Subgroups — C₅×#71696 #14301762

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 380 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	C₂³×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#835	C₂	1	2	yes	maximal, complemented
4	C₅×#5212	C₂	1	1	yes	maximal, characteristic
5	C₅×#4529	C₂	1	2	yes	maximal, complemented
6	C₅×#1892	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
10	C₃×C₅×C₂²⋊Q₈	C₄	1	4	yes	complemented
11	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
12	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
14	C₂×C₅×#217	—	2	1	no	—
15	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
16	C₂²×C₅×C₃⋊C₈	—	2	2	no	—
17	C₂²×C₅×C₃⋊C₈	—	2	4	no	—
18	C₂²×C₅×C₃⋊C₈	C₂²	1	2	yes	—
19	C₅×#835	—	2	4	no	—
20	C₅×C₃⋊#95	—	2	1	no	—
21	#71696	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₅×C₈	—	3	1	no	—
23	C₂×C₅×C₂²⋊Q₈	D₃	1	1	yes	characteristic
24	C₂×C₅×#103	—	3	2	no	—
25	C₅×#380	—	3	1	no	—
26	C₅×#340	—	3	2	no	—
27	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
28	C₂×C₃×C₅×Q₈	—	2	1	no	—
29	C₂×C₃×C₅×Q₈	—	2	2	no	—
30	C₂×C₃×C₅×Q₈	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	2	1	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂²×C₅×Dic₃	—	2	2	no	—
41	C₃×C₅×C₄⋊C₄	—	2	4	no	—
42	C₃×C₅×C₄⋊C₄	—	2	1	no	—
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
44	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
45	C₅×#217	—	4	2	no	—
46	C₅×C₄⋊Dic₃	—	2	2	no	—
47	C₅×C₄⋊Dic₃	—	2	2	no	—
48	C₂×C₅×C₃⋊C₈	—	2	8	no	—
49	C₂×C₅×C₃⋊C₈	—	2	2	no	—
50	C₂×C₅×C₃⋊C₈	—	2	2	no	—
51	C₂×C₅×C₃⋊C₈	D₄	1	4	yes	—
52	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
53	C₂³×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic
54	C₂×#835	C₂×C₅	1	2	yes	complemented
55	#5212	C₂×C₅	1	1	yes	characteristic
56	#4529	C₂×C₅	1	2	yes	complemented
57	C₂²×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
58	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
59	C₂²×C₅×C₈	—	3	2	no	—
60	C₂²×C₅×C₈	—	6	4	no	—
61	C₂²×C₅×C₈	—	6	2	no	—
62	C₅×C₂²⋊Q₈	—	2	2	no	—
63	C₅×C₂²⋊Q₈	Dic₃	1	4	yes	complemented
64	C₂×C₅×C₄⋊C₄	—	2	1	no	—
65	C₂×C₅×C₄⋊C₄	—	3	2	no	—
66	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
67	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
68	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
69	C₅×#103	—	6	4	no	—
70	C₅×#95	—	6	1	no	—
71	#1892	—	3	1	no	Sylow
72	C₂³×C₃×C₅	—	2	2	no	—
73	C₂³×C₃×C₅	—	2	2	no	—
74	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
75	C₂³×C₃×C₅	SD₁₆	1	2	yes	—
76	C₂³×C₃×C₅	Q₁₆	1	2	yes	—
77	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
78	C₃×C₅×Q₈	—	2	4	no	—
79	C₃×C₅×Q₈	—	4	1	no	—
80	C₃×C₅×Q₈	—	4	1	no	—
81	C₂×C₃×C₄×C₅	—	2	2	no	—
82	C₂×C₃×C₄×C₅	—	2	4	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	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	4	2	no	—
88	C₂×C₃×C₄×C₅	—	4	2	no	—
89	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
90	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
93	C₂×C₃×C₄×C₅	#41	1	2	yes	—
94	C₂×C₅×Dic₃	—	4	2	no	—
95	C₂×C₅×Dic₃	—	4	2	no	—
96	C₂×C₅×Dic₃	—	4	2	no	—
97	C₅×C₃⋊C₈	—	2	4	no	—
98	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
99	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
100	C₃×C₂²⋊Q₈	—	2	2	no	—
101	C₃×C₂²⋊Q₈	C₄×C₅	1	4	yes	complemented
102	C₂×C₃×C₄⋊C₄	—	2	1	no	—
103	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
104	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
105	C₂×#217	—	2	1	no	—
106	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
107	C₂²×C₃⋊C₈	—	2	2	no	—
108	C₂²×C₃⋊C₈	—	2	4	no	—
109	C₂²×C₃⋊C₈	C₂²×C₅	1	2	yes	—
110	#835	—	2	4	no	—
111	C₃⋊#95	—	2	1	no	—
112	C₂⁴×C₅	#67	1	1	yes	characteristic
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×Q₈	—	2	2	no	—
116	C₂×C₅×Q₈	C₂×Dic₃	1	2	yes	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	6	2	no	—
122	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
123	C₂²×C₄×C₅	#67	1	1	yes	characteristic
124	C₂²×C₄×C₅	#67	1	2	yes	—
125	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
126	C₂×C₅×C₈	—	3	4	no	—
127	C₂×C₅×C₈	—	6	8	no	—
128	C₂×C₅×C₈	—	6	2	no	—
129	C₂×C₅×C₈	—	6	2	no	—
130	C₅×C₄⋊C₄	—	2	4	no	—
131	C₅×C₄⋊C₄	—	2	1	no	—
132	C₅×C₄⋊C₄	—	6	2	no	—
133	C₅×C₄⋊C₄	—	6	2	no	—
134	C₅×C₄⋊C₄	C₂×Dic₃	1	2	yes	—
135	C₅×C₂²⋊C₄	—	2	4	no	—
136	C₅×C₂²⋊C₄	—	12	2	no	—
137	C₂³×C₈	—	3	1	no	—
138	C₂×C₂²⋊Q₈	C₅×D₃	1	1	yes	characteristic
139	C₂×#103	—	3	2	no	—
140	#380	—	3	1	no	—
141	#340	—	3	2	no	—
142	C₂²×C₃×C₅	—	2	2	no	—
143	C₂²×C₃×C₅	—	2	2	no	—
144	C₂²×C₃×C₅	—	2	4	no	—
145	C₂²×C₃×C₅	—	2	4	no	—
146	C₂²×C₃×C₅	#103	1	4	yes	complemented
147	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	#121	1	2	yes	—
149	C₂²×C₃×C₅	C₂×SD₁₆	1	1	yes	characteristic
150	C₂²×C₃×C₅	C₂×Q₁₆	1	1	yes	characteristic
151	C₂²×C₃×C₅	#135	1	2	yes	—
152	C₃×C₄×C₅	—	2	2	no	—
153	C₃×C₄×C₅	—	4	2	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
156	C₃×C₄×C₅	#120	1	1	yes	characteristic
157	C₃×C₄×C₅	#123	1	1	yes	characteristic
158	C₅×Dic₃	—	8	2	no	—
159	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
160	C₂×C₃×Q₈	—	2	1	no	—
161	C₂×C₃×Q₈	—	2	2	no	—
162	C₂×C₃×Q₈	—	2	2	no	—
163	C₂×C₃×Q₈	C₂×C₄×C₅	1	2	yes	—
164	C₂²×C₃×C₄	—	2	2	no	—
165	C₂²×C₃×C₄	—	2	2	no	—
166	C₂²×C₃×C₄	—	2	1	no	—
167	C₂²×C₃×C₄	—	2	1	no	—
168	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
169	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
171	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
172	C₂²×Dic₃	—	2	2	no	—
173	C₃×C₄⋊C₄	—	2	4	no	—
174	C₃×C₄⋊C₄	—	2	1	no	—
175	C₃×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
176	C₃×C₂²⋊C₄	—	2	4	no	—
177	#217	—	4	2	no	—
178	C₄⋊Dic₃	—	2	2	no	—
179	C₄⋊Dic₃	—	2	2	no	—
180	C₂×C₃⋊C₈	—	2	8	no	—
181	C₂×C₃⋊C₈	—	2	2	no	—
182	C₂×C₃⋊C₈	—	2	2	no	—
183	C₂×C₃⋊C₈	C₅×D₄	1	4	yes	—
184	C₂³×C₅	—	2	2	no	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	#215	1	2	yes	—
187	C₂³×C₅	#216	1	2	yes	—
188	C₂³×C₅	#217	1	2	yes	—
189	C₂³×C₅	C₂×#67	1	1	yes	characteristic
190	C₅×Q₈	—	2	4	no	—
191	C₅×Q₈	—	4	1	no	—
192	C₅×Q₈	—	4	1	no	—
193	C₂×C₄×C₅	—	2	2	no	—
194	C₂×C₄×C₅	—	2	4	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	12	2	no	—
202	C₂×C₄×C₅	—	12	2	no	—
203	C₂×C₄×C₅	—	12	2	no	—
204	C₂×C₄×C₅	#217	1	2	yes	—
205	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
206	C₂×C₄×C₅	#237	1	2	yes	—
207	C₂×C₄×C₅	C₂²×Dic₃	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
209	C₅×C₈	—	6	4	no	—
210	C₂²×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
211	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
212	C₂²×C₈	—	3	2	no	—
213	C₂²×C₈	—	6	4	no	—
214	C₂²×C₈	—	6	2	no	—
215	C₂²⋊Q₈	—	2	2	no	—
216	C₂²⋊Q₈	C₅×Dic₃	1	4	yes	complemented
217	C₂×C₄⋊C₄	—	2	1	no	—
218	C₂×C₄⋊C₄	—	3	2	no	—
219	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
220	C₂×C₂²⋊C₄	—	2	1	no	—
221	C₂×C₂²⋊C₄	—	6	1	no	—
222	#103	—	6	4	no	—
223	#95	—	6	1	no	—
224	C₂×C₃×C₅	—	2	4	no	—
225	C₂×C₃×C₅	#386	1	1	yes	characteristic
226	C₂×C₃×C₅	C₂×#103	1	1	yes	characteristic
227	C₂×C₃×C₅	#416	1	1	yes	characteristic
228	C₂×C₃×C₅	#465	1	2	yes	—
229	C₂×C₃×C₅	#467	1	2	yes	—
230	C₂³×C₃	—	2	2	no	—
231	C₂³×C₃	—	2	2	no	—
232	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
233	C₂³×C₃	C₅×SD₁₆	1	2	yes	—
234	C₂³×C₃	C₅×Q₁₆	1	2	yes	—
235	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
236	C₃×Q₈	—	2	4	no	—
237	C₃×Q₈	—	4	1	no	—
238	C₃×Q₈	—	4	1	no	—
239	C₂×C₃×C₄	—	2	2	no	—
240	C₂×C₃×C₄	—	2	4	no	—
241	C₂×C₃×C₄	—	2	2	no	—
242	C₂×C₃×C₄	—	2	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	4	2	no	—
246	C₂×C₃×C₄	—	4	2	no	—
247	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	—
248	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
249	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
250	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
251	C₂×C₃×C₄	C₅×#41	1	2	yes	—
252	C₂×Dic₃	—	4	2	no	—
253	C₂×Dic₃	—	4	2	no	—
254	C₂×Dic₃	—	4	2	no	—
255	C₃⋊C₈	—	2	4	no	—
256	C₂²×C₅	—	2	2	no	—
257	C₂²×C₅	—	2	2	no	—
258	C₂²×C₅	—	2	4	no	—
259	C₂²×C₅	—	2	4	no	—
260	C₂²×C₅	#835	1	4	yes	complemented
261	C₂²×C₅	#939	1	2	yes	—
262	C₂²×C₅	C₂×#215	1	1	yes	characteristic
263	C₂²×C₅	C₂×#216	1	1	yes	characteristic
264	C₂²×C₅	#950	1	2	yes	—
265	C₂²×C₅	C₂×#217	1	1	yes	characteristic
266	C₄×C₅	—	2	2	no	—
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	24	2	no	—
270	C₄×C₅	D₄×Dic₃	1	2	yes	—
271	C₄×C₅	#935	1	1	yes	characteristic
272	C₄×C₅	#937	1	1	yes	characteristic
273	C₂⁴	C₅×#67	1	1	yes	characteristic
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	C₂×C₅×Dic₃	1	2	yes	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	6	2	no	—
283	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
284	C₂²×C₄	C₅×#67	1	1	yes	characteristic
285	C₂²×C₄	C₅×#67	1	2	yes	—
286	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
287	C₂×C₈	—	3	4	no	—
288	C₂×C₈	—	6	8	no	—
289	C₂×C₈	—	6	2	no	—
290	C₂×C₈	—	6	2	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	1	no	—
293	C₄⋊C₄	—	6	2	no	—
294	C₄⋊C₄	—	6	2	no	—
295	C₄⋊C₄	C₂×C₅×Dic₃	1	2	yes	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	12	2	no	—
298	C₃×C₅	#1892	1	1	yes	characteristic, complemented, Hall
299	C₂²×C₃	—	2	2	no	—
300	C₂²×C₃	—	2	2	no	—
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	2	4	no	—
303	C₂²×C₃	C₅×#103	1	4	yes	complemented
304	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
305	C₂²×C₃	C₅×#121	1	2	yes	—
306	C₂²×C₃	C₂×C₅×SD₁₆	1	1	yes	characteristic
307	C₂²×C₃	C₂×C₅×Q₁₆	1	1	yes	characteristic
308	C₂²×C₃	C₅×#135	1	2	yes	—
309	C₃×C₄	—	2	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
313	C₃×C₄	C₅×#120	1	1	yes	characteristic
314	C₃×C₄	C₅×#123	1	1	yes	characteristic
315	Dic₃	—	8	2	no	—
316	C₂×C₅	—	2	4	no	—
317	C₂×C₅	#5048	1	2	yes	—
318	C₂×C₅	#5051	1	2	yes	—
319	C₂×C₅	#5220	1	1	yes	characteristic
320	C₂×C₅	C₂×#835	1	1	yes	characteristic
321	C₂×C₅	#5233	1	1	yes	characteristic
322	C₂³	—	2	2	no	—
323	C₂³	—	2	2	no	—
324	C₂³	C₅×#215	1	2	yes	—
325	C₂³	C₅×#216	1	2	yes	—
326	C₂³	C₅×#217	1	2	yes	—
327	C₂³	C₂×C₅×#67	1	1	yes	characteristic
328	Q₈	—	2	4	no	—
329	Q₈	—	4	1	no	—
330	Q₈	—	4	1	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	12	2	no	—
340	C₂×C₄	—	12	2	no	—
341	C₂×C₄	—	12	2	no	—
342	C₂×C₄	C₅×#217	1	2	yes	—
343	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
344	C₂×C₄	C₅×#237	1	2	yes	—
345	C₂×C₄	C₂²×C₅×Dic₃	1	1	yes	characteristic
346	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
347	C₈	—	6	4	no	—
348	C₂×C₃	—	2	4	no	—
349	C₂×C₃	C₅×#386	1	1	yes	characteristic
350	C₂×C₃	C₂×C₅×#103	1	1	yes	characteristic
351	C₂×C₃	C₅×#416	1	1	yes	characteristic
352	C₂×C₃	C₅×#465	1	2	yes	—
353	C₂×C₃	C₅×#467	1	2	yes	—
354	C₅	#71696	1	1	yes	characteristic, direct product factor, Sylow
355	C₂²	—	2	2	no	—
356	C₂²	—	2	2	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	C₅×#835	1	4	yes	complemented
360	C₂²	C₅×#939	1	2	yes	—
361	C₂²	C₂×C₅×#215	1	1	yes	characteristic
362	C₂²	C₂×C₅×#216	1	1	yes	characteristic
363	C₂²	C₅×#950	1	2	yes	—
364	C₂²	C₂×C₅×#217	1	1	yes	characteristic
365	C₄	—	2	2	no	—
366	C₄	—	4	2	no	—
367	C₄	—	4	2	no	—
368	C₄	—	24	2	no	—
369	C₄	C₅×D₄×Dic₃	1	2	yes	—
370	C₄	C₅×#935	1	1	yes	characteristic
371	C₄	C₅×#937	1	1	yes	characteristic
372	C₃	C₅×#1892	1	1	yes	characteristic, complemented, Sylow
373	C₂	—	2	4	no	—
374	C₂	C₅×#5048	1	2	yes	—
375	C₂	C₅×#5051	1	2	yes	—
376	C₂	C₅×#5220	1	1	yes	characteristic
377	C₂	C₂×C₅×#835	1	1	yes	characteristic
378	C₂	C₅×#5233	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂×#67
commutator	C₂×C₃×C₄	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×C₂²⋊Q₈	C₂
socle	C₂³×C₃×C₅	C₂×D₄
prime radical	C₂⁴×C₃×C₅	D₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×C₂²⋊Q₈	D₃
hypocenter	C₃	C₅×#1892
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
3. C₂×C₅×#835	C₂	semidirect
5. C₅×#4529	C₂	semidirect
10. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
21. #71696	C₅	direct (N × H)
54. C₂×#835	C₂×C₅	semidirect
56. #4529	C₂×C₅	semidirect
63. C₅×C₂²⋊Q₈	Dic₃	semidirect
101. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
146. C₂²×C₃×C₅	#103	semidirect
216. C₂²⋊Q₈	C₅×Dic₃	semidirect
260. C₂²×C₅	#835	semidirect
298. C₃×C₅	#1892	semidirect
303. C₂²×C₃	C₅×#103	semidirect
354. C₅	#71696	direct (N × H)
359. C₂²	C₅×#835	semidirect
372. C₃	C₅×#1892	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
C₂³×C₅×C₃⋊C₈	2
C₂×C₅×#835	2
C₅×#5212	2
C₅×#4529	2
C₅×#1892	3
#71696	5

Subgroups — C5×#71696 #14301762

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71696 #14301762