Subgroups — C₂²×C₅×#805 #14412797

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×C₅×#235	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄²×C₅	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#805	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₅×#104	—	3	1	no	maximal, Hall
6	C₂³×C₃×C₄×C₅	—	2	1	no	—
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×#67	—	2	1	no	—
9	C₂×C₅×#235	—	2	3	no	—
10	C₂×C₅×#235	—	2	3	no	—
11	C₂×C₅×#235	C₄	1	6	yes	complemented
12	C₂×C₅×#235	C₂²	1	6	yes	—
13	C₂²×C₅×D₁₂	C₄	1	1	yes	characteristic, complemented
14	C₂²×C₄×C₅×D₃	—	2	1	no	—
15	C₂²×C₅×Dic₆	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×C₅×#208	—	2	3	no	—
19	C₂×C₅×#208	C₂²	1	6	yes	complemented
20	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
21	C₅×#805	C₂²	1	16	yes	direct product factor
22	C₂²×#805	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₅×#41	—	3	1	no	—
24	C₂²×C₅×M₁₆	—	3	1	no	—
25	C₂²×C₄²×C₅	D₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#104	—	3	12	no	—
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂³×C₅×D₃	—	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×C₅×#67	—	2	6	no	—
38	C₂×C₅×#67	—	2	6	no	—
39	C₂²×C₅×Dic₃	—	2	1	no	—
40	C₅×#235	—	2	12	no	—
41	C₅×#235	—	2	6	no	—
42	C₅×#235	—	2	6	no	—
43	C₅×#235	C₂×C₄	1	12	yes	complemented
44	C₅×#235	C₂³	1	4	yes	—
45	C₂×C₅×D₁₂	—	2	3	no	—
46	C₂×C₅×D₁₂	C₂×C₄	1	6	yes	complemented
47	C₂×C₄×C₅×D₃	—	2	6	no	—
48	C₂×C₄×C₅×D₃	—	2	6	no	—
49	C₂×C₅×Dic₆	—	2	3	no	—
50	C₂×C₅×Dic₆	C₂×C₄	1	6	yes	complemented
51	C₃×C₄²×C₅	—	2	6	no	—
52	C₃×C₄²×C₅	C₂³	1	4	yes	complemented
53	C₅×#208	—	2	6	no	—
54	C₅×#208	C₂³	1	4	yes	complemented
55	C₂×C₅×C₃⋊C₈	—	2	6	no	—
56	C₂²×#235	C₂×C₅	1	1	yes	characteristic
57	C₂²×C₃×C₄²	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×#805	C₂×C₅	1	12	yes	direct product factor
60	C₂×C₅×#41	—	3	6	no	—
61	C₂×C₅×#41	—	3	6	no	—
62	C₂×C₅×#41	—	6	3	no	—
63	C₂×C₅×#41	—	6	3	no	—
64	C₂²×C₅×Q₈	—	3	1	no	—
65	C₂²×C₅×D₄	—	3	1	no	—
66	C₂²×C₅×D₄	—	6	1	no	—
67	C₂³×C₄×C₅	—	2	1	no	—
68	C₂³×C₄×C₅	—	6	1	no	—
69	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
70	C₂×C₅×M₁₆	—	3	6	no	—
71	C₂×C₅×M₁₆	—	6	3	no	—
72	C₂²×C₅×C₈	—	6	1	no	—
73	C₂×C₄²×C₅	—	2	3	no	—
74	C₂×C₄²×C₅	C₂×D₃	1	6	yes	complemented
75	C₅×#104	—	3	16	no	—
76	C₂²×#104	—	3	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×C₅×D₃	—	2	6	no	—
82	C₂²×C₅×D₃	—	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	C₅×#67	—	2	12	no	—
95	C₅×#67	—	2	4	no	—
96	C₂×C₅×Dic₃	—	2	6	no	—
97	C₅×D₁₂	—	2	6	no	—
98	C₅×D₁₂	C₂²×C₄	1	4	yes	complemented
99	C₄×C₅×D₃	—	2	12	no	—
100	C₄×C₅×D₃	—	2	4	no	—
101	C₅×Dic₆	—	2	6	no	—
102	C₅×Dic₆	C₂²×C₄	1	4	yes	complemented
103	C₅×C₃⋊C₈	—	2	4	no	—
104	C₂³×C₃×C₄	—	2	1	no	—
105	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
106	C₂²×#67	—	2	1	no	—
107	C₂×#235	—	2	3	no	—
108	C₂×#235	—	2	3	no	—
109	C₂×#235	C₄×C₅	1	6	yes	complemented
110	C₂×#235	C₂²×C₅	1	6	yes	—
111	C₂²×D₁₂	C₄×C₅	1	1	yes	characteristic, complemented
112	C₂²×C₄×D₃	—	2	1	no	—
113	C₂²×Dic₆	C₄×C₅	1	1	yes	characteristic, complemented
114	C₂×C₃×C₄²	—	2	3	no	—
115	C₂×C₃×C₄²	C₂²×C₅	1	6	yes	complemented
116	C₂×#208	—	2	3	no	—
117	C₂×#208	C₂²×C₅	1	6	yes	complemented
118	C₂²×C₃⋊C₈	—	2	1	no	—
119	#805	C₂²×C₅	1	16	yes	direct product factor
120	C₂⁴×C₅	—	6	1	no	—
121	C₂⁴×C₅	#67	1	1	yes	characteristic
122	C₅×#41	—	3	12	no	—
123	C₅×#41	—	3	4	no	—
124	C₅×#41	—	6	12	no	—
125	C₅×#41	—	6	6	no	—
126	C₅×#41	—	6	6	no	—
127	C₂×C₅×Q₈	—	3	6	no	—
128	C₂×C₅×Q₈	—	6	3	no	—
129	C₂×C₅×D₄	—	3	6	no	—
130	C₂×C₅×D₄	—	6	6	no	—
131	C₂×C₅×D₄	—	6	6	no	—
132	C₂×C₅×D₄	—	6	3	no	—
133	C₂²×C₄×C₅	—	2	8	no	—
134	C₂²×C₄×C₅	—	2	6	no	—
135	C₂²×C₄×C₅	—	6	1	no	—
136	C₂²×C₄×C₅	—	6	6	no	—
137	C₂²×C₄×C₅	—	6	6	no	—
138	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₄×D₃	1	3	yes	—
140	C₂²×C₄×C₅	D₁₂	1	3	yes	—
141	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
142	C₂²×C₄×C₅	#67	1	3	yes	—
143	C₂²×C₄×C₅	C₂²×D₃	1	3	yes	—
144	C₅×M₁₆	—	3	4	no	—
145	C₅×M₁₆	—	6	6	no	—
146	C₂×C₅×C₈	—	6	6	no	—
147	C₄²×C₅	—	2	6	no	—
148	C₄²×C₅	C₂²×D₃	1	4	yes	complemented
149	C₂²×#41	—	3	1	no	—
150	C₂²×M₁₆	—	3	1	no	—
151	C₂²×C₄²	C₅×D₃	1	1	yes	characteristic, complemented
152	C₂×#104	—	3	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×C₅×D₃	—	2	4	no	—
160	C₂×C₅×D₃	—	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	C₅×Dic₃	—	2	4	no	—
167	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
168	C₂³×D₃	—	2	1	no	—
169	C₂²×C₃×C₄	—	2	8	no	—
170	C₂²×C₃×C₄	—	2	6	no	—
171	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
173	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
174	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
175	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
176	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
177	C₂×#67	—	2	6	no	—
178	C₂×#67	—	2	6	no	—
179	C₂²×Dic₃	—	2	1	no	—
180	#235	—	2	12	no	—
181	#235	—	2	6	no	—
182	#235	—	2	6	no	—
183	#235	C₂×C₄×C₅	1	12	yes	complemented
184	#235	C₂³×C₅	1	4	yes	—
185	C₂×D₁₂	—	2	3	no	—
186	C₂×D₁₂	C₂×C₄×C₅	1	6	yes	complemented
187	C₂×C₄×D₃	—	2	6	no	—
188	C₂×C₄×D₃	—	2	6	no	—
189	C₂×Dic₆	—	2	3	no	—
190	C₂×Dic₆	C₂×C₄×C₅	1	6	yes	complemented
191	C₃×C₄²	—	2	6	no	—
192	C₃×C₄²	C₂³×C₅	1	4	yes	complemented
193	#208	—	2	6	no	—
194	#208	C₂³×C₅	1	4	yes	complemented
195	C₂×C₃⋊C₈	—	2	6	no	—
196	C₂³×C₅	—	2	4	no	—
197	C₂³×C₅	—	6	6	no	—
198	C₂³×C₅	—	12	4	no	—
199	C₂³×C₅	(C₂×D₃)⋊C₄	1	3	yes	—
200	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
201	C₂³×C₅	C₂×#67	1	3	yes	—
202	C₅×Q₈	—	3	4	no	—
203	C₅×Q₈	—	6	6	no	—
204	C₅×D₄	—	3	4	no	—
205	C₅×D₄	—	6	12	no	—
206	C₅×D₄	—	6	4	no	—
207	C₅×D₄	—	6	6	no	—
208	C₂×C₄×C₅	—	2	24	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	6	6	no	—
211	C₂×C₄×C₅	—	6	12	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	3	yes	—
214	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	3	yes	—
215	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	6	yes	—
216	C₂×C₄×C₅	C₂×C₄×D₃	1	3	yes	—
217	C₂×C₄×C₅	C₂×C₄×D₃	1	3	yes	—
218	C₂×C₄×C₅	C₂×D₁₂	1	3	yes	—
219	C₂×C₄×C₅	C₂×D₁₂	1	3	yes	—
220	C₂×C₄×C₅	C₂×#67	1	3	yes	—
221	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
222	C₅×C₈	—	6	4	no	—
223	C₂×#41	—	3	6	no	—
224	C₂×#41	—	3	6	no	—
225	C₂×#41	—	6	3	no	—
226	C₂×#41	—	6	3	no	—
227	C₂²×Q₈	—	3	1	no	—
228	C₂²×D₄	—	3	1	no	—
229	C₂²×D₄	—	6	1	no	—
230	C₂³×C₄	—	2	1	no	—
231	C₂³×C₄	—	6	1	no	—
232	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
233	C₂×M₁₆	—	3	6	no	—
234	C₂×M₁₆	—	6	3	no	—
235	C₂²×C₈	—	6	1	no	—
236	C₂×C₄²	—	2	3	no	—
237	C₂×C₄²	C₂×C₅×D₃	1	6	yes	complemented
238	#104	—	3	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	C₅×D₃	—	4	4	no	—
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	C₅×C₂²⋊C₄	1	3	yes	—
246	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
247	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
248	C₂²×D₃	—	2	6	no	—
249	C₂²×D₃	—	4	4	no	—
250	C₂×C₃×C₄	—	2	24	no	—
251	C₂×C₃×C₄	—	2	4	no	—
252	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	3	yes	—
253	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	3	yes	—
254	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	6	yes	—
255	C₂×C₃×C₄	C₂²×C₄×C₅	1	3	yes	—
256	C₂×C₃×C₄	C₂²×C₄×C₅	1	3	yes	—
257	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
258	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
259	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
260	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
261	#67	—	2	12	no	—
262	#67	—	2	4	no	—
263	C₂×Dic₃	—	2	6	no	—
264	D₁₂	—	2	6	no	—
265	D₁₂	C₂²×C₄×C₅	1	4	yes	complemented
266	C₄×D₃	—	2	12	no	—
267	C₄×D₃	—	2	4	no	—
268	Dic₆	—	2	6	no	—
269	Dic₆	C₂²×C₄×C₅	1	4	yes	complemented
270	C₃⋊C₈	—	2	4	no	—
271	C₂²×C₅	—	2	6	no	—
272	C₂²×C₅	—	2	6	no	—
273	C₂²×C₅	—	6	4	no	—
274	C₂²×C₅	—	12	12	no	—
275	C₂²×C₅	#805	1	4	yes	direct product factor
276	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
277	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
278	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
279	C₄×C₅	—	2	8	no	—
280	C₄×C₅	—	6	4	no	—
281	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
282	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	3	yes	—
283	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
284	C₄×C₅	C₂²×D₁₂	1	1	yes	characteristic
285	C₂⁴	—	6	1	no	—
286	C₂⁴	C₅×#67	1	1	yes	characteristic
287	#41	—	3	12	no	—
288	#41	—	3	4	no	—
289	#41	—	6	12	no	—
290	#41	—	6	6	no	—
291	#41	—	6	6	no	—
292	C₂×Q₈	—	3	6	no	—
293	C₂×Q₈	—	6	3	no	—
294	C₂×D₄	—	3	6	no	—
295	C₂×D₄	—	6	6	no	—
296	C₂×D₄	—	6	6	no	—
297	C₂×D₄	—	6	3	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	—	6	1	no	—
301	C₂²×C₄	—	6	6	no	—
302	C₂²×C₄	—	6	6	no	—
303	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
304	C₂²×C₄	C₄×C₅×D₃	1	3	yes	—
305	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
306	C₂²×C₄	C₅×D₁₂	1	3	yes	—
307	C₂²×C₄	C₅×#67	1	3	yes	—
308	C₂²×C₄	C₂²×C₅×D₃	1	3	yes	—
309	M₁₆	—	3	4	no	—
310	M₁₆	—	6	6	no	—
311	C₂×C₈	—	6	6	no	—
312	C₄²	—	2	6	no	—
313	C₄²	C₂²×C₅×D₃	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	C₅×#104	1	4	yes	complemented
318	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	3	yes	—
319	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	3	yes	—
320	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
321	C₂×D₃	—	2	4	no	—
322	C₂×D₃	—	4	12	no	—
323	C₃×C₄	—	2	8	no	—
324	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	3	yes	—
325	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	3	yes	—
326	C₃×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
327	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
328	Dic₃	—	2	4	no	—
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	2	3	no	—
331	C₂×C₅	—	12	4	no	—
332	C₂×C₅	C₂×#805	1	6	yes	direct product factor
333	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
334	C₂³	—	2	4	no	—
335	C₂³	—	6	6	no	—
336	C₂³	—	12	4	no	—
337	C₂³	C₅×(C₂×D₃)⋊C₄	1	3	yes	—
338	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
339	C₂³	C₂×C₅×#67	1	3	yes	—
340	Q₈	—	3	4	no	—
341	Q₈	—	6	6	no	—
342	D₄	—	3	4	no	—
343	D₄	—	6	12	no	—
344	D₄	—	6	4	no	—
345	D₄	—	6	6	no	—
346	C₂×C₄	—	2	24	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	6	6	no	—
349	C₂×C₄	—	6	12	no	—
350	C₂×C₄	—	6	4	no	—
351	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	3	yes	—
352	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	3	yes	—
353	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	6	yes	—
354	C₂×C₄	C₂×C₄×C₅×D₃	1	3	yes	—
355	C₂×C₄	C₂×C₄×C₅×D₃	1	3	yes	—
356	C₂×C₄	C₂×C₅×D₁₂	1	3	yes	—
357	C₂×C₄	C₂×C₅×D₁₂	1	3	yes	—
358	C₂×C₄	C₂×C₅×#67	1	3	yes	—
359	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
360	C₈	—	6	4	no	—
361	C₂×C₃	—	2	1	no	—
362	C₂×C₃	—	2	3	no	—
363	C₂×C₃	C₂×C₅×#104	1	6	yes	complemented
364	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
365	D₃	—	4	4	no	—
366	C₅	C₂²×#805	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	6	no	—
368	C₂²	—	2	6	no	—
369	C₂²	—	6	4	no	—
370	C₂²	—	12	12	no	—
371	C₂²	C₅×#805	1	4	yes	direct product factor
372	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
373	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
374	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
375	C₄	—	2	8	no	—
376	C₄	—	6	4	no	—
377	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
378	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	3	yes	—
379	C₄	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
380	C₄	C₂²×C₅×D₁₂	1	1	yes	characteristic
381	C₃	C₂²×C₅×#104	1	1	yes	characteristic, complemented, Sylow
382	C₂	—	2	1	no	—
383	C₂	—	2	3	no	—
384	C₂	—	12	4	no	—
385	C₂	C₂×C₅×#805	1	6	yes	direct product factor
386	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	D₁₂
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₂²×C₃×C₄²×C₅	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
prime radical	C₂²×C₅×#235	C₂
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₄²×C₅	D₃
hypocenter	C₃	C₂²×C₅×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₄×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×#208	C₂	semidirect
4. C₂×C₅×#805	C₂	direct (N × H)
11. C₂×C₅×#235	C₄	semidirect
13. C₂²×C₅×D₁₂	C₄	semidirect
15. C₂²×C₅×Dic₆	C₄	semidirect
17. C₂×C₃×C₄²×C₅	C₂²	semidirect
19. C₂×C₅×#208	C₂²	semidirect
21. C₅×#805	C₂²	direct (N × H)
22. C₂²×#805	C₅	direct (N × H)
25. C₂²×C₄²×C₅	D₃	semidirect
43. C₅×#235	C₂×C₄	semidirect
46. C₂×C₅×D₁₂	C₂×C₄	semidirect
50. C₂×C₅×Dic₆	C₂×C₄	semidirect
52. C₃×C₄²×C₅	C₂³	semidirect
54. C₅×#208	C₂³	semidirect
57. C₂²×C₃×C₄²	C₂×C₅	semidirect
58. C₂²×#208	C₂×C₅	semidirect
59. C₂×#805	C₂×C₅	direct (N × H)
74. C₂×C₄²×C₅	C₂×D₃	semidirect
98. C₅×D₁₂	C₂²×C₄	semidirect
102. C₅×Dic₆	C₂²×C₄	semidirect
109. C₂×#235	C₄×C₅	semidirect
111. C₂²×D₁₂	C₄×C₅	semidirect
113. C₂²×Dic₆	C₄×C₅	semidirect
115. C₂×C₃×C₄²	C₂²×C₅	semidirect
117. C₂×#208	C₂²×C₅	semidirect
119. #805	C₂²×C₅	direct (N × H)
148. C₄²×C₅	C₂²×D₃	semidirect
151. C₂²×C₄²	C₅×D₃	semidirect
155. C₂²×C₃×C₅	#104	semidirect
183. #235	C₂×C₄×C₅	semidirect
186. C₂×D₁₂	C₂×C₄×C₅	semidirect
190. C₂×Dic₆	C₂×C₄×C₅	semidirect
192. C₃×C₄²	C₂³×C₅	semidirect
194. #208	C₂³×C₅	semidirect
237. C₂×C₄²	C₂×C₅×D₃	semidirect
241. C₂×C₃×C₅	C₂×#104	semidirect
265. D₁₂	C₂²×C₄×C₅	semidirect
269. Dic₆	C₂²×C₄×C₅	semidirect
275. C₂²×C₅	#805	direct (N × H)
313. C₄²	C₂²×C₅×D₃	semidirect
314. C₃×C₅	C₂²×#104	semidirect
317. C₂²×C₃	C₅×#104	semidirect
332. C₂×C₅	C₂×#805	direct (N × H)
363. C₂×C₃	C₂×C₅×#104	semidirect
366. C₅	C₂²×#805	direct (N × H)
371. C₂²	C₅×#805	direct (N × H)
381. C₃	C₂²×C₅×#104	semidirect
385. C₂	C₂×C₅×#805	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×C₅×#235	2
C₂²×C₃×C₄²×C₅	2
C₂²×C₅×#208	2
C₂×C₅×#805	2
C₂²×C₅×#104	3
C₂²×#805	5

Subgroups — C22×C5×#805 #14412797

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#805 #14412797