Subgroups — C₅×#8593 #11931313

Order 1280.

476 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₅×#1831	C₂	1	1	yes	maximal, characteristic
3	C₅×#1831	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#332	C₂	1	2	yes	maximal
5	C₅×#1296	C₂	1	2	yes	maximal
6	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₅×Q₈	—	2	1	no	—
8	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
9	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
10	C₅×#391	—	2	1	no	—
11	C₅×#389	—	2	1	no	—
12	C₅×#389	C₄	1	2	yes	—
13	C₅×#384	C₂²	1	1	yes	characteristic
14	C₄×C₅×C₄⋊C₄	—	2	1	no	—
15	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
16	C₄³×C₅	C₂²	1	1	yes	characteristic
17	C₅×#336	—	2	1	no	—
18	C₅×#336	—	2	1	no	—
19	C₅×#336	—	2	1	no	—
20	C₅×#336	—	2	1	no	—
21	C₅×#332	—	2	4	no	—
22	#8593	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
23	C₂²×C₅×Q₈	—	2	1	no	—
24	C₂²×C₅×C₈	—	2	2	no	—
25	C₂²×C₅×C₈	—	2	2	no	—
26	C₅×C₄⋊Q₈	—	2	1	no	—
27	C₅×C₄⋊Q₈	—	2	1	no	—
28	C₅×C₄⋊Q₈	D₄	1	2	yes	—
29	C₅×C₄⋊Q₈	Q₈	1	2	yes	—
30	C₄×C₅×Q₈	—	4	4	no	—
31	C₂×C₅×C₄⋊C₄	—	2	1	no	—
32	C₂×C₅×C₄⋊C₄	—	2	2	no	—
33	C₂×C₅×C₄⋊C₄	—	2	1	no	—
34	C₂×C₅×C₄⋊C₄	—	2	1	no	—
35	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
36	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
37	C₂×C₄²×C₅	—	2	2	no	—
38	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
43	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
45	C₅×C₄⋊C₈	—	2	2	no	—
46	C₅×C₄⋊C₈	—	2	2	no	—
47	C₅×C₄⋊C₈	—	2	2	no	—
48	C₅×C₄⋊C₈	—	2	2	no	—
49	C₅×#95	—	2	2	no	—
50	C₅×#95	—	2	2	no	—
51	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
52	#1831	C₂×C₅	1	1	yes	characteristic
53	#1831	C₂×C₅	1	1	yes	characteristic
54	C₂×#332	C₂×C₅	1	2	yes	—
55	#1296	C₂×C₅	1	2	yes	—
56	C₂×C₅×Q₈	—	2	2	no	—
57	C₂×C₅×Q₈	—	2	2	no	—
58	C₂×C₅×Q₈	—	4	2	no	—
59	C₂×C₅×Q₈	—	4	2	no	—
60	C₂²×C₄×C₅	—	2	2	no	—
61	C₂²×C₄×C₅	—	2	2	no	—
62	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
63	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
67	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
69	C₂×C₅×C₈	—	4	2	no	—
70	C₂×C₅×C₈	—	4	2	no	—
71	C₂×C₅×C₈	—	4	2	no	—
72	C₂×C₅×C₈	—	4	2	no	—
73	C₂×C₅×C₈	—	4	2	no	—
74	C₂×C₅×C₈	—	4	2	no	—
75	C₅×C₄⋊C₄	—	2	2	no	—
76	C₅×C₄⋊C₄	—	2	2	no	—
77	C₅×C₄⋊C₄	—	2	2	no	—
78	C₅×C₄⋊C₄	—	4	2	no	—
79	C₅×C₄⋊C₄	—	4	4	no	—
80	C₅×C₄⋊C₄	—	4	2	no	—
81	C₅×C₄⋊C₄	—	4	2	no	—
82	C₅×C₄⋊C₄	C₄⋊C₄	1	4	yes	—
83	C₄²×C₅	—	2	2	no	—
84	C₄²×C₅	—	2	2	no	—
85	C₄²×C₅	—	2	2	no	—
86	C₄²×C₅	—	2	2	no	—
87	C₄²×C₅	—	2	2	no	—
88	C₄²×C₅	—	4	1	no	—
89	C₄²×C₅	—	4	4	no	—
90	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₅	C₂×Q₈	1	1	yes	characteristic
92	C₄²×C₅	#41	1	1	yes	characteristic
93	C₄²×C₅	#41	1	1	yes	characteristic
94	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
95	C₂×C₄×Q₈	—	2	1	no	—
96	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
97	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
98	#391	—	2	1	no	—
99	#389	—	2	1	no	—
100	#389	C₄×C₅	1	2	yes	—
101	#384	C₂²×C₅	1	1	yes	characteristic
102	C₄×C₄⋊C₄	—	2	1	no	—
103	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
104	C₄³	C₂²×C₅	1	1	yes	characteristic
105	#336	—	2	1	no	—
106	#336	—	2	1	no	—
107	#336	—	2	1	no	—
108	#336	—	2	1	no	—
109	#332	—	2	4	no	—
110	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₅×Q₈	—	4	4	no	—
112	C₅×Q₈	—	4	4	no	—
113	C₂×C₄×C₅	—	2	1	no	—
114	C₂×C₄×C₅	—	2	1	no	—
115	C₂×C₄×C₅	—	2	1	no	—
116	C₂×C₄×C₅	—	2	1	no	—
117	C₂×C₄×C₅	—	2	4	no	—
118	C₂×C₄×C₅	—	2	1	no	—
119	C₂×C₄×C₅	—	2	1	no	—
120	C₂×C₄×C₅	—	2	1	no	—
121	C₂×C₄×C₅	—	2	1	no	—
122	C₂×C₄×C₅	—	2	1	no	—
123	C₂×C₄×C₅	—	2	1	no	—
124	C₂×C₄×C₅	—	2	1	no	—
125	C₂×C₄×C₅	—	2	1	no	—
126	C₂×C₄×C₅	—	2	1	no	—
127	C₂×C₄×C₅	—	4	2	no	—
128	C₂×C₄×C₅	—	4	2	no	—
129	C₂×C₄×C₅	—	4	2	no	—
130	C₂×C₄×C₅	—	4	2	no	—
131	C₂×C₄×C₅	—	4	2	no	—
132	C₂×C₄×C₅	#101	1	2	yes	—
133	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₅	#117	1	1	yes	characteristic
135	C₂×C₄×C₅	#121	1	1	yes	characteristic
136	C₂×C₄×C₅	#121	1	1	yes	characteristic
137	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
138	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
139	C₂×C₄×C₅	#135	1	2	yes	—
140	C₂×C₄×C₅	#135	1	2	yes	—
141	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
142	C₂×C₄×C₅	#137	1	2	yes	—
143	C₅×C₈	—	8	2	no	—
144	C₅×C₈	—	8	2	no	—
145	C₂²×Q₈	—	2	1	no	—
146	C₂²×C₈	—	2	2	no	—
147	C₂²×C₈	—	2	2	no	—
148	C₄⋊Q₈	—	2	1	no	—
149	C₄⋊Q₈	—	2	1	no	—
150	C₄⋊Q₈	C₅×D₄	1	2	yes	—
151	C₄⋊Q₈	C₅×Q₈	1	2	yes	—
152	C₄×Q₈	—	4	4	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	—	2	2	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	—	2	1	no	—
157	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
158	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
159	C₂×C₄²	—	2	2	no	—
160	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
161	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
162	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
163	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
164	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
165	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
166	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
167	C₄⋊C₈	—	2	2	no	—
168	C₄⋊C₈	—	2	2	no	—
169	C₄⋊C₈	—	2	2	no	—
170	C₄⋊C₈	—	2	2	no	—
171	#95	—	2	2	no	—
172	#95	—	2	2	no	—
173	C₂²×C₅	#380	1	1	yes	characteristic
174	C₂²×C₅	C₂×#101	1	1	yes	characteristic
175	C₂²×C₅	#413	1	1	yes	characteristic
176	C₂²×C₅	#416	1	1	yes	characteristic
177	C₂²×C₅	#416	1	1	yes	characteristic
178	C₂²×C₅	#418	1	1	yes	characteristic
179	C₂²×C₅	#419	1	1	yes	characteristic
180	C₄×C₅	—	2	1	no	—
181	C₄×C₅	—	2	1	no	—
182	C₄×C₅	—	2	2	no	—
183	C₄×C₅	—	4	1	no	—
184	C₄×C₅	—	4	4	no	—
185	C₄×C₅	—	4	1	no	—
186	C₄×C₅	—	4	1	no	—
187	C₄×C₅	—	8	2	no	—
188	C₄×C₅	#463	1	2	yes	—
189	C₄×C₅	#464	1	2	yes	—
190	C₄×C₅	#478	1	2	yes	—
191	C₄×C₅	#479	1	2	yes	—
192	C₂×Q₈	—	2	2	no	—
193	C₂×Q₈	—	2	2	no	—
194	C₂×Q₈	—	4	2	no	—
195	C₂×Q₈	—	4	2	no	—
196	C₂²×C₄	—	2	2	no	—
197	C₂²×C₄	—	2	2	no	—
198	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
201	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
202	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
203	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
204	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
205	C₂×C₈	—	4	2	no	—
206	C₂×C₈	—	4	2	no	—
207	C₂×C₈	—	4	2	no	—
208	C₂×C₈	—	4	2	no	—
209	C₂×C₈	—	4	2	no	—
210	C₂×C₈	—	4	2	no	—
211	C₄⋊C₄	—	2	2	no	—
212	C₄⋊C₄	—	2	2	no	—
213	C₄⋊C₄	—	2	2	no	—
214	C₄⋊C₄	—	4	2	no	—
215	C₄⋊C₄	—	4	4	no	—
216	C₄⋊C₄	—	4	2	no	—
217	C₄⋊C₄	—	4	2	no	—
218	C₄⋊C₄	C₅×C₄⋊C₄	1	4	yes	—
219	C₄²	—	2	2	no	—
220	C₄²	—	2	2	no	—
221	C₄²	—	2	2	no	—
222	C₄²	—	2	2	no	—
223	C₄²	—	2	2	no	—
224	C₄²	—	4	1	no	—
225	C₄²	—	4	4	no	—
226	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
227	C₄²	C₂×C₅×Q₈	1	1	yes	characteristic
228	C₄²	C₅×#41	1	1	yes	characteristic
229	C₄²	C₅×#41	1	1	yes	characteristic
230	C₂×C₅	#1544	1	1	yes	characteristic
231	C₂×C₅	#1553	1	1	yes	characteristic
232	C₂×C₅	#1554	1	1	yes	characteristic
233	C₂×C₅	#1556	1	1	yes	characteristic
234	C₂×C₅	#1801	1	1	yes	characteristic
235	C₂×C₅	#1804	1	1	yes	characteristic
236	C₂×C₅	#1805	1	1	yes	characteristic
237	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
238	Q₈	—	4	4	no	—
239	Q₈	—	4	4	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	2	1	no	—
242	C₂×C₄	—	2	1	no	—
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	4	no	—
245	C₂×C₄	—	2	1	no	—
246	C₂×C₄	—	2	1	no	—
247	C₂×C₄	—	2	1	no	—
248	C₂×C₄	—	2	1	no	—
249	C₂×C₄	—	2	1	no	—
250	C₂×C₄	—	2	1	no	—
251	C₂×C₄	—	2	1	no	—
252	C₂×C₄	—	2	1	no	—
253	C₂×C₄	—	2	1	no	—
254	C₂×C₄	—	4	2	no	—
255	C₂×C₄	—	4	2	no	—
256	C₂×C₄	—	4	2	no	—
257	C₂×C₄	—	4	2	no	—
258	C₂×C₄	—	4	2	no	—
259	C₂×C₄	C₅×#101	1	2	yes	—
260	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
261	C₂×C₄	C₅×#117	1	1	yes	characteristic
262	C₂×C₄	C₅×#121	1	1	yes	characteristic
263	C₂×C₄	C₅×#121	1	1	yes	characteristic
264	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
265	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
266	C₂×C₄	C₅×#135	1	2	yes	—
267	C₂×C₄	C₅×#135	1	2	yes	—
268	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
269	C₂×C₄	C₅×#137	1	2	yes	—
270	C₈	—	8	2	no	—
271	C₈	—	8	2	no	—
272	C₅	#8593	1	1	yes	characteristic, direct product factor, Sylow
273	C₂²	C₅×#380	1	1	yes	characteristic
274	C₂²	C₂×C₅×#101	1	1	yes	characteristic
275	C₂²	C₅×#413	1	1	yes	characteristic
276	C₂²	C₅×#416	1	1	yes	characteristic
277	C₂²	C₅×#416	1	1	yes	characteristic
278	C₂²	C₅×#418	1	1	yes	characteristic
279	C₂²	C₅×#419	1	1	yes	characteristic
280	C₄	—	2	1	no	—
281	C₄	—	2	1	no	—
282	C₄	—	2	2	no	—
283	C₄	—	4	1	no	—
284	C₄	—	4	4	no	—
285	C₄	—	4	1	no	—
286	C₄	—	4	1	no	—
287	C₄	—	8	2	no	—
288	C₄	C₅×#463	1	2	yes	—
289	C₄	C₅×#464	1	2	yes	—
290	C₄	C₅×#478	1	2	yes	—
291	C₄	C₅×#479	1	2	yes	—
292	C₂	C₅×#1544	1	1	yes	characteristic
293	C₂	C₅×#1553	1	1	yes	characteristic
294	C₂	C₅×#1554	1	1	yes	characteristic
295	C₂	C₅×#1556	1	1	yes	characteristic
296	C₂	C₅×#1801	1	1	yes	characteristic
297	C₂	C₅×#1804	1	1	yes	characteristic
298	C₂	C₅×#1805	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂×C₂²⋊C₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂×C₄²	C₂³×C₅
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
22. #8593	C₅	direct (N × H)
272. C₅	#8593	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×C₅×C₄⋊Q₈	2
C₅×#1831	2
C₂×C₅×#332	2
C₅×#1296	2
#8593	5

Subgroups — C5×#8593 #11931313

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#8593 #11931313