Subgroups — C₅×#17525 #11940245

Order 1280.

934 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3482	C₂	1	1	yes	maximal, characteristic
2	C₅×#2991	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2922	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1495	C₂	1	2	yes	maximal, complemented
5	C₅×#1493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1489	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1487	C₂	1	2	yes	maximal, complemented
8	C₅×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1482	C₂	1	2	yes	maximal, complemented
10	C₅×#1479	C₂	1	2	yes	maximal, complemented
11	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#557	C₄	1	1	yes	characteristic
13	C₅×#556	—	2	1	no	—
14	C₅×#556	C₄	1	1	yes	characteristic
15	C₅×#552	—	2	2	no	—
16	C₅×#552	C₄	1	2	yes	—
17	C₅×D₄×Q₈	C₄	1	1	yes	characteristic
18	C₅×#548	C₄	1	2	yes	—
19	C₅×#547	—	2	1	no	—
20	C₅×#547	C₄	1	1	yes	characteristic
21	C₅×#533	—	2	1	no	—
22	C₅×#533	C₂²	1	1	yes	characteristic
23	C₅×#529	—	2	2	no	—
24	C₅×#529	C₂²	1	2	yes	—
25	C₄×C₅×#41	—	2	1	no	—
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	2	yes	—
29	C₅×C₈×Q₈	—	2	1	no	—
30	C₅×#436	—	2	1	no	—
31	C₅×#436	—	2	2	no	—
32	C₅×#433	—	2	2	no	—
33	C₅×#431	C₂²	1	1	yes	characteristic
34	C₅×#431	C₂²	1	2	yes	—
35	C₅×#431	C₂²	1	2	yes	—
36	C₅×#431	C₂²	1	2	yes	—
37	C₅×#424	—	2	1	no	—
38	C₅×#423	C₂²	1	2	yes	—
39	C₅×#423	C₂²	1	1	yes	characteristic
40	C₅×#408	—	2	1	no	—
41	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
44	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
45	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
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	#17525	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₅×#41	—	2	1	no	—
55	C₂×C₅×#41	C₂×C₄	1	1	yes	characteristic
56	C₂×C₅×#41	D₄	1	1	yes	characteristic
57	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂²×C₅×C₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
65	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
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	2	no	—
71	C₅×#125	—	2	1	no	—
72	C₅×#125	C₂×C₄	1	2	yes	—
73	C₅×#124	—	2	2	no	—
74	C₅×#124	C₂×C₄	1	2	yes	—
75	C₅×#123	—	2	2	no	—
76	C₅×#123	—	2	2	no	—
77	C₅×#123	—	2	2	no	—
78	C₅×C₂²⋊Q₈	—	2	1	no	—
79	C₅×C₂²⋊Q₈	—	2	1	no	—
80	C₅×C₂²⋊Q₈	—	2	1	no	—
81	C₅×C₂²⋊Q₈	—	2	2	no	—
82	C₅×C₂²⋊Q₈	—	2	2	no	—
83	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
84	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
85	C₅×#121	—	2	2	no	—
86	C₅×#121	C₂×C₄	1	2	yes	—
87	C₄×C₅×Q₈	—	2	1	no	—
88	C₄×C₅×Q₈	—	2	2	no	—
89	C₄×C₅×Q₈	—	2	2	no	—
90	C₄×C₅×Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
92	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
93	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
96	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×Q₈	C₂³	1	2	yes	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	2	no	—
100	C₄×C₅×D₄	—	2	1	no	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	2	no	—
103	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
104	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
105	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
106	C₄×C₅×D₄	D₄	1	1	yes	characteristic
107	C₄×C₅×D₄	D₄	1	2	yes	—
108	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
109	C₅×#117	—	2	1	no	—
110	C₅×#117	—	2	1	no	—
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	D₄	1	1	yes	characteristic
116	C₅×#117	D₄	1	2	yes	—
117	C₂×C₅×C₄⋊C₄	—	2	2	no	—
118	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
119	C₂×C₄²×C₅	—	2	2	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	2	no	—
126	C₅×C₄⋊C₈	—	2	2	no	—
127	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
128	C₅×C₄⋊C₈	C₂³	1	2	yes	—
129	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
130	C₅×C₂²⋊C₈	—	2	2	no	—
131	C₅×C₂²⋊C₈	—	2	2	no	—
132	C₅×C₂²⋊C₈	—	2	2	no	—
133	C₅×C₂²⋊C₈	—	2	1	no	—
134	C₅×#97	—	2	1	no	—
135	C₄×C₅×C₈	—	2	1	no	—
136	C₄×C₅×C₈	—	2	1	no	—
137	C₄×C₅×C₈	—	2	2	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	#3482	C₂×C₅	1	1	yes	characteristic
142	#2991	C₂×C₅	1	1	yes	characteristic, complemented
143	#2922	C₂×C₅	1	1	yes	characteristic, complemented
144	#1495	C₂×C₅	1	2	yes	complemented
145	#1493	C₂×C₅	1	1	yes	characteristic, complemented
146	#1489	C₂×C₅	1	1	yes	characteristic, complemented
147	#1487	C₂×C₅	1	2	yes	complemented
148	#1485	C₂×C₅	1	1	yes	characteristic, complemented
149	#1482	C₂×C₅	1	2	yes	complemented
150	#1479	C₂×C₅	1	2	yes	complemented
151	#1476	C₂×C₅	1	1	yes	characteristic, complemented
152	C₅×#41	—	2	2	no	—
153	C₅×#41	—	4	1	no	—
154	C₅×#41	—	4	2	no	—
155	C₅×#41	—	4	4	no	—
156	C₂×C₅×Q₈	—	2	2	no	—
157	C₂×C₅×Q₈	—	2	1	no	—
158	C₂×C₅×Q₈	—	2	4	no	—
159	C₂×C₅×Q₈	—	4	2	no	—
160	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
162	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	2	2	no	—
165	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
166	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
167	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	—	2	2	no	—
169	C₂²×C₄×C₅	—	2	2	no	—
170	C₂²×C₄×C₅	—	2	1	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
174	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
179	C₅×M₁₆	—	4	2	no	—
180	C₅×M₁₆	—	8	2	no	—
181	C₅×M₁₆	—	8	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	2	no	—
185	C₂×C₅×C₈	—	2	1	no	—
186	C₂×C₅×C₈	—	2	2	no	—
187	C₂×C₅×C₈	—	2	1	no	—
188	C₂×C₅×C₈	—	4	2	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	1	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	1	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	1	no	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
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	2	yes	—
206	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
208	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
209	C₅×C₂²⋊C₄	—	2	2	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	2	1	no	—
212	C₅×C₂²⋊C₄	—	2	2	no	—
213	C₅×C₂²⋊C₄	—	2	1	no	—
214	C₅×C₂²⋊C₄	—	2	2	no	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
218	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
219	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	2	no	—
222	C₄²×C₅	—	2	1	no	—
223	C₄²×C₅	—	2	2	no	—
224	C₄²×C₅	—	2	1	no	—
225	C₄²×C₅	—	2	2	no	—
226	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
227	C₄²×C₅	C₂²×C₄	1	2	yes	—
228	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₅	C₂×D₄	1	2	yes	—
230	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₅	C₂×D₄	1	2	yes	—
232	C₄²×C₅	C₂⁴	1	1	yes	characteristic
233	#557	C₄×C₅	1	1	yes	characteristic
234	#556	—	2	1	no	—
235	#556	C₄×C₅	1	1	yes	characteristic
236	#552	—	2	2	no	—
237	#552	C₄×C₅	1	2	yes	—
238	D₄×Q₈	C₄×C₅	1	1	yes	characteristic
239	#548	C₄×C₅	1	2	yes	—
240	#547	—	2	1	no	—
241	#547	C₄×C₅	1	1	yes	characteristic
242	#533	—	2	1	no	—
243	#533	C₂²×C₅	1	1	yes	characteristic
244	#529	—	2	2	no	—
245	#529	C₂²×C₅	1	2	yes	—
246	C₄×#41	—	2	1	no	—
247	C₄×#41	C₂²×C₅	1	1	yes	characteristic
248	C₄×#41	C₂²×C₅	1	1	yes	characteristic
249	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
250	C₈×Q₈	—	2	1	no	—
251	#436	—	2	1	no	—
252	#436	—	2	2	no	—
253	#433	—	2	2	no	—
254	#431	C₂²×C₅	1	1	yes	characteristic
255	#431	C₂²×C₅	1	2	yes	—
256	#431	C₂²×C₅	1	2	yes	—
257	#431	C₂²×C₅	1	2	yes	—
258	#424	—	2	1	no	—
259	#423	C₂²×C₅	1	2	yes	—
260	#423	C₂²×C₅	1	1	yes	characteristic
261	#408	—	2	1	no	—
262	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
263	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
264	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
267	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
268	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
269	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
270	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
271	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
273	D₄⋊C₈	C₂²×C₅	1	2	yes	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
277	C₅×Q₈	—	2	1	no	—
278	C₅×Q₈	—	2	2	no	—
279	C₅×Q₈	—	2	2	no	—
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	—	4	4	no	—
282	C₅×Q₈	—	4	2	no	—
283	C₅×Q₈	#131	1	2	yes	—
284	C₅×D₄	—	2	1	no	—
285	C₅×D₄	—	2	1	no	—
286	C₅×D₄	—	2	2	no	—
287	C₅×D₄	—	4	2	no	—
288	C₅×D₄	—	4	2	no	—
289	C₅×D₄	—	4	4	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	4	2	no	—
305	C₂×C₄×C₅	—	4	2	no	—
306	C₂×C₄×C₅	—	4	4	no	—
307	C₂×C₄×C₅	—	4	4	no	—
308	C₂×C₄×C₅	—	4	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
312	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
315	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
320	C₅×C₈	—	4	1	no	—
321	C₅×C₈	—	4	1	no	—
322	C₅×C₈	—	4	2	no	—
323	C₅×C₈	—	4	1	no	—
324	C₅×C₈	—	4	2	no	—
325	C₅×C₈	—	4	1	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
328	C₂×#41	C₅×D₄	1	1	yes	characteristic
329	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₄⋊Q₈	—	2	1	no	—
335	C₄⋊Q₈	—	2	1	no	—
336	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
337	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
338	#126	—	2	2	no	—
339	#126	—	2	2	no	—
340	#126	—	2	2	no	—
341	#125	—	2	2	no	—
342	#125	—	2	2	no	—
343	#125	—	2	1	no	—
344	#125	C₂×C₄×C₅	1	2	yes	—
345	#124	—	2	2	no	—
346	#124	C₂×C₄×C₅	1	2	yes	—
347	#123	—	2	2	no	—
348	#123	—	2	2	no	—
349	#123	—	2	2	no	—
350	C₂²⋊Q₈	—	2	1	no	—
351	C₂²⋊Q₈	—	2	1	no	—
352	C₂²⋊Q₈	—	2	1	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	—	2	2	no	—
355	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
356	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
357	#121	—	2	2	no	—
358	#121	C₂×C₄×C₅	1	2	yes	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	2	no	—
361	C₄×Q₈	—	2	2	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
364	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
365	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
366	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
367	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
368	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₅	1	2	yes	—
370	C₄×D₄	—	2	1	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
376	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
377	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
378	C₄×D₄	C₅×D₄	1	1	yes	characteristic
379	C₄×D₄	C₅×D₄	1	2	yes	—
380	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
381	#117	—	2	1	no	—
382	#117	—	2	1	no	—
383	#117	—	2	2	no	—
384	#117	—	2	1	no	—
385	#117	—	2	2	no	—
386	#117	C₂×C₄×C₅	1	1	yes	characteristic
387	#117	C₅×D₄	1	2	yes	—
388	#117	C₅×D₄	1	1	yes	characteristic
389	C₂×C₄⋊C₄	—	2	2	no	—
390	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	—	2	1	no	—
393	C₂×C₄²	C₂³×C₅	1	2	yes	—
394	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	2	no	—
397	C₄⋊C₈	—	2	2	no	—
398	C₄⋊C₈	—	2	2	no	—
399	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
400	C₄⋊C₈	C₂³×C₅	1	2	yes	—
401	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
402	C₂²⋊C₈	—	2	2	no	—
403	C₂²⋊C₈	—	2	2	no	—
404	C₂²⋊C₈	—	2	2	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	#97	—	2	1	no	—
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	—	2	2	no	—
410	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
412	C₄×C₈	C₂³×C₅	1	2	yes	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	4	1	no	—
420	C₂²×C₅	—	4	1	no	—
421	C₂²×C₅	—	4	1	no	—
422	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
423	C₄×C₅	—	2	1	no	—
424	C₄×C₅	—	2	2	no	—
425	C₄×C₅	—	2	2	no	—
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	4	2	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	—	4	1	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	#421	1	2	yes	—
435	C₄×C₅	C₂×#131	1	1	yes	characteristic
436	C₄×C₅	#568	1	1	yes	characteristic
437	C₄×C₅	#577	1	1	yes	characteristic
438	C₄×C₅	#578	1	1	yes	characteristic
439	#41	—	2	2	no	—
440	#41	—	4	1	no	—
441	#41	—	4	2	no	—
442	#41	—	4	4	no	—
443	C₂×Q₈	—	2	2	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	4	no	—
446	C₂×Q₈	—	4	2	no	—
447	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
448	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
449	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
450	C₂×D₄	—	2	1	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
453	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
454	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
461	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
466	M₁₆	—	4	2	no	—
467	M₁₆	—	8	2	no	—
468	M₁₆	—	8	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	4	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	2	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
490	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
491	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
492	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
493	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
495	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
496	C₂²⋊C₄	—	2	2	no	—
497	C₂²⋊C₄	—	2	2	no	—
498	C₂²⋊C₄	—	2	1	no	—
499	C₂²⋊C₄	—	2	2	no	—
500	C₂²⋊C₄	—	2	1	no	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
505	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
506	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
507	C₄²	—	2	1	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	1	no	—
512	C₄²	—	2	2	no	—
513	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
514	C₄²	C₂²×C₄×C₅	1	2	yes	—
515	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
516	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
517	C₄²	C₂×C₅×D₄	1	2	yes	—
518	C₄²	C₂×C₅×D₄	1	2	yes	—
519	C₄²	C₂⁴×C₅	1	1	yes	characteristic
520	C₂×C₅	—	4	2	no	—
521	C₂×C₅	—	4	1	no	—
522	C₂×C₅	—	8	1	no	—
523	C₂×C₅	#2880	1	1	yes	characteristic
524	C₂×C₅	#2898	1	1	yes	characteristic
525	C₂×C₅	C₂×#421	1	1	yes	characteristic
526	C₂³	—	2	1	no	—
527	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
528	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
529	Q₈	—	2	2	no	—
530	Q₈	—	2	1	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	2	2	no	—
533	Q₈	—	4	4	no	—
534	Q₈	—	4	2	no	—
535	Q₈	C₅×#131	1	2	yes	—
536	D₄	—	2	2	no	—
537	D₄	—	2	1	no	—
538	D₄	—	2	1	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	2	no	—
541	D₄	—	4	4	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	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	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	1	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
564	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
567	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
568	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
570	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
571	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	2	no	—
575	C₈	—	4	1	no	—
576	C₈	—	4	2	no	—
577	C₈	—	4	1	no	—
578	C₅	#17525	1	1	yes	characteristic, direct product factor, Sylow
579	C₂²	—	2	2	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	2	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	4	1	no	—
588	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
589	C₄	—	2	1	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	2	2	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	2	no	—
596	C₄	—	4	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	C₅×#421	1	2	yes	—
601	C₄	C₂×C₅×#131	1	1	yes	characteristic
602	C₄	C₅×#568	1	1	yes	characteristic
603	C₄	C₅×#577	1	1	yes	characteristic
604	C₄	C₅×#578	1	1	yes	characteristic
605	C₂	—	4	2	no	—
606	C₂	—	4	1	no	—
607	C₂	—	8	1	no	—
608	C₂	C₅×#2880	1	1	yes	characteristic
609	C₂	C₅×#2898	1	1	yes	characteristic
610	C₂	C₂×C₅×#421	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×#3482	C₂
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×#2991	C₂	semidirect
3. C₅×#2922	C₂	semidirect
4. C₅×#1495	C₂	semidirect
5. C₅×#1493	C₂	semidirect
6. C₅×#1489	C₂	semidirect
7. C₅×#1487	C₂	semidirect
8. C₅×#1485	C₂	semidirect
9. C₅×#1482	C₂	semidirect
10. C₅×#1479	C₂	semidirect
11. C₅×#1476	C₂	semidirect
53. #17525	C₅	direct (N × H)
142. #2991	C₂×C₅	semidirect
143. #2922	C₂×C₅	semidirect
144. #1495	C₂×C₅	semidirect
145. #1493	C₂×C₅	semidirect
146. #1489	C₂×C₅	semidirect
147. #1487	C₂×C₅	semidirect
148. #1485	C₂×C₅	semidirect
149. #1482	C₂×C₅	semidirect
150. #1479	C₂×C₅	semidirect
151. #1476	C₂×C₅	semidirect
578. C₅	#17525	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×#3482	2
C₅×#2991	2
C₅×#2922	2
C₅×#1495	2
C₅×#1493	2
C₅×#1489	2
C₅×#1487	2
C₅×#1485	2
C₅×#1482	2
C₅×#1479	2
C₅×#1476	2
#17525	5

Subgroups — C5×#17525 #11940245

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17525 #11940245