Subgroups — C₅×#71701 #14307483

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#5212	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×#217	C₂	1	1	yes	maximal, characteristic
4	C₅×#4526	C₂	1	4	yes	maximal
5	C₅×#1996	—	3	1	no	maximal, Hall
6	C₂²×C₃×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
9	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
10	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
11	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic, complemented
13	C₂×C₃×C₅×C₄⋊C₄	C₄	1	2	yes	complemented
14	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
15	C₂×C₅×#217	C₂²	1	2	yes	—
16	C₂×C₅×#217	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Dic₃	—	2	1	no	—
18	C₂×C₄×C₅×Dic₃	—	2	1	no	—
19	C₅×C₃⋊#95	—	2	1	no	—
20	C₅×C₃⋊#95	—	2	1	no	—
21	#71701	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic
23	C₅×#380	—	3	1	no	—
24	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
25	C₅×#342	—	3	4	no	—
26	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
27	C₂×C₃×C₅×Q₈	—	2	1	no	—
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	—	4	2	no	—
30	C₂²×C₃×C₄×C₅	—	4	2	no	—
31	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₅×Dic₃	—	2	2	no	—
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₃×C₅×C₄⋊C₄	—	2	1	no	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	—	2	2	no	—
44	C₃×C₅×C₄⋊C₄	—	2	2	no	—
45	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
46	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
47	C₅×#217	—	2	2	no	—
48	C₅×#217	—	2	4	no	—
49	C₅×#217	Q₈	1	4	yes	complemented
50	C₅×C₄⋊Dic₃	—	4	2	no	—
51	C₄×C₅×Dic₃	—	4	2	no	—
52	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
53	#5212	C₂×C₅	1	1	yes	characteristic
54	C₄×#217	C₂×C₅	1	1	yes	characteristic
55	#4526	C₂×C₅	1	4	yes	—
56	C₂²×C₅×Q₈	Dic₃	1	1	yes	characteristic, complemented
57	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
58	C₅×C₂²⋊Q₈	—	2	1	no	—
59	C₅×C₂²⋊Q₈	—	2	1	no	—
60	C₅×C₂²⋊Q₈	—	2	1	no	—
61	C₅×C₂²⋊Q₈	—	2	1	no	—
62	C₂×C₅×C₄⋊C₄	—	6	1	no	—
63	C₂×C₅×C₄⋊C₄	Dic₃	1	1	yes	characteristic, complemented
64	C₂×C₅×C₄⋊C₄	Dic₃	1	2	yes	complemented
65	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
66	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
67	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
68	C₂×C₄²×C₅	—	6	1	no	—
69	C₅×#95	—	6	1	no	—
70	C₅×#95	—	6	1	no	—
71	#1996	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	4	1	no	—
73	C₂³×C₃×C₅	—	4	1	no	—
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
78	C₂³×C₃×C₅	#41	1	2	yes	—
79	C₃×C₅×Q₈	—	4	2	no	—
80	C₃×C₅×Q₈	—	4	2	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	2	no	—
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	4	1	no	—
87	C₂×C₃×C₄×C₅	—	4	1	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	2	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₅×Dic₃	—	2	4	no	—
96	C₂×C₅×Dic₃	—	4	2	no	—
97	C₂×C₅×Dic₃	—	4	2	no	—
98	C₂×C₅×Dic₃	—	4	2	no	—
99	C₂×C₅×Dic₃	—	4	2	no	—
100	C₂×C₅×Dic₃	—	4	2	no	—
101	C₂²×C₃×Q₈	C₄×C₅	1	1	yes	characteristic, complemented
102	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
103	C₃×C₂²⋊Q₈	—	2	1	no	—
104	C₃×C₂²⋊Q₈	—	2	1	no	—
105	C₃×C₂²⋊Q₈	—	2	1	no	—
106	C₃×C₂²⋊Q₈	—	2	1	no	—
107	C₂×C₃×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic, complemented
108	C₂×C₃×C₄⋊C₄	C₄×C₅	1	2	yes	complemented
109	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
110	C₂×#217	C₂²×C₅	1	2	yes	—
111	C₂×#217	C₂²×C₅	1	2	yes	—
112	C₂×C₄⋊Dic₃	—	2	1	no	—
113	C₂×C₄×Dic₃	—	2	1	no	—
114	C₃⋊#95	—	2	1	no	—
115	C₃⋊#95	—	2	1	no	—
116	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	1	no	—
119	C₂×C₅×Q₈	—	4	2	no	—
120	C₂²×C₄×C₅	—	4	2	no	—
121	C₂²×C₄×C₅	—	6	2	no	—
122	C₂²×C₄×C₅	—	6	2	no	—
123	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
125	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
126	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
127	C₂²×C₄×C₅	#67	1	1	yes	characteristic
128	C₂²×C₄×C₅	#67	1	1	yes	characteristic
129	C₂²×C₄×C₅	#67	1	1	yes	characteristic
130	C₂²×C₄×C₅	#67	1	1	yes	characteristic
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	2	1	no	—
133	C₅×C₄⋊C₄	—	2	2	no	—
134	C₅×C₄⋊C₄	—	2	2	no	—
135	C₅×C₄⋊C₄	—	12	2	no	—
136	C₅×C₂²⋊C₄	—	2	2	no	—
137	C₅×C₂²⋊C₄	—	2	2	no	—
138	C₅×C₂²⋊C₄	—	3	4	no	—
139	C₅×C₂²⋊C₄	—	6	2	no	—
140	C₅×C₂²⋊C₄	—	6	4	no	—
141	C₄²×C₅	—	12	2	no	—
142	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic
143	#380	—	3	1	no	—
144	C₄×C₂²⋊C₄	—	3	1	no	—
145	#342	—	3	4	no	—
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	2	1	no	—
148	C₂²×C₃×C₅	—	2	1	no	—
149	C₂²×C₃×C₅	—	2	1	no	—
150	C₂²×C₃×C₅	—	2	1	no	—
151	C₂²×C₃×C₅	—	2	1	no	—
152	C₂²×C₃×C₅	—	4	2	no	—
153	C₂²×C₃×C₅	—	4	2	no	—
154	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₃×C₅	C₄×Q₈	1	2	yes	—
156	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
157	C₂²×C₃×C₅	#124	1	1	yes	characteristic
158	C₂²×C₃×C₅	C₄⋊Q₈	1	1	yes	characteristic
159	C₃×C₄×C₅	—	2	1	no	—
160	C₃×C₄×C₅	—	2	1	no	—
161	C₃×C₄×C₅	—	2	1	no	—
162	C₃×C₄×C₅	—	4	2	no	—
163	C₃×C₄×C₅	—	4	2	no	—
164	C₃×C₄×C₅	#99	1	2	yes	—
165	C₅×Dic₃	—	4	4	no	—
166	C₅×Dic₃	—	8	2	no	—
167	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
168	C₂×C₃×Q₈	—	2	1	no	—
169	C₂×C₃×Q₈	—	2	1	no	—
170	C₂×C₃×Q₈	—	4	2	no	—
171	C₂²×C₃×C₄	—	4	2	no	—
172	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
173	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
174	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
175	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
178	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
179	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
180	C₂²×Dic₃	—	2	2	no	—
181	C₂²×Dic₃	—	2	2	no	—
182	C₃×C₄⋊C₄	—	2	1	no	—
183	C₃×C₄⋊C₄	—	2	1	no	—
184	C₃×C₄⋊C₄	—	2	2	no	—
185	C₃×C₄⋊C₄	—	2	2	no	—
186	C₃×C₂²⋊C₄	—	2	2	no	—
187	C₃×C₂²⋊C₄	—	2	2	no	—
188	#217	—	2	2	no	—
189	#217	—	2	4	no	—
190	#217	C₅×Q₈	1	4	yes	complemented
191	C₄⋊Dic₃	—	4	2	no	—
192	C₄×Dic₃	—	4	2	no	—
193	C₂³×C₅	—	4	1	no	—
194	C₂³×C₅	—	4	1	no	—
195	C₂³×C₅	D₃×Q₈	1	2	yes	—
196	C₂³×C₅	#239	1	2	yes	—
197	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
198	C₂³×C₅	C₂×#67	1	1	yes	characteristic
199	C₂³×C₅	C₂×#67	1	1	yes	characteristic
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	4	1	no	—
208	C₂×C₄×C₅	—	4	1	no	—
209	C₂×C₄×C₅	—	4	1	no	—
210	C₂×C₄×C₅	—	4	2	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	6	4	no	—
213	C₂×C₄×C₅	—	12	2	no	—
214	C₂×C₄×C₅	—	12	2	no	—
215	C₂×C₄×C₅	—	12	2	no	—
216	C₂×C₄×C₅	—	12	2	no	—
217	C₂×C₄×C₅	—	12	2	no	—
218	C₂×C₄×C₅	#217	1	1	yes	characteristic
219	C₂×C₄×C₅	#217	1	1	yes	characteristic
220	C₂×C₄×C₅	#217	1	1	yes	characteristic
221	C₂×C₄×C₅	#217	1	1	yes	characteristic
222	C₂²×Q₈	C₅×Dic₃	1	1	yes	characteristic, complemented
223	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
224	C₂²⋊Q₈	—	2	1	no	—
225	C₂²⋊Q₈	—	2	1	no	—
226	C₂²⋊Q₈	—	2	1	no	—
227	C₂²⋊Q₈	—	2	1	no	—
228	C₂×C₄⋊C₄	—	6	1	no	—
229	C₂×C₄⋊C₄	C₅×Dic₃	1	1	yes	characteristic, complemented
230	C₂×C₄⋊C₄	C₅×Dic₃	1	2	yes	complemented
231	C₂×C₂²⋊C₄	—	3	2	no	—
232	C₂×C₂²⋊C₄	—	3	2	no	—
233	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
234	C₂×C₄²	—	6	1	no	—
235	#95	—	6	1	no	—
236	#95	—	6	1	no	—
237	C₂×C₃×C₅	—	2	2	no	—
238	C₂×C₃×C₅	—	2	1	no	—
239	C₂×C₃×C₅	—	2	2	no	—
240	C₂×C₃×C₅	—	2	1	no	—
241	C₂×C₃×C₅	#391	1	1	yes	characteristic
242	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
243	C₂×C₃×C₅	#410	1	1	yes	characteristic
244	C₂³×C₃	—	4	1	no	—
245	C₂³×C₃	—	4	1	no	—
246	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
247	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
248	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
249	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
250	C₂³×C₃	C₅×#41	1	2	yes	—
251	C₃×Q₈	—	4	2	no	—
252	C₃×Q₈	—	4	2	no	—
253	C₂×C₃×C₄	—	2	2	no	—
254	C₂×C₃×C₄	—	2	2	no	—
255	C₂×C₃×C₄	—	2	2	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	2	no	—
258	C₂×C₃×C₄	—	4	1	no	—
259	C₂×C₃×C₄	—	4	1	no	—
260	C₂×C₃×C₄	—	4	1	no	—
261	C₂×C₃×C₄	—	4	2	no	—
262	C₂×C₃×C₄	—	4	2	no	—
263	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
266	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×Dic₃	—	2	4	no	—
268	C₂×Dic₃	—	4	2	no	—
269	C₂×Dic₃	—	4	2	no	—
270	C₂×Dic₃	—	4	2	no	—
271	C₂×Dic₃	—	4	2	no	—
272	C₂×Dic₃	—	4	2	no	—
273	C₂²×C₅	—	2	1	no	—
274	C₂²×C₅	—	2	1	no	—
275	C₂²×C₅	—	2	1	no	—
276	C₂²×C₅	—	2	1	no	—
277	C₂²×C₅	—	2	1	no	—
278	C₂²×C₅	—	2	1	no	—
279	C₂²×C₅	—	4	2	no	—
280	C₂²×C₅	—	4	2	no	—
281	C₂²×C₅	#944	1	1	yes	characteristic
282	C₂²×C₅	Q₈×Dic₃	1	2	yes	—
283	C₂²×C₅	#946	1	2	yes	—
284	C₂²×C₅	#947	1	1	yes	characteristic
285	C₂²×C₅	C₂×#217	1	1	yes	characteristic
286	C₄×C₅	—	2	1	no	—
287	C₄×C₅	—	2	1	no	—
288	C₄×C₅	—	2	1	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	—	12	4	no	—
292	C₄×C₅	—	24	2	no	—
293	C₄×C₅	#834	1	2	yes	—
294	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
295	C₂×Q₈	—	2	1	no	—
296	C₂×Q₈	—	2	1	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂²×C₄	—	4	2	no	—
299	C₂²×C₄	—	6	2	no	—
300	C₂²×C₄	—	6	2	no	—
301	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
302	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
303	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
304	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
305	C₂²×C₄	C₅×#67	1	1	yes	characteristic
306	C₂²×C₄	C₅×#67	1	1	yes	characteristic
307	C₂²×C₄	C₅×#67	1	1	yes	characteristic
308	C₂²×C₄	C₅×#67	1	1	yes	characteristic
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	12	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	3	4	no	—
317	C₂²⋊C₄	—	6	2	no	—
318	C₂²⋊C₄	—	6	4	no	—
319	C₄²	—	12	2	no	—
320	C₃×C₅	#1996	1	1	yes	characteristic, complemented, Hall
321	C₂²×C₃	—	2	1	no	—
322	C₂²×C₃	—	2	1	no	—
323	C₂²×C₃	—	2	1	no	—
324	C₂²×C₃	—	2	1	no	—
325	C₂²×C₃	—	2	1	no	—
326	C₂²×C₃	—	2	1	no	—
327	C₂²×C₃	—	4	2	no	—
328	C₂²×C₃	—	4	2	no	—
329	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
330	C₂²×C₃	C₄×C₅×Q₈	1	2	yes	—
331	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
332	C₂²×C₃	C₅×#124	1	1	yes	characteristic
333	C₂²×C₃	C₅×C₄⋊Q₈	1	1	yes	characteristic
334	C₃×C₄	—	2	1	no	—
335	C₃×C₄	—	2	1	no	—
336	C₃×C₄	—	2	1	no	—
337	C₃×C₄	—	4	2	no	—
338	C₃×C₄	—	4	2	no	—
339	C₃×C₄	C₅×#99	1	2	yes	—
340	Dic₃	—	4	4	no	—
341	Dic₃	—	8	2	no	—
342	C₂×C₅	—	2	2	no	—
343	C₂×C₅	—	2	1	no	—
344	C₂×C₅	—	2	1	no	—
345	C₂×C₅	—	2	2	no	—
346	C₂×C₅	C₂×#834	1	1	yes	characteristic
347	C₂×C₅	#5229	1	1	yes	characteristic
348	C₂×C₅	#5240	1	1	yes	characteristic
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	C₅×D₃×Q₈	1	2	yes	—
352	C₂³	C₅×#239	1	2	yes	—
353	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
354	C₂³	C₂×C₅×#67	1	1	yes	characteristic
355	C₂³	C₂×C₅×#67	1	1	yes	characteristic
356	Q₈	—	4	2	no	—
357	Q₈	—	4	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	6	4	no	—
369	C₂×C₄	—	12	2	no	—
370	C₂×C₄	—	12	2	no	—
371	C₂×C₄	—	12	2	no	—
372	C₂×C₄	—	12	2	no	—
373	C₂×C₄	—	12	2	no	—
374	C₂×C₄	C₅×#217	1	1	yes	characteristic
375	C₂×C₄	C₅×#217	1	1	yes	characteristic
376	C₂×C₄	C₅×#217	1	1	yes	characteristic
377	C₂×C₄	C₅×#217	1	1	yes	characteristic
378	C₂×C₃	—	2	2	no	—
379	C₂×C₃	—	2	1	no	—
380	C₂×C₃	—	2	2	no	—
381	C₂×C₃	—	2	1	no	—
382	C₂×C₃	C₅×#391	1	1	yes	characteristic
383	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
384	C₂×C₃	C₅×#410	1	1	yes	characteristic
385	C₅	#71701	1	1	yes	characteristic, direct product factor, Sylow
386	C₂²	—	2	1	no	—
387	C₂²	—	2	1	no	—
388	C₂²	—	2	1	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	2	no	—
394	C₂²	C₅×#944	1	1	yes	characteristic
395	C₂²	C₅×Q₈×Dic₃	1	2	yes	—
396	C₂²	C₅×#946	1	2	yes	—
397	C₂²	C₅×#947	1	1	yes	characteristic
398	C₂²	C₂×C₅×#217	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	12	4	no	—
405	C₄	—	24	2	no	—
406	C₄	C₅×#834	1	2	yes	—
407	C₃	C₅×#1996	1	1	yes	characteristic, complemented, Sylow
408	C₂	—	2	2	no	—
409	C₂	—	2	1	no	—
410	C₂	—	2	1	no	—
411	C₂	—	2	2	no	—
412	C₂	C₂×C₅×#834	1	1	yes	characteristic
413	C₂	C₅×#5229	1	1	yes	characteristic
414	C₂	C₅×#5240	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×#217
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₅×#1996
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
6. C₂²×C₃×C₅×Q₈	C₄	semidirect
12. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
13. C₂×C₃×C₅×C₄⋊C₄	C₄	semidirect
21. #71701	C₅	direct (N × H)
49. C₅×#217	Q₈	semidirect
56. C₂²×C₅×Q₈	Dic₃	semidirect
63. C₂×C₅×C₄⋊C₄	Dic₃	semidirect
64. C₂×C₅×C₄⋊C₄	Dic₃	semidirect
101. C₂²×C₃×Q₈	C₄×C₅	semidirect
107. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
108. C₂×C₃×C₄⋊C₄	C₄×C₅	semidirect
190. #217	C₅×Q₈	semidirect
222. C₂²×Q₈	C₅×Dic₃	semidirect
229. C₂×C₄⋊C₄	C₅×Dic₃	semidirect
230. C₂×C₄⋊C₄	C₅×Dic₃	semidirect
320. C₃×C₅	#1996	semidirect
385. C₅	#71701	direct (N × H)
407. C₃	C₅×#1996	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×C₅×C₂²⋊Q₈	2
C₅×#5212	2
C₄×C₅×#217	2
C₅×#4526	2
C₅×#1996	3
#71701	5

Subgroups — C5×#71701 #14307483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71701 #14307483