Subgroups — C₅×#21713 #11944433

Order 1280.

802 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#446	C₂	1	2	yes	maximal
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#1985	C₂	1	2	yes	maximal
4	C₅×#1940	C₂	1	2	yes	maximal
5	C₅×#1939	C₂	1	1	yes	maximal, characteristic
6	C₅×#1939	C₂	1	1	yes	maximal, characteristic
7	C₅×#1842	C₂	1	1	yes	maximal, characteristic
8	C₅×#1771	C₂	1	2	yes	maximal
9	C₅×#1770	C₂	1	1	yes	maximal, characteristic
10	C₅×C₈×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic
12	C₂×C₅×C₄⋊Q₈	C₄	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₅×#446	—	2	8	no	—
15	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
16	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
20	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₅×#97	C₂²	1	2	yes	—
22	C₂×C₅×#97	C₂²	1	1	yes	characteristic
23	C₂×C₅×#97	C₂²	1	1	yes	characteristic
24	C₂×C₅×#97	C₂²	1	1	yes	characteristic
25	C₂×C₅×#97	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
27	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
29	C₅×#391	C₄	1	2	yes	—
30	C₅×#389	C₄	1	1	yes	characteristic
31	C₅×#389	C₄	1	1	yes	characteristic
32	C₅×#389	C₄	1	2	yes	—
33	C₅×#384	C₄	1	1	yes	characteristic
34	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄³×C₅	C₂²	1	1	yes	characteristic
38	C₅×#336	C₂²	1	2	yes	—
39	C₅×#336	C₂²	1	2	yes	—
40	C₅×#336	C₂²	1	2	yes	—
41	C₅×#336	C₂²	1	2	yes	—
42	#21713	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
44	C₂²×C₅×C₈	C₂³	1	2	yes	—
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
50	C₅×C₄⋊Q₈	—	2	4	no	—
51	C₄×C₅×Q₈	—	2	4	no	—
52	C₄×C₅×Q₈	—	2	4	no	—
53	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
61	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	C₂³	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₅×C₄⋊C₈	—	2	4	no	—
72	C₅×C₄⋊C₈	—	2	4	no	—
73	C₅×C₄⋊C₈	—	2	4	no	—
74	C₅×C₄⋊C₈	—	2	2	no	—
75	C₅×C₄⋊C₈	—	2	2	no	—
76	C₅×C₄⋊C₈	—	2	4	no	—
77	C₅×#97	—	2	4	no	—
78	C₅×#97	—	2	2	no	—
79	C₅×#97	—	2	2	no	—
80	C₅×#97	D₄	1	4	yes	—
81	C₅×#97	Q₈	1	4	yes	complemented
82	C₄×C₅×C₈	—	2	4	no	—
83	C₄×C₅×C₈	—	2	2	no	—
84	C₄×C₅×C₈	Q₈	1	4	yes	complemented
85	C₅×#95	C₂×C₄	1	2	yes	—
86	C₅×#95	C₂×C₄	1	2	yes	—
87	C₅×#95	C₂×C₄	1	2	yes	—
88	C₅×#95	C₂×C₄	1	2	yes	—
89	C₂×#446	C₂×C₅	1	2	yes	—
90	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
91	#1985	C₂×C₅	1	2	yes	—
92	#1940	C₂×C₅	1	2	yes	—
93	#1939	C₂×C₅	1	1	yes	characteristic
94	#1939	C₂×C₅	1	1	yes	characteristic
95	#1842	C₂×C₅	1	1	yes	characteristic
96	#1771	C₂×C₅	1	2	yes	—
97	#1770	C₂×C₅	1	1	yes	characteristic
98	C₈×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
99	C₄×#97	C₂×C₅	1	1	yes	characteristic
100	C₂×C₅×Q₈	—	2	4	no	—
101	C₂×C₅×Q₈	—	2	4	no	—
102	C₂×C₅×Q₈	—	4	2	no	—
103	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
114	C₂×C₅×C₈	—	2	1	no	—
115	C₂×C₅×C₈	—	2	1	no	—
116	C₂×C₅×C₈	—	2	1	no	—
117	C₂×C₅×C₈	—	2	1	no	—
118	C₂×C₅×C₈	—	2	1	no	—
119	C₂×C₅×C₈	—	2	1	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
127	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
128	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
129	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
130	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
131	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
132	C₅×C₄⋊C₄	—	2	4	no	—
133	C₅×C₄⋊C₄	—	2	4	no	—
134	C₅×C₄⋊C₄	—	2	4	no	—
135	C₅×C₄⋊C₄	—	2	4	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₄⋊C₄	—	2	2	no	—
139	C₅×C₄⋊C₄	—	4	2	no	—
140	C₅×C₄⋊C₄	M₁₆	1	4	yes	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	2	2	no	—
143	C₄²×C₅	—	2	2	no	—
144	C₄²×C₅	—	2	2	no	—
145	C₄²×C₅	—	2	2	no	—
146	C₄²×C₅	—	2	2	no	—
147	C₄²×C₅	—	4	1	no	—
148	C₄²×C₅	—	4	1	no	—
149	C₄²×C₅	C₂×D₄	1	2	yes	—
150	C₄²×C₅	C₂×Q₈	1	2	yes	—
151	C₄²×C₅	C₂×Q₈	1	2	yes	—
152	C₄²×C₅	#41	1	2	yes	—
153	C₄²×C₅	#41	1	2	yes	—
154	C₄²×C₅	#41	1	2	yes	—
155	C₂×C₄⋊Q₈	C₄×C₅	1	1	yes	characteristic
156	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
157	#446	—	2	8	no	—
158	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
159	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
162	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
163	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
164	C₂×#97	C₂²×C₅	1	2	yes	—
165	C₂×#97	C₂²×C₅	1	1	yes	characteristic
166	C₂×#97	C₂²×C₅	1	1	yes	characteristic
167	C₂×#97	C₂²×C₅	1	1	yes	characteristic
168	C₂×#97	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
170	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
172	#391	C₄×C₅	1	2	yes	—
173	#389	C₄×C₅	1	1	yes	characteristic
174	#389	C₄×C₅	1	1	yes	characteristic
175	#389	C₄×C₅	1	2	yes	—
176	#384	C₄×C₅	1	1	yes	characteristic
177	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
179	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
180	C₄³	C₂²×C₅	1	1	yes	characteristic
181	#336	C₂²×C₅	1	2	yes	—
182	#336	C₂²×C₅	1	2	yes	—
183	#336	C₂²×C₅	1	2	yes	—
184	#336	C₂²×C₅	1	2	yes	—
185	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
186	C₅×Q₈	—	4	8	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	no	—
197	C₂×C₄×C₅	—	2	1	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	2	2	no	—
201	C₂×C₄×C₅	—	2	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	—	2	2	no	—
208	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
211	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
212	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
213	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
214	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
215	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
216	C₂×C₄×C₅	#131	1	2	yes	—
217	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
219	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
223	C₅×C₈	—	2	2	no	—
224	C₅×C₈	—	2	2	no	—
225	C₅×C₈	—	2	2	no	—
226	C₅×C₈	—	4	2	no	—
227	C₅×C₈	—	4	2	no	—
228	C₅×C₈	C₄⋊Q₈	1	4	yes	complemented
229	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
230	C₂²×C₈	C₂³×C₅	1	2	yes	—
231	C₂²×C₈	C₂³×C₅	1	2	yes	—
232	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
233	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
234	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
235	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
236	C₄⋊Q₈	—	2	4	no	—
237	C₄×Q₈	—	2	4	no	—
238	C₄×Q₈	—	2	4	no	—
239	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
240	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
241	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
242	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
244	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
245	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
246	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
247	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
248	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
250	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₅	1	2	yes	—
253	C₂×C₄²	C₂³×C₅	1	2	yes	—
254	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	C₄⋊C₈	—	2	4	no	—
258	C₄⋊C₈	—	2	4	no	—
259	C₄⋊C₈	—	2	4	no	—
260	C₄⋊C₈	—	2	2	no	—
261	C₄⋊C₈	—	2	2	no	—
262	C₄⋊C₈	—	2	4	no	—
263	#97	—	2	4	no	—
264	#97	—	2	2	no	—
265	#97	—	2	2	no	—
266	#97	C₅×D₄	1	4	yes	—
267	#97	C₅×Q₈	1	4	yes	complemented
268	C₄×C₈	—	2	4	no	—
269	C₄×C₈	—	2	2	no	—
270	C₄×C₈	C₅×Q₈	1	4	yes	complemented
271	#95	C₂×C₄×C₅	1	2	yes	—
272	#95	C₂×C₄×C₅	1	2	yes	—
273	#95	C₂×C₄×C₅	1	2	yes	—
274	#95	C₂×C₄×C₅	1	2	yes	—
275	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
276	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
277	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
278	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
279	C₂²×C₅	C₂×#131	1	1	yes	characteristic
280	C₂²×C₅	#568	1	1	yes	characteristic
281	C₂²×C₅	#568	1	1	yes	characteristic
282	C₄×C₅	—	2	2	no	—
283	C₄×C₅	—	2	4	no	—
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	2	2	no	—
287	C₄×C₅	—	2	2	no	—
288	C₄×C₅	—	4	2	no	—
289	C₄×C₅	—	4	2	no	—
290	C₄×C₅	—	4	2	no	—
291	C₄×C₅	#446	1	4	yes	complemented
292	C₄×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
293	C₄×C₅	#532	1	1	yes	characteristic
294	C₄×C₅	#533	1	1	yes	characteristic
295	C₄×C₅	#533	1	1	yes	characteristic
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	4	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
303	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
304	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
305	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
307	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
308	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	1	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
323	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
324	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
325	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
326	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
327	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	C₅×M₁₆	1	4	yes	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	2	no	—
343	C₄²	—	4	1	no	—
344	C₄²	—	4	1	no	—
345	C₄²	C₂×C₅×D₄	1	2	yes	—
346	C₄²	C₂×C₅×Q₈	1	2	yes	—
347	C₄²	C₂×C₅×Q₈	1	2	yes	—
348	C₄²	C₅×#41	1	2	yes	—
349	C₄²	C₅×#41	1	2	yes	—
350	C₄²	C₅×#41	1	2	yes	—
351	C₂×C₅	C₄×C₄⋊Q₈	1	1	yes	characteristic
352	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
353	C₂×C₅	#2935	1	1	yes	characteristic
354	C₂×C₅	C₂×#446	1	1	yes	characteristic
355	C₂×C₅	#2961	1	1	yes	characteristic
356	C₂×C₅	#2962	1	1	yes	characteristic
357	C₂×C₅	Q₈×M₁₆	1	1	yes	characteristic
358	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
359	Q₈	—	4	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
382	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
383	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
384	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
385	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
386	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
387	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
388	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
389	C₂×C₄	C₅×#131	1	2	yes	—
390	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
391	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
393	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
394	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
395	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	2	2	no	—
399	C₈	—	4	2	no	—
400	C₈	—	4	2	no	—
401	C₈	C₅×C₄⋊Q₈	1	4	yes	complemented
402	C₅	#21713	1	1	yes	characteristic, direct product factor, Sylow
403	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
404	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
405	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
406	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
407	C₂²	C₂×C₅×#131	1	1	yes	characteristic
408	C₂²	C₅×#568	1	1	yes	characteristic
409	C₂²	C₅×#568	1	1	yes	characteristic
410	C₄	—	2	2	no	—
411	C₄	—	2	4	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	2	2	no	—
415	C₄	—	2	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	4	2	no	—
419	C₄	C₅×#446	1	4	yes	complemented
420	C₄	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
421	C₄	C₅×#532	1	1	yes	characteristic
422	C₄	C₅×#533	1	1	yes	characteristic
423	C₄	C₅×#533	1	1	yes	characteristic
424	C₂	C₄×C₅×C₄⋊Q₈	1	1	yes	characteristic
425	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
426	C₂	C₅×#2935	1	1	yes	characteristic
427	C₂	C₂×C₅×#446	1	1	yes	characteristic
428	C₂	C₅×#2961	1	1	yes	characteristic
429	C₂	C₅×#2962	1	1	yes	characteristic
430	C₂	C₅×Q₈×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂⁴
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂³×C₅	C₂³×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
42. #21713	C₅	direct (N × H)
81. C₅×#97	Q₈	semidirect
84. C₄×C₅×C₈	Q₈	semidirect
228. C₅×C₈	C₄⋊Q₈	semidirect
267. #97	C₅×Q₈	semidirect
270. C₄×C₈	C₅×Q₈	semidirect
291. C₄×C₅	#446	semidirect
401. C₈	C₅×C₄⋊Q₈	semidirect
402. C₅	#21713	direct (N × H)
419. C₄	C₅×#446	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#446	2
C₄×C₅×C₄⋊Q₈	2
C₅×#1985	2
C₅×#1940	2
C₅×#1939	2
C₅×#1842	2
C₅×#1771	2
C₅×#1770	2
C₅×C₈×C₄⋊C₄	2
C₄×C₅×#97	2
#21713	5

Subgroups — C5×#21713 #11944433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21713 #11944433