Subgroups — C₅×#18639 #11941359

Order 1280.

890 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3247	C₂	1	1	yes	maximal, characteristic
3	C₅×#3131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1638	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1637	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1636	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1636	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1626	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1626	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#557	—	2	1	no	—
17	C₅×#557	C₂²	1	1	yes	characteristic
18	C₅×#557	C₂²	1	1	yes	characteristic
19	C₅×#556	—	2	1	no	—
20	C₅×#556	C₂²	1	1	yes	characteristic
21	C₅×#552	—	2	2	no	—
22	C₅×#552	—	2	1	no	—
23	C₅×D₄×Q₈	—	2	1	no	—
24	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
25	C₅×#541	—	2	2	no	—
26	C₅×#541	—	2	1	no	—
27	C₅×#533	—	2	1	no	—
28	C₅×#533	C₂²	1	1	yes	characteristic
29	C₅×#532	C₂²	1	1	yes	characteristic
30	C₅×#529	—	2	1	no	—
31	C₅×#529	C₂²	1	1	yes	characteristic
32	C₅×#519	—	2	1	no	—
33	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₅×#488	—	2	2	no	—
35	C₅×#487	C₂²	1	1	yes	characteristic
36	C₅×#487	C₂²	1	1	yes	characteristic
37	C₅×#486	C₂²	1	1	yes	characteristic
38	C₅×#486	C₂²	1	1	yes	characteristic
39	C₅×#480	—	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×#466	—	2	1	no	—
46	C₅×#465	—	2	1	no	—
47	C₅×#463	—	2	1	no	—
48	C₅×#460	C₂²	1	1	yes	characteristic
49	C₅×#460	C₂²	1	1	yes	characteristic
50	C₅×#460	C₂²	1	1	yes	characteristic
51	C₅×#459	C₂²	1	1	yes	characteristic
52	C₅×#448	—	2	1	no	—
53	C₅×#440	—	2	1	no	—
54	C₅×#440	—	2	1	no	—
55	C₅×#432	C₂²	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×#416	—	2	2	no	—
58	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
59	C₅×#332	C₂²	1	1	yes	characteristic
60	C₅×#332	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	#18639	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	—	2	1	no	—
73	C₂²×C₅×Q₈	—	2	1	no	—
74	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
75	C₂×C₅×SD₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	—	2	1	no	—
77	C₂×C₅×SD₁₆	—	2	1	no	—
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₂²×C₅×C₈	—	2	1	no	—
81	C₅×C₄⋊Q₈	—	2	2	no	—
82	C₅×C₄⋊Q₈	—	2	1	no	—
83	C₅×C₄⋊Q₈	—	2	1	no	—
84	C₅×C₄⋊Q₈	—	2	1	no	—
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
88	C₅×#127	C₂³	1	1	yes	characteristic
89	C₅×#126	—	2	2	no	—
90	C₅×#126	—	2	2	no	—
91	C₅×#126	—	2	2	no	—
92	C₅×#126	—	2	2	no	—
93	C₅×#126	—	2	1	no	—
94	C₅×#125	—	2	2	no	—
95	C₅×#125	—	2	2	no	—
96	C₅×#125	—	2	2	no	—
97	C₅×#125	—	2	1	no	—
98	C₅×#125	—	2	2	no	—
99	C₅×#125	—	2	2	no	—
100	C₅×#125	—	2	1	no	—
101	C₅×#125	D₄	1	1	yes	characteristic
102	C₅×#125	D₄	1	2	yes	—
103	C₅×#124	—	2	1	no	—
104	C₅×#124	—	2	1	no	—
105	C₅×#124	D₄	1	1	yes	characteristic
106	C₅×#123	—	2	2	no	—
107	C₅×#123	—	2	1	no	—
108	C₅×C₂²⋊Q₈	—	2	2	no	—
109	C₅×C₂²⋊Q₈	—	2	2	no	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×C₂²⋊Q₈	—	2	1	no	—
112	C₅×C₂²⋊Q₈	—	2	1	no	—
113	C₅×C₂²⋊Q₈	—	2	1	no	—
114	C₅×C₂²⋊Q₈	—	2	2	no	—
115	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
116	C₅×#121	—	2	1	no	—
117	C₅×#121	—	2	1	no	—
118	C₅×#121	D₄	1	1	yes	characteristic
119	C₄×C₅×Q₈	—	2	2	no	—
120	C₄×C₅×Q₈	—	2	2	no	—
121	C₄×C₅×Q₈	—	2	1	no	—
122	C₄×C₅×Q₈	—	2	1	no	—
123	C₄×C₅×Q₈	—	2	1	no	—
124	C₄×C₅×Q₈	—	2	1	no	—
125	C₄×C₅×Q₈	—	2	1	no	—
126	C₄×C₅×Q₈	—	2	1	no	—
127	C₄×C₅×Q₈	—	2	1	no	—
128	C₄×C₅×Q₈	—	2	1	no	—
129	C₄×C₅×Q₈	—	2	1	no	—
130	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
131	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
132	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
133	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
134	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
135	C₄×C₅×D₄	—	2	2	no	—
136	C₄×C₅×D₄	—	2	1	no	—
137	C₄×C₅×D₄	—	2	1	no	—
138	C₄×C₅×D₄	—	2	1	no	—
139	C₄×C₅×D₄	—	2	1	no	—
140	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
141	C₅×#117	—	2	2	no	—
142	C₅×#117	—	2	2	no	—
143	C₅×#117	—	2	2	no	—
144	C₅×#117	—	2	1	no	—
145	C₅×#117	—	2	1	no	—
146	C₅×#117	D₄	1	2	yes	—
147	C₂×C₅×C₄⋊C₄	—	2	1	no	—
148	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
149	C₂×C₄²×C₅	—	2	1	no	—
150	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
151	C₅×#107	—	2	1	no	—
152	C₅×#107	—	2	1	no	—
153	C₅×#107	—	2	1	no	—
154	C₅×#106	—	2	1	no	—
155	C₅×C₄⋊C₈	—	2	1	no	—
156	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
157	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
158	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
159	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₅×#103	—	2	1	no	—
161	C₅×#103	—	2	1	no	—
162	C₅×#103	—	2	1	no	—
163	C₅×#103	—	2	2	no	—
164	C₅×#103	—	2	2	no	—
165	C₅×#102	—	2	1	no	—
166	C₅×#102	—	2	2	no	—
167	C₅×#102	—	2	2	no	—
168	C₅×#102	—	2	1	no	—
169	C₅×#102	—	2	1	no	—
170	C₅×#102	—	2	1	no	—
171	C₅×#102	—	2	1	no	—
172	C₅×C₂²⋊C₈	—	2	1	no	—
173	C₅×#97	—	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	#3523	C₂×C₅	1	1	yes	characteristic, complemented
178	#3247	C₂×C₅	1	1	yes	characteristic
179	#3131	C₂×C₅	1	1	yes	characteristic, complemented
180	#3112	C₂×C₅	1	1	yes	characteristic, complemented
181	#1638	C₂×C₅	1	1	yes	characteristic, complemented
182	#1637	C₂×C₅	1	1	yes	characteristic, complemented
183	#1636	C₂×C₅	1	1	yes	characteristic, complemented
184	#1636	C₂×C₅	1	1	yes	characteristic, complemented
185	#1628	C₂×C₅	1	1	yes	characteristic, complemented
186	#1627	C₂×C₅	1	1	yes	characteristic, complemented
187	#1626	C₂×C₅	1	1	yes	characteristic, complemented
188	#1626	C₂×C₅	1	1	yes	characteristic, complemented
189	#1552	C₂×C₅	1	1	yes	characteristic, complemented
190	#1494	C₂×C₅	1	1	yes	characteristic, complemented
191	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
192	C₅×#41	—	4	4	no	—
193	C₂×C₅×Q₈	—	2	2	no	—
194	C₂×C₅×Q₈	—	2	1	no	—
195	C₂×C₅×Q₈	—	2	1	no	—
196	C₂×C₅×Q₈	—	2	1	no	—
197	C₂×C₅×Q₈	—	2	2	no	—
198	C₂×C₅×Q₈	—	2	1	no	—
199	C₂×C₅×Q₈	—	4	1	no	—
200	C₂×C₅×Q₈	—	4	2	no	—
201	C₂×C₅×Q₈	—	4	2	no	—
202	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	1	no	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	—	2	1	no	—
208	C₂×C₅×D₄	—	2	1	no	—
209	C₂×C₅×D₄	—	4	1	no	—
210	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
211	C₂²×C₄×C₅	—	2	2	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	—	2	1	no	—
215	C₂²×C₄×C₅	—	4	1	no	—
216	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₅×SD₁₆	—	4	2	no	—
220	C₅×SD₁₆	—	4	2	no	—
221	C₅×SD₁₆	—	8	1	no	—
222	C₅×D₈	—	8	1	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	—	8	1	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	1	no	—
241	C₅×C₄⋊C₄	—	2	1	no	—
242	C₅×C₄⋊C₄	—	2	2	no	—
243	C₅×C₄⋊C₄	—	2	1	no	—
244	C₅×C₄⋊C₄	—	2	1	no	—
245	C₅×C₄⋊C₄	—	2	1	no	—
246	C₅×C₄⋊C₄	—	2	2	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	C₂×D₄	1	1	yes	characteristic
255	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
256	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
257	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
258	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
259	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
260	C₅×C₂²⋊C₄	—	2	2	no	—
261	C₅×C₂²⋊C₄	—	2	2	no	—
262	C₅×C₂²⋊C₄	—	2	2	no	—
263	C₅×C₂²⋊C₄	—	2	1	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	—	2	1	no	—
269	C₅×C₂²⋊C₄	—	4	1	no	—
270	C₅×C₂²⋊C₄	—	4	1	no	—
271	C₄²×C₅	—	2	2	no	—
272	C₄²×C₅	—	2	2	no	—
273	C₄²×C₅	—	2	2	no	—
274	C₄²×C₅	—	2	1	no	—
275	C₄²×C₅	—	2	1	no	—
276	C₄²×C₅	—	2	2	no	—
277	C₄²×C₅	—	2	1	no	—
278	C₄²×C₅	—	2	1	no	—
279	C₄²×C₅	—	2	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	#557	—	2	1	no	—
285	#557	C₂²×C₅	1	1	yes	characteristic
286	#557	C₂²×C₅	1	1	yes	characteristic
287	#556	—	2	1	no	—
288	#556	C₂²×C₅	1	1	yes	characteristic
289	#552	—	2	2	no	—
290	#552	—	2	1	no	—
291	D₄×Q₈	—	2	1	no	—
292	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
293	#541	—	2	2	no	—
294	#541	—	2	1	no	—
295	#533	—	2	1	no	—
296	#533	C₂²×C₅	1	1	yes	characteristic
297	#532	C₂²×C₅	1	1	yes	characteristic
298	#529	—	2	1	no	—
299	#529	C₂²×C₅	1	1	yes	characteristic
300	#519	—	2	1	no	—
301	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
302	#488	—	2	2	no	—
303	#487	C₂²×C₅	1	1	yes	characteristic
304	#487	C₂²×C₅	1	1	yes	characteristic
305	#486	C₂²×C₅	1	1	yes	characteristic
306	#486	C₂²×C₅	1	1	yes	characteristic
307	#480	—	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	#466	—	2	1	no	—
314	#465	—	2	1	no	—
315	#463	—	2	1	no	—
316	#460	C₂²×C₅	1	1	yes	characteristic
317	#460	C₂²×C₅	1	1	yes	characteristic
318	#460	C₂²×C₅	1	1	yes	characteristic
319	#459	C₂²×C₅	1	1	yes	characteristic
320	#448	—	2	1	no	—
321	#440	—	2	1	no	—
322	#440	—	2	1	no	—
323	#432	C₂²×C₅	1	1	yes	characteristic
324	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
325	#416	—	2	2	no	—
326	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
327	#332	C₂²×C₅	1	1	yes	characteristic
328	#332	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	—	4	1	no	—
341	C₂³×C₅	#120	1	1	yes	characteristic
342	C₅×Q₈	—	2	1	no	—
343	C₅×Q₈	—	2	1	no	—
344	C₅×Q₈	—	2	1	no	—
345	C₅×Q₈	—	2	1	no	—
346	C₅×Q₈	—	2	1	no	—
347	C₅×Q₈	—	4	2	no	—
348	C₅×Q₈	—	4	4	no	—
349	C₅×Q₈	—	4	2	no	—
350	C₅×Q₈	—	4	1	no	—
351	C₅×Q₈	—	4	1	no	—
352	C₅×Q₈	—	4	1	no	—
353	C₅×Q₈	—	4	1	no	—
354	C₅×Q₈	#135	1	2	yes	—
355	C₅×D₄	—	2	1	no	—
356	C₅×D₄	—	2	1	no	—
357	C₅×D₄	—	4	2	no	—
358	C₅×D₄	—	4	2	no	—
359	C₅×D₄	—	4	1	no	—
360	C₅×D₄	—	4	1	no	—
361	C₅×D₄	—	4	1	no	—
362	C₅×D₄	—	4	1	no	—
363	C₅×D₄	—	8	2	no	—
364	C₂×C₄×C₅	—	2	1	no	—
365	C₂×C₄×C₅	—	2	2	no	—
366	C₂×C₄×C₅	—	2	1	no	—
367	C₂×C₄×C₅	—	2	1	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	—	2	1	no	—
372	C₂×C₄×C₅	—	2	2	no	—
373	C₂×C₄×C₅	—	2	1	no	—
374	C₂×C₄×C₅	—	2	1	no	—
375	C₂×C₄×C₅	—	2	1	no	—
376	C₂×C₄×C₅	—	2	1	no	—
377	C₂×C₄×C₅	—	2	2	no	—
378	C₂×C₄×C₅	—	4	2	no	—
379	C₂×C₄×C₅	—	4	4	no	—
380	C₂×C₄×C₅	—	4	2	no	—
381	C₂×C₄×C₅	—	4	1	no	—
382	C₂×C₄×C₅	—	4	1	no	—
383	C₂×C₄×C₅	—	4	1	no	—
384	C₂×C₄×C₅	—	8	2	no	—
385	C₂×C₄×C₅	#120	1	1	yes	characteristic
386	C₂×C₄×C₅	#120	1	1	yes	characteristic
387	C₂×C₄×C₅	#120	1	1	yes	characteristic
388	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
389	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
390	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
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	C₅×C₈	—	4	1	no	—
396	C₅×C₈	—	4	1	no	—
397	C₂×#41	—	2	1	no	—
398	C₂²×Q₈	—	2	1	no	—
399	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
400	C₂×SD₁₆	—	2	1	no	—
401	C₂×SD₁₆	—	2	1	no	—
402	C₂×SD₁₆	—	2	1	no	—
403	C₂×D₈	—	2	1	no	—
404	C₂²×C₈	—	2	1	no	—
405	C₂²×C₈	—	2	1	no	—
406	C₄⋊Q₈	—	2	2	no	—
407	C₄⋊Q₈	—	2	1	no	—
408	C₄⋊Q₈	—	2	1	no	—
409	C₄⋊Q₈	—	2	1	no	—
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	#127	C₂³×C₅	1	1	yes	characteristic
414	#126	—	2	2	no	—
415	#126	—	2	2	no	—
416	#126	—	2	2	no	—
417	#126	—	2	2	no	—
418	#126	—	2	1	no	—
419	#125	—	2	2	no	—
420	#125	—	2	2	no	—
421	#125	—	2	2	no	—
422	#125	—	2	1	no	—
423	#125	—	2	2	no	—
424	#125	—	2	2	no	—
425	#125	—	2	1	no	—
426	#125	C₅×D₄	1	1	yes	characteristic
427	#125	C₅×D₄	1	2	yes	—
428	#124	—	2	1	no	—
429	#124	—	2	1	no	—
430	#124	C₅×D₄	1	1	yes	characteristic
431	#123	—	2	2	no	—
432	#123	—	2	1	no	—
433	C₂²⋊Q₈	—	2	2	no	—
434	C₂²⋊Q₈	—	2	2	no	—
435	C₂²⋊Q₈	—	2	1	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	2	no	—
440	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
441	#121	—	2	1	no	—
442	#121	—	2	1	no	—
443	#121	C₅×D₄	1	1	yes	characteristic
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	—	2	2	no	—
446	C₄×Q₈	—	2	1	no	—
447	C₄×Q₈	—	2	1	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	—	2	1	no	—
452	C₄×Q₈	—	2	1	no	—
453	C₄×Q₈	—	2	1	no	—
454	C₄×Q₈	—	2	1	no	—
455	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
456	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
457	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
458	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
459	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
460	C₄×D₄	—	2	2	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	—	2	1	no	—
463	C₄×D₄	—	2	1	no	—
464	C₄×D₄	—	2	1	no	—
465	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
466	#117	—	2	2	no	—
467	#117	—	2	2	no	—
468	#117	—	2	2	no	—
469	#117	—	2	1	no	—
470	#117	—	2	1	no	—
471	#117	C₅×D₄	1	2	yes	—
472	C₂×C₄⋊C₄	—	2	1	no	—
473	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
474	C₂×C₄²	—	2	1	no	—
475	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
476	#107	—	2	1	no	—
477	#107	—	2	1	no	—
478	#107	—	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	2	no	—
489	#103	—	2	2	no	—
490	#102	—	2	1	no	—
491	#102	—	2	2	no	—
492	#102	—	2	2	no	—
493	#102	—	2	1	no	—
494	#102	—	2	1	no	—
495	#102	—	2	1	no	—
496	#102	—	2	1	no	—
497	C₂²⋊C₈	—	2	1	no	—
498	#97	—	2	1	no	—
499	C₄×C₈	—	2	1	no	—
500	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
501	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
502	C₂²×C₅	—	2	1	no	—
503	C₂²×C₅	—	2	1	no	—
504	C₂²×C₅	—	4	1	no	—
505	C₂²×C₅	—	4	1	no	—
506	C₂²×C₅	—	4	1	no	—
507	C₂²×C₅	—	8	1	no	—
508	C₂²×C₅	—	8	1	no	—
509	C₂²×C₅	—	8	1	no	—
510	C₂²×C₅	#454	1	2	yes	—
511	C₂²×C₅	C₂×#120	1	1	yes	characteristic
512	C₄×C₅	—	2	1	no	—
513	C₄×C₅	—	2	2	no	—
514	C₄×C₅	—	2	1	no	—
515	C₄×C₅	—	2	1	no	—
516	C₄×C₅	—	2	1	no	—
517	C₄×C₅	—	4	1	no	—
518	C₄×C₅	—	4	2	no	—
519	C₄×C₅	—	4	1	no	—
520	C₄×C₅	—	4	1	no	—
521	C₄×C₅	—	4	2	no	—
522	C₄×C₅	—	4	1	no	—
523	C₄×C₅	—	4	1	no	—
524	C₄×C₅	—	4	1	no	—
525	C₄×C₅	—	8	1	no	—
526	C₄×C₅	C₂×#135	1	1	yes	characteristic
527	C₄×C₅	#575	1	1	yes	characteristic
528	C₄×C₅	#577	1	1	yes	characteristic
529	C₄×C₅	#578	1	1	yes	characteristic
530	#41	—	4	4	no	—
531	C₂×Q₈	—	2	2	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	1	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	2	no	—
536	C₂×Q₈	—	2	1	no	—
537	C₂×Q₈	—	4	1	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	—	4	2	no	—
540	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
543	C₂×D₄	—	2	1	no	—
544	C₂×D₄	—	2	1	no	—
545	C₂×D₄	—	2	1	no	—
546	C₂×D₄	—	2	1	no	—
547	C₂×D₄	—	4	1	no	—
548	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂²×C₄	—	2	2	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	4	1	no	—
554	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
556	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
557	SD₁₆	—	4	2	no	—
558	SD₁₆	—	4	2	no	—
559	SD₁₆	—	8	1	no	—
560	D₈	—	8	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	2	1	no	—
563	C₂×C₈	—	2	1	no	—
564	C₂×C₈	—	2	1	no	—
565	C₂×C₈	—	2	1	no	—
566	C₂×C₈	—	2	1	no	—
567	C₂×C₈	—	4	2	no	—
568	C₂×C₈	—	8	1	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	2	no	—
574	C₄⋊C₄	—	2	2	no	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	1	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	1	no	—
584	C₄⋊C₄	—	2	2	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	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
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	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
597	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	1	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₄²	—	2	2	no	—
610	C₄²	—	2	2	no	—
611	C₄²	—	2	2	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
619	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
620	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
621	C₄²	C₂⁴×C₅	1	1	yes	characteristic
622	C₂×C₅	—	2	2	no	—
623	C₂×C₅	—	8	1	no	—
624	C₂×C₅	—	16	1	no	—
625	C₂×C₅	#3002	1	1	yes	characteristic
626	C₂×C₅	#3013	1	1	yes	characteristic
627	C₂×C₅	C₂×#454	1	1	yes	characteristic
628	C₂³	—	2	1	no	—
629	C₂³	—	4	1	no	—
630	C₂³	C₅×#120	1	1	yes	characteristic
631	Q₈	—	2	1	no	—
632	Q₈	—	2	1	no	—
633	Q₈	—	2	1	no	—
634	Q₈	—	2	1	no	—
635	Q₈	—	2	1	no	—
636	Q₈	—	4	2	no	—
637	Q₈	—	4	4	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	4	1	no	—
640	Q₈	—	4	1	no	—
641	Q₈	—	4	1	no	—
642	Q₈	—	4	1	no	—
643	Q₈	C₅×#135	1	2	yes	—
644	D₄	—	2	1	no	—
645	D₄	—	2	1	no	—
646	D₄	—	4	2	no	—
647	D₄	—	4	2	no	—
648	D₄	—	4	1	no	—
649	D₄	—	4	1	no	—
650	D₄	—	4	1	no	—
651	D₄	—	4	1	no	—
652	D₄	—	8	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	1	no	—
671	C₂×C₄	—	4	1	no	—
672	C₂×C₄	—	4	1	no	—
673	C₂×C₄	—	8	2	no	—
674	C₂×C₄	C₅×#120	1	1	yes	characteristic
675	C₂×C₄	C₅×#120	1	1	yes	characteristic
676	C₂×C₄	C₅×#120	1	1	yes	characteristic
677	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
678	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
680	C₈	—	4	1	no	—
681	C₈	—	4	1	no	—
682	C₈	—	4	1	no	—
683	C₈	—	4	1	no	—
684	C₈	—	4	1	no	—
685	C₈	—	4	1	no	—
686	C₅	#18639	1	1	yes	characteristic, direct product factor, Sylow
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	4	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	8	1	no	—
693	C₂²	—	8	1	no	—
694	C₂²	—	8	1	no	—
695	C₂²	C₅×#454	1	2	yes	—
696	C₂²	C₂×C₅×#120	1	1	yes	characteristic
697	C₄	—	2	1	no	—
698	C₄	—	2	2	no	—
699	C₄	—	2	1	no	—
700	C₄	—	2	1	no	—
701	C₄	—	2	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	2	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	—	4	2	no	—
707	C₄	—	4	1	no	—
708	C₄	—	4	1	no	—
709	C₄	—	4	1	no	—
710	C₄	—	8	1	no	—
711	C₄	C₂×C₅×#135	1	1	yes	characteristic
712	C₄	C₅×#575	1	1	yes	characteristic
713	C₄	C₅×#577	1	1	yes	characteristic
714	C₄	C₅×#578	1	1	yes	characteristic
715	C₂	—	2	2	no	—
716	C₂	—	8	1	no	—
717	C₂	—	16	1	no	—
718	C₂	C₅×#3002	1	1	yes	characteristic
719	C₂	C₅×#3013	1	1	yes	characteristic
720	C₂	C₂×C₅×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3247	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3523	C₂	semidirect
3. C₅×#3131	C₂	semidirect
4. C₅×#3112	C₂	semidirect
5. C₅×#1638	C₂	semidirect
6. C₅×#1637	C₂	semidirect
7. C₅×#1636	C₂	semidirect
8. C₅×#1636	C₂	semidirect
9. C₅×#1628	C₂	semidirect
10. C₅×#1627	C₂	semidirect
11. C₅×#1626	C₂	semidirect
12. C₅×#1626	C₂	semidirect
13. C₅×#1552	C₂	semidirect
14. C₅×#1494	C₂	semidirect
15. C₂×C₅×Q₈⋊C₈	C₂	semidirect
71. #18639	C₅	direct (N × H)
177. #3523	C₂×C₅	semidirect
179. #3131	C₂×C₅	semidirect
180. #3112	C₂×C₅	semidirect
181. #1638	C₂×C₅	semidirect
182. #1637	C₂×C₅	semidirect
183. #1636	C₂×C₅	semidirect
184. #1636	C₂×C₅	semidirect
185. #1628	C₂×C₅	semidirect
186. #1627	C₂×C₅	semidirect
187. #1626	C₂×C₅	semidirect
188. #1626	C₂×C₅	semidirect
189. #1552	C₂×C₅	semidirect
190. #1494	C₂×C₅	semidirect
191. C₂×Q₈⋊C₈	C₂×C₅	semidirect
686. C₅	#18639	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×#3523	2
C₅×#3247	2
C₅×#3131	2
C₅×#3112	2
C₅×#1638	2
C₅×#1637	2
C₅×#1636	2
C₅×#1628	2
C₅×#1627	2
C₅×#1626	2
C₅×#1552	2
C₅×#1494	2
C₂×C₅×Q₈⋊C₈	2
#18639	5

Subgroups — C5×#18639 #11941359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18639 #11941359