
145	C₂²×C₄×C₂₃	—	2	2	no	—
146	C₂²×C₄×C₂₃	—	2	4	no	—
147	C₂²×C₄×C₂₃	—	2	2	no	—
148	C₂²×C₄×C₂₃	—	2	2	no	—
149	C₂²×C₄×C₂₃	—	2	1	no	—
150	C₂²×C₄×C₂₃	—	2	4	no	—
151	C₂²×C₄×C₂₃	—	4	4	no	—
152	C₂²×C₄×C₂₃	—	4	4	no	—
153	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₂₃	#41	1	4	yes	—
158	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
160	Q₁₆×C₂₃	—	2	32	no	—
161	Q₁₆×C₂₃	—	2	16	no	—
162	SD₁₆×C₂₃	—	2	16	no	—
163	M₁₆×C₂₃	—	2	8	no	—
164	C₂×C₈×C₂₃	—	2	4	no	—
165	C₂×C₈×C₂₃	—	2	8	no	—
166	C₂×C₈×C₂₃	—	2	4	no	—
167	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
168	C₂×C₈×C₂₃	C₂⁴	1	4	yes	—
169	C₄⋊C₄×C₂₃	—	2	16	no	—
170	C₄⋊C₄×C₂₃	—	2	16	no	—
171	C₄⋊C₄×C₂₃	—	2	2	no	—
172	C₄⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
173	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
174	C₂²⋊C₄×C₂₃	—	2	4	no	—
175	C₂²⋊C₄×C₂₃	—	2	16	no	—
176	C₂²⋊C₄×C₂₃	C₂×D₄	1	8	yes	—
177	C₄²×C₂₃	—	2	16	no	—
178	C₄²×C₂₃	—	2	4	no	—
179	C₄²×C₂₃	C₂×D₄	1	4	yes	—
180	C₄²×C₂₃	C₂⁴	1	4	yes	—
181	C₂×#3044	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₂₃	—	2	4	no	—
183	C₂³×C₂₃	—	2	2	no	—
184	C₂³×C₂₃	—	4	2	no	—
185	C₂³×C₂₃	—	4	4	no	—
186	C₂³×C₂₃	#121	1	4	yes	—
187	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
188	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
189	Q₈×C₂₃	—	2	16	no	—
190	Q₈×C₂₃	—	2	8	no	—
191	Q₈×C₂₃	—	2	4	no	—
192	Q₈×C₂₃	—	2	4	no	—
193	Q₈×C₂₃	—	2	2	no	—
194	Q₈×C₂₃	—	2	4	no	—
195	Q₈×C₂₃	—	2	2	no	—
196	Q₈×C₂₃	—	4	8	no	—
197	Q₈×C₂₃	—	4	4	no	—
198	Q₈×C₂₃	—	4	2	no	—
199	Q₈×C₂₃	C₂²×D₄	1	8	yes	—
200	D₄×C₂₃	—	2	2	no	—
201	D₄×C₂₃	—	2	2	no	—
202	D₄×C₂₃	—	4	8	no	—
203	D₄×C₂₃	—	4	2	no	—
204	C₂×C₄×C₂₃	—	2	16	no	—
205	C₂×C₄×C₂₃	—	2	8	no	—
206	C₂×C₄×C₂₃	—	2	8	no	—
207	C₂×C₄×C₂₃	—	2	4	no	—
208	C₂×C₄×C₂₃	—	2	4	no	—
209	C₂×C₄×C₂₃	—	2	4	no	—
210	C₂×C₄×C₂₃	—	2	2	no	—
211	C₂×C₄×C₂₃	—	4	2	no	—
212	C₂×C₄×C₂₃	—	4	8	no	—
213	C₂×C₄×C₂₃	—	4	4	no	—
214	C₂×C₄×C₂₃	—	4	4	no	—
215	C₂×C₄×C₂₃	—	4	8	no	—
216	C₂×C₄×C₂₃	#121	1	4	yes	—
217	C₂×C₄×C₂₃	#121	1	8	yes	—
218	C₂×C₄×C₂₃	C₂²×D₄	1	8	yes	—
219	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
223	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
224	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
225	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
226	C₈×C₂₃	—	2	4	no	—
227	C₈×C₂₃	—	2	4	no	—
228	C₂²×#137	C₂×C₂₃	1	1	yes	characteristic
229	C₂³×Q₁₆	C₂×C₂₃	1	1	yes	characteristic, complemented
230	C₂×#536	C₂×C₂₃	1	1	yes	characteristic
231	C₂×#519	C₂×C₂₃	1	1	yes	characteristic, complemented
232	#3044	C₂×C₂₃	1	16	yes	direct product factor
233	C₂×#464	C₂×C₂₃	1	4	yes	complemented
234	C₂×#462	C₂×C₂₃	1	4	yes	complemented
235	C₂×#424	C₂×C₂₃	1	1	yes	characteristic, complemented
236	C₂×#419	C₂×C₂₃	1	1	yes	characteristic, complemented
237	C₂×#416	C₂×C₂₃	1	1	yes	characteristic
238	C₂²×C₂₃	—	2	8	no	—
239	C₂²×C₂₃	—	2	4	no	—
240	C₂²×C₂₃	—	4	2	no	—
241	C₂²×C₂₃	—	4	4	no	—
242	C₂²×C₂₃	—	8	4	no	—
243	C₂²×C₂₃	C₂×#121	1	4	yes	—
244	C₂²×C₂₃	C₂×#121	1	2	yes	—
245	C₂²×C₂₃	#578	1	4	yes	—
246	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
247	C₄×C₂₃	—	2	8	no	—
248	C₄×C₂₃	—	2	8	no	—
249	C₄×C₂₃	—	4	2	no	—
250	C₄×C₂₃	—	4	4	no	—
251	C₄×C₂₃	—	4	4	no	—
252	C₄×C₂₃	C₂×#121	1	4	yes	—
253	C₄×C₂₃	C₂×#121	1	2	yes	—
254	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
255	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
256	C₂²×#41	C₂²×C₂₃	1	1	yes	characteristic
257	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
258	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
259	C₂×#137	—	2	8	no	—
260	C₂×#137	C₂²×C₂₃	1	8	yes	—
261	C₂²×Q₁₆	—	2	8	no	—
262	C₂²×Q₁₆	C₂²×C₂₃	1	2	yes	—
263	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	—
264	C₂²×Q₁₆	C₂²×C₂₃	1	8	yes	complemented
265	C₂²×SD₁₆	C₂²×C₂₃	1	2	yes	—
266	C₂²×M₁₆	C₂²×C₂₃	1	1	yes	characteristic
267	C₂³×C₈	C₂²×C₂₃	1	1	yes	characteristic
268	#536	—	2	4	no	—
269	#536	C₂²×C₂₃	1	8	yes	—
270	C₂×C₄⋊Q₈	C₂²×C₂₃	1	2	yes	—
271	C₂×#124	C₂²×C₂₃	1	2	yes	—
272	C₂×#123	—	2	2	no	—
273	C₂×C₂²⋊Q₈	—	2	2	no	—
274	#519	—	2	4	no	—
275	#519	C₂²×C₂₃	1	8	yes	complemented
276	C₂×C₄×Q₈	—	2	2	no	—
277	C₂×C₄×Q₈	C₂²×C₂₃	1	4	yes	—
278	C₂×#117	—	2	2	no	—
279	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
280	C₂×#117	C₂²×C₂₃	1	1	yes	characteristic
281	#464	C₂²×C₂₃	1	32	yes	complemented
282	#462	C₂²×C₂₃	1	32	yes	complemented
283	#424	C₂²×C₂₃	1	8	yes	complemented
284	C₂×C₄⋊C₈	C₂²×C₂₃	1	4	yes	—
285	#419	C₂²×C₂₃	1	8	yes	complemented
286	#416	C₂²×C₂₃	1	8	yes	—
287	C₂×#103	C₂²×C₂₃	1	2	yes	—
288	C₂×#103	C₂²×C₂₃	1	4	yes	—
289	C₂×#102	C₂²×C₂₃	1	2	yes	—
290	C₂×C₂₃	—	2	4	no	—
291	C₂×C₂₃	—	8	2	no	—
292	C₂×C₂₃	#3044	1	4	yes	direct product factor
293	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
294	C₂×C₂₃	C₂×#578	1	2	yes	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	4	no	—
297	C₂×#41	—	2	4	no	—
298	C₂×#41	C₂³×C₂₃	1	4	yes	—
299	C₂²×Q₈	—	2	1	no	—
300	C₂²×Q₈	—	2	2	no	—
301	C₂²×Q₈	—	2	1	no	—
302	C₂²×Q₈	—	2	2	no	—
303	C₂²×Q₈	—	2	4	no	—
304	C₂²×Q₈	—	2	4	no	—
305	C₂²×Q₈	—	2	4	no	—
306	C₂²×Q₈	D₄×C₂₃	1	8	yes	—
307	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
308	C₂²×Q₈	C₂³×C₂₃	1	1	yes	characteristic
309	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
310	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
311	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₂₃	1	1	yes	characteristic
314	C₂³×C₄	—	2	1	no	—
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
318	#137	—	2	32	no	—
319	C₂×Q₁₆	—	2	16	no	—
320	C₂×Q₁₆	—	2	32	no	—
321	C₂×Q₁₆	—	2	8	no	—
322	C₂×Q₁₆	C₂³×C₂₃	1	16	yes	—
323	C₂×Q₁₆	C₂³×C₂₃	1	8	yes	—
324	C₂×SD₁₆	—	2	8	no	—
325	C₂×SD₁₆	C₂³×C₂₃	1	8	yes	—
326	C₂×M₁₆	—	2	4	no	—
327	C₂×M₁₆	C₂³×C₂₃	1	4	yes	—
328	C₂²×C₈	—	2	4	no	—
329	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
330	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
331	C₂²×C₈	C₂³×C₂₃	1	2	yes	—
332	C₄⋊Q₈	—	2	4	no	—
333	C₄⋊Q₈	C₂³×C₂₃	1	8	yes	—
334	#124	—	2	4	no	—
335	#124	C₂³×C₂₃	1	8	yes	—
336	#123	—	2	16	no	—
337	C₂²⋊Q₈	—	2	16	no	—
338	C₄×Q₈	—	2	16	no	—
339	C₄×Q₈	—	2	8	no	—
340	C₄×Q₈	C₂³×C₂₃	1	16	yes	—
341	#117	—	2	2	no	—
342	#117	—	2	16	no	—
343	#117	D₄×C₂₃	1	4	yes	—
344	#117	C₂³×C₂₃	1	4	yes	—
345	#117	C₂³×C₂₃	1	4	yes	—
346	C₂×C₄⋊C₄	—	2	4	no	—
347	C₂×C₄⋊C₄	—	2	4	no	—
348	C₂×C₄⋊C₄	D₄×C₂₃	1	2	yes	—
349	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
350	C₂×C₂²⋊C₄	—	2	1	no	—
351	C₂×C₂²⋊C₄	—	2	4	no	—
352	C₂×C₂²⋊C₄	D₄×C₂₃	1	2	yes	—
353	C₂×C₄²	—	2	4	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	C₂³×C₂₃	1	2	yes	—
356	C₄⋊C₈	C₂³×C₂₃	1	16	yes	—
357	#103	C₂³×C₂₃	1	8	yes	—
358	#103	C₂³×C₂₃	1	16	yes	—
359	#102	C₂³×C₂₃	1	8	yes	—
360	C₂₃	C₂×#3044	1	1	yes	characteristic, direct product factor, Sylow
361	C₂⁴	—	2	1	no	—
362	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
363	#41	—	2	8	no	—
364	#41	—	2	8	no	—
365	#41	—	4	8	no	—
366	C₂×Q₈	—	2	8	no	—
367	C₂×Q₈	—	2	16	no	—
368	C₂×Q₈	—	2	4	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	4	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	4	no	—
379	C₂×Q₈	—	2	8	no	—
380	C₂×Q₈	—	2	2	no	—
381	C₂×Q₈	—	4	4	no	—
382	C₂×Q₈	—	4	8	no	—
383	C₂×Q₈	C₂×D₄×C₂₃	1	8	yes	—
384	C₂×Q₈	C₂×D₄×C₂₃	1	16	yes	—
385	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
386	C₂×Q₈	C₂⁴×C₂₃	1	2	yes	—
387	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	4	4	no	—
393	C₂×D₄	C₂⁴×C₂₃	1	2	yes	—
394	C₂²×C₄	—	2	8	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	4	4	no	—
403	C₂²×C₄	—	4	4	no	—
404	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
405	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
407	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
408	C₂²×C₄	#41×C₂₃	1	4	yes	—
409	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
410	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
411	Q₁₆	—	2	32	no	—
412	Q₁₆	—	2	16	no	—
413	SD₁₆	—	2	16	no	—
414	M₁₆	—	2	8	no	—
415	C₂×C₈	—	2	4	no	—
416	C₂×C₈	—	2	8	no	—
417	C₂×C₈	—	2	4	no	—
418	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
419	C₂×C₈	C₂⁴×C₂₃	1	4	yes	—
420	C₄⋊C₄	—	2	16	no	—
421	C₄⋊C₄	—	2	16	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
424	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
425	C₂²⋊C₄	—	2	4	no	—
426	C₂²⋊C₄	—	2	16	no	—
427	C₂²⋊C₄	C₂×D₄×C₂₃	1	8	yes	—
428	C₄²	—	2	16	no	—
429	C₄²	—	2	4	no	—
430	C₄²	C₂×D₄×C₂₃	1	4	yes	—
431	C₄²	C₂⁴×C₂₃	1	4	yes	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	4	4	no	—
435	C₂³	—	4	2	no	—
436	C₂³	C₂₃×#121	1	4	yes	—
437	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
438	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
439	Q₈	—	2	4	no	—
440	Q₈	—	2	16	no	—
441	Q₈	—	2	8	no	—
442	Q₈	—	2	4	no	—
443	Q₈	—	2	2	no	—
444	Q₈	—	2	4	no	—
445	Q₈	—	2	2	no	—
446	Q₈	—	4	8	no	—
447	Q₈	—	4	4	no	—
448	Q₈	—	4	2	no	—
449	Q₈	C₂²×D₄×C₂₃	1	8	yes	—
450	D₄	—	2	2	no	—
451	D₄	—	2	2	no	—
452	D₄	—	4	8	no	—
453	D₄	—	4	2	no	—
454	C₂×C₄	—	2	8	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	16	no	—
457	C₂×C₄	—	2	8	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	4	4	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	8	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	C₂₃×#121	1	4	yes	—
467	C₂×C₄	C₂₃×#121	1	8	yes	—
468	C₂×C₄	C₂²×D₄×C₂₃	1	8	yes	—
469	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
470	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
471	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
473	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
474	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
475	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
476	C₈	—	2	4	no	—
477	C₈	—	2	4	no	—
478	C₂²	—	2	8	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	4	no	—
482	C₂²	—	8	4	no	—
483	C₂²	C₂×C₂₃×#121	1	4	yes	—
484	C₂²	C₂×C₂₃×#121	1	2	yes	—
485	C₂²	C₂₃×#578	1	4	yes	—
486	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
487	C₄	—	2	8	no	—
488	C₄	—	2	8	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	4	4	no	—
492	C₄	C₂×C₂₃×#121	1	4	yes	—
493	C₄	C₂×C₂₃×#121	1	2	yes	—
494	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
495	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
496	C₂	—	2	4	no	—
497	C₂	—	8	2	no	—
498	C₂	C₂₃×#3044	1	4	yes	direct product factor
499	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
500	C₂	C₂×C₂₃×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₂₃
prime radical	C₂²×#41×C₂₃	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. C₂³×Q₁₆×C₂₃	C₂	semidirect
4. C₂×C₂₃×#519	C₂	semidirect
5. C₂₃×#3044	C₂	direct (N × H)
6. C₂×C₂₃×#464	C₂	semidirect
7. C₂×C₂₃×#462	C₂	semidirect
8. C₂×C₂₃×#424	C₂	semidirect
9. C₂×C₂₃×#419	C₂	semidirect
19. C₂²×Q₁₆×C₂₃	C₂²	semidirect
30. C₂₃×#519	C₂²	semidirect
36. C₂₃×#464	C₂²	semidirect
37. C₂₃×#462	C₂²	semidirect
38. C₂₃×#424	C₂²	semidirect
40. C₂₃×#419	C₂²	semidirect
181. C₂×#3044	C₂₃	direct (N × H)
229. C₂³×Q₁₆	C₂×C₂₃	semidirect
231. C₂×#519	C₂×C₂₃	semidirect
232. #3044	C₂×C₂₃	direct (N × H)
233. C₂×#464	C₂×C₂₃	semidirect
234. C₂×#462	C₂×C₂₃	semidirect
235. C₂×#424	C₂×C₂₃	semidirect
236. C₂×#419	C₂×C₂₃	semidirect
264. C₂²×Q₁₆	C₂²×C₂₃	semidirect
275. #519	C₂²×C₂₃	semidirect
281. #464	C₂²×C₂₃	semidirect
282. #462	C₂²×C₂₃	semidirect
283. #424	C₂²×C₂₃	semidirect
285. #419	C₂²×C₂₃	semidirect
292. C₂×C₂₃	#3044	direct (N × H)
360. C₂₃	C₂×#3044	direct (N × H)
498. C₂	C₂₃×#3044	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₂₃×#137	2
C₂³×Q₁₆×C₂₃	2
C₂×C₂₃×#536	2
C₂×C₂₃×#519	2
C₂₃×#3044	2
C₂×C₂₃×#464	2
C₂×C₂₃×#462	2
C₂×C₂₃×#424	2
C₂×C₂₃×#419	2
C₂×C₂₃×#416	2
C₂×#3044	23

Subgroups — C2×C23×#3044 #19208045

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3044 #19208045