Subgroups — C₅×#17519 #11940239

Order 1280.

1022 conjugacy classes of subgroups.

The subgroup lattice has 618 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×#2990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1494	C₂	1	2	yes	maximal, complemented
5	C₅×#1493	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1491	C₂	1	2	yes	maximal, complemented
7	C₅×#1489	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1485	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1483	C₂	1	2	yes	maximal, complemented
10	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₅×Q₈⋊C₈	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#131	—	2	1	no	—
13	C₅×#557	C₄	1	1	yes	characteristic
14	C₅×#556	—	2	1	no	—
15	C₅×#556	C₄	1	1	yes	characteristic
16	C₅×#552	—	2	2	no	—
17	C₅×#552	C₄	1	2	yes	—
18	C₅×D₄×Q₈	C₄	1	1	yes	characteristic
19	C₅×#548	C₄	1	2	yes	—
20	C₅×#547	—	2	1	no	—
21	C₅×#547	C₄	1	1	yes	characteristic
22	C₅×#533	—	2	1	no	—
23	C₅×#533	C₂²	1	1	yes	characteristic
24	C₅×#529	—	2	2	no	—
25	C₅×#529	C₂²	1	2	yes	—
26	C₄×C₅×#41	—	2	1	no	—
27	C₄×C₅×#41	C₂²	1	1	yes	characteristic
28	C₄×C₅×#41	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
30	C₅×#446	—	2	1	no	—
31	C₅×#435	—	2	2	no	—
32	C₅×C₈×D₄	—	2	1	no	—
33	C₅×#432	C₂²	1	2	yes	—
34	C₅×#431	C₂²	1	1	yes	characteristic
35	C₅×#423	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
37	C₅×#405	—	2	2	no	—
38	C₅×#405	—	2	1	no	—
39	C₄×C₅×M₁₆	C₂²	1	2	yes	—
40	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
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	2	yes	—
45	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
46	C₅×Q₈⋊C₈	C₂²	1	2	yes	—
47	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
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	#17519	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	C₅×#131	—	2	8	no	—
59	C₂×C₅×M₁₆	—	2	2	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂²×C₅×C₈	—	2	2	no	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	2	no	—
65	C₅×C₄⋊Q₈	—	2	1	no	—
66	C₅×C₄⋊Q₈	—	2	1	no	—
67	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
68	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
69	C₅×#126	—	2	2	no	—
70	C₅×#126	—	2	2	no	—
71	C₅×#126	—	2	2	no	—
72	C₅×#125	—	2	2	no	—
73	C₅×#125	—	2	2	no	—
74	C₅×#125	—	2	1	no	—
75	C₅×#125	C₂×C₄	1	2	yes	—
76	C₅×#124	—	2	2	no	—
77	C₅×#124	C₂×C₄	1	2	yes	—
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	1	no	—
83	C₅×C₂²⋊Q₈	—	2	1	no	—
84	C₅×C₂²⋊Q₈	—	2	2	no	—
85	C₅×C₂²⋊Q₈	—	2	2	no	—
86	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
87	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
88	C₅×#121	—	2	2	no	—
89	C₅×#121	C₂×C₄	1	2	yes	—
90	C₄×C₅×Q₈	—	2	1	no	—
91	C₄×C₅×Q₈	—	2	2	no	—
92	C₄×C₅×Q₈	—	2	2	no	—
93	C₄×C₅×Q₈	—	2	1	no	—
94	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
95	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
96	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
98	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
99	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂³	1	2	yes	—
101	C₄×C₅×D₄	—	2	1	no	—
102	C₄×C₅×D₄	—	2	2	no	—
103	C₄×C₅×D₄	—	2	1	no	—
104	C₄×C₅×D₄	—	2	1	no	—
105	C₄×C₅×D₄	—	2	2	no	—
106	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
107	C₄×C₅×D₄	C₂×C₄	1	1	yes	characteristic
108	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
109	C₄×C₅×D₄	D₄	1	1	yes	characteristic
110	C₄×C₅×D₄	D₄	1	2	yes	—
111	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
112	C₅×#117	—	2	1	no	—
113	C₅×#117	—	2	1	no	—
114	C₅×#117	—	2	2	no	—
115	C₅×#117	—	2	1	no	—
116	C₅×#117	—	2	2	no	—
117	C₅×#117	C₂×C₄	1	1	yes	characteristic
118	C₅×#117	D₄	1	2	yes	—
119	C₅×#117	D₄	1	1	yes	characteristic
120	C₂×C₅×C₄⋊C₄	—	2	2	no	—
121	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
122	C₂×C₄²×C₅	—	2	2	no	—
123	C₂×C₄²×C₅	—	2	1	no	—
124	C₂×C₄²×C₅	C₂³	1	2	yes	—
125	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
126	C₅×C₄⋊C₈	—	2	2	no	—
127	C₅×C₄⋊C₈	—	2	1	no	—
128	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
129	C₅×C₄⋊C₈	C₂³	1	2	yes	—
130	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
131	C₅×C₂²⋊C₈	—	2	1	no	—
132	C₅×C₂²⋊C₈	—	2	2	no	—
133	C₅×#97	—	2	1	no	—
134	C₅×#97	—	2	2	no	—
135	C₅×#97	—	2	2	no	—
136	C₄×C₅×C₈	—	2	1	no	—
137	C₄×C₅×C₈	—	2	2	no	—
138	C₄×C₅×C₈	—	2	1	no	—
139	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
140	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
141	C₄×C₅×C₈	C₂³	1	2	yes	—
142	#3482	C₂×C₅	1	1	yes	characteristic
143	#2990	C₂×C₅	1	1	yes	characteristic, complemented
144	C₄×#131	C₂×C₅	1	1	yes	characteristic, complemented
145	#1494	C₂×C₅	1	2	yes	complemented
146	#1493	C₂×C₅	1	1	yes	characteristic, complemented
147	#1491	C₂×C₅	1	2	yes	complemented
148	#1489	C₂×C₅	1	1	yes	characteristic, complemented
149	#1485	C₂×C₅	1	1	yes	characteristic, complemented
150	#1483	C₂×C₅	1	2	yes	complemented
151	#1476	C₂×C₅	1	1	yes	characteristic, complemented
152	C₂×Q₈⋊C₈	C₂×C₅	1	2	yes	complemented
153	C₅×#41	—	2	4	no	—
154	C₅×#41	—	2	2	no	—
155	C₅×#41	—	4	1	no	—
156	C₅×#41	—	4	4	no	—
157	C₂×C₅×Q₈	—	2	2	no	—
158	C₂×C₅×Q₈	—	2	1	no	—
159	C₂×C₅×Q₈	—	2	4	no	—
160	C₂×C₅×Q₈	—	4	2	no	—
161	C₂×C₅×Q₈	C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
163	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₅×D₄	—	2	1	no	—
165	C₂×C₅×D₄	—	2	2	no	—
166	C₂×C₅×D₄	C₂²⋊C₄	1	2	yes	—
167	C₂×C₅×D₄	C₂²⋊C₄	1	1	yes	characteristic
168	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	—	2	2	no	—
170	C₂²×C₄×C₅	—	2	2	no	—
171	C₂²×C₄×C₅	—	2	1	no	—
172	C₂²×C₄×C₅	—	2	1	no	—
173	C₂²×C₄×C₅	—	2	1	no	—
174	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
175	C₂²×C₄×C₅	C₂²×C₄	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	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₅×M₁₆	—	2	8	no	—
181	C₅×M₁₆	—	2	4	no	—
182	C₅×M₁₆	—	8	1	no	—
183	C₂×C₅×C₈	—	2	8	no	—
184	C₂×C₅×C₈	—	2	4	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	—	2	1	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	—	2	1	no	—
191	C₂×C₅×C₈	—	8	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	1	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	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	2	no	—
201	C₅×C₄⋊C₄	—	2	1	no	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	2	no	—
205	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
206	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
207	C₅×C₄⋊C₄	C₂²⋊C₄	1	1	yes	characteristic
208	C₅×C₄⋊C₄	C₂²⋊C₄	1	2	yes	—
209	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
210	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
211	C₅×C₄⋊C₄	C₂²×C₄	1	1	yes	characteristic
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	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
221	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
222	C₅×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
223	C₄²×C₅	—	2	1	no	—
224	C₄²×C₅	—	2	2	no	—
225	C₄²×C₅	—	2	1	no	—
226	C₄²×C₅	—	2	2	no	—
227	C₄²×C₅	—	2	1	no	—
228	C₄²×C₅	—	2	2	no	—
229	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
230	C₄²×C₅	C₂²×C₄	1	2	yes	—
231	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
232	C₄²×C₅	C₂×D₄	1	2	yes	—
233	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₅	C₂×D₄	1	2	yes	—
235	C₄²×C₅	C₂⁴	1	1	yes	characteristic
236	C₂×#131	—	2	1	no	—
237	#557	C₄×C₅	1	1	yes	characteristic
238	#556	—	2	1	no	—
239	#556	C₄×C₅	1	1	yes	characteristic
240	#552	—	2	2	no	—
241	#552	C₄×C₅	1	2	yes	—
242	D₄×Q₈	C₄×C₅	1	1	yes	characteristic
243	#548	C₄×C₅	1	2	yes	—
244	#547	—	2	1	no	—
245	#547	C₄×C₅	1	1	yes	characteristic
246	#533	—	2	1	no	—
247	#533	C₂²×C₅	1	1	yes	characteristic
248	#529	—	2	2	no	—
249	#529	C₂²×C₅	1	2	yes	—
250	C₄×#41	—	2	1	no	—
251	C₄×#41	C₂²×C₅	1	1	yes	characteristic
252	C₄×#41	C₂²×C₅	1	1	yes	characteristic
253	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
254	#446	—	2	1	no	—
255	#435	—	2	2	no	—
256	C₈×D₄	—	2	1	no	—
257	#432	C₂²×C₅	1	2	yes	—
258	#431	C₂²×C₅	1	1	yes	characteristic
259	#423	C₂²×C₅	1	1	yes	characteristic
260	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
261	#405	—	2	2	no	—
262	#405	—	2	1	no	—
263	C₄×M₁₆	C₂²×C₅	1	2	yes	—
264	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
265	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
266	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
267	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
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	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
272	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
273	Q₈⋊C₈	C₂²×C₅	1	2	yes	—
274	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
275	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	D₄⋊C₈	C₂²×C₅	1	2	yes	—
277	C₂³×C₅	—	2	1	no	—
278	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₅	C₂×C₂²⋊C₄	1	2	yes	—
280	C₅×Q₈	—	2	1	no	—
281	C₅×Q₈	—	2	2	no	—
282	C₅×Q₈	—	2	2	no	—
283	C₅×Q₈	—	2	2	no	—
284	C₅×Q₈	—	4	4	no	—
285	C₅×Q₈	—	4	2	no	—
286	C₅×Q₈	#131	1	2	yes	complemented
287	C₅×D₄	—	2	4	no	—
288	C₅×D₄	—	2	1	no	—
289	C₅×D₄	—	2	1	no	—
290	C₅×D₄	—	4	2	no	—
291	C₅×D₄	—	4	4	no	—
292	C₅×D₄	#104	1	4	yes	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	4	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	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	4	2	no	—
309	C₂×C₄×C₅	—	4	4	no	—
310	C₂×C₄×C₅	—	4	4	no	—
311	C₂×C₄×C₅	—	4	1	no	—
312	C₂×C₄×C₅	—	4	1	no	—
313	C₂×C₄×C₅	—	4	2	no	—
314	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
315	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
318	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
319	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
322	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
323	C₅×C₈	—	2	2	no	—
324	C₅×C₈	—	2	4	no	—
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	4	1	no	—
327	C₅×C₈	—	4	2	no	—
328	C₅×C₈	—	4	1	no	—
329	C₂×#41	—	2	1	no	—
330	C₂×#41	C₂×C₄×C₅	1	1	yes	characteristic
331	C₂×#41	C₅×D₄	1	1	yes	characteristic
332	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
333	#131	—	2	8	no	—
334	C₂×M₁₆	—	2	2	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂²×C₈	—	2	2	no	—
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	2	2	no	—
340	C₄⋊Q₈	—	2	1	no	—
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
343	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
344	#126	—	2	2	no	—
345	#126	—	2	2	no	—
346	#126	—	2	2	no	—
347	#125	—	2	2	no	—
348	#125	—	2	2	no	—
349	#125	—	2	1	no	—
350	#125	C₂×C₄×C₅	1	2	yes	—
351	#124	—	2	2	no	—
352	#124	C₂×C₄×C₅	1	2	yes	—
353	#123	—	2	2	no	—
354	#123	—	2	2	no	—
355	#123	—	2	2	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	1	no	—
358	C₂²⋊Q₈	—	2	1	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	2	no	—
361	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
362	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
363	#121	—	2	2	no	—
364	#121	C₂×C₄×C₅	1	2	yes	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	1	no	—
369	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
370	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
371	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
372	C₄×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
373	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
374	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₅	1	2	yes	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
382	C₄×D₄	C₂×C₄×C₅	1	1	yes	characteristic
383	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
384	C₄×D₄	C₅×D₄	1	1	yes	characteristic
385	C₄×D₄	C₅×D₄	1	2	yes	—
386	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
387	#117	—	2	1	no	—
388	#117	—	2	1	no	—
389	#117	—	2	2	no	—
390	#117	—	2	1	no	—
391	#117	—	2	2	no	—
392	#117	C₂×C₄×C₅	1	1	yes	characteristic
393	#117	C₅×D₄	1	2	yes	—
394	#117	C₅×D₄	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	2	2	no	—
396	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
397	C₂×C₄²	—	2	2	no	—
398	C₂×C₄²	—	2	1	no	—
399	C₂×C₄²	C₂³×C₅	1	2	yes	—
400	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
401	C₄⋊C₈	—	2	2	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₅	1	2	yes	—
405	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
406	C₂²⋊C₈	—	2	1	no	—
407	C₂²⋊C₈	—	2	2	no	—
408	#97	—	2	1	no	—
409	#97	—	2	2	no	—
410	#97	—	2	2	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	—	2	2	no	—
413	C₄×C₈	—	2	1	no	—
414	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
416	C₄×C₈	C₂³×C₅	1	2	yes	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	—	2	2	no	—
419	C₂²×C₅	—	2	1	no	—
420	C₂²×C₅	—	2	1	no	—
421	C₂²×C₅	—	2	1	no	—
422	C₂²×C₅	—	4	1	no	—
423	C₂²×C₅	—	4	1	no	—
424	C₂²×C₅	—	4	1	no	—
425	C₂²×C₅	C₂×#104	1	4	yes	—
426	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	2	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	—	4	1	no	—
436	C₄×C₅	—	4	1	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	C₂×#104	1	2	yes	—
439	C₄×C₅	C₂×#131	1	1	yes	characteristic
440	C₄×C₅	#568	1	1	yes	characteristic
441	C₄×C₅	#577	1	1	yes	characteristic
442	C₄×C₅	#578	1	1	yes	characteristic
443	#41	—	2	4	no	—
444	#41	—	2	2	no	—
445	#41	—	4	1	no	—
446	#41	—	4	4	no	—
447	C₂×Q₈	—	2	2	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	2	4	no	—
450	C₂×Q₈	—	4	2	no	—
451	C₂×Q₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
452	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
453	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	C₅×C₂²⋊C₄	1	2	yes	—
457	C₂×D₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
458	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	1	no	—
462	C₂²×C₄	—	2	1	no	—
463	C₂²×C₄	—	2	1	no	—
464	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
465	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
467	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
469	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	M₁₆	—	2	8	no	—
471	M₁₆	—	2	4	no	—
472	M₁₆	—	8	1	no	—
473	C₂×C₈	—	2	8	no	—
474	C₂×C₈	—	2	4	no	—
475	C₂×C₈	—	2	1	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	2	no	—
481	C₂×C₈	—	8	2	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	1	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
496	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
497	C₄⋊C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
498	C₄⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
499	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
501	C₄⋊C₄	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	1	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	1	no	—
510	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
511	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
512	C₂²⋊C₄	C₅×C₂²⋊C₄	1	2	yes	—
513	C₄²	—	2	1	no	—
514	C₄²	—	2	2	no	—
515	C₄²	—	2	1	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	1	no	—
518	C₄²	—	2	2	no	—
519	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
520	C₄²	C₂²×C₄×C₅	1	2	yes	—
521	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
522	C₄²	C₂×C₅×D₄	1	2	yes	—
523	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
524	C₄²	C₂×C₅×D₄	1	2	yes	—
525	C₄²	C₂⁴×C₅	1	1	yes	characteristic
526	C₂×C₅	—	2	4	no	—
527	C₂×C₅	—	4	1	no	—
528	C₂×C₅	—	8	1	no	—
529	C₂×C₅	#2880	1	1	yes	characteristic
530	C₂×C₅	#2898	1	1	yes	characteristic
531	C₂×C₅	C₂²×#104	1	1	yes	characteristic
532	C₂³	—	2	1	no	—
533	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
534	C₂³	C₂×C₅×C₂²⋊C₄	1	2	yes	—
535	Q₈	—	2	2	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	2	no	—
538	Q₈	—	2	2	no	—
539	Q₈	—	4	4	no	—
540	Q₈	—	4	2	no	—
541	Q₈	C₅×#131	1	2	yes	complemented
542	D₄	—	2	4	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	1	no	—
545	D₄	—	4	2	no	—
546	D₄	—	4	4	no	—
547	D₄	C₅×#104	1	4	yes	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	1	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	2	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	4	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	1	no	—
569	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
570	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
571	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
573	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	2	yes	—
574	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
575	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
576	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
577	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
578	C₈	—	2	2	no	—
579	C₈	—	2	4	no	—
580	C₈	—	2	2	no	—
581	C₈	—	4	1	no	—
582	C₈	—	4	2	no	—
583	C₈	—	4	1	no	—
584	C₅	#17519	1	1	yes	characteristic, direct product factor, Sylow
585	C₂²	—	2	2	no	—
586	C₂²	—	2	2	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂×C₅×#104	1	4	yes	—
594	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	1	no	—
600	C₄	—	2	1	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	2	no	—
606	C₄	C₂×C₅×#104	1	2	yes	—
607	C₄	C₂×C₅×#131	1	1	yes	characteristic
608	C₄	C₅×#568	1	1	yes	characteristic
609	C₄	C₅×#577	1	1	yes	characteristic
610	C₄	C₅×#578	1	1	yes	characteristic
611	C₂	—	2	4	no	—
612	C₂	—	4	1	no	—
613	C₂	—	8	1	no	—
614	C₂	C₅×#2880	1	1	yes	characteristic
615	C₂	C₅×#2898	1	1	yes	characteristic
616	C₂	C₂²×C₅×#104	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×#2990	C₂	semidirect
3. C₄×C₅×#131	C₂	semidirect
4. C₅×#1494	C₂	semidirect
5. C₅×#1493	C₂	semidirect
6. C₅×#1491	C₂	semidirect
7. C₅×#1489	C₂	semidirect
8. C₅×#1485	C₂	semidirect
9. C₅×#1483	C₂	semidirect
10. C₅×#1476	C₂	semidirect
11. C₂×C₅×Q₈⋊C₈	C₂	semidirect
53. #17519	C₅	direct (N × H)
143. #2990	C₂×C₅	semidirect
144. C₄×#131	C₂×C₅	semidirect
145. #1494	C₂×C₅	semidirect
146. #1493	C₂×C₅	semidirect
147. #1491	C₂×C₅	semidirect
148. #1489	C₂×C₅	semidirect
149. #1485	C₂×C₅	semidirect
150. #1483	C₂×C₅	semidirect
151. #1476	C₂×C₅	semidirect
152. C₂×Q₈⋊C₈	C₂×C₅	semidirect
286. C₅×Q₈	#131	semidirect
541. Q₈	C₅×#131	semidirect
584. C₅	#17519	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×#2990	2
C₄×C₅×#131	2
C₅×#1494	2
C₅×#1493	2
C₅×#1491	2
C₅×#1489	2
C₅×#1485	2
C₅×#1483	2
C₅×#1476	2
C₂×C₅×Q₈⋊C₈	2
#17519	5

Subgroups — C5×#17519 #11940239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17519 #11940239