Subgroups — C₂²×C₃×#3937 #14412798

Order 1920.

1712 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×#681	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3937	C₂	1	12	yes	maximal, direct product factor
5	C₂²×#3937	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂³×C₃×C₄×C₅	—	2	1	no	—
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
9	C₂×C₃×#709	—	2	3	no	—
10	C₂×C₃×#709	—	2	3	no	—
11	C₂×C₃×#709	C₄	1	6	yes	complemented
12	C₂×C₃×#709	C₂²	1	6	yes	—
13	C₂²×C₃×D₂₀	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₃×C₄×D₅	—	2	1	no	—
15	C₂²×C₃×Dic₁₀	C₄	1	1	yes	characteristic, complemented
16	C₂×C₃×C₄²×C₅	—	2	3	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	6	yes	complemented
18	C₂×C₃×#681	—	2	3	no	—
19	C₂×C₃×#681	C₂²	1	6	yes	complemented
20	C₂²×C₃×#168	—	2	1	no	—
21	C₃×#3937	C₂²	1	16	yes	direct product factor
22	C₂²×C₃×#104	—	5	1	no	maximal, Hall
23	C₂²×#709	C₂×C₃	1	1	yes	characteristic
24	C₂²×C₄²×C₅	C₂×C₃	1	1	yes	characteristic, complemented
25	C₂²×#681	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#3937	C₂×C₃	1	12	yes	direct product factor
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂³×C₃×D₅	—	2	1	no	—
29	C₂²×C₃×C₄×C₅	—	2	8	no	—
30	C₂²×C₃×C₄×C₅	—	2	6	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
33	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
34	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
37	C₂×C₃×C₂²⋊D₅	—	2	6	no	—
38	C₂×C₃×C₂²⋊D₅	—	2	6	no	—
39	C₂²×C₃×Dic₅	—	2	1	no	—
40	C₃×#709	—	2	12	no	—
41	C₃×#709	—	2	6	no	—
42	C₃×#709	—	2	6	no	—
43	C₃×#709	C₂×C₄	1	12	yes	complemented
44	C₃×#709	C₂³	1	4	yes	—
45	C₂×C₃×D₂₀	—	2	3	no	—
46	C₂×C₃×D₂₀	C₂×C₄	1	6	yes	complemented
47	C₂×C₃×C₄×D₅	—	2	6	no	—
48	C₂×C₃×C₄×D₅	—	2	6	no	—
49	C₂×C₃×Dic₁₀	—	2	3	no	—
50	C₂×C₃×Dic₁₀	C₂×C₄	1	6	yes	complemented
51	C₃×C₄²×C₅	—	2	6	no	—
52	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
53	C₃×#681	—	2	6	no	—
54	C₃×#681	C₂³	1	4	yes	complemented
55	C₂×C₃×#168	—	2	6	no	—
56	C₂²×C₃×#41	—	5	1	no	—
57	C₂²×C₃×M₁₆	—	5	1	no	—
58	C₂²×C₃×C₄²	D₅	1	1	yes	characteristic, complemented
59	C₂×C₃×#104	—	5	12	no	—
60	C₂³×C₄×C₅	—	2	1	no	—
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂²×C₂²⋊D₅	—	2	1	no	—
63	C₂×#709	—	2	3	no	—
64	C₂×#709	—	2	3	no	—
65	C₂×#709	C₃×C₄	1	6	yes	complemented
66	C₂×#709	C₂²×C₃	1	6	yes	—
67	C₂²×D₂₀	C₃×C₄	1	1	yes	characteristic, complemented
68	C₂²×C₄×D₅	—	2	1	no	—
69	C₂²×Dic₁₀	C₃×C₄	1	1	yes	characteristic, complemented
70	C₂×C₄²×C₅	—	2	3	no	—
71	C₂×C₄²×C₅	C₂²×C₃	1	6	yes	complemented
72	C₂×#681	—	2	3	no	—
73	C₂×#681	C₂²×C₃	1	6	yes	complemented
74	C₂²×#168	—	2	1	no	—
75	#3937	C₂²×C₃	1	16	yes	direct product factor
76	C₂²×#104	—	5	1	no	Sylow
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	C₂²⋊C₄	1	3	yes	—
79	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
80	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
81	C₂²×C₃×D₅	—	2	6	no	—
82	C₂²×C₃×D₅	—	4	4	no	—
83	C₂×C₃×C₄×C₅	—	2	24	no	—
84	C₂×C₃×C₄×C₅	—	2	4	no	—
85	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
86	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
87	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	6	yes	—
88	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
89	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
90	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
91	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
93	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
94	C₃×C₂²⋊D₅	—	2	12	no	—
95	C₃×C₂²⋊D₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	6	no	—
97	C₃×D₂₀	—	2	6	no	—
98	C₃×D₂₀	C₂²×C₄	1	4	yes	complemented
99	C₃×C₄×D₅	—	2	12	no	—
100	C₃×C₄×D₅	—	2	4	no	—
101	C₃×Dic₁₀	—	2	6	no	—
102	C₃×Dic₁₀	C₂²×C₄	1	4	yes	complemented
103	C₃×#168	—	2	4	no	—
104	C₂×C₃×#41	—	5	6	no	—
105	C₂×C₃×#41	—	5	6	no	—
106	C₂×C₃×#41	—	10	3	no	—
107	C₂×C₃×#41	—	10	3	no	—
108	C₂²×C₃×Q₈	—	5	1	no	—
109	C₂²×C₃×D₄	—	5	1	no	—
110	C₂²×C₃×D₄	—	10	1	no	—
111	C₂³×C₃×C₄	—	2	1	no	—
112	C₂³×C₃×C₄	—	10	1	no	—
113	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
114	C₂×C₃×M₁₆	—	5	6	no	—
115	C₂×C₃×M₁₆	—	10	3	no	—
116	C₂²×C₃×C₈	—	10	1	no	—
117	C₂×C₃×C₄²	—	2	3	no	—
118	C₂×C₃×C₄²	C₂×D₅	1	6	yes	complemented
119	C₃×#104	—	5	16	no	—
120	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
121	C₂³×D₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	8	no	—
123	C₂²×C₄×C₅	—	2	6	no	—
124	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×C₃×C₄	1	3	yes	—
126	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₃×D₄	1	3	yes	—
128	C₂²×C₄×C₅	C₃×D₄	1	3	yes	—
129	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
130	C₂×C₂²⋊D₅	—	2	6	no	—
131	C₂×C₂²⋊D₅	—	2	6	no	—
132	C₂²×Dic₅	—	2	1	no	—
133	#709	—	2	12	no	—
134	#709	—	2	6	no	—
135	#709	—	2	6	no	—
136	#709	C₂×C₃×C₄	1	12	yes	complemented
137	#709	C₂³×C₃	1	4	yes	—
138	C₂×D₂₀	—	2	3	no	—
139	C₂×D₂₀	C₂×C₃×C₄	1	6	yes	complemented
140	C₂×C₄×D₅	—	2	6	no	—
141	C₂×C₄×D₅	—	2	6	no	—
142	C₂×Dic₁₀	—	2	3	no	—
143	C₂×Dic₁₀	C₂×C₃×C₄	1	6	yes	complemented
144	C₄²×C₅	—	2	6	no	—
145	C₄²×C₅	C₂³×C₃	1	4	yes	complemented
146	#681	—	2	6	no	—
147	#681	C₂³×C₃	1	4	yes	complemented
148	C₂×#168	—	2	6	no	—
149	C₂²×#41	—	5	1	no	—
150	C₂²×M₁₆	—	5	1	no	—
151	C₂²×C₄²	C₃×D₅	1	1	yes	characteristic, complemented
152	C₂×#104	—	5	12	no	—
153	C₂²×C₃×C₅	—	2	6	no	—
154	C₂²×C₃×C₅	—	2	6	no	—
155	C₂²×C₃×C₅	#104	1	4	yes	complemented
156	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
157	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
158	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₃×D₅	—	2	4	no	—
160	C₂×C₃×D₅	—	4	12	no	—
161	C₃×C₄×C₅	—	2	8	no	—
162	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
163	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	3	yes	—
164	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
165	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
166	C₃×Dic₅	—	2	4	no	—
167	C₂⁴×C₃	—	10	1	no	—
168	C₂⁴×C₃	C₂²⋊D₅	1	1	yes	characteristic
169	C₃×#41	—	5	12	no	—
170	C₃×#41	—	5	4	no	—
171	C₃×#41	—	10	12	no	—
172	C₃×#41	—	10	6	no	—
173	C₃×#41	—	10	6	no	—
174	C₂×C₃×Q₈	—	5	6	no	—
175	C₂×C₃×Q₈	—	10	3	no	—
176	C₂×C₃×D₄	—	5	6	no	—
177	C₂×C₃×D₄	—	10	6	no	—
178	C₂×C₃×D₄	—	10	6	no	—
179	C₂×C₃×D₄	—	10	3	no	—
180	C₂²×C₃×C₄	—	2	8	no	—
181	C₂²×C₃×C₄	—	2	6	no	—
182	C₂²×C₃×C₄	—	10	1	no	—
183	C₂²×C₃×C₄	—	10	6	no	—
184	C₂²×C₃×C₄	—	10	6	no	—
185	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
186	C₂²×C₃×C₄	C₄×D₅	1	3	yes	—
187	C₂²×C₃×C₄	D₂₀	1	3	yes	—
188	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
189	C₂²×C₃×C₄	C₂²⋊D₅	1	3	yes	—
190	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
191	C₃×M₁₆	—	5	4	no	—
192	C₃×M₁₆	—	10	6	no	—
193	C₂×C₃×C₈	—	10	6	no	—
194	C₃×C₄²	—	2	6	no	—
195	C₃×C₄²	C₂²×D₅	1	4	yes	complemented
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	C₃×C₂²⋊C₄	1	3	yes	—
198	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
199	C₂³×C₅	C₂×C₃×D₄	1	3	yes	—
200	C₂²×D₅	—	2	6	no	—
201	C₂²×D₅	—	4	4	no	—
202	C₂×C₄×C₅	—	2	24	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	3	yes	—
205	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	3	yes	—
206	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	6	yes	—
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	3	yes	—
208	C₂×C₄×C₅	C₂²×C₃×C₄	1	3	yes	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
210	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
211	C₂×C₄×C₅	C₂×C₃×D₄	1	3	yes	—
212	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
213	C₂²⋊D₅	—	2	12	no	—
214	C₂²⋊D₅	—	2	4	no	—
215	C₂×Dic₅	—	2	6	no	—
216	D₂₀	—	2	6	no	—
217	D₂₀	C₂²×C₃×C₄	1	4	yes	complemented
218	C₄×D₅	—	2	12	no	—
219	C₄×D₅	—	2	4	no	—
220	Dic₁₀	—	2	6	no	—
221	Dic₁₀	C₂²×C₃×C₄	1	4	yes	complemented
222	#168	—	2	4	no	—
223	C₂×#41	—	5	6	no	—
224	C₂×#41	—	5	6	no	—
225	C₂×#41	—	10	3	no	—
226	C₂×#41	—	10	3	no	—
227	C₂²×Q₈	—	5	1	no	—
228	C₂²×D₄	—	5	1	no	—
229	C₂²×D₄	—	10	1	no	—
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	—	10	1	no	—
232	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
233	C₂×M₁₆	—	5	6	no	—
234	C₂×M₁₆	—	10	3	no	—
235	C₂²×C₈	—	10	1	no	—
236	C₂×C₄²	—	2	3	no	—
237	C₂×C₄²	C₂×C₃×D₅	1	6	yes	complemented
238	#104	—	5	16	no	—
239	C₂×C₃×C₅	—	2	1	no	—
240	C₂×C₃×C₅	—	2	3	no	—
241	C₂×C₃×C₅	C₂×#104	1	6	yes	complemented
242	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
243	C₃×D₅	—	4	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	10	6	no	—
246	C₂³×C₃	—	20	4	no	—
247	C₂³×C₃	#685	1	3	yes	—
248	C₂³×C₃	#685	1	1	yes	characteristic
249	C₂³×C₃	C₂×C₂²⋊D₅	1	3	yes	—
250	C₃×Q₈	—	5	4	no	—
251	C₃×Q₈	—	10	6	no	—
252	C₃×D₄	—	5	4	no	—
253	C₃×D₄	—	10	4	no	—
254	C₃×D₄	—	10	12	no	—
255	C₃×D₄	—	10	6	no	—
256	C₂×C₃×C₄	—	2	24	no	—
257	C₂×C₃×C₄	—	2	4	no	—
258	C₂×C₃×C₄	—	10	6	no	—
259	C₂×C₃×C₄	—	10	4	no	—
260	C₂×C₃×C₄	—	10	12	no	—
261	C₂×C₃×C₄	#685	1	3	yes	—
262	C₂×C₃×C₄	#685	1	3	yes	—
263	C₂×C₃×C₄	#685	1	6	yes	—
264	C₂×C₃×C₄	C₂×C₄×D₅	1	3	yes	—
265	C₂×C₃×C₄	C₂×C₄×D₅	1	3	yes	—
266	C₂×C₃×C₄	C₂×D₂₀	1	3	yes	—
267	C₂×C₃×C₄	C₂×D₂₀	1	3	yes	—
268	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	3	yes	—
269	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
270	C₃×C₈	—	10	4	no	—
271	C₂²×C₅	—	2	6	no	—
272	C₂²×C₅	—	2	6	no	—
273	C₂²×C₅	C₃×#104	1	4	yes	complemented
274	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
275	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
276	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
277	C₂×D₅	—	2	4	no	—
278	C₂×D₅	—	4	12	no	—
279	C₄×C₅	—	2	8	no	—
280	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
281	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	3	yes	—
282	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
283	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
284	Dic₅	—	2	4	no	—
285	C₂⁴	—	10	1	no	—
286	C₂⁴	C₃×C₂²⋊D₅	1	1	yes	characteristic
287	#41	—	5	12	no	—
288	#41	—	5	4	no	—
289	#41	—	10	12	no	—
290	#41	—	10	6	no	—
291	#41	—	10	6	no	—
292	C₂×Q₈	—	5	6	no	—
293	C₂×Q₈	—	10	3	no	—
294	C₂×D₄	—	5	6	no	—
295	C₂×D₄	—	10	6	no	—
296	C₂×D₄	—	10	6	no	—
297	C₂×D₄	—	10	3	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	—	10	1	no	—
301	C₂²×C₄	—	10	6	no	—
302	C₂²×C₄	—	10	6	no	—
303	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
304	C₂²×C₄	C₃×C₄×D₅	1	3	yes	—
305	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
306	C₂²×C₄	C₃×D₂₀	1	3	yes	—
307	C₂²×C₄	C₃×C₂²⋊D₅	1	3	yes	—
308	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
309	M₁₆	—	5	4	no	—
310	M₁₆	—	10	6	no	—
311	C₂×C₈	—	10	6	no	—
312	C₄²	—	2	6	no	—
313	C₄²	C₂²×C₃×D₅	1	4	yes	complemented
314	C₃×C₅	C₂²×#104	1	1	yes	characteristic, complemented, Hall
315	C₂²×C₃	—	2	6	no	—
316	C₂²×C₃	—	2	6	no	—
317	C₂²×C₃	—	10	4	no	—
318	C₂²×C₃	—	20	12	no	—
319	C₂²×C₃	#3937	1	4	yes	direct product factor
320	C₂²×C₃	C₂×#685	1	3	yes	—
321	C₂²×C₃	C₂×#685	1	3	yes	—
322	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
323	C₃×C₄	—	2	8	no	—
324	C₃×C₄	—	10	4	no	—
325	C₃×C₄	C₂×#685	1	3	yes	—
326	C₃×C₄	C₂×#685	1	3	yes	—
327	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
328	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	2	3	no	—
331	C₂×C₅	C₂×C₃×#104	1	6	yes	complemented
332	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
333	D₅	—	4	4	no	—
334	C₂³	—	2	4	no	—
335	C₂³	—	10	6	no	—
336	C₂³	—	20	4	no	—
337	C₂³	C₃×#685	1	3	yes	—
338	C₂³	C₃×#685	1	1	yes	characteristic
339	C₂³	C₂×C₃×C₂²⋊D₅	1	3	yes	—
340	Q₈	—	5	4	no	—
341	Q₈	—	10	6	no	—
342	D₄	—	5	4	no	—
343	D₄	—	10	4	no	—
344	D₄	—	10	12	no	—
345	D₄	—	10	6	no	—
346	C₂×C₄	—	2	24	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	10	6	no	—
349	C₂×C₄	—	10	4	no	—
350	C₂×C₄	—	10	12	no	—
351	C₂×C₄	C₃×#685	1	3	yes	—
352	C₂×C₄	C₃×#685	1	3	yes	—
353	C₂×C₄	C₃×#685	1	6	yes	—
354	C₂×C₄	C₂×C₃×C₄×D₅	1	3	yes	—
355	C₂×C₄	C₂×C₃×C₄×D₅	1	3	yes	—
356	C₂×C₄	C₂×C₃×D₂₀	1	3	yes	—
357	C₂×C₄	C₂×C₃×D₂₀	1	3	yes	—
358	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	3	yes	—
359	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
360	C₈	—	10	4	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	3	no	—
363	C₂×C₃	—	20	4	no	—
364	C₂×C₃	C₂×#3937	1	6	yes	direct product factor
365	C₂×C₃	C₂²×#685	1	1	yes	characteristic
366	C₅	C₂²×C₃×#104	1	1	yes	characteristic, complemented, Sylow
367	C₂²	—	2	6	no	—
368	C₂²	—	2	6	no	—
369	C₂²	—	10	4	no	—
370	C₂²	—	20	12	no	—
371	C₂²	C₃×#3937	1	4	yes	direct product factor
372	C₂²	C₂×C₃×#685	1	3	yes	—
373	C₂²	C₂×C₃×#685	1	3	yes	—
374	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
375	C₄	—	2	8	no	—
376	C₄	—	10	4	no	—
377	C₄	C₂×C₃×#685	1	3	yes	—
378	C₄	C₂×C₃×#685	1	3	yes	—
379	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
380	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
381	C₃	C₂²×#3937	1	1	yes	characteristic, direct product factor, Sylow
382	C₂	—	2	1	no	—
383	C₂	—	2	3	no	—
384	C₂	—	20	4	no	—
385	C₂	C₂×C₃×#3937	1	6	yes	direct product factor
386	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₄²×C₅	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂²×C₃×#709	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄²	D₅
hypocenter	C₅	C₂²×C₃×#104
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×C₄²

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₄²×C₅	C₂	semidirect
3. C₂²×C₃×#681	C₂	semidirect
4. C₂×C₃×#3937	C₂	direct (N × H)
5. C₂²×#3937	C₃	direct (N × H)
11. C₂×C₃×#709	C₄	semidirect
13. C₂²×C₃×D₂₀	C₄	semidirect
15. C₂²×C₃×Dic₁₀	C₄	semidirect
17. C₂×C₃×C₄²×C₅	C₂²	semidirect
19. C₂×C₃×#681	C₂²	semidirect
21. C₃×#3937	C₂²	direct (N × H)
24. C₂²×C₄²×C₅	C₂×C₃	semidirect
25. C₂²×#681	C₂×C₃	semidirect
26. C₂×#3937	C₂×C₃	direct (N × H)
43. C₃×#709	C₂×C₄	semidirect
46. C₂×C₃×D₂₀	C₂×C₄	semidirect
50. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
52. C₃×C₄²×C₅	C₂³	semidirect
54. C₃×#681	C₂³	semidirect
58. C₂²×C₃×C₄²	D₅	semidirect
65. C₂×#709	C₃×C₄	semidirect
67. C₂²×D₂₀	C₃×C₄	semidirect
69. C₂²×Dic₁₀	C₃×C₄	semidirect
71. C₂×C₄²×C₅	C₂²×C₃	semidirect
73. C₂×#681	C₂²×C₃	semidirect
75. #3937	C₂²×C₃	direct (N × H)
98. C₃×D₂₀	C₂²×C₄	semidirect
102. C₃×Dic₁₀	C₂²×C₄	semidirect
118. C₂×C₃×C₄²	C₂×D₅	semidirect
136. #709	C₂×C₃×C₄	semidirect
139. C₂×D₂₀	C₂×C₃×C₄	semidirect
143. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
145. C₄²×C₅	C₂³×C₃	semidirect
147. #681	C₂³×C₃	semidirect
151. C₂²×C₄²	C₃×D₅	semidirect
155. C₂²×C₃×C₅	#104	semidirect
195. C₃×C₄²	C₂²×D₅	semidirect
217. D₂₀	C₂²×C₃×C₄	semidirect
221. Dic₁₀	C₂²×C₃×C₄	semidirect
237. C₂×C₄²	C₂×C₃×D₅	semidirect
241. C₂×C₃×C₅	C₂×#104	semidirect
273. C₂²×C₅	C₃×#104	semidirect
313. C₄²	C₂²×C₃×D₅	semidirect
314. C₃×C₅	C₂²×#104	semidirect
319. C₂²×C₃	#3937	direct (N × H)
331. C₂×C₅	C₂×C₃×#104	semidirect
364. C₂×C₃	C₂×#3937	direct (N × H)
366. C₅	C₂²×C₃×#104	semidirect
371. C₂²	C₃×#3937	direct (N × H)
381. C₃	C₂²×#3937	direct (N × H)
385. C₂	C₂×C₃×#3937	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×C₃×#709	2
C₂²×C₃×C₄²×C₅	2
C₂²×C₃×#681	2
C₂×C₃×#3937	2
C₂²×#3937	3
C₂²×C₃×#104	5

Subgroups — C22×C3×#3937 #14412798

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₃×#3937 #14412798