Subgroups — C₅×#18673 #11941393

Order 1280.

872 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×#3518	C₂	1	1	yes	maximal, characteristic
2	C₅×#3233	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3170	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3116	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1650	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1649	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1646	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1645	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1638	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1637	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1634	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1633	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1554	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1494	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1476	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×Q₈²	C₂²	1	1	yes	characteristic
17	C₅×#556	—	2	1	no	—
18	C₅×#556	—	2	2	no	—
19	C₅×#556	—	2	1	no	—
20	C₅×#556	C₂²	1	1	yes	characteristic
21	C₅×#555	—	2	1	no	—
22	C₅×#555	C₂²	1	1	yes	characteristic
23	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
24	C₅×#548	—	2	1	no	—
25	C₅×#542	—	2	2	no	—
26	C₅×#542	—	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	C₅×#529	—	2	1	no	—
31	C₅×#529	C₂²	1	1	yes	characteristic
32	C₅×#519	—	2	1	no	—
33	C₄×C₅×#41	C₂²	1	1	yes	characteristic
34	C₅×#500	C₂²	1	1	yes	characteristic
35	C₅×#499	—	2	1	no	—
36	C₅×#494	C₂²	1	1	yes	characteristic
37	C₅×#488	—	2	1	no	—
38	C₅×#487	C₂²	1	1	yes	characteristic
39	C₅×#487	C₂²	1	1	yes	characteristic
40	C₅×#485	—	2	1	no	—
41	C₅×#485	—	2	1	no	—
42	C₅×#482	—	2	1	no	—
43	C₅×#477	C₂²	1	1	yes	characteristic
44	C₅×#477	C₂²	1	1	yes	characteristic
45	C₅×#476	C₂²	1	1	yes	characteristic
46	C₅×#476	C₂²	1	1	yes	characteristic
47	C₅×#475	C₂²	1	1	yes	characteristic
48	C₅×#474	C₂²	1	1	yes	characteristic
49	C₅×#467	—	2	2	no	—
50	C₅×#462	C₂²	1	1	yes	characteristic
51	C₅×#461	C₂²	1	1	yes	characteristic
52	C₅×#452	—	2	1	no	—
53	C₅×#441	—	2	1	no	—
54	C₅×#440	—	2	1	no	—
55	C₄×C₅×Q₁₆	—	2	2	no	—
56	C₅×#432	C₂²	1	1	yes	characteristic
57	C₅×#431	C₂²	1	1	yes	characteristic
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×D₄⋊C₈	C₂²	1	1	yes	characteristic
68	C₅×D₄⋊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	#18673	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	C₂×C₅×Q₁₆	—	2	2	no	—
75	C₂×C₅×Q₁₆	—	2	1	no	—
76	C₂×C₅×SD₁₆	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₅×C₄⋊Q₈	—	2	2	no	—
79	C₅×C₄⋊Q₈	—	2	1	no	—
80	C₅×C₄⋊Q₈	—	2	1	no	—
81	C₅×C₄⋊Q₈	—	2	1	no	—
82	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₅×#126	—	2	2	no	—
87	C₅×#126	—	2	2	no	—
88	C₅×#126	—	2	2	no	—
89	C₅×#126	—	2	2	no	—
90	C₅×#126	—	2	1	no	—
91	C₅×#125	—	2	1	no	—
92	C₅×#125	—	2	1	no	—
93	C₅×#125	D₄	1	1	yes	characteristic
94	C₅×#124	—	2	2	no	—
95	C₅×#124	—	2	2	no	—
96	C₅×#124	—	2	2	no	—
97	C₅×#124	—	2	2	no	—
98	C₅×#124	—	2	1	no	—
99	C₅×#124	D₄	1	1	yes	characteristic
100	C₅×#123	—	2	2	no	—
101	C₅×#123	—	2	1	no	—
102	C₅×C₂²⋊Q₈	—	2	2	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	1	no	—
107	C₅×C₂²⋊Q₈	—	2	2	no	—
108	C₅×C₂²⋊Q₈	—	2	1	no	—
109	C₅×C₂²⋊Q₈	—	2	1	no	—
110	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
111	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
112	C₅×#121	—	2	2	no	—
113	C₅×#121	—	2	1	no	—
114	C₅×#121	—	2	1	no	—
115	C₅×#121	D₄	1	1	yes	characteristic
116	C₄×C₅×Q₈	—	2	2	no	—
117	C₄×C₅×Q₈	—	2	2	no	—
118	C₄×C₅×Q₈	—	2	2	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	—	2	1	no	—
123	C₄×C₅×Q₈	—	2	1	no	—
124	C₄×C₅×Q₈	—	2	1	no	—
125	C₄×C₅×Q₈	D₄	1	2	yes	—
126	C₄×C₅×Q₈	D₄	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	1	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	D₄	1	1	yes	characteristic
135	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
136	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
137	C₅×#117	—	2	2	no	—
138	C₅×#117	—	2	2	no	—
139	C₅×#117	—	2	1	no	—
140	C₅×#117	—	2	1	no	—
141	C₅×#117	—	2	1	no	—
142	C₅×#117	—	2	1	no	—
143	C₅×#117	—	2	1	no	—
144	C₅×#117	—	2	1	no	—
145	C₅×#117	—	2	1	no	—
146	C₅×#117	D₄	1	1	yes	characteristic
147	C₂×C₄²×C₅	—	2	1	no	—
148	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
149	C₅×#107	—	2	2	no	—
150	C₅×#107	—	2	1	no	—
151	C₅×#107	—	2	1	no	—
152	C₅×#107	—	2	1	no	—
153	C₅×#106	—	2	1	no	—
154	C₅×#106	—	2	1	no	—
155	C₅×#106	—	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	2	no	—
161	C₅×#103	—	2	1	no	—
162	C₅×#103	—	2	1	no	—
163	C₅×#103	—	2	1	no	—
164	C₅×#103	—	2	2	no	—
165	C₅×#103	—	2	1	no	—
166	C₅×#103	—	2	1	no	—
167	C₅×#102	—	2	1	no	—
168	C₅×#102	—	2	1	no	—
169	C₅×#102	—	2	1	no	—
170	C₅×C₂²⋊C₈	—	2	1	no	—
171	C₅×C₂²⋊C₈	—	2	1	no	—
172	C₅×#97	—	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	#3518	C₂×C₅	1	1	yes	characteristic
178	#3233	C₂×C₅	1	1	yes	characteristic, complemented
179	#3170	C₂×C₅	1	1	yes	characteristic, complemented
180	#3116	C₂×C₅	1	1	yes	characteristic, complemented
181	#1650	C₂×C₅	1	1	yes	characteristic, complemented
182	#1649	C₂×C₅	1	1	yes	characteristic, complemented
183	#1646	C₂×C₅	1	1	yes	characteristic, complemented
184	#1645	C₂×C₅	1	1	yes	characteristic, complemented
185	#1638	C₂×C₅	1	1	yes	characteristic, complemented
186	#1637	C₂×C₅	1	1	yes	characteristic, complemented
187	#1634	C₂×C₅	1	1	yes	characteristic, complemented
188	#1633	C₂×C₅	1	1	yes	characteristic, complemented
189	#1554	C₂×C₅	1	1	yes	characteristic, complemented
190	#1494	C₂×C₅	1	1	yes	characteristic, complemented
191	#1476	C₂×C₅	1	1	yes	characteristic, complemented
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	4	1	no	—
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	1	no	—
199	C₂×C₅×Q₈	—	4	2	no	—
200	C₂×C₅×Q₈	—	4	2	no	—
201	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
202	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
203	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
204	C₂×C₅×D₄	—	2	1	no	—
205	C₂×C₅×D₄	—	2	2	no	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
208	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	—	2	1	no	—
211	C₂²×C₄×C₅	—	2	1	no	—
212	C₂²×C₄×C₅	—	2	1	no	—
213	C₂²×C₄×C₅	—	2	1	no	—
214	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₅×Q₁₆	—	4	4	no	—
218	C₅×Q₁₆	—	4	2	no	—
219	C₅×SD₁₆	—	4	2	no	—
220	C₂×C₅×C₈	—	2	1	no	—
221	C₂×C₅×C₈	—	2	1	no	—
222	C₂×C₅×C₈	—	2	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	—	4	2	no	—
227	C₅×C₄⋊C₄	—	2	2	no	—
228	C₅×C₄⋊C₄	—	2	2	no	—
229	C₅×C₄⋊C₄	—	2	2	no	—
230	C₅×C₄⋊C₄	—	2	2	no	—
231	C₅×C₄⋊C₄	—	2	1	no	—
232	C₅×C₄⋊C₄	—	2	1	no	—
233	C₅×C₄⋊C₄	—	2	2	no	—
234	C₅×C₄⋊C₄	—	2	1	no	—
235	C₅×C₄⋊C₄	—	2	1	no	—
236	C₅×C₄⋊C₄	—	2	2	no	—
237	C₅×C₄⋊C₄	—	2	1	no	—
238	C₅×C₄⋊C₄	—	2	1	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	1	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	—	4	1	no	—
247	C₅×C₄⋊C₄	—	4	1	no	—
248	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
249	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
250	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
251	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
252	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
253	C₅×C₂²⋊C₄	—	2	2	no	—
254	C₅×C₂²⋊C₄	—	2	2	no	—
255	C₅×C₂²⋊C₄	—	2	2	no	—
256	C₅×C₂²⋊C₄	—	2	2	no	—
257	C₅×C₂²⋊C₄	—	2	2	no	—
258	C₅×C₂²⋊C₄	—	2	2	no	—
259	C₅×C₂²⋊C₄	—	2	1	no	—
260	C₅×C₂²⋊C₄	—	2	1	no	—
261	C₅×C₂²⋊C₄	—	2	1	no	—
262	C₅×C₂²⋊C₄	—	2	1	no	—
263	C₅×C₂²⋊C₄	—	2	1	no	—
264	C₅×C₂²⋊C₄	—	2	1	no	—
265	C₅×C₂²⋊C₄	—	2	1	no	—
266	C₅×C₂²⋊C₄	—	2	1	no	—
267	C₅×C₂²⋊C₄	—	4	1	no	—
268	C₄²×C₅	—	2	2	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	—	4	1	no	—
277	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
278	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
279	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₅	C₂⁴	1	1	yes	characteristic
281	Q₈²	C₂²×C₅	1	1	yes	characteristic
282	#556	—	2	1	no	—
283	#556	—	2	2	no	—
284	#556	—	2	1	no	—
285	#556	C₂²×C₅	1	1	yes	characteristic
286	#555	—	2	1	no	—
287	#555	C₂²×C₅	1	1	yes	characteristic
288	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
289	#548	—	2	1	no	—
290	#542	—	2	2	no	—
291	#542	—	2	1	no	—
292	#533	—	2	1	no	—
293	#533	C₂²×C₅	1	1	yes	characteristic
294	#533	C₂²×C₅	1	1	yes	characteristic
295	#529	—	2	1	no	—
296	#529	C₂²×C₅	1	1	yes	characteristic
297	#519	—	2	1	no	—
298	C₄×#41	C₂²×C₅	1	1	yes	characteristic
299	#500	C₂²×C₅	1	1	yes	characteristic
300	#499	—	2	1	no	—
301	#494	C₂²×C₅	1	1	yes	characteristic
302	#488	—	2	1	no	—
303	#487	C₂²×C₅	1	1	yes	characteristic
304	#487	C₂²×C₅	1	1	yes	characteristic
305	#485	—	2	1	no	—
306	#485	—	2	1	no	—
307	#482	—	2	1	no	—
308	#477	C₂²×C₅	1	1	yes	characteristic
309	#477	C₂²×C₅	1	1	yes	characteristic
310	#476	C₂²×C₅	1	1	yes	characteristic
311	#476	C₂²×C₅	1	1	yes	characteristic
312	#475	C₂²×C₅	1	1	yes	characteristic
313	#474	C₂²×C₅	1	1	yes	characteristic
314	#467	—	2	2	no	—
315	#462	C₂²×C₅	1	1	yes	characteristic
316	#461	C₂²×C₅	1	1	yes	characteristic
317	#452	—	2	1	no	—
318	#441	—	2	1	no	—
319	#440	—	2	1	no	—
320	C₄×Q₁₆	—	2	2	no	—
321	#432	C₂²×C₅	1	1	yes	characteristic
322	#431	C₂²×C₅	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
324	#333	C₂²×C₅	1	1	yes	characteristic
325	#333	C₂²×C₅	1	1	yes	characteristic
326	#332	C₂²×C₅	1	1	yes	characteristic
327	#332	C₂²×C₅	1	1	yes	characteristic
328	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
329	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
330	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
332	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
333	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
334	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
335	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
336	C₂³×C₅	—	2	1	no	—
337	C₂³×C₅	—	2	1	no	—
338	C₂³×C₅	#120	1	1	yes	characteristic
339	C₅×Q₈	—	2	1	no	—
340	C₅×Q₈	—	2	1	no	—
341	C₅×Q₈	—	2	1	no	—
342	C₅×Q₈	—	4	2	no	—
343	C₅×Q₈	—	4	4	no	—
344	C₅×Q₈	—	4	2	no	—
345	C₅×Q₈	—	4	1	no	—
346	C₅×Q₈	—	4	1	no	—
347	C₅×Q₈	—	4	1	no	—
348	C₅×Q₈	—	4	1	no	—
349	C₅×Q₈	—	8	2	no	—
350	C₅×Q₈	#135	1	2	yes	—
351	C₅×D₄	—	2	1	no	—
352	C₅×D₄	—	2	1	no	—
353	C₅×D₄	—	2	1	no	—
354	C₅×D₄	—	2	1	no	—
355	C₅×D₄	—	4	2	no	—
356	C₅×D₄	—	8	1	no	—
357	C₅×D₄	—	8	2	no	—
358	C₂×C₄×C₅	—	2	1	no	—
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	1	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	2	no	—
369	C₂×C₄×C₅	—	2	1	no	—
370	C₂×C₄×C₅	—	4	1	no	—
371	C₂×C₄×C₅	—	4	2	no	—
372	C₂×C₄×C₅	—	4	4	no	—
373	C₂×C₄×C₅	—	4	1	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	—	4	1	no	—
379	C₂×C₄×C₅	—	8	1	no	—
380	C₂×C₄×C₅	#120	1	1	yes	characteristic
381	C₂×C₄×C₅	#120	1	1	yes	characteristic
382	C₂×C₄×C₅	#120	1	1	yes	characteristic
383	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
384	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
385	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
386	C₅×C₈	—	2	2	no	—
387	C₅×C₈	—	4	1	no	—
388	C₅×C₈	—	4	1	no	—
389	C₅×C₈	—	4	1	no	—
390	C₅×C₈	—	4	1	no	—
391	C₅×C₈	—	4	1	no	—
392	C₂×#41	C₅×D₄	1	1	yes	characteristic
393	C₂²×Q₈	—	2	1	no	—
394	C₂×Q₁₆	—	2	2	no	—
395	C₂×Q₁₆	—	2	1	no	—
396	C₂×SD₁₆	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₄⋊Q₈	—	2	2	no	—
399	C₄⋊Q₈	—	2	1	no	—
400	C₄⋊Q₈	—	2	1	no	—
401	C₄⋊Q₈	—	2	1	no	—
402	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
403	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
404	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
405	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
406	#126	—	2	2	no	—
407	#126	—	2	2	no	—
408	#126	—	2	2	no	—
409	#126	—	2	2	no	—
410	#126	—	2	1	no	—
411	#125	—	2	1	no	—
412	#125	—	2	1	no	—
413	#125	C₅×D₄	1	1	yes	characteristic
414	#124	—	2	2	no	—
415	#124	—	2	2	no	—
416	#124	—	2	2	no	—
417	#124	—	2	2	no	—
418	#124	—	2	1	no	—
419	#124	C₅×D₄	1	1	yes	characteristic
420	#123	—	2	2	no	—
421	#123	—	2	1	no	—
422	C₂²⋊Q₈	—	2	2	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	—	2	1	no	—
425	C₂²⋊Q₈	—	2	1	no	—
426	C₂²⋊Q₈	—	2	1	no	—
427	C₂²⋊Q₈	—	2	2	no	—
428	C₂²⋊Q₈	—	2	1	no	—
429	C₂²⋊Q₈	—	2	1	no	—
430	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
431	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
432	#121	—	2	2	no	—
433	#121	—	2	1	no	—
434	#121	—	2	1	no	—
435	#121	C₅×D₄	1	1	yes	characteristic
436	C₄×Q₈	—	2	2	no	—
437	C₄×Q₈	—	2	2	no	—
438	C₄×Q₈	—	2	2	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	2	yes	—
447	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
448	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
449	C₄×D₄	—	2	2	no	—
450	C₄×D₄	—	2	1	no	—
451	C₄×D₄	—	2	1	no	—
452	C₄×D₄	—	2	1	no	—
453	C₄×D₄	—	2	1	no	—
454	C₄×D₄	C₅×D₄	1	1	yes	characteristic
455	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
456	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
457	#117	—	2	2	no	—
458	#117	—	2	2	no	—
459	#117	—	2	1	no	—
460	#117	—	2	1	no	—
461	#117	—	2	1	no	—
462	#117	—	2	1	no	—
463	#117	—	2	1	no	—
464	#117	—	2	1	no	—
465	#117	—	2	1	no	—
466	#117	C₅×D₄	1	1	yes	characteristic
467	C₂×C₄²	—	2	1	no	—
468	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
469	#107	—	2	2	no	—
470	#107	—	2	1	no	—
471	#107	—	2	1	no	—
472	#107	—	2	1	no	—
473	#106	—	2	1	no	—
474	#106	—	2	1	no	—
475	#106	—	2	1	no	—
476	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
477	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
478	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
479	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
480	#103	—	2	2	no	—
481	#103	—	2	1	no	—
482	#103	—	2	1	no	—
483	#103	—	2	1	no	—
484	#103	—	2	2	no	—
485	#103	—	2	1	no	—
486	#103	—	2	1	no	—
487	#102	—	2	1	no	—
488	#102	—	2	1	no	—
489	#102	—	2	1	no	—
490	C₂²⋊C₈	—	2	1	no	—
491	C₂²⋊C₈	—	2	1	no	—
492	#97	—	2	1	no	—
493	C₄×C₈	—	2	1	no	—
494	C₄×C₈	—	2	1	no	—
495	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
496	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
497	C₂²×C₅	—	2	1	no	—
498	C₂²×C₅	—	2	1	no	—
499	C₂²×C₅	—	2	1	no	—
500	C₂²×C₅	—	4	1	no	—
501	C₂²×C₅	—	4	1	no	—
502	C₂²×C₅	—	4	1	no	—
503	C₂²×C₅	—	4	1	no	—
504	C₂²×C₅	—	4	1	no	—
505	C₂²×C₅	—	4	1	no	—
506	C₂²×C₅	C₂×#120	1	1	yes	characteristic
507	C₄×C₅	—	2	1	no	—
508	C₄×C₅	—	2	2	no	—
509	C₄×C₅	—	2	1	no	—
510	C₄×C₅	—	2	1	no	—
511	C₄×C₅	—	2	1	no	—
512	C₄×C₅	—	4	2	no	—
513	C₄×C₅	—	4	1	no	—
514	C₄×C₅	—	4	1	no	—
515	C₄×C₅	—	4	1	no	—
516	C₄×C₅	—	4	1	no	—
517	C₄×C₅	—	4	2	no	—
518	C₄×C₅	—	4	1	no	—
519	C₄×C₅	—	8	1	no	—
520	C₄×C₅	—	8	1	no	—
521	C₄×C₅	C₂×#135	1	1	yes	characteristic
522	C₄×C₅	#575	1	1	yes	characteristic
523	C₄×C₅	#578	1	1	yes	characteristic
524	C₄×C₅	#578	1	1	yes	characteristic
525	#41	—	2	2	no	—
526	#41	—	4	1	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	2	1	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	4	2	no	—
533	C₂×Q₈	—	4	2	no	—
534	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
535	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
536	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
537	C₂×D₄	—	2	1	no	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
541	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
542	C₂²×C₄	—	2	2	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
548	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
549	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
550	Q₁₆	—	4	4	no	—
551	Q₁₆	—	4	2	no	—
552	SD₁₆	—	4	2	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	4	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	1	no	—
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	1	no	—
568	C₄⋊C₄	—	2	1	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	1	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	4	1	no	—
580	C₄⋊C₄	—	4	1	no	—
581	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
582	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
583	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
584	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
585	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
586	C₂²⋊C₄	—	2	2	no	—
587	C₂²⋊C₄	—	2	2	no	—
588	C₂²⋊C₄	—	2	2	no	—
589	C₂²⋊C₄	—	2	2	no	—
590	C₂²⋊C₄	—	2	2	no	—
591	C₂²⋊C₄	—	2	2	no	—
592	C₂²⋊C₄	—	2	1	no	—
593	C₂²⋊C₄	—	2	1	no	—
594	C₂²⋊C₄	—	2	1	no	—
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	4	1	no	—
601	C₄²	—	2	2	no	—
602	C₄²	—	2	2	no	—
603	C₄²	—	2	2	no	—
604	C₄²	—	2	1	no	—
605	C₄²	—	2	1	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	—	4	1	no	—
610	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
611	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
612	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
613	C₄²	C₂⁴×C₅	1	1	yes	characteristic
614	C₂×C₅	—	4	1	no	—
615	C₂×C₅	—	8	1	no	—
616	C₂×C₅	—	8	1	no	—
617	C₂×C₅	#3002	1	1	yes	characteristic
618	C₂×C₅	#3011	1	1	yes	characteristic
619	C₂×C₅	#3018	1	1	yes	characteristic
620	C₂³	—	2	1	no	—
621	C₂³	—	2	1	no	—
622	C₂³	C₅×#120	1	1	yes	characteristic
623	Q₈	—	2	1	no	—
624	Q₈	—	2	1	no	—
625	Q₈	—	2	1	no	—
626	Q₈	—	4	2	no	—
627	Q₈	—	4	4	no	—
628	Q₈	—	4	2	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	8	2	no	—
634	Q₈	C₅×#135	1	2	yes	—
635	D₄	—	2	1	no	—
636	D₄	—	2	1	no	—
637	D₄	—	2	1	no	—
638	D₄	—	2	1	no	—
639	D₄	—	4	2	no	—
640	D₄	—	8	1	no	—
641	D₄	—	8	2	no	—
642	C₂×C₄	—	2	1	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	4	1	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	1	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	—	4	1	no	—
663	C₂×C₄	—	8	1	no	—
664	C₂×C₄	C₅×#120	1	1	yes	characteristic
665	C₂×C₄	C₅×#120	1	1	yes	characteristic
666	C₂×C₄	C₅×#120	1	1	yes	characteristic
667	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
668	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
669	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
670	C₈	—	2	2	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₅	#18673	1	1	yes	characteristic, direct product factor, Sylow
677	C₂²	—	2	1	no	—
678	C₂²	—	2	1	no	—
679	C₂²	—	2	1	no	—
680	C₂²	—	4	1	no	—
681	C₂²	—	4	1	no	—
682	C₂²	—	4	1	no	—
683	C₂²	—	4	1	no	—
684	C₂²	—	4	1	no	—
685	C₂²	—	4	1	no	—
686	C₂²	C₂×C₅×#120	1	1	yes	characteristic
687	C₄	—	2	1	no	—
688	C₄	—	2	2	no	—
689	C₄	—	2	1	no	—
690	C₄	—	2	1	no	—
691	C₄	—	2	1	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	1	no	—
694	C₄	—	4	1	no	—
695	C₄	—	4	1	no	—
696	C₄	—	4	1	no	—
697	C₄	—	4	2	no	—
698	C₄	—	4	1	no	—
699	C₄	—	8	1	no	—
700	C₄	—	8	1	no	—
701	C₄	C₂×C₅×#135	1	1	yes	characteristic
702	C₄	C₅×#575	1	1	yes	characteristic
703	C₄	C₅×#578	1	1	yes	characteristic
704	C₄	C₅×#578	1	1	yes	characteristic
705	C₂	—	4	1	no	—
706	C₂	—	8	1	no	—
707	C₂	—	8	1	no	—
708	C₂	C₅×#3002	1	1	yes	characteristic
709	C₂	C₅×#3011	1	1	yes	characteristic
710	C₂	C₅×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3518	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
2. C₅×#3233	C₂	semidirect
3. C₅×#3170	C₂	semidirect
4. C₅×#3116	C₂	semidirect
5. C₅×#1650	C₂	semidirect
6. C₅×#1649	C₂	semidirect
7. C₅×#1646	C₂	semidirect
8. C₅×#1645	C₂	semidirect
9. C₅×#1638	C₂	semidirect
10. C₅×#1637	C₂	semidirect
11. C₅×#1634	C₂	semidirect
12. C₅×#1633	C₂	semidirect
13. C₅×#1554	C₂	semidirect
14. C₅×#1494	C₂	semidirect
15. C₅×#1476	C₂	semidirect
71. #18673	C₅	direct (N × H)
178. #3233	C₂×C₅	semidirect
179. #3170	C₂×C₅	semidirect
180. #3116	C₂×C₅	semidirect
181. #1650	C₂×C₅	semidirect
182. #1649	C₂×C₅	semidirect
183. #1646	C₂×C₅	semidirect
184. #1645	C₂×C₅	semidirect
185. #1638	C₂×C₅	semidirect
186. #1637	C₂×C₅	semidirect
187. #1634	C₂×C₅	semidirect
188. #1633	C₂×C₅	semidirect
189. #1554	C₂×C₅	semidirect
190. #1494	C₂×C₅	semidirect
191. #1476	C₂×C₅	semidirect
676. C₅	#18673	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×#3518	2
C₅×#3233	2
C₅×#3170	2
C₅×#3116	2
C₅×#1650	2
C₅×#1649	2
C₅×#1646	2
C₅×#1645	2
C₅×#1638	2
C₅×#1637	2
C₅×#1634	2
C₅×#1633	2
C₅×#1554	2
C₅×#1494	2
C₅×#1476	2
#18673	5

Subgroups — C5×#18673 #11941393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18673 #11941393