Subgroups — C₂²×C₅×#837 #14412794

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×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#837	C₂	1	12	yes	maximal, direct product factor
5	C₂²×C₅×#104	—	3	1	no	maximal, Hall
6	C₂×C₃×C₅×#41	—	2	3	no	—
7	C₂×C₃×C₅×#41	—	2	3	no	—
8	C₂×C₃×C₅×#41	C₄	1	6	yes	complemented
9	C₂×C₃×C₅×#41	C₂²	1	6	yes	—
10	C₂²×C₃×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
11	C₂²×C₃×C₅×D₄	—	2	1	no	—
12	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic, complemented
13	C₂³×C₃×C₄×C₅	—	2	1	no	—
14	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₂³×C₅×Dic₃	—	2	1	no	—
16	C₂×C₄×C₅×Dic₃	—	2	3	no	—
17	C₂×C₄×C₅×Dic₃	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×#837	C₂²	1	16	yes	direct product factor
22	C₂²×#837	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
23	C₂²×C₅×#41	D₃	1	1	yes	characteristic
24	C₂²×C₅×M₁₆	—	3	1	no	—
25	C₂²×C₄²×C₅	—	3	1	no	—
26	C₂×C₅×#104	—	3	12	no	—
27	C₂⁴×C₃×C₅	—	2	1	no	—
28	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
29	C₃×C₅×#41	—	2	12	no	—
30	C₃×C₅×#41	—	2	6	no	—
31	C₃×C₅×#41	—	2	6	no	—
32	C₃×C₅×#41	C₂×C₄	1	12	yes	complemented
33	C₃×C₅×#41	C₂³	1	4	yes	—
34	C₂×C₃×C₅×Q₈	—	2	3	no	—
35	C₂×C₃×C₅×Q₈	C₂×C₄	1	6	yes	complemented
36	C₂×C₃×C₅×D₄	—	2	6	no	—
37	C₂×C₃×C₅×D₄	—	2	6	no	—
38	C₂×C₃×C₅×D₄	—	2	3	no	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	6	yes	complemented
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	6	no	—
42	C₂²×C₃×C₄×C₅	—	2	6	no	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	3	yes	—
45	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
46	C₂²×C₃×C₄×C₅	D₄	1	3	yes	—
47	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
49	C₂²×C₅×Dic₃	—	2	8	no	—
50	C₂²×C₅×Dic₃	—	2	6	no	—
51	C₄×C₅×Dic₃	—	2	6	no	—
52	C₄×C₅×Dic₃	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×C₃×#41	C₂×C₅	1	1	yes	characteristic
57	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
59	C₂×#837	C₂×C₅	1	12	yes	direct product factor
60	C₂×C₅×#41	—	2	3	no	—
61	C₂×C₅×#41	—	2	3	no	—
62	C₂×C₅×#41	Dic₃	1	6	yes	complemented
63	C₂×C₅×#41	C₂×D₃	1	6	yes	—
64	C₂²×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
65	C₂²×C₅×D₄	—	2	1	no	—
66	C₂²×C₅×D₄	Dic₃	1	1	yes	characteristic, complemented
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	—	3	6	no	—
74	C₂×C₄²×C₅	—	6	3	no	—
75	C₅×#104	—	3	16	no	—
76	C₂²×#104	—	3	1	no	Sylow
77	C₂³×C₃×C₅	—	2	4	no	—
78	C₂³×C₃×C₅	—	2	6	no	—
79	C₂³×C₃×C₅	—	4	4	no	—
80	C₂³×C₃×C₅	C₂²⋊C₄	1	3	yes	—
81	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
82	C₂³×C₃×C₅	C₂×D₄	1	3	yes	—
83	C₃×C₅×Q₈	—	2	6	no	—
84	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	complemented
85	C₃×C₅×D₄	—	2	12	no	—
86	C₃×C₅×D₄	—	2	4	no	—
87	C₃×C₅×D₄	—	2	6	no	—
88	C₃×C₅×D₄	C₂²×C₄	1	4	yes	complemented
89	C₂×C₃×C₄×C₅	—	2	6	no	—
90	C₂×C₃×C₄×C₅	—	2	12	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	3	yes	—
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	6	yes	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
96	C₂×C₃×C₄×C₅	C₂²×C₄	1	3	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
98	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
99	C₂×C₃×C₄×C₅	C₂×D₄	1	3	yes	—
100	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
101	C₂×C₅×Dic₃	—	2	24	no	—
102	C₂×C₅×Dic₃	—	2	4	no	—
103	C₅×C₃⋊C₈	—	2	4	no	—
104	C₂×C₃×#41	—	2	3	no	—
105	C₂×C₃×#41	—	2	3	no	—
106	C₂×C₃×#41	C₄×C₅	1	6	yes	complemented
107	C₂×C₃×#41	C₂²×C₅	1	6	yes	—
108	C₂²×C₃×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
109	C₂²×C₃×D₄	—	2	1	no	—
110	C₂²×C₃×D₄	C₄×C₅	1	1	yes	characteristic, complemented
111	C₂³×C₃×C₄	—	2	1	no	—
112	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
113	C₂³×Dic₃	—	2	1	no	—
114	C₂×C₄×Dic₃	—	2	3	no	—
115	C₂×C₄×Dic₃	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	#837	C₂²×C₅	1	16	yes	direct product factor
120	C₂⁴×C₅	—	2	1	no	—
121	C₂⁴×C₅	#67	1	1	yes	characteristic
122	C₅×#41	—	2	12	no	—
123	C₅×#41	—	2	6	no	—
124	C₅×#41	—	2	6	no	—
125	C₅×#41	C₂×Dic₃	1	12	yes	complemented
126	C₅×#41	C₂²×D₃	1	4	yes	—
127	C₂×C₅×Q₈	—	2	3	no	—
128	C₂×C₅×Q₈	C₂×Dic₃	1	6	yes	complemented
129	C₂×C₅×D₄	—	2	6	no	—
130	C₂×C₅×D₄	—	2	6	no	—
131	C₂×C₅×D₄	—	2	3	no	—
132	C₂×C₅×D₄	C₂×Dic₃	1	6	yes	complemented
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	6	no	—
135	C₂²×C₄×C₅	—	2	6	no	—
136	C₂²×C₄×C₅	—	6	8	no	—
137	C₂²×C₄×C₅	—	6	6	no	—
138	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂×Dic₃	1	3	yes	—
140	C₂²×C₄×C₅	#67	1	3	yes	—
141	C₂²×C₄×C₅	#67	1	3	yes	—
142	C₂²×C₄×C₅	#67	1	1	yes	characteristic
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	—	3	4	no	—
148	C₄²×C₅	—	6	6	no	—
149	C₂²×#41	C₅×D₃	1	1	yes	characteristic
150	C₂²×M₁₆	—	3	1	no	—
151	C₂²×C₄²	—	3	1	no	—
152	C₂×#104	—	3	12	no	—
153	C₂²×C₃×C₅	—	2	6	no	—
154	C₂²×C₃×C₅	—	2	6	no	—
155	C₂²×C₃×C₅	—	2	4	no	—
156	C₂²×C₃×C₅	—	4	12	no	—
157	C₂²×C₃×C₅	#104	1	4	yes	complemented
158	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
159	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	3	yes	—
160	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
161	C₃×C₄×C₅	—	2	4	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	8	no	—
167	C₂⁴×C₃	—	2	1	no	—
168	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
169	C₃×#41	—	2	12	no	—
170	C₃×#41	—	2	6	no	—
171	C₃×#41	—	2	6	no	—
172	C₃×#41	C₂×C₄×C₅	1	12	yes	complemented
173	C₃×#41	C₂³×C₅	1	4	yes	—
174	C₂×C₃×Q₈	—	2	3	no	—
175	C₂×C₃×Q₈	C₂×C₄×C₅	1	6	yes	complemented
176	C₂×C₃×D₄	—	2	6	no	—
177	C₂×C₃×D₄	—	2	6	no	—
178	C₂×C₃×D₄	—	2	3	no	—
179	C₂×C₃×D₄	C₂×C₄×C₅	1	6	yes	complemented
180	C₂²×C₃×C₄	—	2	1	no	—
181	C₂²×C₃×C₄	—	2	6	no	—
182	C₂²×C₃×C₄	—	2	6	no	—
183	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
184	C₂²×C₃×C₄	C₂×C₄×C₅	1	3	yes	—
185	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
186	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
187	C₂²×C₃×C₄	C₅×D₄	1	3	yes	—
188	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
189	C₂²×Dic₃	—	2	8	no	—
190	C₂²×Dic₃	—	2	6	no	—
191	C₄×Dic₃	—	2	6	no	—
192	C₄×Dic₃	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	—	2	6	no	—
198	C₂³×C₅	—	4	4	no	—
199	C₂³×C₅	#217	1	3	yes	—
200	C₂³×C₅	#217	1	1	yes	characteristic
201	C₂³×C₅	C₂×#67	1	3	yes	—
202	C₅×Q₈	—	2	6	no	—
203	C₅×Q₈	C₂²×Dic₃	1	4	yes	complemented
204	C₅×D₄	—	2	12	no	—
205	C₅×D₄	—	2	4	no	—
206	C₅×D₄	—	2	6	no	—
207	C₅×D₄	C₂²×Dic₃	1	4	yes	complemented
208	C₂×C₄×C₅	—	2	6	no	—
209	C₂×C₄×C₅	—	2	12	no	—
210	C₂×C₄×C₅	—	2	4	no	—
211	C₂×C₄×C₅	—	6	24	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	#217	1	3	yes	—
214	C₂×C₄×C₅	#217	1	3	yes	—
215	C₂×C₄×C₅	#217	1	6	yes	—
216	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
217	C₂×C₄×C₅	C₂²×Dic₃	1	3	yes	—
218	C₂×C₄×C₅	C₂×#67	1	3	yes	—
219	C₂×C₄×C₅	C₂×#67	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	—	2	3	no	—
224	C₂×#41	—	2	3	no	—
225	C₂×#41	C₅×Dic₃	1	6	yes	complemented
226	C₂×#41	C₂×C₅×D₃	1	6	yes	—
227	C₂²×Q₈	C₅×Dic₃	1	1	yes	characteristic, complemented
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	C₅×Dic₃	1	1	yes	characteristic, complemented
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	—	3	6	no	—
237	C₂×C₄²	—	6	3	no	—
238	#104	—	3	16	no	—
239	C₂×C₃×C₅	—	2	1	no	—
240	C₂×C₃×C₅	—	2	3	no	—
241	C₂×C₃×C₅	—	4	4	no	—
242	C₂×C₃×C₅	C₂×#104	1	6	yes	complemented
243	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
244	C₂³×C₃	—	2	4	no	—
245	C₂³×C₃	—	2	6	no	—
246	C₂³×C₃	—	4	4	no	—
247	C₂³×C₃	C₅×C₂²⋊C₄	1	3	yes	—
248	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
249	C₂³×C₃	C₂×C₅×D₄	1	3	yes	—
250	C₃×Q₈	—	2	6	no	—
251	C₃×Q₈	C₂²×C₄×C₅	1	4	yes	complemented
252	C₃×D₄	—	2	12	no	—
253	C₃×D₄	—	2	4	no	—
254	C₃×D₄	—	2	6	no	—
255	C₃×D₄	C₂²×C₄×C₅	1	4	yes	complemented
256	C₂×C₃×C₄	—	2	6	no	—
257	C₂×C₃×C₄	—	2	12	no	—
258	C₂×C₃×C₄	—	2	4	no	—
259	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	3	yes	—
260	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	3	yes	—
261	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	6	yes	—
262	C₂×C₃×C₄	C₂²×C₄×C₅	1	3	yes	—
263	C₂×C₃×C₄	C₂²×C₄×C₅	1	3	yes	—
264	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
265	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
266	C₂×C₃×C₄	C₂×C₅×D₄	1	3	yes	—
267	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
268	C₂×Dic₃	—	2	24	no	—
269	C₂×Dic₃	—	2	4	no	—
270	C₃⋊C₈	—	2	4	no	—
271	C₂²×C₅	—	2	6	no	—
272	C₂²×C₅	—	2	6	no	—
273	C₂²×C₅	—	2	4	no	—
274	C₂²×C₅	—	4	12	no	—
275	C₂²×C₅	#837	1	4	yes	direct product factor
276	C₂²×C₅	C₂×#217	1	3	yes	—
277	C₂²×C₅	C₂×#217	1	3	yes	—
278	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
279	C₄×C₅	—	2	4	no	—
280	C₄×C₅	—	6	8	no	—
281	C₄×C₅	C₂×#217	1	3	yes	—
282	C₄×C₅	C₂×#217	1	3	yes	—
283	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
284	C₄×C₅	C₂²×#67	1	1	yes	characteristic
285	C₂⁴	—	2	1	no	—
286	C₂⁴	C₅×#67	1	1	yes	characteristic
287	#41	—	2	12	no	—
288	#41	—	2	6	no	—
289	#41	—	2	6	no	—
290	#41	C₂×C₅×Dic₃	1	12	yes	complemented
291	#41	C₂²×C₅×D₃	1	4	yes	—
292	C₂×Q₈	—	2	3	no	—
293	C₂×Q₈	C₂×C₅×Dic₃	1	6	yes	complemented
294	C₂×D₄	—	2	6	no	—
295	C₂×D₄	—	2	6	no	—
296	C₂×D₄	—	2	3	no	—
297	C₂×D₄	C₂×C₅×Dic₃	1	6	yes	complemented
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	6	no	—
300	C₂²×C₄	—	2	6	no	—
301	C₂²×C₄	—	6	8	no	—
302	C₂²×C₄	—	6	6	no	—
303	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₅×Dic₃	1	3	yes	—
305	C₂²×C₄	C₅×#67	1	3	yes	—
306	C₂²×C₄	C₅×#67	1	1	yes	characteristic
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	—	3	4	no	—
313	C₄²	—	6	6	no	—
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	—	2	4	no	—
318	C₂²×C₃	—	4	12	no	—
319	C₂²×C₃	C₅×#104	1	4	yes	complemented
320	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	3	yes	—
321	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	3	yes	—
322	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
323	C₃×C₄	—	2	4	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	8	no	—
329	C₂×C₅	—	2	1	no	—
330	C₂×C₅	—	2	3	no	—
331	C₂×C₅	—	4	4	no	—
332	C₂×C₅	C₂×#837	1	6	yes	direct product factor
333	C₂×C₅	C₂²×#217	1	1	yes	characteristic
334	C₂³	—	2	4	no	—
335	C₂³	—	2	6	no	—
336	C₂³	—	4	4	no	—
337	C₂³	C₅×#217	1	3	yes	—
338	C₂³	C₅×#217	1	1	yes	characteristic
339	C₂³	C₂×C₅×#67	1	3	yes	—
340	Q₈	—	2	6	no	—
341	Q₈	C₂²×C₅×Dic₃	1	4	yes	complemented
342	D₄	—	2	12	no	—
343	D₄	—	2	4	no	—
344	D₄	—	2	6	no	—
345	D₄	C₂²×C₅×Dic₃	1	4	yes	complemented
346	C₂×C₄	—	2	6	no	—
347	C₂×C₄	—	2	12	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	6	24	no	—
350	C₂×C₄	—	6	4	no	—
351	C₂×C₄	C₅×#217	1	3	yes	—
352	C₂×C₄	C₅×#217	1	3	yes	—
353	C₂×C₄	C₅×#217	1	6	yes	—
354	C₂×C₄	C₂²×C₅×Dic₃	1	3	yes	—
355	C₂×C₄	C₂²×C₅×Dic₃	1	3	yes	—
356	C₂×C₄	C₂×C₅×#67	1	3	yes	—
357	C₂×C₄	C₂×C₅×#67	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	—	4	4	no	—
364	C₂×C₃	C₂×C₅×#104	1	6	yes	complemented
365	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
366	C₅	C₂²×#837	1	1	yes	characteristic, direct product factor, Sylow
367	C₂²	—	2	6	no	—
368	C₂²	—	2	6	no	—
369	C₂²	—	2	4	no	—
370	C₂²	—	4	12	no	—
371	C₂²	C₅×#837	1	4	yes	direct product factor
372	C₂²	C₂×C₅×#217	1	3	yes	—
373	C₂²	C₂×C₅×#217	1	3	yes	—
374	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
375	C₄	—	2	4	no	—
376	C₄	—	6	8	no	—
377	C₄	C₂×C₅×#217	1	3	yes	—
378	C₄	C₂×C₅×#217	1	3	yes	—
379	C₄	C₂³×C₅×Dic₃	1	1	yes	characteristic
380	C₄	C₂²×C₅×#67	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	—	4	4	no	—
385	C₂	C₂×C₅×#837	1	6	yes	direct product factor
386	C₂	C₂²×C₅×#217	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	#67
commutator	C₃×C₄	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting, prime radical	C₂²×C₃×C₅×#41	C₂
socle	C₂³×C₃×C₅	C₂²⋊C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₂²×C₅×#41	D₃
hypocenter	C₃	C₂²×C₅×#104
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×#41

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×C₅×Dic₃	C₂	semidirect
3. C₂²×C₅×#208	C₂	semidirect
4. C₂×C₅×#837	C₂	direct (N × H)
8. C₂×C₃×C₅×#41	C₄	semidirect
10. C₂²×C₃×C₅×Q₈	C₄	semidirect
12. C₂²×C₃×C₅×D₄	C₄	semidirect
17. C₂×C₄×C₅×Dic₃	C₂²	semidirect
19. C₂×C₅×#208	C₂²	semidirect
21. C₅×#837	C₂²	direct (N × H)
22. C₂²×#837	C₅	direct (N × H)
32. C₃×C₅×#41	C₂×C₄	semidirect
35. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
39. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
52. C₄×C₅×Dic₃	C₂³	semidirect
54. C₅×#208	C₂³	semidirect
57. C₂²×C₄×Dic₃	C₂×C₅	semidirect
58. C₂²×#208	C₂×C₅	semidirect
59. C₂×#837	C₂×C₅	direct (N × H)
62. C₂×C₅×#41	Dic₃	semidirect
64. C₂²×C₅×Q₈	Dic₃	semidirect
66. C₂²×C₅×D₄	Dic₃	semidirect
84. C₃×C₅×Q₈	C₂²×C₄	semidirect
88. C₃×C₅×D₄	C₂²×C₄	semidirect
106. C₂×C₃×#41	C₄×C₅	semidirect
108. C₂²×C₃×Q₈	C₄×C₅	semidirect
110. C₂²×C₃×D₄	C₄×C₅	semidirect
115. C₂×C₄×Dic₃	C₂²×C₅	semidirect
117. C₂×#208	C₂²×C₅	semidirect
119. #837	C₂²×C₅	direct (N × H)
125. C₅×#41	C₂×Dic₃	semidirect
128. C₂×C₅×Q₈	C₂×Dic₃	semidirect
132. C₂×C₅×D₄	C₂×Dic₃	semidirect
157. C₂²×C₃×C₅	#104	semidirect
172. C₃×#41	C₂×C₄×C₅	semidirect
175. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
179. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
192. C₄×Dic₃	C₂³×C₅	semidirect
194. #208	C₂³×C₅	semidirect
203. C₅×Q₈	C₂²×Dic₃	semidirect
207. C₅×D₄	C₂²×Dic₃	semidirect
225. C₂×#41	C₅×Dic₃	semidirect
227. C₂²×Q₈	C₅×Dic₃	semidirect
229. C₂²×D₄	C₅×Dic₃	semidirect
242. C₂×C₃×C₅	C₂×#104	semidirect
251. C₃×Q₈	C₂²×C₄×C₅	semidirect
255. C₃×D₄	C₂²×C₄×C₅	semidirect
275. C₂²×C₅	#837	direct (N × H)
290. #41	C₂×C₅×Dic₃	semidirect
293. C₂×Q₈	C₂×C₅×Dic₃	semidirect
297. C₂×D₄	C₂×C₅×Dic₃	semidirect
314. C₃×C₅	C₂²×#104	semidirect
319. C₂²×C₃	C₅×#104	semidirect
332. C₂×C₅	C₂×#837	direct (N × H)
341. Q₈	C₂²×C₅×Dic₃	semidirect
345. D₄	C₂²×C₅×Dic₃	semidirect
364. C₂×C₃	C₂×C₅×#104	semidirect
366. C₅	C₂²×#837	direct (N × H)
371. C₂²	C₅×#837	direct (N × H)
381. C₃	C₂²×C₅×#104	semidirect
385. C₂	C₂×C₅×#837	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×C₅×#41	2
C₂²×C₄×C₅×Dic₃	2
C₂²×C₅×#208	2
C₂×C₅×#837	2
C₂²×C₅×#104	3
C₂²×#837	5

Subgroups — C22×C5×#837 #14412794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₅×#837 #14412794