Subgroups — C₂×C₅×#4939 #14320772

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×C₅×D₁₂	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
4	C₂²×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4939	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#390	—	3	1	no	maximal, Hall
7	C₂⁴×C₅×D₃	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×C₅×Dic₃	C₂²	1	2	yes	—
11	C₂²×C₅×D₁₂	—	2	4	no	—
12	C₂²×C₅×D₁₂	—	2	4	no	—
13	C₂²×C₅×D₁₂	C₄	1	8	yes	complemented
14	C₂²×C₅×D₁₂	C₂²	1	4	yes	—
15	C₂×C₃×C₄²×C₅	—	2	4	no	—
16	C₂×C₃×C₄²×C₅	C₂²	1	4	yes	complemented
17	C₂×C₅×(C₂×D₃)⋊C₄	—	2	16	no	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	16	yes	complemented
19	C₂×C₅×C₄⋊Dic₃	—	2	4	no	—
20	C₂×C₅×C₄⋊Dic₃	C₂²	1	4	yes	complemented
21	C₂×#4939	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₅×D₄	—	3	1	no	—
23	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
24	C₂²×C₅×C₂²⋊C₄	—	3	4	no	—
25	C₂²×C₄²×C₅	D₃	1	1	yes	characteristic, complemented
26	C₅×#390	—	3	8	no	—
27	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
28	C₂³×C₅×D₃	—	2	8	no	—
29	C₂³×C₅×D₃	—	2	4	no	—
30	C₂³×C₅×D₃	—	2	4	no	—
31	C₂³×C₅×D₃	—	2	8	no	—
32	C₂³×C₅×D₃	C₂×C₄	1	8	yes	—
33	C₂³×C₅×D₃	C₂³	1	4	yes	—
34	C₂²×C₃×C₄×C₅	—	2	4	no	—
35	C₂²×C₃×C₄×C₅	—	2	4	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	D₄	1	8	yes	complemented
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₅×Dic₃	—	2	4	no	—
43	C₂²×C₅×Dic₃	—	2	8	no	—
44	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
45	C₂×C₅×D₁₂	—	2	32	no	—
46	C₂×C₅×D₁₂	—	2	8	no	—
47	C₂×C₅×D₁₂	—	2	8	no	—
48	C₂×C₅×D₁₂	C₂×C₄	1	16	yes	complemented
49	C₃×C₄²×C₅	—	2	8	no	—
50	C₅×(C₂×D₃)⋊C₄	—	2	32	no	—
51	C₅×C₄⋊Dic₃	—	2	8	no	—
52	C₂³×D₁₂	C₂×C₅	1	1	yes	characteristic
53	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
54	C₂²×(C₂×D₃)⋊C₄	C₂×C₅	1	4	yes	complemented
55	C₂²×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
56	#4939	C₂×C₅	1	8	yes	direct product factor
57	C₂⁵×C₅	—	3	2	no	—
58	C₂²×C₅×D₄	—	3	8	no	—
59	C₂²×C₅×D₄	—	3	4	no	—
60	C₂²×C₅×D₄	—	6	4	no	—
61	C₂²×C₅×D₄	—	6	4	no	—
62	C₂³×C₄×C₅	—	3	2	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
64	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
65	C₂×C₅×C₄⋊C₄	—	3	4	no	—
66	C₂×C₅×C₄⋊C₄	—	6	4	no	—
67	C₂×C₅×C₂²⋊C₄	—	3	16	no	—
68	C₂×C₅×C₂²⋊C₄	—	6	16	no	—
69	C₂×C₄²×C₅	—	2	4	no	—
70	C₂×C₄²×C₅	C₂×D₃	1	4	yes	complemented
71	C₂×#390	—	3	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×C₅×D₃	—	2	16	no	—
79	C₂²×C₅×D₃	—	2	32	no	—
80	C₂²×C₅×D₃	—	2	8	no	—
81	C₂²×C₅×D₃	—	2	4	no	—
82	C₂²×C₅×D₃	—	2	4	no	—
83	C₂²×C₅×D₃	—	2	8	no	—
84	C₂²×C₅×D₃	—	4	16	no	—
85	C₂²×C₅×D₃	—	4	8	no	—
86	C₂²×C₅×D₃	—	4	8	no	—
87	C₂²×C₅×D₃	C₂²×C₄	1	8	yes	—
88	C₂×C₃×C₄×C₅	—	2	16	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	2	4	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×C₄×C₅	C₂×D₄	1	8	yes	complemented
96	C₂×C₅×Dic₃	—	2	4	no	—
97	C₂×C₅×Dic₃	—	2	8	no	—
98	C₂×C₅×Dic₃	—	4	8	no	—
99	C₅×D₁₂	—	2	32	no	—
100	C₂⁴×D₃	C₂²×C₅	1	2	yes	—
101	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
104	C₂²×D₁₂	—	2	4	no	—
105	C₂²×D₁₂	—	2	4	no	—
106	C₂²×D₁₂	C₄×C₅	1	8	yes	complemented
107	C₂²×D₁₂	C₂²×C₅	1	4	yes	—
108	C₂×C₃×C₄²	—	2	4	no	—
109	C₂×C₃×C₄²	C₂²×C₅	1	4	yes	complemented
110	C₂×(C₂×D₃)⋊C₄	—	2	16	no	—
111	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	16	yes	complemented
112	C₂×C₄⋊Dic₃	—	2	4	no	—
113	C₂×C₄⋊Dic₃	C₂²×C₅	1	4	yes	complemented
114	C₂⁴×C₅	—	3	8	no	—
115	C₂⁴×C₅	—	3	4	no	—
116	C₂⁴×C₅	—	6	8	no	—
117	C₂⁴×C₅	—	6	4	no	—
118	C₂⁴×C₅	—	6	8	no	—
119	C₂⁴×C₅	—	6	4	no	—
120	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
121	C₂×C₅×D₄	—	3	16	no	—
122	C₂×C₅×D₄	—	6	32	no	—
123	C₂×C₅×D₄	—	6	8	no	—
124	C₂×C₅×D₄	—	6	8	no	—
125	C₂²×C₄×C₅	—	2	4	no	—
126	C₂²×C₄×C₅	—	2	4	no	—
127	C₂²×C₄×C₅	—	3	4	no	—
128	C₂²×C₄×C₅	—	6	8	no	—
129	C₂²×C₄×C₅	—	6	4	no	—
130	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
131	C₂²×C₄×C₅	D₁₂	1	4	yes	—
132	C₂²×C₄×C₅	D₁₂	1	8	yes	complemented
133	C₂²×C₄×C₅	#67	1	4	yes	—
134	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
135	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
136	C₅×C₄⋊C₄	—	6	8	no	—
137	C₅×C₂²⋊C₄	—	6	32	no	—
138	C₄²×C₅	—	2	8	no	—
139	C₂³×D₄	—	3	1	no	—
140	C₂²×C₄⋊C₄	—	3	1	no	—
141	C₂²×C₂²⋊C₄	—	3	4	no	—
142	C₂²×C₄²	C₅×D₃	1	1	yes	characteristic, complemented
143	#390	—	3	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×C₅×D₃	—	2	8	no	—
155	C₂×C₅×D₃	—	2	16	no	—
156	C₂×C₅×D₃	—	4	8	no	—
157	C₂×C₅×D₃	—	4	4	no	—
158	C₂×C₅×D₃	—	4	4	no	—
159	C₂×C₅×D₃	—	4	32	no	—
160	C₃×C₄×C₅	—	2	8	no	—
161	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
162	C₅×Dic₃	—	4	4	no	—
163	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
164	C₂³×D₃	—	2	8	no	—
165	C₂³×D₃	—	2	4	no	—
166	C₂³×D₃	—	2	4	no	—
167	C₂³×D₃	—	2	8	no	—
168	C₂³×D₃	C₂×C₄×C₅	1	8	yes	—
169	C₂³×D₃	C₂³×C₅	1	4	yes	—
170	C₂²×C₃×C₄	—	2	4	no	—
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
173	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
174	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
175	C₂²×C₃×C₄	C₅×D₄	1	8	yes	complemented
176	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
177	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
178	C₂²×Dic₃	—	2	4	no	—
179	C₂²×Dic₃	—	2	8	no	—
180	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
181	C₂×D₁₂	—	2	32	no	—
182	C₂×D₁₂	—	2	8	no	—
183	C₂×D₁₂	—	2	8	no	—
184	C₂×D₁₂	C₂×C₄×C₅	1	16	yes	complemented
185	C₃×C₄²	—	2	8	no	—
186	(C₂×D₃)⋊C₄	—	2	32	no	—
187	C₄⋊Dic₃	—	2	8	no	—
188	C₂³×C₅	—	3	8	no	—
189	C₂³×C₅	—	6	32	no	—
190	C₂³×C₅	—	6	16	no	—
191	C₂³×C₅	—	6	8	no	—
192	C₂³×C₅	—	6	4	no	—
193	C₂³×C₅	—	6	8	no	—
194	C₂³×C₅	—	6	4	no	—
195	C₂³×C₅	—	12	8	no	—
196	C₂³×C₅	—	12	8	no	—
197	C₂³×C₅	—	12	16	no	—
198	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
199	C₂³×C₅	C₂×D₁₂	1	4	yes	—
200	C₂³×C₅	C₂×D₁₂	1	2	yes	—
201	C₂³×C₅	#235	1	4	yes	—
202	C₂³×C₅	C₂×#67	1	2	yes	—
203	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
204	C₅×D₄	—	6	32	no	—
205	C₂×C₄×C₅	—	2	16	no	—
206	C₂×C₄×C₅	—	2	4	no	—
207	C₂×C₄×C₅	—	2	4	no	—
208	C₂×C₄×C₅	—	6	8	no	—
209	C₂×C₄×C₅	—	6	4	no	—
210	C₂×C₄×C₅	—	12	8	no	—
211	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	16	yes	complemented
212	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
213	C₂×C₄×C₅	C₂×D₁₂	1	4	yes	—
214	C₂×C₄×C₅	C₂×D₁₂	1	8	yes	complemented
215	C₂×C₄×C₅	C₂×#67	1	4	yes	—
216	C₂⁵	—	3	2	no	—
217	C₂²×D₄	—	3	8	no	—
218	C₂²×D₄	—	3	4	no	—
219	C₂²×D₄	—	6	4	no	—
220	C₂²×D₄	—	6	4	no	—
221	C₂³×C₄	—	3	2	no	—
222	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
223	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
224	C₂×C₄⋊C₄	—	3	4	no	—
225	C₂×C₄⋊C₄	—	6	4	no	—
226	C₂×C₂²⋊C₄	—	3	16	no	—
227	C₂×C₂²⋊C₄	—	6	16	no	—
228	C₂×C₄²	—	2	4	no	—
229	C₂×C₄²	C₂×C₅×D₃	1	4	yes	complemented
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	C₅×D₃	—	4	8	no	—
237	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
238	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
239	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
240	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
241	C₂³×C₃	C₅×#41	1	4	yes	—
242	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
243	C₂²×D₃	—	2	16	no	—
244	C₂²×D₃	—	2	32	no	—
245	C₂²×D₃	—	2	8	no	—
246	C₂²×D₃	—	2	4	no	—
247	C₂²×D₃	—	2	4	no	—
248	C₂²×D₃	—	2	8	no	—
249	C₂²×D₃	—	4	16	no	—
250	C₂²×D₃	—	4	8	no	—
251	C₂²×D₃	—	4	8	no	—
252	C₂²×D₃	C₂²×C₄×C₅	1	8	yes	—
253	C₂×C₃×C₄	—	2	16	no	—
254	C₂×C₃×C₄	—	2	4	no	—
255	C₂×C₃×C₄	—	2	4	no	—
256	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	16	yes	complemented
257	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
260	C₂×C₃×C₄	C₂×C₅×D₄	1	8	yes	complemented
261	C₂×Dic₃	—	2	4	no	—
262	C₂×Dic₃	—	2	8	no	—
263	C₂×Dic₃	—	4	8	no	—
264	D₁₂	—	2	32	no	—
265	C₂²×C₅	—	6	16	no	—
266	C₂²×C₅	—	6	8	no	—
267	C₂²×C₅	—	12	32	no	—
268	C₂²×C₅	—	12	4	no	—
269	C₂²×C₅	—	12	4	no	—
270	C₂²×C₅	—	12	8	no	—
271	C₂²×C₅	C₄×D₁₂	1	8	yes	—
272	C₂²×C₅	#874	1	4	yes	—
273	C₂²×C₅	#875	1	4	yes	—
274	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
275	C₂²×C₅	#930	1	8	yes	—
276	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
277	C₂²×C₅	C₂²×D₁₂	1	2	yes	—
278	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
279	C₂²×C₅	C₂×#235	1	2	yes	—
280	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
281	C₄×C₅	—	2	8	no	—
282	C₄×C₅	—	12	4	no	—
283	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	8	yes	complemented
284	C₂⁴	—	3	8	no	—
285	C₂⁴	—	3	4	no	—
286	C₂⁴	—	6	8	no	—
287	C₂⁴	—	6	4	no	—
288	C₂⁴	—	6	8	no	—
289	C₂⁴	—	6	4	no	—
290	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
291	C₂×D₄	—	3	16	no	—
292	C₂×D₄	—	6	32	no	—
293	C₂×D₄	—	6	8	no	—
294	C₂×D₄	—	6	8	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	3	4	no	—
298	C₂²×C₄	—	6	8	no	—
299	C₂²×C₄	—	6	4	no	—
300	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
301	C₂²×C₄	C₅×D₁₂	1	4	yes	—
302	C₂²×C₄	C₅×D₁₂	1	8	yes	complemented
303	C₂²×C₄	C₅×#67	1	4	yes	—
304	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
305	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
306	C₄⋊C₄	—	6	8	no	—
307	C₂²⋊C₄	—	6	32	no	—
308	C₄²	—	2	8	no	—
309	C₃×C₅	C₂×#390	1	1	yes	characteristic, complemented, Hall
310	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
311	C₂²×C₃	C₄×C₅×D₄	1	8	yes	—
312	C₂²×C₃	C₅×#121	1	8	yes	—
313	C₂²×C₃	C₅×#124	1	4	yes	—
314	C₂²×C₃	C₅×#127	1	4	yes	—
315	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
316	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
317	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
318	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
319	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
320	C₂×D₃	—	2	8	no	—
321	C₂×D₃	—	2	16	no	—
322	C₂×D₃	—	4	32	no	—
323	C₂×D₃	—	4	8	no	—
324	C₂×D₃	—	4	4	no	—
325	C₂×D₃	—	4	4	no	—
326	C₃×C₄	—	2	8	no	—
327	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
328	Dic₃	—	4	4	no	—
329	C₂×C₅	—	12	8	no	—
330	C₂×C₅	#4939	1	8	yes	direct product factor
331	C₂×C₅	C₂×C₄×D₁₂	1	2	yes	—
332	C₂×C₅	C₂×#874	1	1	yes	characteristic
333	C₂×C₅	C₂×#875	1	1	yes	characteristic
334	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
335	C₂×C₅	C₂×#930	1	2	yes	—
336	C₂³	—	3	8	no	—
337	C₂³	—	6	32	no	—
338	C₂³	—	6	16	no	—
339	C₂³	—	6	8	no	—
340	C₂³	—	6	4	no	—
341	C₂³	—	6	8	no	—
342	C₂³	—	6	4	no	—
343	C₂³	—	12	8	no	—
344	C₂³	—	12	8	no	—
345	C₂³	—	12	16	no	—
346	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
347	C₂³	C₂×C₅×D₁₂	1	4	yes	—
348	C₂³	C₂×C₅×D₁₂	1	2	yes	—
349	C₂³	C₅×#235	1	4	yes	—
350	C₂³	C₂×C₅×#67	1	2	yes	—
351	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
352	D₄	—	6	32	no	—
353	C₂×C₄	—	2	16	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	6	8	no	—
357	C₂×C₄	—	6	4	no	—
358	C₂×C₄	—	12	8	no	—
359	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	16	yes	complemented
360	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
361	C₂×C₄	C₂×C₅×D₁₂	1	4	yes	—
362	C₂×C₄	C₂×C₅×D₁₂	1	8	yes	complemented
363	C₂×C₄	C₂×C₅×#67	1	4	yes	—
364	C₂×C₃	C₅×#390	1	8	yes	complemented
365	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₂×C₃	C₂×C₄×C₅×D₄	1	2	yes	—
367	C₂×C₃	C₂×C₅×#121	1	2	yes	—
368	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
369	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
370	D₃	—	4	8	no	—
371	C₅	C₂×#4939	1	1	yes	characteristic, direct product factor, Sylow
372	C₂²	—	6	16	no	—
373	C₂²	—	6	8	no	—
374	C₂²	—	12	32	no	—
375	C₂²	—	12	4	no	—
376	C₂²	—	12	4	no	—
377	C₂²	—	12	8	no	—
378	C₂²	C₄×C₅×D₁₂	1	8	yes	—
379	C₂²	C₅×#874	1	4	yes	—
380	C₂²	C₅×#875	1	4	yes	—
381	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
382	C₂²	C₅×#930	1	8	yes	—
383	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
384	C₂²	C₂²×C₅×D₁₂	1	2	yes	—
385	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
386	C₂²	C₂×C₅×#235	1	2	yes	—
387	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
388	C₄	—	2	8	no	—
389	C₄	—	12	4	no	—
390	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	8	yes	complemented
391	C₃	C₂×C₅×#390	1	1	yes	characteristic, complemented, Sylow
392	C₂	—	12	8	no	—
393	C₂	C₅×#4939	1	8	yes	direct product factor
394	C₂	C₂×C₄×C₅×D₁₂	1	2	yes	—
395	C₂	C₂×C₅×#874	1	1	yes	characteristic
396	C₂	C₂×C₅×#875	1	1	yes	characteristic
397	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
398	C₂	C₂×C₅×#930	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₄²×C₅	C₂
socle	C₂⁴×C₃×C₅	C₂³
prime radical	C₂³×C₅×D₁₂	C₂
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂²×C₄²×C₅	D₃
hypocenter	C₃	C₂×C₅×#390
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂²×C₄²×C₅

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×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
4. C₂²×C₅×C₄⋊Dic₃	C₂	semidirect
5. C₅×#4939	C₂	direct (N × H)
13. C₂²×C₅×D₁₂	C₄	semidirect
16. C₂×C₃×C₄²×C₅	C₂²	semidirect
18. C₂×C₅×(C₂×D₃)⋊C₄	C₂²	semidirect
20. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
21. C₂×#4939	C₅	direct (N × H)
25. C₂²×C₄²×C₅	D₃	semidirect
39. C₂²×C₃×C₄×C₅	D₄	semidirect
48. C₂×C₅×D₁₂	C₂×C₄	semidirect
53. C₂²×C₃×C₄²	C₂×C₅	semidirect
54. C₂²×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
55. C₂²×C₄⋊Dic₃	C₂×C₅	semidirect
56. #4939	C₂×C₅	direct (N × H)
70. C₂×C₄²×C₅	C₂×D₃	semidirect
91. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
95. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
106. C₂²×D₁₂	C₄×C₅	semidirect
109. C₂×C₃×C₄²	C₂²×C₅	semidirect
111. C₂×(C₂×D₃)⋊C₄	C₂²×C₅	semidirect
113. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
132. C₂²×C₄×C₅	D₁₂	semidirect
142. C₂²×C₄²	C₅×D₃	semidirect
161. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
175. C₂²×C₃×C₄	C₅×D₄	semidirect
184. C₂×D₁₂	C₂×C₄×C₅	semidirect
211. C₂×C₄×C₅	(C₂×D₃)⋊C₄	semidirect
214. C₂×C₄×C₅	C₂×D₁₂	semidirect
229. C₂×C₄²	C₂×C₅×D₃	semidirect
230. C₂×C₃×C₅	#390	semidirect
256. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
260. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
283. C₄×C₅	C₂×(C₂×D₃)⋊C₄	semidirect
302. C₂²×C₄	C₅×D₁₂	semidirect
309. C₃×C₅	C₂×#390	semidirect
327. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
330. C₂×C₅	#4939	direct (N × H)
359. C₂×C₄	C₅×(C₂×D₃)⋊C₄	semidirect
362. C₂×C₄	C₂×C₅×D₁₂	semidirect
364. C₂×C₃	C₅×#390	semidirect
371. C₅	C₂×#4939	direct (N × H)
390. C₄	C₂×C₅×(C₂×D₃)⋊C₄	semidirect
391. C₃	C₂×C₅×#390	semidirect
393. C₂	C₅×#4939	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×C₅×D₁₂	2
C₂²×C₃×C₄²×C₅	2
C₂²×C₅×(C₂×D₃)⋊C₄	2
C₂²×C₅×C₄⋊Dic₃	2
C₅×#4939	2
C₂×C₅×#390	3
C₂×#4939	5

Subgroups — C2×C5×#4939 #14320772

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#4939 #14320772