Subgroups — C₅×#18519 #11941239

Order 1280.

914 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×Q₈×#41	C₂	1	1	yes	maximal, characteristic
2	C₅×#3170	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3104	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3076	C₂	1	1	yes	maximal, characteristic
5	C₅×#1649	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1648	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1645	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1644	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1637	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1636	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1633	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1632	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1542	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1476	C₂	1	1	yes	maximal, characteristic
15	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×Q₈²	C₂²	1	1	yes	characteristic
17	C₅×#557	—	2	1	no	—
18	C₅×#557	C₂²	1	1	yes	characteristic
19	C₅×#554	—	2	2	no	—
20	C₅×#554	—	2	1	no	—
21	C₅×#554	—	2	1	no	—
22	C₅×#554	C₂²	1	1	yes	characteristic
23	C₅×D₄×Q₈	—	2	1	no	—
24	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
25	C₅×#533	—	2	2	no	—
26	C₅×#533	—	2	1	no	—
27	C₅×#533	—	2	1	no	—
28	C₅×#533	C₂²	1	1	yes	characteristic
29	C₅×#533	C₂²	1	1	yes	characteristic
30	C₄×C₅×#41	—	2	1	no	—
31	C₄×C₅×#41	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Q₈	—	2	1	no	—
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₅×#500	C₂²	1	1	yes	characteristic
35	C₅×#494	C₂²	1	1	yes	characteristic
36	C₅×#487	C₂²	1	1	yes	characteristic
37	C₅×#487	C₂²	1	1	yes	characteristic
38	C₅×#484	—	2	1	no	—
39	C₅×#479	—	2	1	no	—
40	C₅×#478	—	2	1	no	—
41	C₅×#477	C₂²	1	1	yes	characteristic
42	C₅×#477	C₂²	1	1	yes	characteristic
43	C₅×#477	C₂²	1	1	yes	characteristic
44	C₅×#476	C₂²	1	1	yes	characteristic
45	C₅×#475	C₂²	1	1	yes	characteristic
46	C₅×#474	C₂²	1	1	yes	characteristic
47	C₅×#467	—	2	2	no	—
48	C₅×#462	C₂²	1	1	yes	characteristic
49	C₅×#462	C₂²	1	1	yes	characteristic
50	C₅×#451	—	2	1	no	—
51	C₄×C₅×Q₁₆	—	2	1	no	—
52	C₄×C₅×Q₁₆	—	2	1	no	—
53	C₄×C₅×Q₁₆	—	2	2	no	—
54	C₅×#431	C₂²	1	1	yes	characteristic
55	C₅×#427	—	2	1	no	—
56	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×#416	—	2	1	no	—
58	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
59	C₅×#333	C₂²	1	1	yes	characteristic
60	C₅×#333	C₂²	1	1	yes	characteristic
61	C₅×#332	C₂²	1	1	yes	characteristic
62	C₅×#332	C₂²	1	1	yes	characteristic
63	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₅×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₅×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	#18519	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	D₄	1	1	yes	characteristic
73	C₂²×C₅×Q₈	—	2	1	no	—
74	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
75	C₂×C₅×Q₁₆	—	2	1	no	—
76	C₂×C₅×Q₁₆	—	2	1	no	—
77	C₂×C₅×Q₁₆	—	2	2	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₅×C₄⋊Q₈	—	2	2	no	—
81	C₅×C₄⋊Q₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	—	2	2	no	—
83	C₅×C₄⋊Q₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	—	2	1	no	—
85	C₅×C₄⋊Q₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
89	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₅×#125	—	2	2	no	—
91	C₅×#125	—	2	2	no	—
92	C₅×#125	—	2	2	no	—
93	C₅×#125	—	2	1	no	—
94	C₅×#125	—	2	1	no	—
95	C₅×#125	—	2	1	no	—
96	C₅×#125	—	2	1	no	—
97	C₅×C₂²⋊Q₈	—	2	2	no	—
98	C₅×C₂²⋊Q₈	—	2	2	no	—
99	C₅×C₂²⋊Q₈	—	2	2	no	—
100	C₅×C₂²⋊Q₈	—	2	2	no	—
101	C₅×C₂²⋊Q₈	—	2	2	no	—
102	C₅×C₂²⋊Q₈	—	2	1	no	—
103	C₅×C₂²⋊Q₈	—	2	2	no	—
104	C₅×C₂²⋊Q₈	—	2	1	no	—
105	C₅×C₂²⋊Q₈	—	2	1	no	—
106	C₅×C₂²⋊Q₈	—	2	2	no	—
107	C₅×C₂²⋊Q₈	—	2	1	no	—
108	C₅×C₂²⋊Q₈	—	2	1	no	—
109	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
110	C₄×C₅×Q₈	—	2	2	no	—
111	C₄×C₅×Q₈	—	2	2	no	—
112	C₄×C₅×Q₈	—	2	2	no	—
113	C₄×C₅×Q₈	—	2	1	no	—
114	C₄×C₅×Q₈	—	2	1	no	—
115	C₄×C₅×Q₈	—	2	1	no	—
116	C₄×C₅×Q₈	—	2	1	no	—
117	C₄×C₅×Q₈	—	2	1	no	—
118	C₄×C₅×Q₈	—	2	1	no	—
119	C₄×C₅×Q₈	—	2	1	no	—
120	C₄×C₅×Q₈	—	2	1	no	—
121	C₄×C₅×Q₈	—	2	1	no	—
122	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
123	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
124	C₄×C₅×Q₈	D₄	1	2	yes	—
125	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
126	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
127	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
128	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
129	C₄×C₅×D₄	—	2	2	no	—
130	C₄×C₅×D₄	—	2	2	no	—
131	C₄×C₅×D₄	—	2	1	no	—
132	C₄×C₅×D₄	—	2	1	no	—
133	C₄×C₅×D₄	—	2	1	no	—
134	C₄×C₅×D₄	—	2	1	no	—
135	C₄×C₅×D₄	D₄	1	1	yes	characteristic
136	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
137	C₅×#117	—	2	2	no	—
138	C₅×#117	—	2	1	no	—
139	C₅×#117	—	2	1	no	—
140	C₅×#117	—	2	1	no	—
141	C₅×#117	D₄	1	1	yes	characteristic
142	C₂×C₅×C₄⋊C₄	—	2	2	no	—
143	C₂×C₅×C₄⋊C₄	—	2	1	no	—
144	C₂×C₅×C₄⋊C₄	—	2	1	no	—
145	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
146	C₂×C₄²×C₅	—	2	2	no	—
147	C₂×C₄²×C₅	—	2	1	no	—
148	C₂×C₄²×C₅	—	2	1	no	—
149	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
150	C₅×#107	—	2	1	no	—
151	C₅×#107	—	2	1	no	—
152	C₅×#107	—	2	2	no	—
153	C₅×#107	—	2	1	no	—
154	C₅×#107	—	2	1	no	—
155	C₅×#106	—	2	1	no	—
156	C₅×#106	—	2	1	no	—
157	C₅×C₄⋊C₈	—	2	1	no	—
158	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₅×#103	—	2	1	no	—
163	C₅×#103	—	2	1	no	—
164	C₅×#103	—	2	1	no	—
165	C₅×#103	—	2	1	no	—
166	C₅×#103	—	2	2	no	—
167	C₅×#103	—	2	1	no	—
168	C₅×#103	—	2	1	no	—
169	C₅×#103	—	2	2	no	—
170	C₅×#102	—	2	1	no	—
171	C₅×#102	—	2	1	no	—
172	C₅×C₂²⋊C₈	—	2	1	no	—
173	C₄×C₅×C₈	—	2	1	no	—
174	C₄×C₅×C₈	—	2	1	no	—
175	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
176	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
177	Q₈×#41	C₂×C₅	1	1	yes	characteristic
178	#3170	C₂×C₅	1	1	yes	characteristic, complemented
179	#3104	C₂×C₅	1	1	yes	characteristic, complemented
180	#3076	C₂×C₅	1	1	yes	characteristic
181	#1649	C₂×C₅	1	1	yes	characteristic, complemented
182	#1648	C₂×C₅	1	1	yes	characteristic, complemented
183	#1645	C₂×C₅	1	1	yes	characteristic, complemented
184	#1644	C₂×C₅	1	1	yes	characteristic, complemented
185	#1637	C₂×C₅	1	1	yes	characteristic, complemented
186	#1636	C₂×C₅	1	1	yes	characteristic, complemented
187	#1633	C₂×C₅	1	1	yes	characteristic, complemented
188	#1632	C₂×C₅	1	1	yes	characteristic, complemented
189	#1542	C₂×C₅	1	1	yes	characteristic, complemented
190	#1476	C₂×C₅	1	1	yes	characteristic
191	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
192	C₅×#41	—	2	2	no	—
193	C₅×#41	Q₁₆	1	4	yes	complemented
194	C₂×C₅×Q₈	—	2	2	no	—
195	C₂×C₅×Q₈	—	2	2	no	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	—	2	1	no	—
198	C₂×C₅×Q₈	—	2	2	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	—	2	1	no	—
201	C₂×C₅×Q₈	—	4	1	no	—
202	C₂×C₅×Q₈	—	4	2	no	—
203	C₂×C₅×Q₈	—	4	2	no	—
204	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
206	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
207	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
208	C₂×C₅×D₄	—	2	1	no	—
209	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	2	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	2	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	2	1	no	—
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
220	C₅×Q₁₆	—	4	4	no	—
221	C₅×Q₁₆	—	4	2	no	—
222	C₅×Q₁₆	—	4	2	no	—
223	C₂×C₅×C₈	—	2	1	no	—
224	C₂×C₅×C₈	—	2	1	no	—
225	C₂×C₅×C₈	—	2	1	no	—
226	C₂×C₅×C₈	—	2	1	no	—
227	C₂×C₅×C₈	—	2	1	no	—
228	C₂×C₅×C₈	—	2	1	no	—
229	C₂×C₅×C₈	—	4	2	no	—
230	C₂×C₅×C₈	—	4	2	no	—
231	C₅×C₄⋊C₄	—	2	2	no	—
232	C₅×C₄⋊C₄	—	2	2	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	2	no	—
235	C₅×C₄⋊C₄	—	2	2	no	—
236	C₅×C₄⋊C₄	—	2	2	no	—
237	C₅×C₄⋊C₄	—	2	2	no	—
238	C₅×C₄⋊C₄	—	2	2	no	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	2	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	—	2	1	no	—
243	C₅×C₄⋊C₄	—	2	1	no	—
244	C₅×C₄⋊C₄	—	2	2	no	—
245	C₅×C₄⋊C₄	—	2	1	no	—
246	C₅×C₄⋊C₄	—	2	1	no	—
247	C₅×C₄⋊C₄	—	2	1	no	—
248	C₅×C₄⋊C₄	—	2	1	no	—
249	C₅×C₄⋊C₄	—	2	1	no	—
250	C₅×C₄⋊C₄	—	2	1	no	—
251	C₅×C₄⋊C₄	—	2	1	no	—
252	C₅×C₄⋊C₄	—	2	1	no	—
253	C₅×C₄⋊C₄	—	2	1	no	—
254	C₅×C₄⋊C₄	—	2	1	no	—
255	C₅×C₄⋊C₄	—	4	1	no	—
256	C₅×C₄⋊C₄	—	4	1	no	—
257	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
258	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
261	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	—	2	2	no	—
264	C₅×C₂²⋊C₄	—	2	2	no	—
265	C₅×C₂²⋊C₄	—	2	1	no	—
266	C₅×C₂²⋊C₄	—	2	1	no	—
267	C₅×C₂²⋊C₄	—	2	1	no	—
268	C₅×C₂²⋊C₄	—	4	1	no	—
269	C₄²×C₅	—	2	2	no	—
270	C₄²×C₅	—	2	2	no	—
271	C₄²×C₅	—	2	1	no	—
272	C₄²×C₅	—	2	1	no	—
273	C₄²×C₅	—	2	2	no	—
274	C₄²×C₅	—	2	1	no	—
275	C₄²×C₅	—	2	1	no	—
276	C₄²×C₅	—	2	1	no	—
277	C₄²×C₅	—	2	1	no	—
278	C₄²×C₅	—	2	1	no	—
279	C₄²×C₅	—	4	1	no	—
280	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₅	C₂⁴	1	1	yes	characteristic
284	Q₈²	C₂²×C₅	1	1	yes	characteristic
285	#557	—	2	1	no	—
286	#557	C₂²×C₅	1	1	yes	characteristic
287	#554	—	2	2	no	—
288	#554	—	2	1	no	—
289	#554	—	2	1	no	—
290	#554	C₂²×C₅	1	1	yes	characteristic
291	D₄×Q₈	—	2	1	no	—
292	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
293	#533	—	2	2	no	—
294	#533	—	2	1	no	—
295	#533	—	2	1	no	—
296	#533	C₂²×C₅	1	1	yes	characteristic
297	#533	C₂²×C₅	1	1	yes	characteristic
298	C₄×#41	—	2	1	no	—
299	C₄×#41	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₄×Q₈	—	2	1	no	—
301	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
302	#500	C₂²×C₅	1	1	yes	characteristic
303	#494	C₂²×C₅	1	1	yes	characteristic
304	#487	C₂²×C₅	1	1	yes	characteristic
305	#487	C₂²×C₅	1	1	yes	characteristic
306	#484	—	2	1	no	—
307	#479	—	2	1	no	—
308	#478	—	2	1	no	—
309	#477	C₂²×C₅	1	1	yes	characteristic
310	#477	C₂²×C₅	1	1	yes	characteristic
311	#477	C₂²×C₅	1	1	yes	characteristic
312	#476	C₂²×C₅	1	1	yes	characteristic
313	#475	C₂²×C₅	1	1	yes	characteristic
314	#474	C₂²×C₅	1	1	yes	characteristic
315	#467	—	2	2	no	—
316	#462	C₂²×C₅	1	1	yes	characteristic
317	#462	C₂²×C₅	1	1	yes	characteristic
318	#451	—	2	1	no	—
319	C₄×Q₁₆	—	2	1	no	—
320	C₄×Q₁₆	—	2	1	no	—
321	C₄×Q₁₆	—	2	2	no	—
322	#431	C₂²×C₅	1	1	yes	characteristic
323	#427	—	2	1	no	—
324	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
325	#416	—	2	1	no	—
326	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
327	#333	C₂²×C₅	1	1	yes	characteristic
328	#333	C₂²×C₅	1	1	yes	characteristic
329	#332	C₂²×C₅	1	1	yes	characteristic
330	#332	C₂²×C₅	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
334	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
335	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
336	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
337	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
338	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
339	C₂³×C₅	—	2	1	no	—
340	C₂³×C₅	#120	1	1	yes	characteristic
341	C₅×Q₈	—	2	1	no	—
342	C₅×Q₈	—	2	1	no	—
343	C₅×Q₈	—	2	1	no	—
344	C₅×Q₈	—	2	1	no	—
345	C₅×Q₈	—	4	2	no	—
346	C₅×Q₈	—	4	2	no	—
347	C₅×Q₈	—	4	4	no	—
348	C₅×Q₈	—	4	2	no	—
349	C₅×Q₈	—	4	1	no	—
350	C₅×Q₈	—	4	1	no	—
351	C₅×Q₈	—	4	1	no	—
352	C₅×Q₈	—	4	1	no	—
353	C₅×Q₈	—	8	2	no	—
354	C₅×Q₈	C₂×Q₁₆	1	2	yes	—
355	C₅×Q₈	#135	1	2	yes	—
356	C₅×D₄	—	2	4	no	—
357	C₅×D₄	—	2	1	no	—
358	C₅×D₄	C₂×Q₁₆	1	2	yes	—
359	C₂×C₄×C₅	—	2	1	no	—
360	C₂×C₄×C₅	—	2	1	no	—
361	C₂×C₄×C₅	—	2	1	no	—
362	C₂×C₄×C₅	—	2	1	no	—
363	C₂×C₄×C₅	—	2	4	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	1	no	—
366	C₂×C₄×C₅	—	2	2	no	—
367	C₂×C₄×C₅	—	2	2	no	—
368	C₂×C₄×C₅	—	2	1	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	2	1	no	—
371	C₂×C₄×C₅	—	4	1	no	—
372	C₂×C₄×C₅	—	4	2	no	—
373	C₂×C₄×C₅	—	4	4	no	—
374	C₂×C₄×C₅	—	4	1	no	—
375	C₂×C₄×C₅	—	4	1	no	—
376	C₂×C₄×C₅	—	4	1	no	—
377	C₂×C₄×C₅	—	4	1	no	—
378	C₂×C₄×C₅	—	8	1	no	—
379	C₂×C₄×C₅	—	8	1	no	—
380	C₂×C₄×C₅	—	8	2	no	—
381	C₂×C₄×C₅	#120	1	1	yes	characteristic
382	C₂×C₄×C₅	#120	1	1	yes	characteristic
383	C₂×C₄×C₅	#120	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂×Q₁₆	1	2	yes	—
385	C₂×C₄×C₅	#137	1	2	yes	—
386	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
387	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
389	C₅×C₈	—	2	2	no	—
390	C₅×C₈	—	4	1	no	—
391	C₅×C₈	—	4	1	no	—
392	C₅×C₈	—	4	1	no	—
393	C₅×C₈	—	4	1	no	—
394	C₅×C₈	—	4	1	no	—
395	C₂×#41	C₅×D₄	1	1	yes	characteristic
396	C₂²×Q₈	—	2	1	no	—
397	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
398	C₂×Q₁₆	—	2	1	no	—
399	C₂×Q₁₆	—	2	1	no	—
400	C₂×Q₁₆	—	2	2	no	—
401	C₂²×C₈	—	2	1	no	—
402	C₂²×C₈	—	2	1	no	—
403	C₄⋊Q₈	—	2	2	no	—
404	C₄⋊Q₈	—	2	1	no	—
405	C₄⋊Q₈	—	2	2	no	—
406	C₄⋊Q₈	—	2	1	no	—
407	C₄⋊Q₈	—	2	1	no	—
408	C₄⋊Q₈	—	2	1	no	—
409	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
410	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
411	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
412	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
413	#125	—	2	2	no	—
414	#125	—	2	2	no	—
415	#125	—	2	2	no	—
416	#125	—	2	1	no	—
417	#125	—	2	1	no	—
418	#125	—	2	1	no	—
419	#125	—	2	1	no	—
420	C₂²⋊Q₈	—	2	2	no	—
421	C₂²⋊Q₈	—	2	2	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	2	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	2	no	—
427	C₂²⋊Q₈	—	2	1	no	—
428	C₂²⋊Q₈	—	2	1	no	—
429	C₂²⋊Q₈	—	2	2	no	—
430	C₂²⋊Q₈	—	2	1	no	—
431	C₂²⋊Q₈	—	2	1	no	—
432	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
433	C₄×Q₈	—	2	2	no	—
434	C₄×Q₈	—	2	2	no	—
435	C₄×Q₈	—	2	2	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	—	2	1	no	—
438	C₄×Q₈	—	2	1	no	—
439	C₄×Q₈	—	2	1	no	—
440	C₄×Q₈	—	2	1	no	—
441	C₄×Q₈	—	2	1	no	—
442	C₄×Q₈	—	2	1	no	—
443	C₄×Q₈	—	2	1	no	—
444	C₄×Q₈	—	2	1	no	—
445	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
446	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
447	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
448	C₄×Q₈	C₅×D₄	1	2	yes	—
449	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
450	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
451	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
452	C₄×D₄	—	2	2	no	—
453	C₄×D₄	—	2	2	no	—
454	C₄×D₄	—	2	1	no	—
455	C₄×D₄	—	2	1	no	—
456	C₄×D₄	—	2	1	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	C₅×D₄	1	1	yes	characteristic
459	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
460	#117	—	2	2	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	#117	—	2	1	no	—
464	#117	C₅×D₄	1	1	yes	characteristic
465	C₂×C₄⋊C₄	—	2	2	no	—
466	C₂×C₄⋊C₄	—	2	1	no	—
467	C₂×C₄⋊C₄	—	2	1	no	—
468	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
469	C₂×C₄²	—	2	2	no	—
470	C₂×C₄²	—	2	1	no	—
471	C₂×C₄²	—	2	1	no	—
472	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
473	#107	—	2	1	no	—
474	#107	—	2	1	no	—
475	#107	—	2	2	no	—
476	#107	—	2	1	no	—
477	#107	—	2	1	no	—
478	#106	—	2	1	no	—
479	#106	—	2	1	no	—
480	C₄⋊C₈	—	2	1	no	—
481	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
482	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
483	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
484	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
485	#103	—	2	1	no	—
486	#103	—	2	1	no	—
487	#103	—	2	1	no	—
488	#103	—	2	1	no	—
489	#103	—	2	2	no	—
490	#103	—	2	1	no	—
491	#103	—	2	1	no	—
492	#103	—	2	2	no	—
493	#102	—	2	1	no	—
494	#102	—	2	1	no	—
495	C₂²⋊C₈	—	2	1	no	—
496	C₄×C₈	—	2	1	no	—
497	C₄×C₈	—	2	1	no	—
498	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
499	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
500	C₂²×C₅	—	2	1	no	—
501	C₂²×C₅	—	2	1	no	—
502	C₂²×C₅	—	2	2	no	—
503	C₂²×C₅	—	4	1	no	—
504	C₂²×C₅	—	4	1	no	—
505	C₂²×C₅	#451	1	2	yes	—
506	C₂²×C₅	C₂×#120	1	1	yes	characteristic
507	C₄×C₅	—	2	2	no	—
508	C₄×C₅	—	2	1	no	—
509	C₄×C₅	—	2	2	no	—
510	C₄×C₅	—	2	1	no	—
511	C₄×C₅	—	2	1	no	—
512	C₄×C₅	—	4	1	no	—
513	C₄×C₅	—	4	2	no	—
514	C₄×C₅	—	4	1	no	—
515	C₄×C₅	—	4	1	no	—
516	C₄×C₅	—	4	2	no	—
517	C₄×C₅	—	4	1	no	—
518	C₄×C₅	—	4	1	no	—
519	C₄×C₅	—	8	1	no	—
520	C₄×C₅	—	8	1	no	—
521	C₄×C₅	#451	1	2	yes	—
522	C₄×C₅	C₂²×Q₁₆	1	1	yes	characteristic
523	C₄×C₅	C₂×#135	1	1	yes	characteristic
524	C₄×C₅	C₂×#137	1	1	yes	characteristic
525	C₄×C₅	#575	1	1	yes	characteristic
526	#41	—	2	2	no	—
527	#41	C₅×Q₁₆	1	4	yes	complemented
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	4	1	no	—
536	C₂×Q₈	—	4	2	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
539	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
540	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	2	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
552	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
553	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
554	Q₁₆	—	4	4	no	—
555	Q₁₆	—	4	2	no	—
556	Q₁₆	—	4	2	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	4	2	no	—
564	C₂×C₈	—	4	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	2	no	—
572	C₄⋊C₄	—	2	2	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	2	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	—	4	1	no	—
591	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
592	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
593	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
594	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
595	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	4	1	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	2	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	4	1	no	—
614	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
615	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
616	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
617	C₄²	C₂⁴×C₅	1	1	yes	characteristic
618	C₂×C₅	—	2	2	no	—
619	C₂×C₅	—	4	2	no	—
620	C₂×C₅	C₂×#451	1	1	yes	characteristic
621	C₂×C₅	#3002	1	1	yes	characteristic
622	C₂×C₅	#3018	1	1	yes	characteristic
623	C₂³	—	2	1	no	—
624	C₂³	C₅×#120	1	1	yes	characteristic
625	Q₈	—	2	1	no	—
626	Q₈	—	2	1	no	—
627	Q₈	—	2	1	no	—
628	Q₈	—	2	1	no	—
629	Q₈	—	4	2	no	—
630	Q₈	—	4	2	no	—
631	Q₈	—	4	4	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	—	8	2	no	—
638	Q₈	C₂×C₅×Q₁₆	1	2	yes	—
639	Q₈	C₅×#135	1	2	yes	—
640	D₄	—	2	4	no	—
641	D₄	—	2	1	no	—
642	D₄	C₂×C₅×Q₁₆	1	2	yes	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	4	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	4	1	no	—
656	C₂×C₄	—	4	2	no	—
657	C₂×C₄	—	4	4	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	—	8	1	no	—
664	C₂×C₄	—	8	2	no	—
665	C₂×C₄	C₅×#120	1	1	yes	characteristic
666	C₂×C₄	C₅×#120	1	1	yes	characteristic
667	C₂×C₄	C₅×#120	1	1	yes	characteristic
668	C₂×C₄	C₂×C₅×Q₁₆	1	2	yes	—
669	C₂×C₄	C₅×#137	1	2	yes	—
670	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
671	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
672	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
673	C₈	—	2	2	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	4	1	no	—
677	C₈	—	4	1	no	—
678	C₈	—	4	1	no	—
679	C₅	#18519	1	1	yes	characteristic, direct product factor, Sylow
680	C₂²	—	2	1	no	—
681	C₂²	—	2	1	no	—
682	C₂²	—	2	2	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	C₅×#451	1	2	yes	—
686	C₂²	C₂×C₅×#120	1	1	yes	characteristic
687	C₄	—	2	2	no	—
688	C₄	—	2	1	no	—
689	C₄	—	2	2	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	2	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	C₅×#451	1	2	yes	—
702	C₄	C₂²×C₅×Q₁₆	1	1	yes	characteristic
703	C₄	C₂×C₅×#135	1	1	yes	characteristic
704	C₄	C₂×C₅×#137	1	1	yes	characteristic
705	C₄	C₅×#575	1	1	yes	characteristic
706	C₂	—	2	2	no	—
707	C₂	—	4	2	no	—
708	C₂	C₂×C₅×#451	1	1	yes	characteristic
709	C₂	C₅×#3002	1	1	yes	characteristic
710	C₂	C₅×#3018	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×#120
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#3170	C₂	semidirect
3. C₅×#3104	C₂	semidirect
5. C₅×#1649	C₂	semidirect
6. C₅×#1648	C₂	semidirect
7. C₅×#1645	C₂	semidirect
8. C₅×#1644	C₂	semidirect
9. C₅×#1637	C₂	semidirect
10. C₅×#1636	C₂	semidirect
11. C₅×#1633	C₂	semidirect
12. C₅×#1632	C₂	semidirect
13. C₅×#1542	C₂	semidirect
15. C₂×C₅×Q₈⋊C₈	C₂	semidirect
71. #18519	C₅	direct (N × H)
178. #3170	C₂×C₅	semidirect
179. #3104	C₂×C₅	semidirect
181. #1649	C₂×C₅	semidirect
182. #1648	C₂×C₅	semidirect
183. #1645	C₂×C₅	semidirect
184. #1644	C₂×C₅	semidirect
185. #1637	C₂×C₅	semidirect
186. #1636	C₂×C₅	semidirect
187. #1633	C₂×C₅	semidirect
188. #1632	C₂×C₅	semidirect
189. #1542	C₂×C₅	semidirect
191. C₂×Q₈⋊C₈	C₂×C₅	semidirect
193. C₅×#41	Q₁₆	semidirect
527. #41	C₅×Q₁₆	semidirect
679. C₅	#18519	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×Q₈×#41	2
C₅×#3170	2
C₅×#3104	2
C₅×#3076	2
C₅×#1649	2
C₅×#1648	2
C₅×#1645	2
C₅×#1644	2
C₅×#1637	2
C₅×#1636	2
C₅×#1633	2
C₅×#1632	2
C₅×#1542	2
C₅×#1476	2
C₂×C₅×Q₈⋊C₈	2
#18519	5

Subgroups — C5×#18519 #11941239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18519 #11941239