Subgroups — C₅×#22521 #11945241

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#557	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×C₈×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#2355	C₂	1	1	yes	maximal, characteristic
4	C₅×#1991	C₂	1	2	yes	maximal
5	C₅×#1990	C₂	1	1	yes	maximal, characteristic
6	C₅×#1989	C₂	1	2	yes	maximal
7	C₅×#1988	C₂	1	1	yes	maximal, characteristic
8	C₅×#1805	C₂	1	2	yes	maximal
9	C₅×#1803	C₂	1	1	yes	maximal, characteristic
10	C₄×C₅×#103	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#103	C₂	1	2	yes	maximal
12	C₅×#557	—	2	4	no	—
13	C₅×#557	C₄	1	8	yes	complemented
14	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×#125	—	2	2	no	—
17	C₂×C₅×#125	C₂²	1	2	yes	—
18	C₂×C₄×C₅×Q₈	—	2	1	no	—
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
21	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
22	C₅×C₈×Q₈	—	2	4	no	—
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	1	yes	characteristic
27	C₂×C₅×#103	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
30	C₅×#391	—	2	1	no	—
31	C₅×#387	—	2	2	no	—
32	C₅×#384	C₂²	1	1	yes	characteristic
33	C₅×#382	C₂²	1	2	yes	—
34	C₄×C₅×C₄⋊C₄	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₅×#340	C₂²	1	2	yes	—
38	C₅×#340	C₂²	1	1	yes	characteristic
39	C₅×#340	C₂²	1	2	yes	—
40	C₅×#340	C₂²	1	1	yes	characteristic
41	C₅×#340	C₂²	1	2	yes	—
42	C₅×#340	C₂²	1	2	yes	—
43	C₅×#340	C₂²	1	2	yes	—
44	#22521	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂²×C₅×Q₈	—	2	1	no	—
46	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
47	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	2	yes	—
50	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
51	C₅×C₄⋊Q₈	—	2	8	no	—
52	C₅×C₄⋊Q₈	—	2	2	no	—
53	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	—
54	C₅×#125	—	2	16	no	—
55	C₅×#125	—	2	4	no	—
56	C₅×#125	C₂×C₄	1	8	yes	—
57	C₄×C₅×Q₈	—	2	8	no	—
58	C₄×C₅×Q₈	—	2	4	no	—
59	C₄×C₅×Q₈	—	2	2	no	—
60	C₄×C₅×Q₈	C₂×C₄	1	8	yes	—
61	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
62	C₄×C₅×Q₈	C₂×C₄	1	4	yes	—
63	C₄×C₅×Q₈	D₄	1	4	yes	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	—	2	1	no	—
68	C₂×C₅×C₄⋊C₄	—	2	2	no	—
69	C₂×C₅×C₄⋊C₄	—	2	1	no	—
70	C₂×C₅×C₄⋊C₄	—	2	1	no	—
71	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
72	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
73	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
74	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
76	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	—	2	2	no	—
79	C₂×C₄²×C₅	—	2	1	no	—
80	C₂×C₄²×C₅	—	2	1	no	—
81	C₂×C₄²×C₅	—	2	2	no	—
82	C₂×C₄²×C₅	C₂³	1	2	yes	—
83	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊C₈	—	2	4	no	—
85	C₅×C₄⋊C₈	—	2	2	no	—
86	C₅×#103	—	2	4	no	—
87	C₅×#103	—	2	2	no	—
88	C₅×#103	Q₈	1	4	yes	complemented
89	C₄×C₅×C₈	—	2	4	no	—
90	C₄×C₅×C₈	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	1	no	—
93	C₅×#95	—	2	2	no	—
94	C₅×#95	—	2	2	no	—
95	C₂×#557	C₂×C₅	1	1	yes	characteristic
96	C₂×C₈×Q₈	C₂×C₅	1	1	yes	characteristic
97	#2355	C₂×C₅	1	1	yes	characteristic
98	#1991	C₂×C₅	1	2	yes	—
99	#1990	C₂×C₅	1	1	yes	characteristic
100	#1989	C₂×C₅	1	2	yes	—
101	#1988	C₂×C₅	1	1	yes	characteristic
102	#1805	C₂×C₅	1	2	yes	—
103	#1803	C₂×C₅	1	1	yes	characteristic
104	C₄×#103	C₂×C₅	1	1	yes	characteristic
105	C₄×#103	C₂×C₅	1	2	yes	—
106	C₂×C₅×Q₈	—	2	4	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	1	no	—
110	C₂×C₅×Q₈	—	2	1	no	—
111	C₂×C₅×Q₈	—	2	1	no	—
112	C₂×C₅×Q₈	—	4	2	no	—
113	C₂×C₅×Q₈	—	4	2	no	—
114	C₂×C₅×Q₈	C₂²⋊C₄	1	4	yes	—
115	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
116	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
117	C₂×C₅×Q₈	#41	1	2	yes	—
118	C₂²×C₄×C₅	—	2	1	no	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	1	no	—
121	C₂²×C₄×C₅	—	2	2	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₂×C₅×C₈	—	2	1	no	—
130	C₂×C₅×C₈	—	2	1	no	—
131	C₂×C₅×C₈	—	2	1	no	—
132	C₂×C₅×C₈	—	2	2	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
138	C₅×C₄⋊C₄	—	2	8	no	—
139	C₅×C₄⋊C₄	—	2	4	no	—
140	C₅×C₄⋊C₄	—	2	8	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	8	no	—
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	—	2	1	no	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	—	8	1	no	—
152	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
153	C₅×C₄⋊C₄	C₂²⋊C₄	1	8	yes	—
154	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
155	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
156	C₅×C₄⋊C₄	C₂×Q₈	1	2	yes	—
157	C₄²×C₅	—	2	8	no	—
158	C₄²×C₅	—	2	4	no	—
159	C₄²×C₅	—	4	2	no	—
160	C₄²×C₅	—	8	2	no	—
161	C₄²×C₅	C₂²×C₄	1	4	yes	—
162	C₄²×C₅	C₂²×C₄	1	2	yes	—
163	C₄²×C₅	C₂×D₄	1	4	yes	—
164	C₄²×C₅	C₂×D₄	1	2	yes	—
165	#557	—	2	4	no	—
166	#557	C₄×C₅	1	8	yes	complemented
167	C₂×C₄⋊Q₈	—	2	1	no	—
168	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
169	C₂×#125	—	2	2	no	—
170	C₂×#125	C₂²×C₅	1	2	yes	—
171	C₂×C₄×Q₈	—	2	1	no	—
172	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
174	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
175	C₈×Q₈	—	2	4	no	—
176	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
178	C₂×#103	C₂²×C₅	1	2	yes	—
179	C₂×#103	C₂²×C₅	1	1	yes	characteristic
180	C₂×#103	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
183	#391	—	2	1	no	—
184	#387	—	2	2	no	—
185	#384	C₂²×C₅	1	1	yes	characteristic
186	#382	C₂²×C₅	1	2	yes	—
187	C₄×C₄⋊C₄	—	2	1	no	—
188	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
189	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
190	#340	C₂²×C₅	1	2	yes	—
191	#340	C₂²×C₅	1	2	yes	—
192	#340	C₂²×C₅	1	2	yes	—
193	#340	C₂²×C₅	1	2	yes	—
194	#340	C₂²×C₅	1	1	yes	characteristic
195	#340	C₂²×C₅	1	2	yes	—
196	#340	C₂²×C₅	1	1	yes	characteristic
197	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
198	C₅×Q₈	—	2	2	no	—
199	C₅×Q₈	—	2	2	no	—
200	C₅×Q₈	—	2	2	no	—
201	C₅×Q₈	—	2	8	no	—
202	C₅×Q₈	—	4	8	no	—
203	C₅×Q₈	C₄×Q₈	1	4	yes	—
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	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	2	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	2	no	—
214	C₂×C₄×C₅	—	2	4	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	2	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	1	no	—
225	C₂×C₄×C₅	—	4	2	no	—
226	C₂×C₄×C₅	—	4	2	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
229	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
231	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
232	C₂×C₄×C₅	#135	1	2	yes	—
233	C₂×C₄×C₅	#135	1	2	yes	—
234	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
239	C₂×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
240	C₅×C₈	—	2	2	no	—
241	C₅×C₈	—	4	1	no	—
242	C₅×C₈	—	4	2	no	—
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
245	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
246	C₂²×C₈	C₂³×C₅	1	2	yes	—
247	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
249	C₄⋊Q₈	—	2	8	no	—
250	C₄⋊Q₈	—	2	2	no	—
251	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	—
252	#125	—	2	16	no	—
253	#125	—	2	4	no	—
254	#125	C₂×C₄×C₅	1	8	yes	—
255	C₄×Q₈	—	2	8	no	—
256	C₄×Q₈	—	2	4	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₄×Q₈	C₂×C₄×C₅	1	8	yes	—
259	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
260	C₄×Q₈	C₂×C₄×C₅	1	4	yes	—
261	C₄×Q₈	C₅×D₄	1	4	yes	—
262	C₂×C₄⋊C₄	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	C₂³×C₅	1	2	yes	—
281	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
282	C₄⋊C₈	—	2	4	no	—
283	C₄⋊C₈	—	2	2	no	—
284	#103	—	2	4	no	—
285	#103	—	2	2	no	—
286	#103	C₅×Q₈	1	4	yes	complemented
287	C₄×C₈	—	2	4	no	—
288	C₄×C₈	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	1	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₅	#548	1	1	yes	characteristic
295	C₂²×C₅	D₄×Q₈	1	1	yes	characteristic
296	C₂²×C₅	C₂×#135	1	1	yes	characteristic
297	C₂²×C₅	C₂×#135	1	1	yes	characteristic
298	C₂²×C₅	#577	1	1	yes	characteristic
299	C₂²×C₅	#578	1	1	yes	characteristic
300	C₄×C₅	—	2	4	no	—
301	C₄×C₅	—	2	4	no	—
302	C₄×C₅	—	2	4	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	4	4	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	8	1	no	—
308	C₄×C₅	—	8	2	no	—
309	C₄×C₅	#416	1	4	yes	—
310	C₄×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
311	C₄×C₅	#519	1	1	yes	characteristic
312	C₄×C₅	#548	1	1	yes	characteristic
313	C₄×C₅	D₄×Q₈	1	1	yes	characteristic
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	1	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	C₅×C₂²⋊C₄	1	4	yes	—
323	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
324	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
325	C₂×Q₈	C₅×#41	1	2	yes	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
333	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
334	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
336	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
346	C₄⋊C₄	—	2	8	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	8	no	—
349	C₄⋊C₄	—	2	4	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	—	8	1	no	—
360	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
361	C₄⋊C₄	C₅×C₂²⋊C₄	1	8	yes	—
362	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
364	C₄⋊C₄	C₂×C₅×Q₈	1	2	yes	—
365	C₄²	—	2	8	no	—
366	C₄²	—	2	4	no	—
367	C₄²	—	4	2	no	—
368	C₄²	—	8	2	no	—
369	C₄²	C₂²×C₄×C₅	1	4	yes	—
370	C₄²	C₂²×C₄×C₅	1	2	yes	—
371	C₄²	C₂×C₅×D₄	1	4	yes	—
372	C₄²	C₂×C₅×D₄	1	2	yes	—
373	C₂×C₅	Q₈×C₂²⋊C₄	1	1	yes	characteristic
374	C₂×C₅	C₂×#416	1	1	yes	characteristic
375	C₂×C₅	#2898	1	1	yes	characteristic
376	C₂×C₅	#3364	1	1	yes	characteristic
377	C₂×C₅	#3365	1	1	yes	characteristic
378	C₂×C₅	#3381	1	1	yes	characteristic
379	C₂×C₅	#3383	1	1	yes	characteristic
380	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
381	Q₈	—	2	8	no	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	2	no	—
384	Q₈	—	2	2	no	—
385	Q₈	—	4	8	no	—
386	Q₈	C₄×C₅×Q₈	1	4	yes	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
412	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
413	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
414	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
415	C₂×C₄	C₅×#135	1	2	yes	—
416	C₂×C₄	C₅×#135	1	2	yes	—
417	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
418	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
419	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
420	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
421	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
422	C₂×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
423	C₈	—	2	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	4	1	no	—
426	C₅	#22521	1	1	yes	characteristic, direct product factor, Sylow
427	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
428	C₂²	C₅×#548	1	1	yes	characteristic
429	C₂²	C₅×D₄×Q₈	1	1	yes	characteristic
430	C₂²	C₂×C₅×#135	1	1	yes	characteristic
431	C₂²	C₂×C₅×#135	1	1	yes	characteristic
432	C₂²	C₅×#577	1	1	yes	characteristic
433	C₂²	C₅×#578	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	4	2	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	2	no	—
443	C₄	C₅×#416	1	4	yes	—
444	C₄	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
445	C₄	C₅×#519	1	1	yes	characteristic
446	C₄	C₅×#548	1	1	yes	characteristic
447	C₄	C₅×D₄×Q₈	1	1	yes	characteristic
448	C₂	C₅×Q₈×C₂²⋊C₄	1	1	yes	characteristic
449	C₂	C₂×C₅×#416	1	1	yes	characteristic
450	C₂	C₅×#2898	1	1	yes	characteristic
451	C₂	C₅×#3364	1	1	yes	characteristic
452	C₂	C₅×#3365	1	1	yes	characteristic
453	C₂	C₅×#3381	1	1	yes	characteristic
454	C₂	C₅×#3383	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₄×C₅×Q₈ ◁ G

Complements

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

N	H ≅ G/N	type
13. C₅×#557	C₄	semidirect
44. #22521	C₅	direct (N × H)
88. C₅×#103	Q₈	semidirect
166. #557	C₄×C₅	semidirect
286. #103	C₅×Q₈	semidirect
426. C₅	#22521	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#557	2
C₂×C₅×C₈×Q₈	2
C₅×#2355	2
C₅×#1991	2
C₅×#1990	2
C₅×#1989	2
C₅×#1988	2
C₅×#1805	2
C₅×#1803	2
C₄×C₅×#103	2
#22521	5

Subgroups — C5×#22521 #11945241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22521 #11945241