Subgroups — C₅×#21146 #11943866

Order 1280.

1114 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#423	C₂	1	2	yes	maximal
3	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₅×#1940	C₂	1	4	yes	maximal, complemented
6	C₅×#1939	C₂	1	4	yes	maximal, complemented
7	C₅×#1728	C₂	1	2	yes	maximal
8	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×C₄⋊C₄	C₄	1	2	yes	—
12	C₂²×C₄²×C₅	C₂²	1	2	yes	—
13	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#423	—	2	8	no	—
15	C₅×#423	—	2	4	no	—
16	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊C₈	C₂²	1	8	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₄×C₅×M₁₆	—	2	4	no	—
20	C₂×C₅×#97	C₂²	1	2	yes	—
21	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
22	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
23	C₄×C₅×C₄⋊C₄	C₄	1	2	yes	—
24	C₄×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
25	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
27	C₂×C₅×#95	C₄	1	2	yes	—
28	C₅×#336	C₂²	1	8	yes	—
29	#21146	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	C₂³×C₄×C₅	C₂×C₄	1	4	yes	—
31	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
34	C₂×C₅×M₁₆	—	2	2	no	—
35	C₂×C₅×M₁₆	—	2	2	no	—
36	C₂×C₅×M₁₆	—	2	2	no	—
37	C₂×C₅×M₁₆	—	2	2	no	—
38	C₂×C₅×M₁₆	—	2	4	no	—
39	C₂×C₅×M₁₆	—	2	4	no	—
40	C₂×C₅×M₁₆	—	2	4	no	—
41	C₂×C₅×M₁₆	D₄	1	4	yes	—
42	C₂×C₅×M₁₆	Q₈	1	4	yes	—
43	C₂²×C₅×C₈	C₂³	1	4	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂×C₅×C₄⋊C₄	—	2	8	no	—
47	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
49	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₅	—	2	4	no	—
51	C₂×C₄²×C₅	—	2	4	no	—
52	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₅	D₄	1	4	yes	—
57	C₂×C₄²×C₅	Q₈	1	4	yes	—
58	C₂×C₄²×C₅	C₂³	1	4	yes	—
59	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
61	C₅×C₄⋊C₈	—	2	16	no	—
62	C₅×C₄⋊C₈	—	2	4	no	—
63	C₅×C₄⋊C₈	—	2	4	no	—
64	C₅×#97	—	2	4	no	—
65	C₄×C₅×C₈	—	2	4	no	—
66	C₅×#95	C₂×C₄	1	2	yes	—
67	C₅×#95	C₂×C₄	1	4	yes	—
68	C₅×#95	C₂×C₄	1	2	yes	—
69	C₂×#423	C₂×C₅	1	1	yes	characteristic
70	C₂×#423	C₂×C₅	1	2	yes	—
71	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
72	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
73	#1940	C₂×C₅	1	4	yes	complemented
74	#1939	C₂×C₅	1	4	yes	complemented
75	#1728	C₂×C₅	1	2	yes	—
76	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₅	—	2	4	no	—
78	C₂²×C₄×C₅	—	2	8	no	—
79	C₂²×C₄×C₅	—	2	8	no	—
80	C₂²×C₄×C₅	—	4	2	no	—
81	C₂²×C₄×C₅	—	4	4	no	—
82	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
83	C₂²×C₄×C₅	C₄⋊C₄	1	4	yes	—
84	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₅	C₂²×C₄	1	4	yes	—
89	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
94	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₅	#41	1	2	yes	—
96	C₂²×C₄×C₅	#41	1	2	yes	—
97	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
98	C₅×M₁₆	—	2	8	no	—
99	C₅×M₁₆	—	2	8	no	—
100	C₅×M₁₆	—	4	8	no	—
101	C₂×C₅×C₈	—	2	2	no	—
102	C₂×C₅×C₈	—	2	2	no	—
103	C₂×C₅×C₈	—	2	2	no	—
104	C₂×C₅×C₈	—	2	2	no	—
105	C₂×C₅×C₈	—	2	4	no	—
106	C₂×C₅×C₈	—	2	4	no	—
107	C₂×C₅×C₈	—	2	4	no	—
108	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
109	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
110	C₅×C₄⋊C₄	—	2	8	no	—
111	C₅×C₄⋊C₄	—	2	4	no	—
112	C₅×C₄⋊C₄	M₁₆	1	8	yes	complemented
113	C₄²×C₅	—	2	4	no	—
114	C₄²×C₅	—	2	4	no	—
115	C₄²×C₅	—	2	4	no	—
116	C₄²×C₅	—	2	4	no	—
117	C₄²×C₅	C₄⋊C₄	1	4	yes	—
118	C₄²×C₅	C₄⋊C₄	1	4	yes	—
119	C₄²×C₅	C₂×D₄	1	2	yes	—
120	C₄²×C₅	C₂×D₄	1	2	yes	—
121	C₄²×C₅	C₂×Q₈	1	2	yes	—
122	C₄²×C₅	C₂×Q₈	1	2	yes	—
123	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
124	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
125	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₄⋊C₄	C₄×C₅	1	2	yes	—
127	C₂²×C₄²	C₂²×C₅	1	2	yes	—
128	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
129	#423	—	2	8	no	—
130	#423	—	2	4	no	—
131	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
132	C₂×C₄⋊C₈	C₂²×C₅	1	8	yes	—
133	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
134	C₄×M₁₆	—	2	4	no	—
135	C₂×#97	C₂²×C₅	1	2	yes	—
136	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
137	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
138	C₄×C₄⋊C₄	C₄×C₅	1	2	yes	—
139	C₄×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
140	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
141	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×#95	C₄×C₅	1	2	yes	—
143	#336	C₂²×C₅	1	8	yes	—
144	C₂³×C₅	—	2	2	no	—
145	C₂³×C₅	—	2	2	no	—
146	C₂³×C₅	C₂×C₄⋊C₄	1	2	yes	—
147	C₂³×C₅	C₄×D₄	1	2	yes	—
148	C₂³×C₅	C₄×Q₈	1	2	yes	—
149	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₅	—	2	4	no	—
151	C₂×C₄×C₅	—	2	2	no	—
152	C₂×C₄×C₅	—	2	2	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	2	4	no	—
155	C₂×C₄×C₅	—	2	8	no	—
156	C₂×C₄×C₅	—	2	4	no	—
157	C₂×C₄×C₅	—	2	4	no	—
158	C₂×C₄×C₅	—	2	4	no	—
159	C₂×C₄×C₅	—	4	4	no	—
160	C₂×C₄×C₅	—	4	16	no	—
161	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
164	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
165	C₂×C₄×C₅	C₂×C₄⋊C₄	1	2	yes	—
166	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
167	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
168	C₂×C₄×C₅	#121	1	4	yes	—
169	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₅	#125	1	4	yes	—
171	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
172	C₂×C₄×C₅	C₂×M₁₆	1	8	yes	—
173	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
174	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
179	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
180	C₅×C₈	—	2	4	no	—
181	C₅×C₈	—	2	4	no	—
182	C₅×C₈	—	4	4	no	—
183	C₂³×C₄	C₂×C₄×C₅	1	4	yes	—
184	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
185	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
186	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
187	C₂×M₁₆	—	2	2	no	—
188	C₂×M₁₆	—	2	2	no	—
189	C₂×M₁₆	—	2	2	no	—
190	C₂×M₁₆	—	2	2	no	—
191	C₂×M₁₆	—	2	4	no	—
192	C₂×M₁₆	—	2	4	no	—
193	C₂×M₁₆	—	2	4	no	—
194	C₂×M₁₆	C₅×D₄	1	4	yes	—
195	C₂×M₁₆	C₅×Q₈	1	4	yes	—
196	C₂²×C₈	C₂³×C₅	1	4	yes	—
197	C₂²×C₈	C₂³×C₅	1	2	yes	—
198	C₂²×C₈	C₂³×C₅	1	2	yes	—
199	C₂×C₄⋊C₄	—	2	8	no	—
200	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
201	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
202	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
203	C₂×C₄²	—	2	4	no	—
204	C₂×C₄²	—	2	4	no	—
205	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
206	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
207	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
208	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
209	C₂×C₄²	C₅×D₄	1	4	yes	—
210	C₂×C₄²	C₅×Q₈	1	4	yes	—
211	C₂×C₄²	C₂³×C₅	1	4	yes	—
212	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
213	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
214	C₄⋊C₈	—	2	16	no	—
215	C₄⋊C₈	—	2	4	no	—
216	C₄⋊C₈	—	2	4	no	—
217	#97	—	2	4	no	—
218	C₄×C₈	—	2	4	no	—
219	#95	C₂×C₄×C₅	1	2	yes	—
220	#95	C₂×C₄×C₅	1	4	yes	—
221	#95	C₂×C₄×C₅	1	2	yes	—
222	C₂²×C₅	—	2	2	no	—
223	C₂²×C₅	—	2	2	no	—
224	C₂²×C₅	—	2	4	no	—
225	C₂²×C₅	—	2	4	no	—
226	C₂²×C₅	#389	1	4	yes	—
227	C₂²×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
228	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
229	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
230	C₂²×C₅	C₂²×M₁₆	1	2	yes	—
231	C₂²×C₅	#568	1	2	yes	—
232	C₄×C₅	—	2	2	no	—
233	C₄×C₅	—	2	2	no	—
234	C₄×C₅	—	2	2	no	—
235	C₄×C₅	—	2	8	no	—
236	C₄×C₅	—	4	4	no	—
237	C₄×C₅	#389	1	4	yes	—
238	C₄×C₅	#423	1	4	yes	complemented
239	C₄×C₅	C₂×#121	1	1	yes	characteristic
240	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
241	C₄×C₅	C₂×#125	1	1	yes	characteristic
242	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
243	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	2	8	no	—
246	C₂²×C₄	—	2	8	no	—
247	C₂²×C₄	—	4	2	no	—
248	C₂²×C₄	—	4	4	no	—
249	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
250	C₂²×C₄	C₅×C₄⋊C₄	1	4	yes	—
251	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
252	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
253	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
254	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
255	C₂²×C₄	C₂²×C₄×C₅	1	4	yes	—
256	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
257	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
259	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
260	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
261	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
262	C₂²×C₄	C₅×#41	1	2	yes	—
263	C₂²×C₄	C₅×#41	1	2	yes	—
264	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
265	M₁₆	—	2	8	no	—
266	M₁₆	—	2	8	no	—
267	M₁₆	—	4	8	no	—
268	C₂×C₈	—	2	2	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	2	no	—
272	C₂×C₈	—	2	4	no	—
273	C₂×C₈	—	2	4	no	—
274	C₂×C₈	—	2	4	no	—
275	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
276	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
277	C₄⋊C₄	—	2	8	no	—
278	C₄⋊C₄	—	2	4	no	—
279	C₄⋊C₄	C₅×M₁₆	1	8	yes	complemented
280	C₄²	—	2	4	no	—
281	C₄²	—	2	4	no	—
282	C₄²	—	2	4	no	—
283	C₄²	—	2	4	no	—
284	C₄²	C₅×C₄⋊C₄	1	4	yes	—
285	C₄²	C₅×C₄⋊C₄	1	4	yes	—
286	C₄²	C₂×C₅×D₄	1	2	yes	—
287	C₄²	C₂×C₅×D₄	1	2	yes	—
288	C₄²	C₂×C₅×Q₈	1	2	yes	—
289	C₄²	C₂×C₅×Q₈	1	2	yes	—
290	C₂×C₅	—	2	4	no	—
291	C₂×C₅	C₂×#389	1	1	yes	characteristic
292	C₂×C₅	C₂×#423	1	1	yes	characteristic
293	C₂×C₅	#2905	1	1	yes	characteristic
294	C₂×C₅	D₄×M₁₆	1	2	yes	—
295	C₂×C₅	Q₈×M₁₆	1	2	yes	—
296	C₂³	—	2	2	no	—
297	C₂³	—	2	2	no	—
298	C₂³	C₂×C₅×C₄⋊C₄	1	2	yes	—
299	C₂³	C₄×C₅×D₄	1	2	yes	—
300	C₂³	C₄×C₅×Q₈	1	2	yes	—
301	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	8	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	4	4	no	—
312	C₂×C₄	—	4	16	no	—
313	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
314	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
315	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
316	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
317	C₂×C₄	C₂×C₅×C₄⋊C₄	1	2	yes	—
318	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
319	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
320	C₂×C₄	C₅×#121	1	4	yes	—
321	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
322	C₂×C₄	C₅×#125	1	4	yes	—
323	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
324	C₂×C₄	C₂×C₅×M₁₆	1	8	yes	—
325	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
326	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
327	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
328	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
329	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
330	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
331	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
332	C₈	—	2	4	no	—
333	C₈	—	2	4	no	—
334	C₈	—	4	4	no	—
335	C₅	#21146	1	1	yes	characteristic, direct product factor, Sylow
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	C₅×#389	1	4	yes	—
341	C₂²	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
342	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
343	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
344	C₂²	C₂²×C₅×M₁₆	1	2	yes	—
345	C₂²	C₅×#568	1	2	yes	—
346	C₄	—	2	2	no	—
347	C₄	—	2	2	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	8	no	—
350	C₄	—	4	4	no	—
351	C₄	C₅×#389	1	4	yes	—
352	C₄	C₅×#423	1	4	yes	complemented
353	C₄	C₂×C₅×#121	1	1	yes	characteristic
354	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
355	C₄	C₂×C₅×#125	1	1	yes	characteristic
356	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
357	C₂	—	2	4	no	—
358	C₂	C₂×C₅×#389	1	1	yes	characteristic
359	C₂	C₂×C₅×#423	1	1	yes	characteristic
360	C₂	C₅×#2905	1	1	yes	characteristic
361	C₂	C₅×D₄×M₁₆	1	2	yes	—
362	C₂	C₅×Q₈×M₁₆	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂³×C₅	C₂³×C₄
prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₅×#1940	C₂	semidirect
6. C₅×#1939	C₂	semidirect
29. #21146	C₅	direct (N × H)
73. #1940	C₂×C₅	semidirect
74. #1939	C₂×C₅	semidirect
112. C₅×C₄⋊C₄	M₁₆	semidirect
238. C₄×C₅	#423	semidirect
279. C₄⋊C₄	C₅×M₁₆	semidirect
335. C₅	#21146	direct (N × H)
352. C₄	C₅×#423	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#423	2
C₂×C₄×C₅×M₁₆	2
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1940	2
C₅×#1939	2
C₅×#1728	2
#21146	5

Subgroups — C5×#21146 #11943866

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21146 #11943866