Subgroups — C₅×#18608 #11941328

Order 1280.

928 conjugacy classes of subgroups.

The subgroup lattice has 748 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, complemented
2	C₅×#3251	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3182	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3035	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×#1628	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1627	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1624	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1623	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1550	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#1489	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#1483	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	—	2	1	no	—
17	C₅×Q₈²	C₂²	1	1	yes	characteristic
18	C₅×#556	—	2	1	no	—
19	C₅×#556	—	2	2	no	—
20	C₅×#556	—	2	1	no	—
21	C₅×#556	C₂²	1	1	yes	characteristic
22	C₅×#555	—	2	1	no	—
23	C₅×#555	C₂²	1	1	yes	characteristic
24	C₅×D₄×Q₈	C₂²	1	1	yes	characteristic
25	C₅×#548	—	2	1	no	—
26	C₅×#542	—	2	2	no	—
27	C₅×#542	—	2	1	no	—
28	C₅×#533	—	2	1	no	—
29	C₅×#533	C₂²	1	1	yes	characteristic
30	C₅×#532	C₂²	1	1	yes	characteristic
31	C₅×#529	—	2	1	no	—
32	C₅×#529	C₂²	1	1	yes	characteristic
33	C₅×#519	—	2	1	no	—
34	C₄×C₅×#41	C₂²	1	1	yes	characteristic
35	C₅×#500	C₂²	1	1	yes	characteristic
36	C₅×#492	C₂²	1	1	yes	characteristic
37	C₅×#487	C₂²	1	1	yes	characteristic
38	C₅×#486	C₂²	1	1	yes	characteristic
39	C₅×#478	—	2	1	no	—
40	C₅×#475	C₂²	1	1	yes	characteristic
41	C₅×#474	C₂²	1	1	yes	characteristic
42	C₅×#469	—	2	1	no	—
43	C₅×#468	—	2	1	no	—
44	C₅×#468	—	2	2	no	—
45	C₅×#464	—	2	1	no	—
46	C₅×#463	—	2	1	no	—
47	C₅×#463	—	2	1	no	—
48	C₅×#462	C₂²	1	1	yes	characteristic
49	C₅×#461	C₂²	1	1	yes	characteristic
50	C₅×#460	C₂²	1	1	yes	characteristic
51	C₅×#460	C₂²	1	1	yes	characteristic
52	C₅×#459	C₂²	1	1	yes	characteristic
53	C₅×#459	C₂²	1	1	yes	characteristic
54	C₅×#440	—	2	2	no	—
55	C₅×#423	C₂²	1	1	yes	characteristic
56	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
57	C₅×#416	—	2	1	no	—
58	C₄×C₅×M₁₆	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	#18608	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	—	2	1	no	—
73	C₂×C₅×#41	D₄	1	1	yes	characteristic
74	C₂²×C₅×Q₈	—	2	1	no	—
75	C₅×#135	—	4	4	no	—
76	C₂×C₅×Q₁₆	—	2	1	no	—
77	C₂×C₅×SD₁₆	—	2	2	no	—
78	C₂×C₅×SD₁₆	—	2	1	no	—
79	C₂×C₅×SD₁₆	—	2	1	no	—
80	C₂×C₅×SD₁₆	—	2	1	no	—
81	C₂×C₅×D₈	—	2	1	no	—
82	C₂×C₅×D₈	—	2	1	no	—
83	C₂×C₅×M₁₆	—	2	1	no	—
84	C₂×C₅×M₁₆	—	2	1	no	—
85	C₂²×C₅×C₈	—	2	1	no	—
86	C₅×C₄⋊Q₈	—	2	2	no	—
87	C₅×C₄⋊Q₈	—	2	1	no	—
88	C₅×C₄⋊Q₈	—	2	1	no	—
89	C₅×C₄⋊Q₈	—	2	1	no	—
90	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₅×#127	C₂³	1	1	yes	characteristic
94	C₅×#126	—	2	2	no	—
95	C₅×#126	—	2	2	no	—
96	C₅×#126	—	2	2	no	—
97	C₅×#126	—	2	2	no	—
98	C₅×#126	—	2	1	no	—
99	C₅×#125	—	2	1	no	—
100	C₅×#125	D₄	1	1	yes	characteristic
101	C₅×#124	—	2	2	no	—
102	C₅×#124	—	2	2	no	—
103	C₅×#124	—	2	2	no	—
104	C₅×#124	—	2	2	no	—
105	C₅×#124	—	2	1	no	—
106	C₅×#124	—	2	1	no	—
107	C₅×#124	D₄	1	1	yes	characteristic
108	C₅×#123	—	2	2	no	—
109	C₅×#123	—	2	1	no	—
110	C₅×C₂²⋊Q₈	—	2	2	no	—
111	C₅×C₂²⋊Q₈	—	2	2	no	—
112	C₅×C₂²⋊Q₈	—	2	1	no	—
113	C₅×C₂²⋊Q₈	—	2	1	no	—
114	C₅×C₂²⋊Q₈	—	2	1	no	—
115	C₅×C₂²⋊Q₈	—	2	2	no	—
116	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
117	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
118	C₅×#121	—	2	2	no	—
119	C₅×#121	—	2	1	no	—
120	C₅×#121	—	2	1	no	—
121	C₅×#121	—	2	1	no	—
122	C₅×#121	—	2	1	no	—
123	C₅×#121	D₄	1	1	yes	characteristic
124	C₄×C₅×Q₈	—	2	2	no	—
125	C₄×C₅×Q₈	—	2	2	no	—
126	C₄×C₅×Q₈	—	2	2	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	—	2	1	no	—
131	C₄×C₅×Q₈	D₄	1	2	yes	—
132	C₄×C₅×Q₈	D₄	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	—	2	1	no	—
141	C₄×C₅×D₄	—	2	1	no	—
142	C₄×C₅×D₄	D₄	1	1	yes	characteristic
143	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
144	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
145	C₅×#117	—	2	2	no	—
146	C₅×#117	—	2	2	no	—
147	C₅×#117	—	2	1	no	—
148	C₅×#117	—	2	1	no	—
149	C₅×#117	—	2	1	no	—
150	C₅×#117	—	2	1	no	—
151	C₅×#117	—	2	1	no	—
152	C₅×#117	—	2	1	no	—
153	C₅×#117	D₄	1	1	yes	characteristic
154	C₂×C₄²×C₅	—	2	1	no	—
155	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
156	C₅×#107	—	2	2	no	—
157	C₅×#107	—	2	1	no	—
158	C₅×#106	—	2	1	no	—
159	C₅×C₄⋊C₈	—	2	1	no	—
160	C₅×C₄⋊C₈	—	2	1	no	—
161	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
164	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
165	C₅×#103	—	2	2	no	—
166	C₅×#103	—	2	1	no	—
167	C₅×#103	—	2	1	no	—
168	C₅×#103	—	2	1	no	—
169	C₅×#102	—	2	1	no	—
170	C₅×#102	—	2	1	no	—
171	C₅×#102	—	2	1	no	—
172	C₅×#102	—	2	2	no	—
173	C₅×#102	—	2	1	no	—
174	C₅×#102	—	2	1	no	—
175	C₅×#97	—	2	1	no	—
176	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
177	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
178	#3518	C₂×C₅	1	1	yes	characteristic, complemented
179	#3251	C₂×C₅	1	1	yes	characteristic, complemented
180	#3182	C₂×C₅	1	1	yes	characteristic, complemented
181	#3035	C₂×C₅	1	1	yes	characteristic, complemented
182	#1650	C₂×C₅	1	1	yes	characteristic, complemented
183	#1649	C₂×C₅	1	1	yes	characteristic, complemented
184	#1646	C₂×C₅	1	1	yes	characteristic, complemented
185	#1645	C₂×C₅	1	1	yes	characteristic, complemented
186	#1628	C₂×C₅	1	1	yes	characteristic, complemented
187	#1627	C₂×C₅	1	1	yes	characteristic, complemented
188	#1624	C₂×C₅	1	1	yes	characteristic, complemented
189	#1623	C₂×C₅	1	1	yes	characteristic, complemented
190	#1550	C₂×C₅	1	1	yes	characteristic, complemented
191	#1489	C₂×C₅	1	1	yes	characteristic, complemented
192	#1483	C₂×C₅	1	1	yes	characteristic, complemented
193	C₅×#41	—	2	2	no	—
194	C₅×#41	—	4	1	no	—
195	C₅×#41	—	4	2	no	—
196	C₅×#41	—	4	2	no	—
197	C₂×C₅×Q₈	—	2	2	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	2	no	—
202	C₂×C₅×Q₈	—	4	2	no	—
203	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
204	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
205	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
206	C₂×C₅×D₄	—	2	1	no	—
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	—	2	1	no	—
209	C₂×C₅×D₄	—	2	1	no	—
210	C₂×C₅×D₄	—	2	1	no	—
211	C₂×C₅×D₄	—	2	1	no	—
212	C₂×C₅×D₄	—	4	1	no	—
213	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
214	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
215	C₂²×C₄×C₅	—	2	2	no	—
216	C₂²×C₄×C₅	—	2	1	no	—
217	C₂²×C₄×C₅	—	2	1	no	—
218	C₂²×C₄×C₅	—	2	1	no	—
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	4	1	no	—
221	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
224	C₅×Q₁₆	—	4	2	no	—
225	C₅×SD₁₆	—	4	4	no	—
226	C₅×SD₁₆	—	4	2	no	—
227	C₅×SD₁₆	—	4	2	no	—
228	C₅×SD₁₆	—	8	1	no	—
229	C₅×D₈	—	4	2	no	—
230	C₅×D₈	—	8	1	no	—
231	C₅×M₁₆	—	4	2	no	—
232	C₅×M₁₆	—	8	1	no	—
233	C₂×C₅×C₈	—	2	1	no	—
234	C₂×C₅×C₈	—	2	1	no	—
235	C₂×C₅×C₈	—	2	1	no	—
236	C₂×C₅×C₈	—	2	1	no	—
237	C₂×C₅×C₈	—	2	1	no	—
238	C₂×C₅×C₈	—	2	1	no	—
239	C₂×C₅×C₈	—	4	2	no	—
240	C₅×C₄⋊C₄	—	2	2	no	—
241	C₅×C₄⋊C₄	—	2	2	no	—
242	C₅×C₄⋊C₄	—	2	2	no	—
243	C₅×C₄⋊C₄	—	2	2	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	2	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	—	2	1	no	—
256	C₅×C₄⋊C₄	—	2	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	2	no	—
266	C₅×C₂²⋊C₄	—	2	2	no	—
267	C₅×C₂²⋊C₄	—	2	2	no	—
268	C₅×C₂²⋊C₄	—	2	1	no	—
269	C₅×C₂²⋊C₄	—	2	1	no	—
270	C₅×C₂²⋊C₄	—	2	1	no	—
271	C₅×C₂²⋊C₄	—	2	1	no	—
272	C₅×C₂²⋊C₄	—	2	1	no	—
273	C₅×C₂²⋊C₄	—	2	1	no	—
274	C₅×C₂²⋊C₄	—	2	1	no	—
275	C₅×C₂²⋊C₄	—	2	1	no	—
276	C₅×C₂²⋊C₄	—	4	1	no	—
277	C₅×C₂²⋊C₄	—	4	1	no	—
278	C₄²×C₅	—	2	2	no	—
279	C₄²×C₅	—	2	2	no	—
280	C₄²×C₅	—	2	2	no	—
281	C₄²×C₅	—	2	1	no	—
282	C₄²×C₅	—	2	1	no	—
283	C₄²×C₅	—	2	2	no	—
284	C₄²×C₅	—	2	1	no	—
285	C₄²×C₅	—	2	1	no	—
286	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
287	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
288	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₅	C₂⁴	1	1	yes	characteristic
290	C₂×#135	—	2	1	no	—
291	Q₈²	C₂²×C₅	1	1	yes	characteristic
292	#556	—	2	1	no	—
293	#556	—	2	2	no	—
294	#556	—	2	1	no	—
295	#556	C₂²×C₅	1	1	yes	characteristic
296	#555	—	2	1	no	—
297	#555	C₂²×C₅	1	1	yes	characteristic
298	D₄×Q₈	C₂²×C₅	1	1	yes	characteristic
299	#548	—	2	1	no	—
300	#542	—	2	2	no	—
301	#542	—	2	1	no	—
302	#533	—	2	1	no	—
303	#533	C₂²×C₅	1	1	yes	characteristic
304	#532	C₂²×C₅	1	1	yes	characteristic
305	#529	—	2	1	no	—
306	#529	C₂²×C₅	1	1	yes	characteristic
307	#519	—	2	1	no	—
308	C₄×#41	C₂²×C₅	1	1	yes	characteristic
309	#500	C₂²×C₅	1	1	yes	characteristic
310	#492	C₂²×C₅	1	1	yes	characteristic
311	#487	C₂²×C₅	1	1	yes	characteristic
312	#486	C₂²×C₅	1	1	yes	characteristic
313	#478	—	2	1	no	—
314	#475	C₂²×C₅	1	1	yes	characteristic
315	#474	C₂²×C₅	1	1	yes	characteristic
316	#469	—	2	1	no	—
317	#468	—	2	2	no	—
318	#468	—	2	1	no	—
319	#464	—	2	1	no	—
320	#463	—	2	1	no	—
321	#463	—	2	1	no	—
322	#462	C₂²×C₅	1	1	yes	characteristic
323	#461	C₂²×C₅	1	1	yes	characteristic
324	#460	C₂²×C₅	1	1	yes	characteristic
325	#460	C₂²×C₅	1	1	yes	characteristic
326	#459	C₂²×C₅	1	1	yes	characteristic
327	#459	C₂²×C₅	1	1	yes	characteristic
328	#440	—	2	2	no	—
329	#423	C₂²×C₅	1	1	yes	characteristic
330	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
331	#416	—	2	1	no	—
332	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
333	#333	C₂²×C₅	1	1	yes	characteristic
334	#333	C₂²×C₅	1	1	yes	characteristic
335	#332	C₂²×C₅	1	1	yes	characteristic
336	#332	C₂²×C₅	1	1	yes	characteristic
337	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
338	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
339	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
340	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
341	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
342	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
343	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
344	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
345	C₂³×C₅	—	2	1	no	—
346	C₂³×C₅	—	2	1	no	—
347	C₂³×C₅	—	4	1	no	—
348	C₂³×C₅	#120	1	1	yes	characteristic
349	C₅×Q₈	—	2	1	no	—
350	C₅×Q₈	—	2	1	no	—
351	C₅×Q₈	—	2	1	no	—
352	C₅×Q₈	—	4	2	no	—
353	C₅×Q₈	—	4	4	no	—
354	C₅×Q₈	—	4	1	no	—
355	C₅×Q₈	—	4	1	no	—
356	C₅×Q₈	—	4	1	no	—
357	C₅×Q₈	—	4	1	no	—
358	C₅×Q₈	—	8	2	no	—
359	C₅×Q₈	AGL(1,ℤ/8)	1	2	yes	—
360	C₅×D₄	—	2	1	no	—
361	C₅×D₄	—	2	1	no	—
362	C₅×D₄	—	2	1	no	—
363	C₅×D₄	—	2	1	no	—
364	C₅×D₄	—	4	2	no	—
365	C₅×D₄	—	4	2	no	—
366	C₅×D₄	—	4	1	no	—
367	C₅×D₄	—	4	1	no	—
368	C₅×D₄	—	4	1	no	—
369	C₅×D₄	—	4	1	no	—
370	C₅×D₄	—	8	1	no	—
371	C₅×D₄	—	8	2	no	—
372	C₅×D₄	—	8	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	1	no	—
378	C₂×C₄×C₅	—	2	1	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	2	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	2	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	4	1	no	—
386	C₂×C₄×C₅	—	4	2	no	—
387	C₂×C₄×C₅	—	4	4	no	—
388	C₂×C₄×C₅	—	4	1	no	—
389	C₂×C₄×C₅	—	4	1	no	—
390	C₂×C₄×C₅	—	4	1	no	—
391	C₂×C₄×C₅	—	4	1	no	—
392	C₂×C₄×C₅	—	4	1	no	—
393	C₂×C₄×C₅	—	8	1	no	—
394	C₂×C₄×C₅	—	8	2	no	—
395	C₂×C₄×C₅	#120	1	1	yes	characteristic
396	C₂×C₄×C₅	#120	1	1	yes	characteristic
397	C₂×C₄×C₅	#120	1	1	yes	characteristic
398	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
400	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
401	C₅×C₈	—	2	2	no	—
402	C₅×C₈	—	4	1	no	—
403	C₅×C₈	—	4	1	no	—
404	C₅×C₈	—	4	1	no	—
405	C₅×C₈	—	4	1	no	—
406	C₅×C₈	—	4	1	no	—
407	C₂×#41	—	2	1	no	—
408	C₂×#41	C₅×D₄	1	1	yes	characteristic
409	C₂²×Q₈	—	2	1	no	—
410	#135	—	4	4	no	—
411	C₂×Q₁₆	—	2	1	no	—
412	C₂×SD₁₆	—	2	1	no	—
413	C₂×SD₁₆	—	2	2	no	—
414	C₂×SD₁₆	—	2	1	no	—
415	C₂×SD₁₆	—	2	1	no	—
416	C₂×D₈	—	2	1	no	—
417	C₂×D₈	—	2	1	no	—
418	C₂×M₁₆	—	2	1	no	—
419	C₂×M₁₆	—	2	1	no	—
420	C₂²×C₈	—	2	1	no	—
421	C₄⋊Q₈	—	2	2	no	—
422	C₄⋊Q₈	—	2	1	no	—
423	C₄⋊Q₈	—	2	1	no	—
424	C₄⋊Q₈	—	2	1	no	—
425	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
426	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
427	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
428	#127	C₂³×C₅	1	1	yes	characteristic
429	#126	—	2	2	no	—
430	#126	—	2	2	no	—
431	#126	—	2	2	no	—
432	#126	—	2	2	no	—
433	#126	—	2	1	no	—
434	#125	—	2	1	no	—
435	#125	C₅×D₄	1	1	yes	characteristic
436	#124	—	2	2	no	—
437	#124	—	2	2	no	—
438	#124	—	2	2	no	—
439	#124	—	2	2	no	—
440	#124	—	2	1	no	—
441	#124	—	2	1	no	—
442	#124	C₅×D₄	1	1	yes	characteristic
443	#123	—	2	2	no	—
444	#123	—	2	1	no	—
445	C₂²⋊Q₈	—	2	2	no	—
446	C₂²⋊Q₈	—	2	2	no	—
447	C₂²⋊Q₈	—	2	1	no	—
448	C₂²⋊Q₈	—	2	1	no	—
449	C₂²⋊Q₈	—	2	1	no	—
450	C₂²⋊Q₈	—	2	2	no	—
451	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
452	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
453	#121	—	2	2	no	—
454	#121	—	2	1	no	—
455	#121	—	2	1	no	—
456	#121	—	2	1	no	—
457	#121	—	2	1	no	—
458	#121	C₅×D₄	1	1	yes	characteristic
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	2	2	no	—
461	C₄×Q₈	—	2	2	no	—
462	C₄×Q₈	—	2	1	no	—
463	C₄×Q₈	—	2	1	no	—
464	C₄×Q₈	—	2	1	no	—
465	C₄×Q₈	—	2	1	no	—
466	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
467	C₄×Q₈	C₅×D₄	1	2	yes	—
468	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
469	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
470	C₄×D₄	—	2	2	no	—
471	C₄×D₄	—	2	1	no	—
472	C₄×D₄	—	2	1	no	—
473	C₄×D₄	—	2	1	no	—
474	C₄×D₄	—	2	1	no	—
475	C₄×D₄	—	2	1	no	—
476	C₄×D₄	—	2	1	no	—
477	C₄×D₄	C₅×D₄	1	1	yes	characteristic
478	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
479	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
480	#117	—	2	2	no	—
481	#117	—	2	2	no	—
482	#117	—	2	1	no	—
483	#117	—	2	1	no	—
484	#117	—	2	1	no	—
485	#117	—	2	1	no	—
486	#117	—	2	1	no	—
487	#117	—	2	1	no	—
488	#117	C₅×D₄	1	1	yes	characteristic
489	C₂×C₄²	—	2	1	no	—
490	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
491	#107	—	2	2	no	—
492	#107	—	2	1	no	—
493	#106	—	2	1	no	—
494	C₄⋊C₈	—	2	1	no	—
495	C₄⋊C₈	—	2	1	no	—
496	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
497	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
498	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
499	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
500	#103	—	2	2	no	—
501	#103	—	2	1	no	—
502	#103	—	2	1	no	—
503	#103	—	2	1	no	—
504	#102	—	2	1	no	—
505	#102	—	2	1	no	—
506	#102	—	2	1	no	—
507	#102	—	2	2	no	—
508	#102	—	2	1	no	—
509	#102	—	2	1	no	—
510	#97	—	2	1	no	—
511	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
512	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
513	C₂²×C₅	—	2	1	no	—
514	C₂²×C₅	—	2	1	no	—
515	C₂²×C₅	—	2	1	no	—
516	C₂²×C₅	—	4	1	no	—
517	C₂²×C₅	—	4	1	no	—
518	C₂²×C₅	—	4	1	no	—
519	C₂²×C₅	—	4	1	no	—
520	C₂²×C₅	—	4	1	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	8	1	no	—
523	C₂²×C₅	—	8	1	no	—
524	C₂²×C₅	—	8	1	no	—
525	C₂²×C₅	C₂×#120	1	1	yes	characteristic
526	C₄×C₅	—	2	1	no	—
527	C₄×C₅	—	2	2	no	—
528	C₄×C₅	—	2	1	no	—
529	C₄×C₅	—	2	1	no	—
530	C₄×C₅	—	2	1	no	—
531	C₄×C₅	—	4	2	no	—
532	C₄×C₅	—	4	1	no	—
533	C₄×C₅	—	4	1	no	—
534	C₄×C₅	—	4	1	no	—
535	C₄×C₅	—	4	1	no	—
536	C₄×C₅	—	4	2	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	8	1	no	—
539	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
540	C₄×C₅	#575	1	1	yes	characteristic
541	C₄×C₅	#577	1	1	yes	characteristic
542	C₄×C₅	#578	1	1	yes	characteristic
543	#41	—	2	2	no	—
544	#41	—	4	1	no	—
545	#41	—	4	2	no	—
546	#41	—	4	2	no	—
547	C₂×Q₈	—	2	2	no	—
548	C₂×Q₈	—	2	2	no	—
549	C₂×Q₈	—	2	1	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	4	2	no	—
552	C₂×Q₈	—	4	2	no	—
553	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
554	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
555	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
556	C₂×D₄	—	2	1	no	—
557	C₂×D₄	—	2	2	no	—
558	C₂×D₄	—	2	1	no	—
559	C₂×D₄	—	2	1	no	—
560	C₂×D₄	—	2	1	no	—
561	C₂×D₄	—	2	1	no	—
562	C₂×D₄	—	4	1	no	—
563	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
564	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
565	C₂²×C₄	—	2	2	no	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	1	no	—
569	C₂²×C₄	—	2	1	no	—
570	C₂²×C₄	—	4	1	no	—
571	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
572	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
573	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
574	Q₁₆	—	4	2	no	—
575	SD₁₆	—	4	4	no	—
576	SD₁₆	—	4	2	no	—
577	SD₁₆	—	4	2	no	—
578	SD₁₆	—	8	1	no	—
579	D₈	—	4	2	no	—
580	D₈	—	8	1	no	—
581	M₁₆	—	4	2	no	—
582	M₁₆	—	8	1	no	—
583	C₂×C₈	—	2	1	no	—
584	C₂×C₈	—	2	1	no	—
585	C₂×C₈	—	2	1	no	—
586	C₂×C₈	—	2	1	no	—
587	C₂×C₈	—	2	1	no	—
588	C₂×C₈	—	2	1	no	—
589	C₂×C₈	—	4	2	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	2	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	2	2	no	—
594	C₄⋊C₄	—	2	1	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	2	no	—
597	C₄⋊C₄	—	2	1	no	—
598	C₄⋊C₄	—	2	1	no	—
599	C₄⋊C₄	—	2	2	no	—
600	C₄⋊C₄	—	2	1	no	—
601	C₄⋊C₄	—	2	1	no	—
602	C₄⋊C₄	—	2	1	no	—
603	C₄⋊C₄	—	2	1	no	—
604	C₄⋊C₄	—	2	1	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
608	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
609	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
610	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
611	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
612	C₂²⋊C₄	—	2	2	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	2	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	2	no	—
617	C₂²⋊C₄	—	2	2	no	—
618	C₂²⋊C₄	—	2	1	no	—
619	C₂²⋊C₄	—	2	1	no	—
620	C₂²⋊C₄	—	2	1	no	—
621	C₂²⋊C₄	—	2	1	no	—
622	C₂²⋊C₄	—	2	1	no	—
623	C₂²⋊C₄	—	2	1	no	—
624	C₂²⋊C₄	—	2	1	no	—
625	C₂²⋊C₄	—	2	1	no	—
626	C₂²⋊C₄	—	4	1	no	—
627	C₂²⋊C₄	—	4	1	no	—
628	C₄²	—	2	2	no	—
629	C₄²	—	2	2	no	—
630	C₄²	—	2	2	no	—
631	C₄²	—	2	1	no	—
632	C₄²	—	2	1	no	—
633	C₄²	—	2	2	no	—
634	C₄²	—	2	1	no	—
635	C₄²	—	2	1	no	—
636	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
637	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
638	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
639	C₄²	C₂⁴×C₅	1	1	yes	characteristic
640	C₂×C₅	—	4	1	no	—
641	C₂×C₅	—	8	1	no	—
642	C₂×C₅	—	8	1	no	—
643	C₂×C₅	—	16	1	no	—
644	C₂×C₅	#3006	1	1	yes	characteristic
645	C₂×C₅	#3013	1	1	yes	characteristic
646	C₂×C₅	#3018	1	1	yes	characteristic
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	4	1	no	—
650	C₂³	C₅×#120	1	1	yes	characteristic
651	Q₈	—	2	1	no	—
652	Q₈	—	2	1	no	—
653	Q₈	—	2	1	no	—
654	Q₈	—	4	2	no	—
655	Q₈	—	4	4	no	—
656	Q₈	—	4	1	no	—
657	Q₈	—	4	1	no	—
658	Q₈	—	4	1	no	—
659	Q₈	—	4	1	no	—
660	Q₈	—	8	2	no	—
661	Q₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
662	D₄	—	2	1	no	—
663	D₄	—	2	1	no	—
664	D₄	—	2	1	no	—
665	D₄	—	2	1	no	—
666	D₄	—	4	2	no	—
667	D₄	—	4	2	no	—
668	D₄	—	4	1	no	—
669	D₄	—	4	1	no	—
670	D₄	—	4	1	no	—
671	D₄	—	4	1	no	—
672	D₄	—	8	1	no	—
673	D₄	—	8	2	no	—
674	D₄	—	8	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	1	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	1	no	—
694	C₂×C₄	—	4	1	no	—
695	C₂×C₄	—	8	1	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	C₅×#120	1	1	yes	characteristic
698	C₂×C₄	C₅×#120	1	1	yes	characteristic
699	C₂×C₄	C₅×#120	1	1	yes	characteristic
700	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
701	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
702	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
703	C₈	—	2	2	no	—
704	C₈	—	4	1	no	—
705	C₈	—	4	1	no	—
706	C₈	—	4	1	no	—
707	C₈	—	4	1	no	—
708	C₈	—	4	1	no	—
709	C₅	#18608	1	1	yes	characteristic, direct product factor, Sylow
710	C₂²	—	2	1	no	—
711	C₂²	—	2	1	no	—
712	C₂²	—	2	1	no	—
713	C₂²	—	4	1	no	—
714	C₂²	—	4	1	no	—
715	C₂²	—	4	1	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	8	1	no	—
720	C₂²	—	8	1	no	—
721	C₂²	—	8	1	no	—
722	C₂²	C₂×C₅×#120	1	1	yes	characteristic
723	C₄	—	2	1	no	—
724	C₄	—	2	2	no	—
725	C₄	—	2	1	no	—
726	C₄	—	2	1	no	—
727	C₄	—	2	1	no	—
728	C₄	—	4	2	no	—
729	C₄	—	4	1	no	—
730	C₄	—	4	1	no	—
731	C₄	—	4	1	no	—
732	C₄	—	4	1	no	—
733	C₄	—	4	2	no	—
734	C₄	—	4	1	no	—
735	C₄	—	8	1	no	—
736	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
737	C₄	C₅×#575	1	1	yes	characteristic
738	C₄	C₅×#577	1	1	yes	characteristic
739	C₄	C₅×#578	1	1	yes	characteristic
740	C₂	—	4	1	no	—
741	C₂	—	8	1	no	—
742	C₂	—	8	1	no	—
743	C₂	—	16	1	no	—
744	C₂	C₅×#3006	1	1	yes	characteristic
745	C₂	C₅×#3013	1	1	yes	characteristic
746	C₂	C₅×#3018	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
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×#3518	C₂	semidirect
2. C₅×#3251	C₂	semidirect
3. C₅×#3182	C₂	semidirect
4. C₅×#3035	C₂	semidirect
5. C₅×#1650	C₂	semidirect
6. C₅×#1649	C₂	semidirect
7. C₅×#1646	C₂	semidirect
8. C₅×#1645	C₂	semidirect
9. C₅×#1628	C₂	semidirect
10. C₅×#1627	C₂	semidirect
11. C₅×#1624	C₂	semidirect
12. C₅×#1623	C₂	semidirect
13. C₅×#1550	C₂	semidirect
14. C₅×#1489	C₂	semidirect
15. C₅×#1483	C₂	semidirect
71. #18608	C₅	direct (N × H)
178. #3518	C₂×C₅	semidirect
179. #3251	C₂×C₅	semidirect
180. #3182	C₂×C₅	semidirect
181. #3035	C₂×C₅	semidirect
182. #1650	C₂×C₅	semidirect
183. #1649	C₂×C₅	semidirect
184. #1646	C₂×C₅	semidirect
185. #1645	C₂×C₅	semidirect
186. #1628	C₂×C₅	semidirect
187. #1627	C₂×C₅	semidirect
188. #1624	C₂×C₅	semidirect
189. #1623	C₂×C₅	semidirect
190. #1550	C₂×C₅	semidirect
191. #1489	C₂×C₅	semidirect
192. #1483	C₂×C₅	semidirect
709. C₅	#18608	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×#3251	2
C₅×#3182	2
C₅×#3035	2
C₅×#1650	2
C₅×#1649	2
C₅×#1646	2
C₅×#1645	2
C₅×#1628	2
C₅×#1627	2
C₅×#1624	2
C₅×#1623	2
C₅×#1550	2
C₅×#1489	2
C₅×#1483	2
#18608	5

Subgroups — C5×#18608 #11941328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18608 #11941328