Subgroups — C₂×C₅×#5816 #14480473

Order 1920.

3024 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#235	C₂	1	1	yes	maximal, characteristic
3	C₅×#5816	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#947	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#946	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#944	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#929	C₂	1	4	yes	maximal, complemented
8	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#536	—	3	1	no	maximal, Hall
10	C₂²×C₃×C₅×Q₈	—	2	8	no	—
11	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×Q₈	C₂²	1	8	yes	complemented
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₅×#67	C₂²	1	2	yes	—
17	C₂×C₅×#235	—	2	8	no	—
18	C₂×C₅×#235	C₂²	1	8	yes	—
19	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
21	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
22	C₂×C₅×#217	C₂²	1	2	yes	—
23	C₅×#947	C₂²	1	16	yes	complemented
24	C₅×#946	C₂²	1	32	yes	complemented
25	C₅×#944	C₂²	1	16	yes	complemented
26	C₅×#929	C₂²	1	32	yes	complemented
27	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
28	C₅×#926	C₂²	1	8	yes	complemented
29	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
30	C₂×C₅×Dic₃⋊C₄	C₂²	1	8	yes	—
31	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
32	C₂×#5816	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₅×#41	—	3	1	no	—
34	C₂³×C₅×Q₈	D₃	1	1	yes	characteristic, complemented
35	C₅×#536	—	3	16	no	—
36	C₂×C₅×C₄⋊Q₈	—	3	2	no	—
37	C₂×C₅×#124	—	3	2	no	—
38	C₂×C₅×#123	—	3	4	no	—
39	C₂×C₅×C₂²⋊Q₈	—	3	4	no	—
40	C₂×C₅×#117	—	3	1	no	—
41	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
42	C₂³×C₅×D₃	C₂³	1	2	yes	—
43	C₂×C₃×C₅×Q₈	—	2	8	no	—
44	C₂×C₃×C₅×Q₈	—	2	8	no	—
45	C₂×C₃×C₅×Q₈	—	2	32	no	—
46	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
47	C₂×C₃×C₅×Q₈	C₂³	1	8	yes	—
48	C₂²×C₃×C₄×C₅	—	2	8	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	8	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
55	C₂×C₅×#67	—	2	8	no	—
56	C₂×C₅×#67	C₂³	1	8	yes	—
57	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
59	C₅×#235	—	2	32	no	—
60	C₂×C₅×D₁₂	—	2	4	no	—
61	C₂×C₅×D₁₂	C₂³	1	4	yes	—
62	C₂×C₄×C₅×D₃	—	2	8	no	—
63	C₂×C₄×C₅×D₃	C₂³	1	8	yes	—
64	C₂×C₅×Dic₆	—	2	4	no	—
65	C₂×C₅×Dic₆	C₂³	1	4	yes	—
66	C₅×#217	C₂³	1	8	yes	—
67	C₅×(C₂×D₃)⋊C₄	C₂³	1	32	yes	—
68	C₅×C₄⋊Dic₃	C₂³	1	8	yes	—
69	C₅×Dic₃⋊C₄	C₂³	1	32	yes	—
70	C₄×C₅×Dic₃	C₂³	1	8	yes	—
71	C₂³×C₃×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂²×#235	C₂×C₅	1	1	yes	characteristic
73	#5816	C₂×C₅	1	16	yes	direct product factor
74	C₂×#947	C₂×C₅	1	2	yes	complemented
75	C₂×#946	C₂×C₅	1	4	yes	complemented
76	C₂×#944	C₂×C₅	1	2	yes	complemented
77	C₂×#929	C₂×C₅	1	4	yes	complemented
78	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂×C₅×#41	—	3	8	no	—
80	C₂×C₅×#41	—	6	8	no	—
81	C₂²×C₅×Q₈	—	2	8	no	—
82	C₂²×C₅×Q₈	—	3	1	no	—
83	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
84	C₂²×C₅×Q₈	C₂×D₃	1	2	yes	—
85	C₂²×C₅×Q₈	C₂×D₃	1	8	yes	complemented
86	C₂²×C₅×D₄	—	3	2	no	—
87	C₂²×C₅×D₄	—	3	1	no	—
88	C₂³×C₄×C₅	—	3	2	no	—
89	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
90	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	—	3	16	no	—
92	C₅×#124	—	3	16	no	—
93	C₅×#123	—	3	32	no	—
94	C₅×C₂²⋊Q₈	—	3	32	no	—
95	C₅×#117	—	3	8	no	—
96	C₂×C₅×C₄⋊C₄	—	3	8	no	—
97	C₂×C₅×C₄⋊C₄	—	3	2	no	—
98	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
99	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
100	C₂×C₄²×C₅	—	3	2	no	—
101	C₂×#536	—	3	1	no	Sylow
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
105	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₂²×C₅×D₃	—	2	4	no	—
107	C₂²×C₅×D₃	—	2	8	no	—
108	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
109	C₃×C₅×Q₈	—	2	16	no	—
110	C₃×C₅×Q₈	—	2	16	no	—
111	C₂×C₃×C₄×C₅	—	2	16	no	—
112	C₂×C₃×C₄×C₅	—	2	8	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	16	yes	—
116	C₂×C₃×C₄×C₅	C₂⁴	1	8	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
119	C₅×#67	—	2	16	no	—
120	C₂×C₅×Dic₃	—	2	4	no	—
121	C₂×C₅×Dic₃	—	2	8	no	—
122	C₂×C₅×Dic₃	C₂⁴	1	8	yes	—
123	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
124	C₅×D₁₂	—	2	8	no	—
125	C₄×C₅×D₃	—	2	16	no	—
126	C₅×Dic₆	—	2	8	no	—
127	C₂²×C₃×Q₈	—	2	8	no	—
128	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
130	C₂²×C₃×Q₈	C₂²×C₅	1	8	yes	complemented
131	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
132	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
133	C₂²×#67	C₂²×C₅	1	2	yes	—
134	C₂×#235	—	2	8	no	—
135	C₂×#235	C₂²×C₅	1	8	yes	—
136	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
137	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
138	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
139	C₂×#217	C₂²×C₅	1	2	yes	—
140	#947	C₂²×C₅	1	16	yes	complemented
141	#946	C₂²×C₅	1	32	yes	complemented
142	#944	C₂²×C₅	1	16	yes	complemented
143	#929	C₂²×C₅	1	32	yes	complemented
144	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	—
145	#926	C₂²×C₅	1	8	yes	complemented
146	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
147	C₂×Dic₃⋊C₄	C₂²×C₅	1	8	yes	—
148	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
149	C₂⁴×C₅	—	3	2	no	—
150	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
151	C₅×#41	—	6	32	no	—
152	C₂×C₅×Q₈	—	2	8	no	—
153	C₂×C₅×Q₈	—	2	8	no	—
154	C₂×C₅×Q₈	—	2	32	no	—
155	C₂×C₅×Q₈	—	3	4	no	—
156	C₂×C₅×Q₈	—	6	4	no	—
157	C₂×C₅×Q₈	C₂²×D₃	1	8	yes	—
158	C₂×C₅×Q₈	C₂²×D₃	1	8	yes	—
159	C₂×C₅×D₄	—	3	8	no	—
160	C₂×C₅×D₄	—	3	4	no	—
161	C₂×C₅×D₄	—	6	8	no	—
162	C₂×C₅×D₄	—	6	4	no	—
163	C₂²×C₄×C₅	—	2	8	no	—
164	C₂²×C₄×C₅	—	3	4	no	—
165	C₂²×C₄×C₅	—	3	2	no	—
166	C₂²×C₄×C₅	—	3	8	no	—
167	C₂²×C₄×C₅	—	6	8	no	—
168	C₂²×C₄×C₅	#67	1	8	yes	—
169	C₂²×C₄×C₅	C₂²×D₃	1	8	yes	—
170	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
171	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
172	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₅×C₄⋊C₄	—	3	8	no	—
175	C₅×C₄⋊C₄	—	3	32	no	—
176	C₅×C₂²⋊C₄	—	3	8	no	—
177	C₅×C₂²⋊C₄	—	3	32	no	—
178	C₄²×C₅	—	3	8	no	—
179	C₂²×#41	—	3	1	no	—
180	C₂³×Q₈	C₅×D₃	1	1	yes	characteristic, complemented
181	#536	—	3	16	no	—
182	C₂×C₄⋊Q₈	—	3	2	no	—
183	C₂×#124	—	3	2	no	—
184	C₂×#123	—	3	4	no	—
185	C₂×C₂²⋊Q₈	—	3	4	no	—
186	C₂×#117	—	3	1	no	—
187	C₂²×C₃×C₅	—	2	8	no	—
188	C₂²×C₃×C₅	—	2	4	no	—
189	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
190	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
191	C₂²×C₃×C₅	2₋¹⁺⁴	1	4	yes	—
192	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
193	C₂×C₅×D₃	—	2	4	no	—
194	C₂×C₅×D₃	—	2	8	no	—
195	C₂×C₅×D₃	—	4	8	no	—
196	C₃×C₄×C₅	—	2	8	no	—
197	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
198	C₃×C₄×C₅	C₂²×D₄	1	4	yes	—
199	C₅×Dic₃	—	2	4	no	—
200	C₅×Dic₃	—	2	8	no	—
201	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
202	C₂³×D₃	C₂³×C₅	1	2	yes	—
203	C₂×C₃×Q₈	—	2	8	no	—
204	C₂×C₃×Q₈	—	2	8	no	—
205	C₂×C₃×Q₈	—	2	32	no	—
206	C₂×C₃×Q₈	C₂³×C₅	1	8	yes	—
207	C₂×C₃×Q₈	C₂³×C₅	1	8	yes	—
208	C₂²×C₃×C₄	—	2	8	no	—
209	C₂²×C₃×C₄	C₅×D₄	1	8	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	8	yes	—
212	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
213	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
214	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
215	C₂×#67	—	2	8	no	—
216	C₂×#67	C₂³×C₅	1	8	yes	—
217	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
218	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
219	#235	—	2	32	no	—
220	C₂×D₁₂	—	2	4	no	—
221	C₂×D₁₂	C₂³×C₅	1	4	yes	—
222	C₂×C₄×D₃	—	2	8	no	—
223	C₂×C₄×D₃	C₂³×C₅	1	8	yes	—
224	C₂×Dic₆	—	2	4	no	—
225	C₂×Dic₆	C₂³×C₅	1	4	yes	—
226	#217	C₂³×C₅	1	8	yes	—
227	(C₂×D₃)⋊C₄	C₂³×C₅	1	32	yes	—
228	C₄⋊Dic₃	C₂³×C₅	1	8	yes	—
229	Dic₃⋊C₄	C₂³×C₅	1	32	yes	—
230	C₄×Dic₃	C₂³×C₅	1	8	yes	—
231	C₂³×C₅	—	2	4	no	—
232	C₂³×C₅	—	3	4	no	—
233	C₂³×C₅	—	6	8	no	—
234	C₂³×C₅	—	6	4	no	—
235	C₂³×C₅	C₂×#67	1	4	yes	—
236	C₂³×C₅	C₂³×D₃	1	2	yes	—
237	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
238	C₅×Q₈	—	2	16	no	—
239	C₅×Q₈	—	2	16	no	—
240	C₅×Q₈	—	6	8	no	—
241	C₅×D₄	—	6	16	no	—
242	C₅×D₄	—	6	8	no	—
243	C₂×C₄×C₅	—	2	16	no	—
244	C₂×C₄×C₅	—	2	8	no	—
245	C₂×C₄×C₅	—	3	8	no	—
246	C₂×C₄×C₅	—	3	4	no	—
247	C₂×C₄×C₅	—	6	8	no	—
248	C₂×C₄×C₅	—	6	4	no	—
249	C₂×C₄×C₅	—	6	16	no	—
250	C₂×C₄×C₅	C₂×#67	1	4	yes	—
251	C₂×C₄×C₅	C₂×#67	1	4	yes	—
252	C₂×C₄×C₅	C₂×#67	1	16	yes	—
253	C₂×C₄×C₅	C₂³×D₃	1	8	yes	—
254	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
255	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
256	C₂×#41	—	3	8	no	—
257	C₂×#41	—	6	8	no	—
258	C₂²×Q₈	—	2	8	no	—
259	C₂²×Q₈	—	3	1	no	—
260	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
261	C₂²×Q₈	C₂×C₅×D₃	1	2	yes	—
262	C₂²×Q₈	C₂×C₅×D₃	1	8	yes	complemented
263	C₂²×D₄	—	3	2	no	—
264	C₂²×D₄	—	3	1	no	—
265	C₂³×C₄	—	3	2	no	—
266	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
267	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
268	C₄⋊Q₈	—	3	16	no	—
269	#124	—	3	16	no	—
270	#123	—	3	32	no	—
271	C₂²⋊Q₈	—	3	32	no	—
272	#117	—	3	8	no	—
273	C₂×C₄⋊C₄	—	3	2	no	—
274	C₂×C₄⋊C₄	—	3	8	no	—
275	C₂×C₂²⋊C₄	—	3	2	no	—
276	C₂×C₂²⋊C₄	—	3	8	no	—
277	C₂×C₄²	—	3	2	no	—
278	C₂×C₃×C₅	—	2	4	no	—
279	C₂×C₃×C₅	#536	1	4	yes	complemented
280	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
281	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
282	C₅×D₃	—	4	4	no	—
283	C₂³×C₃	—	2	4	no	—
284	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
285	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
286	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
287	C₂²×D₃	—	2	4	no	—
288	C₂²×D₃	—	2	8	no	—
289	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
290	C₃×Q₈	—	2	16	no	—
291	C₃×Q₈	—	2	16	no	—
292	C₂×C₃×C₄	—	2	16	no	—
293	C₂×C₃×C₄	—	2	8	no	—
294	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
296	C₂×C₃×C₄	C₂×C₅×D₄	1	16	yes	—
297	C₂×C₃×C₄	C₂⁴×C₅	1	8	yes	—
298	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
299	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
300	#67	—	2	16	no	—
301	C₂×Dic₃	—	2	4	no	—
302	C₂×Dic₃	—	2	8	no	—
303	C₂×Dic₃	C₂⁴×C₅	1	8	yes	—
304	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
305	D₁₂	—	2	8	no	—
306	C₄×D₃	—	2	16	no	—
307	Dic₆	—	2	8	no	—
308	C₂²×C₅	—	2	4	no	—
309	C₂²×C₅	—	2	8	no	—
310	C₂²×C₅	—	6	8	no	—
311	C₂²×C₅	—	6	4	no	—
312	C₂²×C₅	—	12	8	no	—
313	C₂²×C₅	#1007	1	4	yes	—
314	C₂²×C₅	C₂²×#67	1	4	yes	—
315	C₂²×C₅	C₂²×#67	1	2	yes	—
316	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
317	C₄×C₅	—	2	8	no	—
318	C₄×C₅	—	6	8	no	—
319	C₄×C₅	—	6	4	no	—
320	C₄×C₅	C₂²×#67	1	4	yes	—
321	C₄×C₅	C₂²×#67	1	4	yes	—
322	C₂⁴	—	3	2	no	—
323	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
324	#41	—	6	32	no	—
325	C₂×Q₈	—	2	8	no	—
326	C₂×Q₈	—	2	8	no	—
327	C₂×Q₈	—	2	32	no	—
328	C₂×Q₈	—	3	4	no	—
329	C₂×Q₈	—	6	4	no	—
330	C₂×Q₈	C₂²×C₅×D₃	1	8	yes	—
331	C₂×Q₈	C₂²×C₅×D₃	1	8	yes	—
332	C₂×D₄	—	3	8	no	—
333	C₂×D₄	—	3	4	no	—
334	C₂×D₄	—	6	8	no	—
335	C₂×D₄	—	6	4	no	—
336	C₂²×C₄	—	2	8	no	—
337	C₂²×C₄	—	3	4	no	—
338	C₂²×C₄	—	3	2	no	—
339	C₂²×C₄	—	3	8	no	—
340	C₂²×C₄	—	6	8	no	—
341	C₂²×C₄	C₅×#67	1	8	yes	—
342	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
343	C₂²×C₄	C₂²×C₅×D₃	1	8	yes	—
344	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
346	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
347	C₄⋊C₄	—	3	8	no	—
348	C₄⋊C₄	—	3	32	no	—
349	C₂²⋊C₄	—	3	8	no	—
350	C₂²⋊C₄	—	3	32	no	—
351	C₄²	—	3	8	no	—
352	C₃×C₅	C₂×#536	1	1	yes	characteristic, complemented, Hall
353	C₂²×C₃	—	2	8	no	—
354	C₂²×C₃	—	2	4	no	—
355	C₂²×C₃	C₂²×C₅×D₄	1	4	yes	—
356	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
357	C₂²×C₃	C₅×2₋¹⁺⁴	1	4	yes	—
358	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
359	C₂×D₃	—	2	4	no	—
360	C₂×D₃	—	2	8	no	—
361	C₂×D₃	—	4	8	no	—
362	C₃×C₄	—	2	8	no	—
363	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
364	C₃×C₄	C₂²×C₅×D₄	1	4	yes	—
365	Dic₃	—	2	4	no	—
366	Dic₃	—	2	8	no	—
367	C₂×C₅	—	2	4	no	—
368	C₂×C₅	—	12	4	no	—
369	C₂×C₅	#5816	1	4	yes	direct product factor
370	C₂×C₅	C₂×#1007	1	2	yes	—
371	C₂×C₅	C₂³×#67	1	1	yes	characteristic
372	C₂³	—	2	4	no	—
373	C₂³	—	3	4	no	—
374	C₂³	—	6	8	no	—
375	C₂³	—	6	4	no	—
376	C₂³	C₂×C₅×#67	1	4	yes	—
377	C₂³	C₂³×C₅×D₃	1	2	yes	—
378	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
379	Q₈	—	2	16	no	—
380	Q₈	—	2	16	no	—
381	Q₈	—	6	8	no	—
382	D₄	—	6	16	no	—
383	D₄	—	6	8	no	—
384	C₂×C₄	—	2	16	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	3	8	no	—
387	C₂×C₄	—	3	4	no	—
388	C₂×C₄	—	6	8	no	—
389	C₂×C₄	—	6	4	no	—
390	C₂×C₄	—	6	16	no	—
391	C₂×C₄	C₂×C₅×#67	1	4	yes	—
392	C₂×C₄	C₂×C₅×#67	1	4	yes	—
393	C₂×C₄	C₂×C₅×#67	1	16	yes	—
394	C₂×C₄	C₂³×C₅×D₃	1	8	yes	—
395	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
396	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
397	C₂×C₃	—	2	4	no	—
398	C₂×C₃	C₅×#536	1	4	yes	complemented
399	C₂×C₃	C₂³×C₅×D₄	1	1	yes	characteristic
400	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
401	D₃	—	4	4	no	—
402	C₅	C₂×#5816	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	—	2	4	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	6	8	no	—
406	C₂²	—	6	4	no	—
407	C₂²	—	12	8	no	—
408	C₂²	C₅×#1007	1	4	yes	—
409	C₂²	C₂²×C₅×#67	1	4	yes	—
410	C₂²	C₂²×C₅×#67	1	2	yes	—
411	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
412	C₄	—	2	8	no	—
413	C₄	—	6	8	no	—
414	C₄	—	6	4	no	—
415	C₄	C₂²×C₅×#67	1	4	yes	—
416	C₄	C₂²×C₅×#67	1	4	yes	—
417	C₃	C₂×C₅×#536	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	2	4	no	—
419	C₂	—	12	4	no	—
420	C₂	C₅×#5816	1	4	yes	direct product factor
421	C₂	C₂×C₅×#1007	1	2	yes	—
422	C₂	C₂³×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₂³×C₃×C₅×Q₈	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#235	C₂
hypercenter	C₂³×C₅×Q₈	D₃
hypocenter	C₃	C₂×C₅×#536
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₅×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂³×C₃×C₅×Q₈	C₂	semidirect
3. C₅×#5816	C₂	direct (N × H)
4. C₂×C₅×#947	C₂	semidirect
5. C₂×C₅×#946	C₂	semidirect
6. C₂×C₅×#944	C₂	semidirect
7. C₂×C₅×#929	C₂	semidirect
8. C₂×C₅×#926	C₂	semidirect
13. C₂²×C₃×C₅×Q₈	C₂²	semidirect
23. C₅×#947	C₂²	semidirect
24. C₅×#946	C₂²	semidirect
25. C₅×#944	C₂²	semidirect
26. C₅×#929	C₂²	semidirect
28. C₅×#926	C₂²	semidirect
32. C₂×#5816	C₅	direct (N × H)
34. C₂³×C₅×Q₈	D₃	semidirect
71. C₂³×C₃×Q₈	C₂×C₅	semidirect
73. #5816	C₂×C₅	direct (N × H)
74. C₂×#947	C₂×C₅	semidirect
75. C₂×#946	C₂×C₅	semidirect
76. C₂×#944	C₂×C₅	semidirect
77. C₂×#929	C₂×C₅	semidirect
78. C₂×#926	C₂×C₅	semidirect
85. C₂²×C₅×Q₈	C₂×D₃	semidirect
130. C₂²×C₃×Q₈	C₂²×C₅	semidirect
140. #947	C₂²×C₅	semidirect
141. #946	C₂²×C₅	semidirect
142. #944	C₂²×C₅	semidirect
143. #929	C₂²×C₅	semidirect
145. #926	C₂²×C₅	semidirect
180. C₂³×Q₈	C₅×D₃	semidirect
262. C₂²×Q₈	C₂×C₅×D₃	semidirect
279. C₂×C₃×C₅	#536	semidirect
352. C₃×C₅	C₂×#536	semidirect
369. C₂×C₅	#5816	direct (N × H)
398. C₂×C₃	C₅×#536	semidirect
402. C₅	C₂×#5816	direct (N × H)
417. C₃	C₂×C₅×#536	semidirect
420. C₂	C₅×#5816	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×C₅×Q₈	2
C₂²×C₅×#235	2
C₅×#5816	2
C₂×C₅×#947	2
C₂×C₅×#946	2
C₂×C₅×#944	2
C₂×C₅×#929	2
C₂×C₅×#926	2
C₂×C₅×#536	3
C₂×#5816	5

Subgroups — C2×C5×#5816 #14480473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#5816 #14480473