Subgroups — C₂×C₂₃×#3037 #19208037

Order 5888.

2810 conjugacy classes of subgroups.

The subgroup lattice has 536 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	2	yes	maximal, complemented
2	C₂×C₂₃×#532	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂₃×#3037	C₂	1	16	yes	maximal, direct product factor
5	C₂×C₂₃×#464	C₂	1	4	yes	maximal, complemented
6	C₂×C₂₃×#462	C₂	1	2	yes	maximal, complemented
7	C₂×C₂₃×#460	C₂	1	2	yes	maximal, complemented
8	C₂×C₂₃×#423	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂₃×#417	C₂	1	2	yes	maximal, complemented
10	C₂²×#41×C₂₃	C₂²	1	2	yes	—
11	C₂³×Q₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₂₃×#137	—	2	16	no	—
13	C₂×C₂₃×#137	C₂²	1	16	yes	complemented
14	C₂²×Q₁₆×C₂₃	C₂²	1	4	yes	—
15	C₂²×SD₁₆×C₂₃	C₂²	1	4	yes	—
16	C₂²×M₁₆×C₂₃	C₂²	1	2	yes	—
17	C₂₃×#532	—	2	4	no	—
18	C₂₃×#532	C₂²	1	8	yes	—
19	C₂×C₂₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₂₃×#127	C₂²	1	1	yes	characteristic
21	C₂×C₂₃×#124	C₂²	1	2	yes	—
22	C₂×C₂₃×#121	—	2	1	no	—
23	C₂×C₂₃×#121	—	2	1	no	—
24	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
25	C₂×C₄×Q₈×C₂₃	—	2	1	no	—
26	C₂×C₄×Q₈×C₂₃	—	2	4	no	—
27	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₂₃	C₂²	1	2	yes	—
29	C₂×C₄×Q₈×C₂₃	C₂²	1	8	yes	complemented
30	C₂×C₄×D₄×C₂₃	—	2	1	no	—
31	C₂×C₄×D₄×C₂₃	—	2	1	no	—
32	C₂²×C₄⋊C₄×C₂₃	—	2	1	no	—
33	C₂²×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
34	C₂²×C₄²×C₂₃	—	2	1	no	—
35	C₂²×C₄²×C₂₃	C₂²	1	1	yes	characteristic
36	C₂₃×#464	C₂²	1	32	yes	complemented
37	C₂₃×#462	C₂²	1	16	yes	complemented
38	C₂₃×#460	C₂²	1	16	yes	complemented
39	C₂₃×#423	C₂²	1	8	yes	complemented
40	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₂₃×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂₃×#417	C₂²	1	16	yes	complemented
43	C₂×C₂₃×#103	C₂²	1	4	yes	—
44	C₂×C₂₃×#102	C₂²	1	4	yes	—
45	C₂×#41×C₂₃	—	2	4	no	—
46	C₂×#41×C₂₃	—	2	8	no	—
47	C₂×#41×C₂₃	—	2	8	no	—
48	C₂×#41×C₂₃	C₂³	1	8	yes	—
49	C₂²×Q₈×C₂₃	—	2	2	no	—
50	C₂²×Q₈×C₂₃	—	2	1	no	—
51	C₂²×Q₈×C₂₃	—	2	4	no	—
52	C₂²×Q₈×C₂₃	D₄	1	8	yes	complemented
53	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
54	C₂²×Q₈×C₂₃	C₂³	1	2	yes	—
55	C₂²×Q₈×C₂₃	C₂³	1	4	yes	—
56	C₂²×D₄×C₂₃	—	2	2	no	—
57	C₂²×D₄×C₂₃	—	2	1	no	—
58	C₂²×D₄×C₂₃	—	2	1	no	—
59	C₂²×D₄×C₂₃	C₂³	1	2	yes	—
60	C₂³×C₄×C₂₃	—	2	1	no	—
61	C₂³×C₄×C₂₃	—	2	1	no	—
62	C₂³×C₄×C₂₃	—	2	2	no	—
63	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₂₃	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₂₃	C₂³	1	1	yes	characteristic
66	C₂₃×#137	—	2	64	no	—
67	C₂×Q₁₆×C₂₃	—	2	16	no	—
68	C₂×Q₁₆×C₂₃	C₂³	1	16	yes	—
69	C₂×SD₁₆×C₂₃	—	2	16	no	—
70	C₂×SD₁₆×C₂₃	C₂³	1	16	yes	—
71	C₂×M₁₆×C₂₃	—	2	8	no	—
72	C₂×M₁₆×C₂₃	C₂³	1	8	yes	—
73	C₂²×C₈×C₂₃	C₂³	1	4	yes	—
74	C₂₃×C₄⋊Q₈	—	2	2	no	—
75	C₂₃×C₄⋊Q₈	C₂³	1	4	yes	—
76	C₂₃×#127	—	2	2	no	—
77	C₂₃×#127	C₂³	1	4	yes	—
78	C₂₃×#124	—	2	4	no	—
79	C₂₃×#124	C₂³	1	8	yes	—
80	C₂₃×#121	—	2	8	no	—
81	C₂₃×#121	—	2	8	no	—
82	C₄×Q₈×C₂₃	—	2	4	no	—
83	C₄×Q₈×C₂₃	—	2	4	no	—
84	C₄×Q₈×C₂₃	—	2	8	no	—
85	C₄×Q₈×C₂₃	—	2	8	no	—
86	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
87	C₄×Q₈×C₂₃	C₂³	1	8	yes	—
88	C₄×D₄×C₂₃	—	2	8	no	—
89	C₄×D₄×C₂₃	—	2	8	no	—
90	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
91	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
92	C₂×C₄⋊C₄×C₂₃	—	2	8	no	—
93	C₂×C₄⋊C₄×C₂₃	—	2	2	no	—
94	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
95	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
96	C₂×C₄⋊C₄×C₂₃	—	2	1	no	—
97	C₂×C₄⋊C₄×C₂₃	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
100	C₂×C₂²⋊C₄×C₂₃	—	2	2	no	—
101	C₂×C₄²×C₂₃	—	2	2	no	—
102	C₂×C₄²×C₂₃	—	2	2	no	—
103	C₂×C₄²×C₂₃	—	2	8	no	—
104	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₂₃	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₂₃	D₄	1	4	yes	—
107	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₂₃	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₂₃	C₂³	1	4	yes	—
110	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
111	C₂₃×C₄⋊C₈	C₂³	1	8	yes	—
112	C₂₃×#103	C₂³	1	16	yes	—
113	C₂₃×#102	C₂³	1	16	yes	—
114	C₂⁴×C₂₃	—	2	2	no	—
115	C₂⁴×C₂₃	C₂×D₄	1	1	yes	characteristic
116	#41×C₂₃	—	2	16	no	—
117	#41×C₂₃	—	2	16	no	—
118	#41×C₂₃	—	4	16	no	—
119	C₂×Q₈×C₂₃	—	2	8	no	—
120	C₂×Q₈×C₂₃	—	2	16	no	—
121	C₂×Q₈×C₂₃	—	2	4	no	—
122	C₂×Q₈×C₂₃	—	2	2	no	—
123	C₂×Q₈×C₂₃	—	2	2	no	—
124	C₂×Q₈×C₂₃	—	2	4	no	—
125	C₂×Q₈×C₂₃	—	2	8	no	—
126	C₂×Q₈×C₂₃	—	2	4	no	—
127	C₂×Q₈×C₂₃	—	2	4	no	—
128	C₂×Q₈×C₂₃	C₂×D₄	1	8	yes	—
129	C₂×Q₈×C₂₃	C₂×D₄	1	16	yes	complemented
130	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
131	C₂×Q₈×C₂₃	C₂⁴	1	4	yes	—
132	C₂×D₄×C₂₃	—	2	8	no	—
133	C₂×D₄×C₂₃	—	2	4	no	—
134	C₂×D₄×C₂₃	—	2	4	no	—
135	C₂×D₄×C₂₃	—	2	4	no	—
136	C₂×D₄×C₂₃	—	2	2	no	—
137	C₂×D₄×C₂₃	—	2	4	no	—
138	C₂×D₄×C₂₃	—	4	4	no	—
139	C₂×D₄×C₂₃	—	4	8	no	—
140	C₂×D₄×C₂₃	—	4	4	no	—
141	C₂×D₄×C₂₃	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₂₃	—	2	8	no	—
143	C₂²×C₄×C₂₃	—	2	4	no	—
144	C₂²×C₄×C₂₃	—	2	2	no	—
145	C₂²×C₄×C₂₃	—	2	4	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	8	no	—
150	C₂²×C₄×C₂₃	—	4	2	no	—
151	C₂²×C₄×C₂₃	—	4	4	no	—
152	C₂²×C₄×C₂₃	—	4	8	no	—
153	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
154	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₂₃	C₂×D₄	1	2	yes	—
159	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₂₃	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₂₃	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₂₃	#41	1	4	yes	—
163	C₂²×C₄×C₂₃	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
165	Q₁₆×C₂₃	—	2	32	no	—
166	SD₁₆×C₂₃	—	2	32	no	—
167	M₁₆×C₂₃	—	2	16	no	—
168	C₂×C₈×C₂₃	—	2	8	no	—
169	C₂×C₈×C₂₃	C₂⁴	1	8	yes	—
170	C₄⋊C₄×C₂₃	—	2	8	no	—
171	C₄⋊C₄×C₂₃	—	2	8	no	—
172	C₄⋊C₄×C₂₃	—	2	4	no	—
173	C₄⋊C₄×C₂₃	—	2	2	no	—
174	C₄⋊C₄×C₂₃	—	2	4	no	—
175	C₄⋊C₄×C₂₃	—	2	4	no	—
176	C₄⋊C₄×C₂₃	C₂⁴	1	4	yes	—
177	C₂²⋊C₄×C₂₃	—	2	8	no	—
178	C₂²⋊C₄×C₂₃	—	2	8	no	—
179	C₄²×C₂₃	—	2	8	no	—
180	C₄²×C₂₃	—	2	8	no	—
181	C₄²×C₂₃	C₂×D₄	1	4	yes	—
182	C₄²×C₂₃	C₂×D₄	1	4	yes	—
183	C₄²×C₂₃	C₂×D₄	1	2	yes	—
184	C₄²×C₂₃	C₂×D₄	1	2	yes	—
185	C₄²×C₂₃	C₂⁴	1	2	yes	—
186	C₄²×C₂₃	C₂⁴	1	2	yes	—
187	C₂×#3037	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂³×C₂₃	—	2	2	no	—
189	C₂³×C₂₃	—	2	2	no	—
190	C₂³×C₂₃	—	2	4	no	—
191	C₂³×C₂₃	—	4	4	no	—
192	C₂³×C₂₃	—	4	4	no	—
193	C₂³×C₂₃	—	4	4	no	—
194	C₂³×C₂₃	#121	1	4	yes	—
195	C₂³×C₂₃	C₂²×D₄	1	2	yes	—
196	C₂³×C₂₃	C₂²×D₄	1	1	yes	characteristic
197	Q₈×C₂₃	—	2	8	no	—
198	Q₈×C₂₃	—	2	16	no	—
199	Q₈×C₂₃	—	2	4	no	—
200	Q₈×C₂₃	—	2	4	no	—
201	Q₈×C₂₃	—	2	4	no	—
202	Q₈×C₂₃	—	4	4	no	—
203	Q₈×C₂₃	C₂²×D₄	1	8	yes	—
204	D₄×C₂₃	—	2	4	no	—
205	D₄×C₂₃	—	2	4	no	—
206	D₄×C₂₃	—	4	8	no	—
207	D₄×C₂₃	—	4	16	no	—
208	D₄×C₂₃	—	4	4	no	—
209	D₄×C₂₃	—	4	8	no	—
210	C₂×C₄×C₂₃	—	2	8	no	—
211	C₂×C₄×C₂₃	—	2	16	no	—
212	C₂×C₄×C₂₃	—	2	2	no	—
213	C₂×C₄×C₂₃	—	2	2	no	—
214	C₂×C₄×C₂₃	—	2	2	no	—
215	C₂×C₄×C₂₃	—	2	4	no	—
216	C₂×C₄×C₂₃	—	2	8	no	—
217	C₂×C₄×C₂₃	—	2	4	no	—
218	C₂×C₄×C₂₃	—	2	4	no	—
219	C₂×C₄×C₂₃	—	4	4	no	—
220	C₂×C₄×C₂₃	—	4	8	no	—
221	C₂×C₄×C₂₃	—	4	4	no	—
222	C₂×C₄×C₂₃	—	4	4	no	—
223	C₂×C₄×C₂₃	—	4	16	no	—
224	C₂×C₄×C₂₃	#121	1	4	yes	—
225	C₂×C₄×C₂₃	#121	1	8	yes	—
226	C₂×C₄×C₂₃	#137	1	4	yes	complemented
227	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
228	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
229	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
231	C₂×C₄×C₂₃	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₂₃	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₂₃	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₂₃	C₂×#41	1	2	yes	—
236	C₂×C₄×C₂₃	C₂×#41	1	4	yes	—
237	C₂×C₄×C₂₃	C₂⁵	1	1	yes	characteristic
238	C₈×C₂₃	—	2	8	no	—
239	C₂²×#137	C₂×C₂₃	1	2	yes	complemented
240	C₂×#532	C₂×C₂₃	1	1	yes	characteristic
241	C₂²×C₄×Q₈	C₂×C₂₃	1	1	yes	characteristic, complemented
242	#3037	C₂×C₂₃	1	16	yes	direct product factor
243	C₂×#464	C₂×C₂₃	1	4	yes	complemented
244	C₂×#462	C₂×C₂₃	1	2	yes	complemented
245	C₂×#460	C₂×C₂₃	1	2	yes	complemented
246	C₂×#423	C₂×C₂₃	1	1	yes	characteristic, complemented
247	C₂×#417	C₂×C₂₃	1	2	yes	complemented
248	C₂²×C₂₃	—	2	8	no	—
249	C₂²×C₂₃	—	2	2	no	—
250	C₂²×C₂₃	—	2	2	no	—
251	C₂²×C₂₃	—	4	4	no	—
252	C₂²×C₂₃	—	4	4	no	—
253	C₂²×C₂₃	—	4	4	no	—
254	C₂²×C₂₃	—	8	8	no	—
255	C₂²×C₂₃	C₂×#121	1	4	yes	—
256	C₂²×C₂₃	C₂×#121	1	2	yes	—
257	C₂²×C₂₃	C₂×#137	1	2	yes	—
258	C₂²×C₂₃	#575	1	2	yes	—
259	C₂²×C₂₃	C₂³×D₄	1	1	yes	characteristic
260	C₄×C₂₃	—	2	8	no	—
261	C₄×C₂₃	—	2	2	no	—
262	C₄×C₂₃	—	2	2	no	—
263	C₄×C₂₃	—	2	2	no	—
264	C₄×C₂₃	—	4	4	no	—
265	C₄×C₂₃	—	4	4	no	—
266	C₄×C₂₃	C₂×#121	1	4	yes	—
267	C₄×C₂₃	C₂×#121	1	2	yes	—
268	C₄×C₂₃	C₂×#137	1	4	yes	complemented
269	C₄×C₂₃	C₂³×D₄	1	1	yes	characteristic
270	C₄×C₂₃	C₂²×#41	1	1	yes	characteristic
271	C₂²×#41	C₂²×C₂₃	1	2	yes	—
272	C₂³×Q₈	C₂²×C₂₃	1	1	yes	characteristic
273	C₂×#137	—	2	16	no	—
274	C₂×#137	C₂²×C₂₃	1	16	yes	complemented
275	C₂²×Q₁₆	C₂²×C₂₃	1	4	yes	—
276	C₂²×SD₁₆	C₂²×C₂₃	1	4	yes	—
277	C₂²×M₁₆	C₂²×C₂₃	1	2	yes	—
278	#532	—	2	4	no	—
279	#532	C₂²×C₂₃	1	8	yes	—
280	C₂×C₄⋊Q₈	C₂²×C₂₃	1	1	yes	characteristic
281	C₂×#127	C₂²×C₂₃	1	1	yes	characteristic
282	C₂×#124	C₂²×C₂₃	1	2	yes	—
283	C₂×#121	—	2	1	no	—
284	C₂×#121	—	2	1	no	—
285	C₂×C₄×Q₈	—	2	1	no	—
286	C₂×C₄×Q₈	—	2	1	no	—
287	C₂×C₄×Q₈	—	2	4	no	—
288	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₂₃	1	2	yes	—
290	C₂×C₄×Q₈	C₂²×C₂₃	1	8	yes	complemented
291	C₂×C₄×D₄	—	2	1	no	—
292	C₂×C₄×D₄	—	2	1	no	—
293	C₂²×C₄⋊C₄	—	2	1	no	—
294	C₂²×C₄⋊C₄	C₂²×C₂₃	1	1	yes	characteristic
295	C₂²×C₄²	—	2	1	no	—
296	C₂²×C₄²	C₂²×C₂₃	1	1	yes	characteristic
297	#464	C₂²×C₂₃	1	32	yes	complemented
298	#462	C₂²×C₂₃	1	16	yes	complemented
299	#460	C₂²×C₂₃	1	16	yes	complemented
300	#423	C₂²×C₂₃	1	8	yes	complemented
301	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
302	C₂×C₄⋊C₈	C₂²×C₂₃	1	2	yes	—
303	#417	C₂²×C₂₃	1	16	yes	complemented
304	C₂×#103	C₂²×C₂₃	1	4	yes	—
305	C₂×#102	C₂²×C₂₃	1	4	yes	—
306	C₂×C₂₃	—	2	4	no	—
307	C₂×C₂₃	—	8	4	no	—
308	C₂×C₂₃	#3037	1	4	yes	direct product factor
309	C₂×C₂₃	C₂²×#121	1	1	yes	characteristic
310	C₂×C₂₃	C₂²×#137	1	1	yes	characteristic
311	C₂×C₂₃	C₂×#575	1	1	yes	characteristic
312	C₂×#41	—	2	4	no	—
313	C₂×#41	—	2	8	no	—
314	C₂×#41	—	2	8	no	—
315	C₂×#41	C₂³×C₂₃	1	8	yes	—
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	—	2	4	no	—
319	C₂²×Q₈	D₄×C₂₃	1	8	yes	complemented
320	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
321	C₂²×Q₈	C₂³×C₂₃	1	2	yes	—
322	C₂²×Q₈	C₂³×C₂₃	1	4	yes	—
323	C₂²×D₄	—	2	2	no	—
324	C₂²×D₄	—	2	1	no	—
325	C₂²×D₄	—	2	1	no	—
326	C₂²×D₄	C₂³×C₂₃	1	2	yes	—
327	C₂³×C₄	—	2	1	no	—
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	—	2	2	no	—
330	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
331	C₂³×C₄	D₄×C₂₃	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₂₃	1	1	yes	characteristic
333	#137	—	2	64	no	—
334	C₂×Q₁₆	—	2	16	no	—
335	C₂×Q₁₆	C₂³×C₂₃	1	16	yes	—
336	C₂×SD₁₆	—	2	16	no	—
337	C₂×SD₁₆	C₂³×C₂₃	1	16	yes	—
338	C₂×M₁₆	—	2	8	no	—
339	C₂×M₁₆	C₂³×C₂₃	1	8	yes	—
340	C₂²×C₈	C₂³×C₂₃	1	4	yes	—
341	C₄⋊Q₈	—	2	2	no	—
342	C₄⋊Q₈	C₂³×C₂₃	1	4	yes	—
343	#127	—	2	2	no	—
344	#127	C₂³×C₂₃	1	4	yes	—
345	#124	—	2	4	no	—
346	#124	C₂³×C₂₃	1	8	yes	—
347	#121	—	2	8	no	—
348	#121	—	2	8	no	—
349	C₄×Q₈	—	2	4	no	—
350	C₄×Q₈	—	2	4	no	—
351	C₄×Q₈	—	2	8	no	—
352	C₄×Q₈	—	2	8	no	—
353	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
354	C₄×Q₈	C₂³×C₂₃	1	8	yes	—
355	C₄×D₄	—	2	8	no	—
356	C₄×D₄	—	2	8	no	—
357	C₂×C₄⋊C₄	—	2	2	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	8	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	2	no	—
362	C₂×C₄⋊C₄	—	2	1	no	—
363	C₂×C₄⋊C₄	—	2	1	no	—
364	C₂×C₄⋊C₄	C₂³×C₂₃	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₂₃	1	4	yes	—
366	C₂×C₂²⋊C₄	—	2	2	no	—
367	C₂×C₂²⋊C₄	—	2	2	no	—
368	C₂×C₄²	—	2	2	no	—
369	C₂×C₄²	—	2	2	no	—
370	C₂×C₄²	—	2	8	no	—
371	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
372	C₂×C₄²	D₄×C₂₃	1	1	yes	characteristic
373	C₂×C₄²	D₄×C₂₃	1	4	yes	—
374	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
375	C₂×C₄²	C₂³×C₂₃	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₂₃	1	4	yes	—
377	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
378	C₄⋊C₈	C₂³×C₂₃	1	8	yes	—
379	#103	C₂³×C₂₃	1	16	yes	—
380	#102	C₂³×C₂₃	1	16	yes	—
381	C₂₃	C₂×#3037	1	1	yes	characteristic, direct product factor, Sylow
382	C₂⁴	—	2	2	no	—
383	C₂⁴	C₂×D₄×C₂₃	1	1	yes	characteristic
384	#41	—	2	16	no	—
385	#41	—	2	16	no	—
386	#41	—	4	16	no	—
387	C₂×Q₈	—	2	8	no	—
388	C₂×Q₈	—	2	16	no	—
389	C₂×Q₈	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	—	2	4	no	—
395	C₂×Q₈	—	2	4	no	—
396	C₂×Q₈	C₂×D₄×C₂₃	1	8	yes	—
397	C₂×Q₈	C₂×D₄×C₂₃	1	16	yes	complemented
398	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
399	C₂×Q₈	C₂⁴×C₂₃	1	4	yes	—
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	4	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	2	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	4	4	no	—
407	C₂×D₄	—	4	8	no	—
408	C₂×D₄	—	4	4	no	—
409	C₂×D₄	C₂⁴×C₂₃	1	4	yes	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	4	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	8	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	8	no	—
421	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
422	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
423	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₂₃	1	2	yes	—
428	C₂²×C₄	C₂×D₄×C₂₃	1	4	yes	—
429	C₂²×C₄	C₂×D₄×C₂₃	1	1	yes	characteristic
430	C₂²×C₄	#41×C₂₃	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
432	C₂²×C₄	C₂⁴×C₂₃	1	2	yes	—
433	Q₁₆	—	2	32	no	—
434	SD₁₆	—	2	32	no	—
435	M₁₆	—	2	16	no	—
436	C₂×C₈	—	2	8	no	—
437	C₂×C₈	C₂⁴×C₂₃	1	8	yes	—
438	C₄⋊C₄	—	2	8	no	—
439	C₄⋊C₄	—	2	8	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	C₂⁴×C₂₃	1	4	yes	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₄²	—	2	8	no	—
448	C₄²	—	2	8	no	—
449	C₄²	C₂×D₄×C₂₃	1	4	yes	—
450	C₄²	C₂×D₄×C₂₃	1	4	yes	—
451	C₄²	C₂×D₄×C₂₃	1	2	yes	—
452	C₄²	C₂×D₄×C₂₃	1	2	yes	—
453	C₄²	C₂⁴×C₂₃	1	2	yes	—
454	C₄²	C₂⁴×C₂₃	1	2	yes	—
455	C₂³	—	2	2	no	—
456	C₂³	—	2	2	no	—
457	C₂³	—	2	4	no	—
458	C₂³	—	4	4	no	—
459	C₂³	—	4	4	no	—
460	C₂³	—	4	4	no	—
461	C₂³	C₂₃×#121	1	4	yes	—
462	C₂³	C₂²×D₄×C₂₃	1	2	yes	—
463	C₂³	C₂²×D₄×C₂₃	1	1	yes	characteristic
464	Q₈	—	2	4	no	—
465	Q₈	—	2	8	no	—
466	Q₈	—	2	16	no	—
467	Q₈	—	2	4	no	—
468	Q₈	—	2	4	no	—
469	Q₈	—	4	4	no	—
470	Q₈	C₂²×D₄×C₂₃	1	8	yes	—
471	D₄	—	2	4	no	—
472	D₄	—	2	4	no	—
473	D₄	—	4	8	no	—
474	D₄	—	4	16	no	—
475	D₄	—	4	8	no	—
476	D₄	—	4	4	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	8	no	—
482	C₂×C₄	—	2	16	no	—
483	C₂×C₄	—	2	8	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	4	4	no	—
487	C₂×C₄	—	4	8	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	4	4	no	—
490	C₂×C₄	—	4	16	no	—
491	C₂×C₄	C₂₃×#121	1	4	yes	—
492	C₂×C₄	C₂₃×#121	1	8	yes	—
493	C₂×C₄	C₂₃×#137	1	4	yes	complemented
494	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
495	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
496	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
497	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
498	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
499	C₂×C₄	C₂²×D₄×C₂₃	1	4	yes	—
500	C₂×C₄	C₂²×D₄×C₂₃	1	2	yes	—
501	C₂×C₄	C₂²×D₄×C₂₃	1	1	yes	characteristic
502	C₂×C₄	C₂×#41×C₂₃	1	2	yes	—
503	C₂×C₄	C₂×#41×C₂₃	1	4	yes	—
504	C₂×C₄	C₂⁵×C₂₃	1	1	yes	characteristic
505	C₈	—	2	8	no	—
506	C₂²	—	2	8	no	—
507	C₂²	—	2	2	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	4	4	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	8	8	no	—
513	C₂²	C₂×C₂₃×#121	1	4	yes	—
514	C₂²	C₂×C₂₃×#121	1	2	yes	—
515	C₂²	C₂×C₂₃×#137	1	2	yes	—
516	C₂²	C₂₃×#575	1	2	yes	—
517	C₂²	C₂³×D₄×C₂₃	1	1	yes	characteristic
518	C₄	—	2	8	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	4	no	—
524	C₄	C₂×C₂₃×#121	1	4	yes	—
525	C₄	C₂×C₂₃×#121	1	2	yes	—
526	C₄	C₂×C₂₃×#137	1	4	yes	complemented
527	C₄	C₂³×D₄×C₂₃	1	1	yes	characteristic
528	C₄	C₂²×#41×C₂₃	1	1	yes	characteristic
529	C₂	—	2	4	no	—
530	C₂	—	8	4	no	—
531	C₂	C₂₃×#3037	1	4	yes	direct product factor
532	C₂	C₂²×C₂₃×#121	1	1	yes	characteristic
533	C₂	C₂²×C₂₃×#137	1	1	yes	characteristic
534	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×#532	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. C₂²×C₂₃×#137	C₂	semidirect
3. C₂²×C₄×Q₈×C₂₃	C₂	semidirect
4. C₂₃×#3037	C₂	direct (N × H)
5. C₂×C₂₃×#464	C₂	semidirect
6. C₂×C₂₃×#462	C₂	semidirect
7. C₂×C₂₃×#460	C₂	semidirect
8. C₂×C₂₃×#423	C₂	semidirect
9. C₂×C₂₃×#417	C₂	semidirect
13. C₂×C₂₃×#137	C₂²	semidirect
29. C₂×C₄×Q₈×C₂₃	C₂²	semidirect
36. C₂₃×#464	C₂²	semidirect
37. C₂₃×#462	C₂²	semidirect
38. C₂₃×#460	C₂²	semidirect
39. C₂₃×#423	C₂²	semidirect
42. C₂₃×#417	C₂²	semidirect
52. C₂²×Q₈×C₂₃	D₄	semidirect
129. C₂×Q₈×C₂₃	C₂×D₄	semidirect
187. C₂×#3037	C₂₃	direct (N × H)
226. C₂×C₄×C₂₃	#137	semidirect
239. C₂²×#137	C₂×C₂₃	semidirect
241. C₂²×C₄×Q₈	C₂×C₂₃	semidirect
242. #3037	C₂×C₂₃	direct (N × H)
243. C₂×#464	C₂×C₂₃	semidirect
244. C₂×#462	C₂×C₂₃	semidirect
245. C₂×#460	C₂×C₂₃	semidirect
246. C₂×#423	C₂×C₂₃	semidirect
247. C₂×#417	C₂×C₂₃	semidirect
268. C₄×C₂₃	C₂×#137	semidirect
274. C₂×#137	C₂²×C₂₃	semidirect
290. C₂×C₄×Q₈	C₂²×C₂₃	semidirect
297. #464	C₂²×C₂₃	semidirect
298. #462	C₂²×C₂₃	semidirect
299. #460	C₂²×C₂₃	semidirect
300. #423	C₂²×C₂₃	semidirect
303. #417	C₂²×C₂₃	semidirect
308. C₂×C₂₃	#3037	direct (N × H)
319. C₂²×Q₈	D₄×C₂₃	semidirect
381. C₂₃	C₂×#3037	direct (N × H)
397. C₂×Q₈	C₂×D₄×C₂₃	semidirect
493. C₂×C₄	C₂₃×#137	semidirect
526. C₄	C₂×C₂₃×#137	semidirect
531. C₂	C₂₃×#3037	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
C₂×C₂₃×#532	2
C₂²×C₄×Q₈×C₂₃	2
C₂₃×#3037	2
C₂×C₂₃×#464	2
C₂×C₂₃×#462	2
C₂×C₂₃×#460	2
C₂×C₂₃×#423	2
C₂×C₂₃×#417	2
C₂×#3037	23

Subgroups — C2×C23×#3037 #19208037

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₂₃×#3037 #19208037