Subgroups — C₂×C₃×#65277 #14320770

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#685	C₂	1	4	yes	maximal, complemented
4	C₂²×C₃×C₄×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65277	C₂	1	8	yes	maximal, direct product factor
6	C₂×#65277	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂⁴×C₃×D₅	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×Dic₅	C₂²	1	2	yes	—
11	C₂²×C₃×D₂₀	—	2	4	no	—
12	C₂²×C₃×D₂₀	—	2	4	no	—
13	C₂²×C₃×D₂₀	C₄	1	8	yes	complemented
14	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	4	yes	complemented
17	C₂×C₃×#685	—	2	16	no	—
18	C₂×C₃×#685	C₂²	1	16	yes	complemented
19	C₂×C₃×C₄×Dic₅	—	2	4	no	—
20	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	complemented
21	C₂×C₃×#390	—	5	1	no	maximal, Hall
22	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic
23	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
24	C₂²×#685	C₂×C₃	1	4	yes	complemented
25	C₂²×C₄×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
26	#65277	C₂×C₃	1	8	yes	direct product factor
27	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
28	C₂³×C₃×D₅	—	2	4	no	—
29	C₂³×C₃×D₅	—	2	4	no	—
30	C₂³×C₃×D₅	—	2	8	no	—
31	C₂³×C₃×D₅	—	2	8	no	—
32	C₂³×C₃×D₅	C₂×C₄	1	8	yes	—
33	C₂³×C₃×D₅	C₂³	1	4	yes	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	2	8	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
38	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×Dic₅	—	2	4	no	—
42	C₂²×C₃×Dic₅	—	2	4	no	—
43	C₂²×C₃×Dic₅	D₄	1	8	yes	complemented
44	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
45	C₂×C₃×D₂₀	—	2	32	no	—
46	C₂×C₃×D₂₀	—	2	8	no	—
47	C₂×C₃×D₂₀	—	2	8	no	—
48	C₂×C₃×D₂₀	C₂×C₄	1	16	yes	complemented
49	C₃×C₅×C₄⋊C₄	—	2	8	no	—
50	C₃×#685	—	2	32	no	—
51	C₃×C₄×Dic₅	—	2	8	no	—
52	C₂³×C₃×D₄	—	5	1	no	—
53	C₂²×C₃×C₄⋊C₄	D₅	1	1	yes	characteristic, complemented
54	C₂²×C₃×C₂²⋊C₄	—	5	4	no	—
55	C₂²×C₃×C₄²	—	5	1	no	—
56	C₃×#390	—	5	8	no	—
57	C₂⁴×D₅	C₂²×C₃	1	2	yes	—
58	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
59	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
60	C₂³×Dic₅	C₂²×C₃	1	2	yes	—
61	C₂²×D₂₀	—	2	4	no	—
62	C₂²×D₂₀	—	2	4	no	—
63	C₂²×D₂₀	C₃×C₄	1	8	yes	complemented
64	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
65	C₂×C₅×C₄⋊C₄	—	2	4	no	—
66	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
67	C₂×#685	—	2	16	no	—
68	C₂×#685	C₂²×C₃	1	16	yes	complemented
69	C₂×C₄×Dic₅	—	2	4	no	—
70	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	complemented
71	C₂×#390	—	5	1	no	Sylow
72	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
73	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
74	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
75	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
76	C₂³×C₃×C₅	#41	1	4	yes	—
77	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
78	C₂²×C₃×D₅	—	2	16	no	—
79	C₂²×C₃×D₅	—	2	32	no	—
80	C₂²×C₃×D₅	—	2	8	no	—
81	C₂²×C₃×D₅	—	2	4	no	—
82	C₂²×C₃×D₅	—	2	4	no	—
83	C₂²×C₃×D₅	—	2	8	no	—
84	C₂²×C₃×D₅	—	4	16	no	—
85	C₂²×C₃×D₅	—	4	8	no	—
86	C₂²×C₃×D₅	—	4	8	no	—
87	C₂²×C₃×D₅	C₂²×C₄	1	8	yes	—
88	C₂×C₃×C₄×C₅	—	2	8	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	4	8	no	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
92	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
93	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
94	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
95	C₂×C₃×Dic₅	—	2	16	no	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂×C₃×Dic₅	—	2	4	no	—
98	C₂×C₃×Dic₅	C₂×D₄	1	8	yes	complemented
99	C₃×D₂₀	—	2	32	no	—
100	C₂⁵×C₃	—	5	2	no	—
101	C₂²×C₃×D₄	—	5	8	no	—
102	C₂²×C₃×D₄	—	5	4	no	—
103	C₂²×C₃×D₄	—	10	4	no	—
104	C₂²×C₃×D₄	—	10	4	no	—
105	C₂³×C₃×C₄	—	5	2	no	—
106	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
107	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
108	C₂×C₃×C₄⋊C₄	—	2	4	no	—
109	C₂×C₃×C₄⋊C₄	C₂×D₅	1	4	yes	complemented
110	C₂×C₃×C₂²⋊C₄	—	5	16	no	—
111	C₂×C₃×C₂²⋊C₄	—	10	16	no	—
112	C₂×C₃×C₄²	—	5	4	no	—
113	C₂×C₃×C₄²	—	10	4	no	—
114	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
115	C₂³×D₅	—	2	4	no	—
116	C₂³×D₅	—	2	4	no	—
117	C₂³×D₅	—	2	8	no	—
118	C₂³×D₅	—	2	8	no	—
119	C₂³×D₅	C₂×C₃×C₄	1	8	yes	—
120	C₂³×D₅	C₂³×C₃	1	4	yes	—
121	C₂²×C₄×C₅	—	2	4	no	—
122	C₂²×C₄×C₅	—	2	8	no	—
123	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
124	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
125	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×Dic₅	—	2	4	no	—
129	C₂²×Dic₅	—	2	4	no	—
130	C₂²×Dic₅	C₃×D₄	1	8	yes	complemented
131	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
132	C₂×D₂₀	—	2	32	no	—
133	C₂×D₂₀	—	2	8	no	—
134	C₂×D₂₀	—	2	8	no	—
135	C₂×D₂₀	C₂×C₃×C₄	1	16	yes	complemented
136	C₅×C₄⋊C₄	—	2	8	no	—
137	#685	—	2	32	no	—
138	C₄×Dic₅	—	2	8	no	—
139	C₂³×D₄	—	5	1	no	—
140	C₂²×C₄⋊C₄	C₃×D₅	1	1	yes	characteristic, complemented
141	C₂²×C₂²⋊C₄	—	5	4	no	—
142	C₂²×C₄²	—	5	1	no	—
143	#390	—	5	8	no	—
144	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
145	C₂²×C₃×C₅	C₄×D₄	1	8	yes	—
146	C₂²×C₃×C₅	#121	1	8	yes	—
147	C₂²×C₃×C₅	#124	1	4	yes	—
148	C₂²×C₃×C₅	#127	1	4	yes	—
149	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
152	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
153	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
154	C₂×C₃×D₅	—	2	8	no	—
155	C₂×C₃×D₅	—	2	16	no	—
156	C₂×C₃×D₅	—	4	8	no	—
157	C₂×C₃×D₅	—	4	4	no	—
158	C₂×C₃×D₅	—	4	4	no	—
159	C₂×C₃×D₅	—	4	32	no	—
160	C₃×C₄×C₅	—	4	4	no	—
161	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
162	C₃×Dic₅	—	2	8	no	—
163	C₂⁴×C₃	—	5	8	no	—
164	C₂⁴×C₃	—	5	4	no	—
165	C₂⁴×C₃	—	10	4	no	—
166	C₂⁴×C₃	—	10	8	no	—
167	C₂⁴×C₃	—	10	8	no	—
168	C₂⁴×C₃	—	10	4	no	—
169	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
170	C₂×C₃×D₄	—	5	16	no	—
171	C₂×C₃×D₄	—	10	32	no	—
172	C₂×C₃×D₄	—	10	8	no	—
173	C₂×C₃×D₄	—	10	8	no	—
174	C₂²×C₃×C₄	—	2	8	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	5	8	no	—
177	C₂²×C₃×C₄	—	5	4	no	—
178	C₂²×C₃×C₄	—	10	4	no	—
179	C₂²×C₃×C₄	—	10	4	no	—
180	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
181	C₂²×C₃×C₄	D₂₀	1	4	yes	—
182	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
184	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
185	C₃×C₄⋊C₄	—	2	8	no	—
186	C₃×C₂²⋊C₄	—	10	32	no	—
187	C₃×C₄²	—	10	8	no	—
188	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
189	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
190	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
191	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
192	C₂³×C₅	C₃×#41	1	4	yes	—
193	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
194	C₂²×D₅	—	2	16	no	—
195	C₂²×D₅	—	2	32	no	—
196	C₂²×D₅	—	2	8	no	—
197	C₂²×D₅	—	2	4	no	—
198	C₂²×D₅	—	2	4	no	—
199	C₂²×D₅	—	2	8	no	—
200	C₂²×D₅	—	4	16	no	—
201	C₂²×D₅	—	4	8	no	—
202	C₂²×D₅	—	4	8	no	—
203	C₂²×D₅	C₂²×C₃×C₄	1	8	yes	—
204	C₂×C₄×C₅	—	2	8	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	4	8	no	—
207	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	16	yes	complemented
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
211	C₂×Dic₅	—	2	16	no	—
212	C₂×Dic₅	—	2	4	no	—
213	C₂×Dic₅	—	2	4	no	—
214	C₂×Dic₅	C₂×C₃×D₄	1	8	yes	complemented
215	D₂₀	—	2	32	no	—
216	C₂⁵	—	5	2	no	—
217	C₂²×D₄	—	5	8	no	—
218	C₂²×D₄	—	5	4	no	—
219	C₂²×D₄	—	10	4	no	—
220	C₂²×D₄	—	10	4	no	—
221	C₂³×C₄	—	5	2	no	—
222	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
223	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
224	C₂×C₄⋊C₄	—	2	4	no	—
225	C₂×C₄⋊C₄	C₂×C₃×D₅	1	4	yes	complemented
226	C₂×C₂²⋊C₄	—	5	16	no	—
227	C₂×C₂²⋊C₄	—	10	16	no	—
228	C₂×C₄²	—	5	4	no	—
229	C₂×C₄²	—	10	4	no	—
230	C₂×C₃×C₅	#390	1	8	yes	complemented
231	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
233	C₂×C₃×C₅	C₂×#121	1	2	yes	—
234	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
235	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
236	C₃×D₅	—	4	8	no	—
237	C₂³×C₃	—	5	8	no	—
238	C₂³×C₃	—	10	4	no	—
239	C₂³×C₃	—	10	8	no	—
240	C₂³×C₃	—	10	8	no	—
241	C₂³×C₃	—	10	4	no	—
242	C₂³×C₃	—	10	32	no	—
243	C₂³×C₃	—	10	16	no	—
244	C₂³×C₃	—	20	16	no	—
245	C₂³×C₃	—	20	8	no	—
246	C₂³×C₃	—	20	8	no	—
247	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
248	C₂³×C₃	C₂×D₂₀	1	2	yes	—
249	C₂³×C₃	D₄×D₅	1	4	yes	—
250	C₂³×C₃	#713	1	4	yes	—
251	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
252	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
253	C₃×D₄	—	10	32	no	—
254	C₂×C₃×C₄	—	2	8	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	—	4	8	no	—
257	C₂×C₃×C₄	—	5	8	no	—
258	C₂×C₃×C₄	—	10	4	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	10	16	no	—
261	C₂×C₃×C₄	#685	1	16	yes	complemented
262	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
263	C₂×C₃×C₄	C₂×D₂₀	1	4	yes	—
264	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
265	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
266	C₂²×C₅	C₃×C₄×D₄	1	8	yes	—
267	C₂²×C₅	C₃×#121	1	8	yes	—
268	C₂²×C₅	C₃×#124	1	4	yes	—
269	C₂²×C₅	C₃×#127	1	4	yes	—
270	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
271	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
272	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
273	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
274	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
275	C₂×D₅	—	2	8	no	—
276	C₂×D₅	—	2	16	no	—
277	C₂×D₅	—	4	32	no	—
278	C₂×D₅	—	4	8	no	—
279	C₂×D₅	—	4	4	no	—
280	C₂×D₅	—	4	4	no	—
281	C₄×C₅	—	4	4	no	—
282	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	8	yes	complemented
283	Dic₅	—	2	8	no	—
284	C₂⁴	—	5	8	no	—
285	C₂⁴	—	5	4	no	—
286	C₂⁴	—	10	4	no	—
287	C₂⁴	—	10	8	no	—
288	C₂⁴	—	10	8	no	—
289	C₂⁴	—	10	4	no	—
290	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
291	C₂×D₄	—	5	16	no	—
292	C₂×D₄	—	10	32	no	—
293	C₂×D₄	—	10	8	no	—
294	C₂×D₄	—	10	8	no	—
295	C₂²×C₄	—	2	8	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	5	8	no	—
298	C₂²×C₄	—	5	4	no	—
299	C₂²×C₄	—	10	4	no	—
300	C₂²×C₄	—	10	4	no	—
301	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
302	C₂²×C₄	C₃×D₂₀	1	4	yes	—
303	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
304	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
305	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
306	C₄⋊C₄	—	2	8	no	—
307	C₂²⋊C₄	—	10	32	no	—
308	C₄²	—	10	8	no	—
309	C₃×C₅	C₂×#390	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	—	10	16	no	—
311	C₂²×C₃	—	10	8	no	—
312	C₂²×C₃	—	20	8	no	—
313	C₂²×C₃	—	20	4	no	—
314	C₂²×C₃	—	20	4	no	—
315	C₂²×C₃	—	20	32	no	—
316	C₂²×C₃	#4039	1	8	yes	—
317	C₂²×C₃	#4041	1	8	yes	—
318	C₂²×C₃	C₂×#685	1	4	yes	—
319	C₂²×C₃	#4086	1	4	yes	—
320	C₂²×C₃	#4093	1	4	yes	—
321	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
322	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
323	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
324	C₂²×C₃	C₂×#713	1	2	yes	—
325	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
326	C₃×C₄	—	4	4	no	—
327	C₃×C₄	—	10	8	no	—
328	C₃×C₄	C₂×#685	1	8	yes	complemented
329	C₂×C₅	C₃×#390	1	8	yes	complemented
330	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×C₅	C₂×C₃×C₄×D₄	1	2	yes	—
332	C₂×C₅	C₂×C₃×#121	1	2	yes	—
333	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
334	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
335	D₅	—	4	8	no	—
336	C₂³	—	5	8	no	—
337	C₂³	—	10	4	no	—
338	C₂³	—	10	8	no	—
339	C₂³	—	10	8	no	—
340	C₂³	—	10	4	no	—
341	C₂³	—	10	32	no	—
342	C₂³	—	10	16	no	—
343	C₂³	—	20	8	no	—
344	C₂³	—	20	8	no	—
345	C₂³	—	20	16	no	—
346	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
347	C₂³	C₂×C₃×D₂₀	1	2	yes	—
348	C₂³	C₃×D₄×D₅	1	4	yes	—
349	C₂³	C₃×#713	1	4	yes	—
350	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
351	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
352	D₄	—	10	32	no	—
353	C₂×C₄	—	2	8	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	5	8	no	—
357	C₂×C₄	—	10	4	no	—
358	C₂×C₄	—	10	4	no	—
359	C₂×C₄	—	10	16	no	—
360	C₂×C₄	C₃×#685	1	16	yes	complemented
361	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
362	C₂×C₄	C₂×C₃×D₂₀	1	4	yes	—
363	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
364	C₂×C₃	—	20	8	no	—
365	C₂×C₃	#65277	1	8	yes	direct product factor
366	C₂×C₃	C₂×#4039	1	2	yes	—
367	C₂×C₃	C₂×#4041	1	2	yes	—
368	C₂×C₃	C₂²×#685	1	1	yes	characteristic
369	C₂×C₃	C₂×#4086	1	1	yes	characteristic
370	C₂×C₃	C₂×#4093	1	1	yes	characteristic
371	C₅	C₂×C₃×#390	1	1	yes	characteristic, complemented, Sylow
372	C₂²	—	10	8	no	—
373	C₂²	—	10	16	no	—
374	C₂²	—	20	4	no	—
375	C₂²	—	20	4	no	—
376	C₂²	—	20	32	no	—
377	C₂²	—	20	8	no	—
378	C₂²	C₃×#4039	1	8	yes	—
379	C₂²	C₃×#4041	1	8	yes	—
380	C₂²	C₂×C₃×#685	1	4	yes	—
381	C₂²	C₃×#4086	1	4	yes	—
382	C₂²	C₃×#4093	1	4	yes	—
383	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
384	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
385	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
386	C₂²	C₂×C₃×#713	1	2	yes	—
387	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
388	C₄	—	4	4	no	—
389	C₄	—	10	8	no	—
390	C₄	C₂×C₃×#685	1	8	yes	complemented
391	C₃	C₂×#65277	1	1	yes	characteristic, direct product factor, Sylow
392	C₂	—	20	8	no	—
393	C₂	C₃×#65277	1	8	yes	direct product factor
394	C₂	C₂×C₃×#4039	1	2	yes	—
395	C₂	C₂×C₃×#4041	1	2	yes	—
396	C₂	C₂²×C₃×#685	1	1	yes	characteristic
397	C₂	C₂×C₃×#4086	1	1	yes	characteristic
398	C₂	C₂×C₃×#4093	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×C₄⋊C₄	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂³×C₃×D₂₀	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄⋊C₄	D₅
hypocenter	C₅	C₂×C₃×#390
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×C₄⋊C₄	C₂	semidirect
3. C₂²×C₃×#685	C₂	semidirect
4. C₂²×C₃×C₄×Dic₅	C₂	semidirect
5. C₃×#65277	C₂	direct (N × H)
6. C₂×#65277	C₃	direct (N × H)
13. C₂²×C₃×D₂₀	C₄	semidirect
16. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
18. C₂×C₃×#685	C₂²	semidirect
20. C₂×C₃×C₄×Dic₅	C₂²	semidirect
23. C₂²×C₅×C₄⋊C₄	C₂×C₃	semidirect
24. C₂²×#685	C₂×C₃	semidirect
25. C₂²×C₄×Dic₅	C₂×C₃	semidirect
26. #65277	C₂×C₃	direct (N × H)
43. C₂²×C₃×Dic₅	D₄	semidirect
48. C₂×C₃×D₂₀	C₂×C₄	semidirect
53. C₂²×C₃×C₄⋊C₄	D₅	semidirect
63. C₂²×D₂₀	C₃×C₄	semidirect
66. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
68. C₂×#685	C₂²×C₃	semidirect
70. C₂×C₄×Dic₅	C₂²×C₃	semidirect
91. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
98. C₂×C₃×Dic₅	C₂×D₄	semidirect
109. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
130. C₂²×Dic₅	C₃×D₄	semidirect
135. C₂×D₂₀	C₂×C₃×C₄	semidirect
140. C₂²×C₄⋊C₄	C₃×D₅	semidirect
161. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
207. C₂×C₄×C₅	C₃×C₂²⋊C₄	semidirect
214. C₂×Dic₅	C₂×C₃×D₄	semidirect
225. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
230. C₂×C₃×C₅	#390	semidirect
261. C₂×C₃×C₄	#685	semidirect
282. C₄×C₅	C₂×C₃×C₂²⋊C₄	semidirect
309. C₃×C₅	C₂×#390	semidirect
328. C₃×C₄	C₂×#685	semidirect
329. C₂×C₅	C₃×#390	semidirect
360. C₂×C₄	C₃×#685	semidirect
365. C₂×C₃	#65277	direct (N × H)
371. C₅	C₂×C₃×#390	semidirect
390. C₄	C₂×C₃×#685	semidirect
391. C₃	C₂×#65277	direct (N × H)
393. C₂	C₃×#65277	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×D₂₀	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₂²×C₃×#685	2
C₂²×C₃×C₄×Dic₅	2
C₃×#65277	2
C₂×#65277	3
C₂×C₃×#390	5

Subgroups — C2×C3×#65277 #14320770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65277 #14320770