Subgroups — C₅×#21599 #11944319

Order 1280.

898 conjugacy classes of subgroups.

The subgroup lattice has 644 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	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₄×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
4	C₅×#1985	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1940	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1917	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1850	C₂	1	1	yes	maximal, characteristic
9	C₅×#1850	C₂	1	1	yes	maximal, characteristic
10	C₅×#1797	C₂	1	1	yes	maximal, characteristic
11	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1771	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1770	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1752	C₂	1	1	yes	maximal, characteristic
15	C₅×C₈×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₂²⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₅×#446	—	2	4	no	—
22	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	—	2	4	no	—
31	C₂×C₅×#97	C₂²	1	1	yes	characteristic
32	C₂×C₅×#97	C₂²	1	1	yes	characteristic
33	C₂×C₅×#97	C₂²	1	1	yes	characteristic
34	C₂×C₅×#97	C₂²	1	1	yes	characteristic
35	C₂×C₅×#97	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
39	C₅×#391	C₄	1	1	yes	characteristic
40	C₅×#389	C₄	1	1	yes	characteristic
41	C₅×#387	C₄	1	1	yes	characteristic
42	C₅×#387	C₄	1	1	yes	characteristic
43	C₅×#385	C₄	1	1	yes	characteristic
44	C₅×#385	C₄	1	1	yes	characteristic
45	C₅×#380	C₄	1	1	yes	characteristic
46	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
51	C₅×#336	C₂²	1	1	yes	characteristic
52	C₅×#336	C₂²	1	1	yes	characteristic
53	C₅×#336	C₂²	1	1	yes	characteristic
54	C₅×#336	C₂²	1	1	yes	characteristic
55	C₅×#336	C₂²	1	1	yes	characteristic
56	C₅×#336	C₂²	1	1	yes	characteristic
57	C₅×#336	C₂²	1	1	yes	characteristic
58	C₅×#336	C₂²	1	1	yes	characteristic
59	C₅×#336	C₂²	1	1	yes	characteristic
60	C₅×#336	C₂²	1	1	yes	characteristic
61	#21599	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
63	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₅×C₈	—	2	2	no	—
67	C₂²×C₅×C₈	—	2	2	no	—
68	C₂²×C₅×C₈	—	2	2	no	—
69	C₂²×C₅×C₈	—	2	2	no	—
70	C₂²×C₅×C₈	—	2	2	no	—
71	C₂²×C₅×C₈	Q₈	1	4	yes	complemented
72	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₅×C₂²⋊Q₈	—	2	4	no	—
81	C₄×C₅×Q₈	—	2	2	no	—
82	C₄×C₅×Q₈	—	2	2	no	—
83	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
91	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	—	2	2	no	—
97	C₂×C₄²×C₅	—	2	2	no	—
98	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
106	C₅×C₄⋊C₈	—	2	2	no	—
107	C₅×C₄⋊C₈	—	2	2	no	—
108	C₅×C₄⋊C₈	—	2	2	no	—
109	C₅×C₄⋊C₈	—	2	2	no	—
110	C₅×C₄⋊C₈	—	2	2	no	—
111	C₅×C₄⋊C₈	—	2	2	no	—
112	C₅×C₂²⋊C₈	—	2	2	no	—
113	C₅×C₂²⋊C₈	—	2	2	no	—
114	C₅×#97	—	2	2	no	—
115	C₅×#97	—	2	2	no	—
116	C₅×#97	—	2	2	no	—
117	C₅×#97	—	2	2	no	—
118	C₅×#97	—	2	2	no	—
119	C₅×#97	D₄	1	4	yes	—
120	C₄×C₅×C₈	—	2	2	no	—
121	C₄×C₅×C₈	—	2	2	no	—
122	C₅×#95	C₂×C₄	1	1	yes	characteristic
123	C₅×#95	C₂×C₄	1	1	yes	characteristic
124	C₅×#95	C₂×C₄	1	1	yes	characteristic
125	C₅×#95	C₂×C₄	1	1	yes	characteristic
126	C₅×#95	C₂×C₄	1	1	yes	characteristic
127	C₅×#95	C₂×C₄	1	1	yes	characteristic
128	C₅×#95	C₂×C₄	1	1	yes	characteristic
129	C₅×#95	C₂×C₄	1	1	yes	characteristic
130	C₅×#95	C₂×C₄	1	1	yes	characteristic
131	C₅×#95	C₂×C₄	1	1	yes	characteristic
132	C₂×#446	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂²×#97	C₂×C₅	1	1	yes	characteristic
134	C₄×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
135	#1985	C₂×C₅	1	1	yes	characteristic, complemented
136	#1940	C₂×C₅	1	1	yes	characteristic, complemented
137	#1917	C₂×C₅	1	1	yes	characteristic, complemented
138	#1917	C₂×C₅	1	1	yes	characteristic, complemented
139	#1850	C₂×C₅	1	1	yes	characteristic
140	#1850	C₂×C₅	1	1	yes	characteristic
141	#1797	C₂×C₅	1	1	yes	characteristic
142	#1771	C₂×C₅	1	1	yes	characteristic, complemented
143	#1771	C₂×C₅	1	1	yes	characteristic, complemented
144	#1770	C₂×C₅	1	1	yes	characteristic, complemented
145	#1752	C₂×C₅	1	1	yes	characteristic
146	C₈×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
147	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	2	no	—
150	C₂×C₅×Q₈	—	4	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	4	1	no	—
160	C₂²×C₄×C₅	—	4	1	no	—
161	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
175	C₂²×C₄×C₅	#41	1	2	yes	—
176	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
177	C₂×C₅×C₈	—	2	8	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	1	no	—
180	C₂×C₅×C₈	—	2	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	8	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	1	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	2	1	no	—
189	C₂×C₅×C₈	—	2	1	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	—	2	1	no	—
196	C₂×C₅×C₈	—	2	1	no	—
197	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
198	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
199	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
200	C₂×C₅×C₈	C₂×Q₈	1	2	yes	—
201	C₂×C₅×C₈	#41	1	2	yes	—
202	C₂×C₅×C₈	#41	1	2	yes	—
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	—	2	2	no	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	4	1	no	—
210	C₅×C₄⋊C₄	—	4	1	no	—
211	C₅×C₄⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	2	2	no	—
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	M₁₆	1	4	yes	—
216	C₄²×C₅	—	2	2	no	—
217	C₄²×C₅	—	2	2	no	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	1	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	C₂×D₄	1	2	yes	—
229	C₄²×C₅	#41	1	2	yes	—
230	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×C₂²⋊Q₈	C₄×C₅	1	1	yes	characteristic
233	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
234	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
235	#446	—	2	4	no	—
236	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
237	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
239	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
242	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
243	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×#97	—	2	4	no	—
245	C₂×#97	C₂²×C₅	1	1	yes	characteristic
246	C₂×#97	C₂²×C₅	1	1	yes	characteristic
247	C₂×#97	C₂²×C₅	1	1	yes	characteristic
248	C₂×#97	C₂²×C₅	1	1	yes	characteristic
249	C₂×#97	C₂²×C₅	1	1	yes	characteristic
250	C₂×#97	C₂²×C₅	1	1	yes	characteristic
251	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
252	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
253	#391	C₄×C₅	1	1	yes	characteristic
254	#389	C₄×C₅	1	1	yes	characteristic
255	#387	C₄×C₅	1	1	yes	characteristic
256	#387	C₄×C₅	1	1	yes	characteristic
257	#385	C₄×C₅	1	1	yes	characteristic
258	#385	C₄×C₅	1	1	yes	characteristic
259	#380	C₄×C₅	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
261	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
262	C₄×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
264	C₄×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
265	#336	C₂²×C₅	1	1	yes	characteristic
266	#336	C₂²×C₅	1	1	yes	characteristic
267	#336	C₂²×C₅	1	1	yes	characteristic
268	#336	C₂²×C₅	1	1	yes	characteristic
269	#336	C₂²×C₅	1	1	yes	characteristic
270	#336	C₂²×C₅	1	1	yes	characteristic
271	#336	C₂²×C₅	1	1	yes	characteristic
272	#336	C₂²×C₅	1	1	yes	characteristic
273	#336	C₂²×C₅	1	1	yes	characteristic
274	#336	C₂²×C₅	1	1	yes	characteristic
275	C₂³×C₅	—	2	1	no	—
276	C₂³×C₅	—	2	1	no	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	—	2	1	no	—
279	C₂³×C₅	C₄×Q₈	1	2	yes	—
280	C₂³×C₅	C₂×M₁₆	1	2	yes	—
281	C₂³×C₅	#131	1	2	yes	—
282	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
283	C₅×Q₈	—	4	4	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	1	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	4	4	no	—
323	C₂×C₄×C₅	—	4	4	no	—
324	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
325	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
326	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
327	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
328	C₂×C₄×C₅	C₂×M₁₆	1	2	yes	—
329	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
332	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
333	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
335	C₅×C₈	—	2	2	no	—
336	C₅×C₈	—	2	2	no	—
337	C₅×C₈	—	2	2	no	—
338	C₅×C₈	—	4	1	no	—
339	C₅×C₈	—	4	1	no	—
340	C₅×C₈	—	4	1	no	—
341	C₅×C₈	—	4	1	no	—
342	C₅×C₈	C₂²⋊Q₈	1	4	yes	complemented
343	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
344	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
345	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
347	C₂²×C₈	—	2	2	no	—
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	—	2	2	no	—
350	C₂²×C₈	—	2	2	no	—
351	C₂²×C₈	—	2	2	no	—
352	C₂²×C₈	C₅×Q₈	1	4	yes	complemented
353	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
354	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
355	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
356	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
357	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
358	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
359	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
360	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
361	C₂²⋊Q₈	—	2	4	no	—
362	C₄×Q₈	—	2	2	no	—
363	C₄×Q₈	—	2	2	no	—
364	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
365	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
367	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
369	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
372	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
374	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
376	C₂×C₂²⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
380	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
387	C₄⋊C₈	—	2	2	no	—
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	2	2	no	—
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	—	2	2	no	—
392	C₄⋊C₈	—	2	2	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	#97	—	2	2	no	—
396	#97	—	2	2	no	—
397	#97	—	2	2	no	—
398	#97	—	2	2	no	—
399	#97	—	2	2	no	—
400	#97	C₅×D₄	1	4	yes	—
401	C₄×C₈	—	2	2	no	—
402	C₄×C₈	—	2	2	no	—
403	#95	C₂×C₄×C₅	1	1	yes	characteristic
404	#95	C₂×C₄×C₅	1	1	yes	characteristic
405	#95	C₂×C₄×C₅	1	1	yes	characteristic
406	#95	C₂×C₄×C₅	1	1	yes	characteristic
407	#95	C₂×C₄×C₅	1	1	yes	characteristic
408	#95	C₂×C₄×C₅	1	1	yes	characteristic
409	#95	C₂×C₄×C₅	1	1	yes	characteristic
410	#95	C₂×C₄×C₅	1	1	yes	characteristic
411	#95	C₂×C₄×C₅	1	1	yes	characteristic
412	#95	C₂×C₄×C₅	1	1	yes	characteristic
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	#446	1	4	yes	complemented
420	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
421	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
422	C₂²×C₅	C₄×#41	1	1	yes	characteristic
423	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
424	C₂²×C₅	C₂×#131	1	1	yes	characteristic
425	C₂²×C₅	#568	1	1	yes	characteristic
426	C₂²×C₅	#568	1	1	yes	characteristic
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	1	no	—
434	C₄×C₅	—	4	1	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	1	no	—
438	C₄×C₅	—	4	1	no	—
439	C₄×C₅	—	4	1	no	—
440	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
441	C₄×C₅	#525	1	1	yes	characteristic
442	C₄×C₅	#529	1	1	yes	characteristic
443	C₄×C₅	#533	1	1	yes	characteristic
444	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
445	C₂×Q₈	—	2	2	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	4	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
460	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
461	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
462	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
464	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
467	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
468	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
469	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
470	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
472	C₂²×C₄	C₅×#41	1	2	yes	—
473	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
474	C₂×C₈	—	2	8	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	1	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	8	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
495	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
496	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
497	C₂×C₈	C₂×C₅×Q₈	1	2	yes	—
498	C₂×C₈	C₅×#41	1	2	yes	—
499	C₂×C₈	C₅×#41	1	2	yes	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	2	no	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	2	2	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	—	4	1	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₂²⋊C₄	—	2	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	C₅×M₁₆	1	4	yes	—
513	C₄²	—	2	2	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	1	no	—
519	C₄²	—	2	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	2	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	C₂×C₅×D₄	1	2	yes	—
526	C₄²	C₅×#41	1	2	yes	—
527	C₂×C₅	—	2	4	no	—
528	C₂×C₅	C₄×C₂²⋊Q₈	1	1	yes	characteristic
529	C₂×C₅	#2933	1	1	yes	characteristic
530	C₂×C₅	D₄×M₁₆	1	1	yes	characteristic
531	C₂×C₅	C₂×#446	1	1	yes	characteristic
532	C₂×C₅	#2961	1	1	yes	characteristic
533	C₂×C₅	#2968	1	1	yes	characteristic
534	C₂×C₅	#2970	1	1	yes	characteristic
535	C₂³	—	2	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	C₄×C₅×Q₈	1	2	yes	—
540	C₂³	C₂×C₅×M₁₆	1	2	yes	—
541	C₂³	C₅×#131	1	2	yes	—
542	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
543	Q₈	—	4	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
585	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
586	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
587	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
588	C₂×C₄	C₂×C₅×M₁₆	1	2	yes	—
589	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
590	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
591	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
592	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
593	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
594	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
595	C₈	—	2	2	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	4	1	no	—
601	C₈	—	4	1	no	—
602	C₈	C₅×C₂²⋊Q₈	1	4	yes	complemented
603	C₅	#21599	1	1	yes	characteristic, direct product factor, Sylow
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	2	2	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	2	2	no	—
610	C₂²	C₅×#446	1	4	yes	complemented
611	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
612	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
613	C₂²	C₄×C₅×#41	1	1	yes	characteristic
614	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
615	C₂²	C₂×C₅×#131	1	1	yes	characteristic
616	C₂²	C₅×#568	1	1	yes	characteristic
617	C₂²	C₅×#568	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	2	no	—
622	C₄	—	2	2	no	—
623	C₄	—	4	1	no	—
624	C₄	—	4	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	4	1	no	—
631	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
632	C₄	C₅×#525	1	1	yes	characteristic
633	C₄	C₅×#529	1	1	yes	characteristic
634	C₄	C₅×#533	1	1	yes	characteristic
635	C₂	—	2	4	no	—
636	C₂	C₄×C₅×C₂²⋊Q₈	1	1	yes	characteristic
637	C₂	C₅×#2933	1	1	yes	characteristic
638	C₂	C₅×D₄×M₁₆	1	1	yes	characteristic
639	C₂	C₂×C₅×#446	1	1	yes	characteristic
640	C₂	C₅×#2961	1	1	yes	characteristic
641	C₂	C₅×#2968	1	1	yes	characteristic
642	C₂	C₅×#2970	1	1	yes	characteristic

	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
1. C₂×C₅×#446	C₂	semidirect
4. C₅×#1985	C₂	semidirect
5. C₅×#1940	C₂	semidirect
6. C₅×#1917	C₂	semidirect
7. C₅×#1917	C₂	semidirect
11. C₅×#1771	C₂	semidirect
12. C₅×#1771	C₂	semidirect
13. C₅×#1770	C₂	semidirect
61. #21599	C₅	direct (N × H)
71. C₂²×C₅×C₈	Q₈	semidirect
132. C₂×#446	C₂×C₅	semidirect
135. #1985	C₂×C₅	semidirect
136. #1940	C₂×C₅	semidirect
137. #1917	C₂×C₅	semidirect
138. #1917	C₂×C₅	semidirect
142. #1771	C₂×C₅	semidirect
143. #1771	C₂×C₅	semidirect
144. #1770	C₂×C₅	semidirect
342. C₅×C₈	C₂²⋊Q₈	semidirect
352. C₂²×C₈	C₅×Q₈	semidirect
419. C₂²×C₅	#446	semidirect
602. C₈	C₅×C₂²⋊Q₈	semidirect
603. C₅	#21599	direct (N × H)
610. C₂²	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
C₂²×C₅×#97	2
C₄×C₅×C₂²⋊Q₈	2
C₅×#1985	2
C₅×#1940	2
C₅×#1917	2
C₅×#1850	2
C₅×#1797	2
C₅×#1771	2
C₅×#1770	2
C₅×#1752	2
C₅×C₈×C₂²⋊C₄	2
#21599	5

Subgroups — C5×#21599 #11944319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21599 #11944319