Subgroups — C₅×#17484 #11940204

Order 1280.

920 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3461	C₂	1	1	yes	maximal, characteristic
2	C₅×#2989	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1497	C₂	1	2	yes	maximal, complemented
5	C₅×#1495	C₂	1	2	yes	maximal, complemented
6	C₅×#1494	C₂	1	2	yes	maximal, complemented
7	C₅×#1493	C₂	1	2	yes	maximal, complemented
8	C₅×#1479	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1477	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#544	C₄	1	1	yes	characteristic
13	C₅×#542	—	2	1	no	—
14	C₅×#542	C₄	1	2	yes	—
15	C₅×#541	—	2	1	no	—
16	C₅×#541	C₄	1	2	yes	—
17	C₅×#539	—	2	2	no	—
18	C₅×#537	C₄	1	1	yes	characteristic
19	C₅×#536	C₄	1	1	yes	characteristic
20	C₅×#536	C₄	1	1	yes	characteristic
21	C₅×#533	—	2	1	no	—
22	C₅×#533	C₂²	1	2	yes	—
23	C₅×#529	—	2	2	no	—
24	C₅×#529	—	2	1	no	—
25	C₅×#529	C₂²	1	2	yes	—
26	C₄×C₅×#41	C₂²	1	1	yes	characteristic
27	C₄×C₅×#41	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
29	C₅×#446	—	2	1	no	—
30	C₅×C₈×Q₈	—	2	1	no	—
31	C₅×#436	—	2	1	no	—
32	C₅×#435	—	2	2	no	—
33	C₅×C₈×D₄	—	2	2	no	—
34	C₅×C₈×D₄	—	2	1	no	—
35	C₅×#432	C₂²	1	2	yes	—
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₅×#431	C₂²	1	2	yes	—
39	C₅×#423	C₂²	1	2	yes	—
40	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
43	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
45	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
46	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
47	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
51	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
52	C₅×D₄⋊C₈	C₂²	1	2	yes	—
53	#17484	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
55	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
65	C₅×#126	—	2	2	no	—
66	C₅×#126	—	2	2	no	—
67	C₅×#126	—	2	2	no	—
68	C₅×#126	—	2	2	no	—
69	C₅×#125	—	2	2	no	—
70	C₅×#125	—	2	1	no	—
71	C₅×#125	—	2	2	no	—
72	C₅×#125	—	2	2	no	—
73	C₅×#125	C₂×C₄	1	2	yes	—
74	C₅×#124	—	2	1	no	—
75	C₅×#124	—	2	2	no	—
76	C₅×#124	C₂×C₄	1	2	yes	—
77	C₅×#123	—	2	2	no	—
78	C₅×#123	—	2	2	no	—
79	C₅×#123	—	2	2	no	—
80	C₅×#123	—	2	2	no	—
81	C₅×C₂²⋊Q₈	—	2	1	no	—
82	C₅×C₂²⋊Q₈	—	2	2	no	—
83	C₅×C₂²⋊Q₈	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	1	no	—
85	C₅×C₂²⋊Q₈	—	2	2	no	—
86	C₅×C₂²⋊Q₈	—	2	2	no	—
87	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
88	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
89	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
90	C₅×#121	—	2	2	no	—
91	C₅×#121	—	2	1	no	—
92	C₅×#121	C₂×C₄	1	2	yes	—
93	C₄×C₅×Q₈	—	2	1	no	—
94	C₄×C₅×Q₈	—	2	1	no	—
95	C₄×C₅×Q₈	—	2	2	no	—
96	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
97	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
99	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂³	1	2	yes	—
101	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
102	C₄×C₅×D₄	—	2	1	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	2	no	—
105	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
106	C₄×C₅×D₄	D₄	1	2	yes	—
107	C₄×C₅×D₄	D₄	1	1	yes	characteristic
108	C₄×C₅×D₄	D₄	1	2	yes	—
109	C₄×C₅×D₄	D₄	1	1	yes	characteristic
110	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
111	C₅×#117	—	2	2	no	—
112	C₅×#117	—	2	1	no	—
113	C₅×#117	—	2	2	no	—
114	C₅×#117	C₂×C₄	1	1	yes	characteristic
115	C₅×#117	C₂×C₄	1	1	yes	characteristic
116	C₅×#117	C₂×C₄	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	—	2	1	no	—
118	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×C₄²×C₅	—	2	1	no	—
120	C₂×C₄²×C₅	—	2	1	no	—
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	2	yes	—
123	C₅×C₄⋊C₈	—	2	1	no	—
124	C₅×C₄⋊C₈	—	2	2	no	—
125	C₅×C₄⋊C₈	—	2	1	no	—
126	C₅×C₄⋊C₈	—	2	2	no	—
127	C₅×C₄⋊C₈	C₂³	1	2	yes	—
128	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
129	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
130	C₅×C₂²⋊C₈	—	2	1	no	—
131	C₅×C₂²⋊C₈	—	2	2	no	—
132	C₅×C₂²⋊C₈	—	2	1	no	—
133	C₅×C₂²⋊C₈	—	2	2	no	—
134	C₅×#97	—	2	2	no	—
135	C₄×C₅×C₈	—	2	1	no	—
136	C₄×C₅×C₈	—	2	2	no	—
137	C₄×C₅×C₈	—	2	1	no	—
138	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
139	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₄×C₅×C₈	C₂³	1	2	yes	—
141	#3461	C₂×C₅	1	1	yes	characteristic
142	#2989	C₂×C₅	1	1	yes	characteristic, complemented
143	C₈×#41	C₂×C₅	1	1	yes	characteristic, complemented
144	#1497	C₂×C₅	1	2	yes	complemented
145	#1495	C₂×C₅	1	2	yes	complemented
146	#1494	C₂×C₅	1	2	yes	complemented
147	#1493	C₂×C₅	1	2	yes	complemented
148	#1479	C₂×C₅	1	1	yes	characteristic, complemented
149	#1477	C₂×C₅	1	1	yes	characteristic, complemented
150	#1476	C₂×C₅	1	1	yes	characteristic, complemented
151	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
152	C₅×#41	—	2	4	no	—
153	C₅×#41	—	2	4	no	—
154	C₂×C₅×Q₈	—	2	1	no	—
155	C₂×C₅×Q₈	—	2	2	no	—
156	C₂×C₅×Q₈	—	2	4	no	—
157	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
158	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
159	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
160	C₂×C₅×D₄	—	2	1	no	—
161	C₂×C₅×D₄	—	2	2	no	—
162	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
163	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	1	no	—
167	C₂²×C₄×C₅	—	2	1	no	—
168	C₂²×C₄×C₅	—	2	1	no	—
169	C₂²×C₄×C₅	—	2	1	no	—
170	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
176	C₅×M₁₆	—	8	2	no	—
177	C₂×C₅×C₈	—	2	1	no	—
178	C₂×C₅×C₈	—	2	1	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	4	2	no	—
184	C₂×C₅×C₈	—	4	4	no	—
185	C₂×C₅×C₈	—	8	1	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	2	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
200	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
201	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
202	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
203	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
204	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	2	1	no	—
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	2	1	no	—
211	C₅×C₂²⋊C₄	—	2	2	no	—
212	C₅×C₂²⋊C₄	—	2	2	no	—
213	C₅×C₂²⋊C₄	—	2	2	no	—
214	C₅×C₂²⋊C₄	—	2	1	no	—
215	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
216	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
217	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	2	no	—
221	C₄²×C₅	—	2	2	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
224	C₄²×C₅	C₂²×C₄	1	2	yes	—
225	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₅	C₂×D₄	1	2	yes	—
227	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
228	C₄²×C₅	C₂×D₄	1	2	yes	—
229	C₄²×C₅	C₂⁴	1	1	yes	characteristic
230	#544	C₄×C₅	1	1	yes	characteristic
231	#542	—	2	1	no	—
232	#542	C₄×C₅	1	2	yes	—
233	#541	—	2	1	no	—
234	#541	C₄×C₅	1	2	yes	—
235	#539	—	2	2	no	—
236	#537	C₄×C₅	1	1	yes	characteristic
237	#536	C₄×C₅	1	1	yes	characteristic
238	#536	C₄×C₅	1	1	yes	characteristic
239	#533	—	2	1	no	—
240	#533	C₂²×C₅	1	2	yes	—
241	#529	—	2	2	no	—
242	#529	—	2	1	no	—
243	#529	C₂²×C₅	1	2	yes	—
244	C₄×#41	C₂²×C₅	1	1	yes	characteristic
245	C₄×#41	C₂²×C₅	1	1	yes	characteristic
246	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
247	#446	—	2	1	no	—
248	C₈×Q₈	—	2	1	no	—
249	#436	—	2	1	no	—
250	#435	—	2	2	no	—
251	C₈×D₄	—	2	2	no	—
252	C₈×D₄	—	2	1	no	—
253	#432	C₂²×C₅	1	2	yes	—
254	#431	C₂²×C₅	1	1	yes	characteristic
255	#431	C₂²×C₅	1	1	yes	characteristic
256	#431	C₂²×C₅	1	2	yes	—
257	#423	C₂²×C₅	1	2	yes	—
258	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
261	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
262	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
263	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
266	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
267	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
268	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
269	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
270	D₄⋊C₈	C₂²×C₅	1	2	yes	—
271	C₂³×C₅	—	2	1	no	—
272	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
273	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₅×Q₈	—	2	2	no	—
275	C₅×Q₈	—	2	4	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	4	2	no	—
278	C₅×Q₈	—	8	2	no	—
279	C₅×D₄	—	2	4	no	—
280	C₅×D₄	—	2	2	no	—
281	C₅×D₄	—	2	2	no	—
282	C₅×D₄	—	4	2	no	—
283	C₅×D₄	—	8	2	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	1	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	2	no	—
296	C₂×C₄×C₅	—	4	2	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	8	1	no	—
301	C₂×C₄×C₅	—	8	1	no	—
302	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
306	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
307	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄×C₅	#131	1	4	yes	—
309	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₅×C₈	—	2	2	no	—
313	C₅×C₈	—	4	1	no	—
314	C₅×C₈	—	4	2	no	—
315	C₅×C₈	—	4	2	no	—
316	C₅×C₈	—	4	1	no	—
317	C₅×C₈	—	4	1	no	—
318	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
319	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
320	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
321	C₂×M₁₆	—	2	2	no	—
322	C₂²×C₈	—	2	1	no	—
323	C₂²×C₈	—	2	2	no	—
324	C₂²×C₈	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
328	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
329	#126	—	2	2	no	—
330	#126	—	2	2	no	—
331	#126	—	2	2	no	—
332	#126	—	2	2	no	—
333	#125	—	2	2	no	—
334	#125	—	2	1	no	—
335	#125	—	2	2	no	—
336	#125	—	2	2	no	—
337	#125	C₂×C₄×C₅	1	2	yes	—
338	#124	—	2	1	no	—
339	#124	—	2	2	no	—
340	#124	C₂×C₄×C₅	1	2	yes	—
341	#123	—	2	2	no	—
342	#123	—	2	2	no	—
343	#123	—	2	2	no	—
344	#123	—	2	2	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	2	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	2	no	—
350	C₂²⋊Q₈	—	2	2	no	—
351	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
352	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
353	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
354	#121	—	2	2	no	—
355	#121	—	2	1	no	—
356	#121	C₂×C₄×C₅	1	2	yes	—
357	C₄×Q₈	—	2	1	no	—
358	C₄×Q₈	—	2	1	no	—
359	C₄×Q₈	—	2	2	no	—
360	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
361	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
362	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
363	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
364	C₄×Q₈	C₂³×C₅	1	2	yes	—
365	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
370	C₄×D₄	C₅×D₄	1	2	yes	—
371	C₄×D₄	C₅×D₄	1	1	yes	characteristic
372	C₄×D₄	C₅×D₄	1	2	yes	—
373	C₄×D₄	C₅×D₄	1	1	yes	characteristic
374	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
375	#117	—	2	2	no	—
376	#117	—	2	1	no	—
377	#117	—	2	2	no	—
378	#117	C₂×C₄×C₅	1	1	yes	characteristic
379	#117	C₂×C₄×C₅	1	1	yes	characteristic
380	#117	C₂×C₄×C₅	1	2	yes	—
381	C₂×C₄⋊C₄	—	2	1	no	—
382	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂×C₄²	—	2	1	no	—
384	C₂×C₄²	—	2	1	no	—
385	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₅	1	2	yes	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	—	2	1	no	—
390	C₄⋊C₈	—	2	2	no	—
391	C₄⋊C₈	C₂³×C₅	1	2	yes	—
392	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
393	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
394	C₂²⋊C₈	—	2	1	no	—
395	C₂²⋊C₈	—	2	2	no	—
396	C₂²⋊C₈	—	2	1	no	—
397	C₂²⋊C₈	—	2	2	no	—
398	#97	—	2	2	no	—
399	C₄×C₈	—	2	1	no	—
400	C₄×C₈	—	2	2	no	—
401	C₄×C₈	—	2	1	no	—
402	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
403	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
404	C₄×C₈	C₂³×C₅	1	2	yes	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	2	2	no	—
408	C₂²×C₅	—	2	2	no	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	4	1	no	—
411	C₂²×C₅	—	4	1	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	#408	1	2	yes	—
414	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
415	C₄×C₅	—	2	2	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	4	1	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	1	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	—	4	1	no	—
426	C₄×C₅	#408	1	2	yes	—
427	C₄×C₅	C₂×#131	1	2	yes	—
428	C₄×C₅	#577	1	1	yes	characteristic
429	C₄×C₅	#578	1	1	yes	characteristic
430	#41	—	2	4	no	—
431	#41	—	2	4	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	4	no	—
435	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
436	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
437	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
441	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
442	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
449	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
452	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
454	M₁₆	—	8	2	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	4	4	no	—
463	C₂×C₈	—	8	1	no	—
464	C₄⋊C₄	—	2	2	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	2	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
478	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
479	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
480	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
481	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
482	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
483	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
494	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
495	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	2	no	—
500	C₄²	—	2	1	no	—
501	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₄²	C₂²×C₄×C₅	1	2	yes	—
503	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
504	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
505	C₄²	C₂×C₅×D₄	1	2	yes	—
506	C₄²	C₂×C₅×D₄	1	2	yes	—
507	C₄²	C₂⁴×C₅	1	1	yes	characteristic
508	C₂×C₅	—	2	2	no	—
509	C₂×C₅	—	4	2	no	—
510	C₂×C₅	—	8	1	no	—
511	C₂×C₅	C₂×#408	1	1	yes	characteristic
512	C₂×C₅	#2898	1	1	yes	characteristic
513	C₂×C₅	#2901	1	1	yes	characteristic
514	C₂³	—	2	1	no	—
515	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
516	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	4	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	8	2	no	—
522	D₄	—	2	4	no	—
523	D₄	—	2	2	no	—
524	D₄	—	2	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	8	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	4	1	no	—
538	C₂×C₄	—	4	2	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	8	1	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
546	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
547	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
548	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
549	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
550	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
551	C₂×C₄	C₅×#131	1	4	yes	—
552	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
553	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	4	1	no	—
557	C₈	—	4	2	no	—
558	C₈	—	4	2	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₅	#17484	1	1	yes	characteristic, direct product factor, Sylow
562	C₂²	—	2	1	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	C₅×#408	1	2	yes	—
571	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
572	C₄	—	2	2	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	2	no	—
575	C₄	—	2	1	no	—
576	C₄	—	2	1	no	—
577	C₄	—	2	2	no	—
578	C₄	—	4	1	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	1	no	—
583	C₄	C₅×#408	1	2	yes	—
584	C₄	C₂×C₅×#131	1	2	yes	—
585	C₄	C₅×#577	1	1	yes	characteristic
586	C₄	C₅×#578	1	1	yes	characteristic
587	C₂	—	2	2	no	—
588	C₂	—	4	2	no	—
589	C₂	—	8	1	no	—
590	C₂	C₂×C₅×#408	1	1	yes	characteristic
591	C₂	C₅×#2898	1	1	yes	characteristic
592	C₂	C₅×#2901	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₅×#537	C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2989	C₂	semidirect
3. C₅×C₈×#41	C₂	semidirect
4. C₅×#1497	C₂	semidirect
5. C₅×#1495	C₂	semidirect
6. C₅×#1494	C₂	semidirect
7. C₅×#1493	C₂	semidirect
8. C₅×#1479	C₂	semidirect
9. C₅×#1477	C₂	semidirect
10. C₅×#1476	C₂	semidirect
11. C₂×C₅×Q₈⋊C₈	C₂	semidirect
53. #17484	C₅	direct (N × H)
142. #2989	C₂×C₅	semidirect
143. C₈×#41	C₂×C₅	semidirect
144. #1497	C₂×C₅	semidirect
145. #1495	C₂×C₅	semidirect
146. #1494	C₂×C₅	semidirect
147. #1493	C₂×C₅	semidirect
148. #1479	C₂×C₅	semidirect
149. #1477	C₂×C₅	semidirect
150. #1476	C₂×C₅	semidirect
151. C₂×Q₈⋊C₈	C₂×C₅	semidirect
561. C₅	#17484	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3461	2
C₅×#2989	2
C₅×C₈×#41	2
C₅×#1497	2
C₅×#1495	2
C₅×#1494	2
C₅×#1493	2
C₅×#1479	2
C₅×#1477	2
C₅×#1476	2
C₂×C₅×Q₈⋊C₈	2
#17484	5

Subgroups — C5×#17484 #11940204

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17484 #11940204