Subgroups — C₅×#18619 #11941339

Order 1280.

1010 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3522	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3247	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3147	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3112	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1633	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1632	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1631	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1630	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1623	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1622	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1621	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#1620	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#1551	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	C₂×C₅×#135	—	2	2	no	—
17	C₅×#559	—	2	1	no	—
18	C₅×#559	C₂²	1	1	yes	characteristic
19	C₅×Q₈²	C₂²	1	1	yes	characteristic
20	C₅×#554	—	2	1	no	—
21	C₅×#554	C₂²	1	1	yes	characteristic
22	C₅×#550	C₂²	1	1	yes	characteristic
23	C₅×#548	—	2	1	no	—
24	C₅×#547	—	2	2	no	—
25	C₅×#547	—	2	1	no	—
26	C₅×#542	—	2	2	no	—
27	C₅×#542	—	2	1	no	—
28	C₅×#532	—	2	1	no	—
29	C₅×#532	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×#520	—	2	1	no	—
34	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
35	C₅×#495	—	2	2	no	—
36	C₅×#494	C₂²	1	1	yes	characteristic
37	C₅×#493	C₂²	1	1	yes	characteristic
38	C₅×#492	C₂²	1	1	yes	characteristic
39	C₅×#492	C₂²	1	1	yes	characteristic
40	C₅×#480	—	2	1	no	—
41	C₅×#478	—	2	1	no	—
42	C₅×#477	C₂²	1	1	yes	characteristic
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×#466	—	2	1	no	—
47	C₅×#465	—	2	1	no	—
48	C₅×#463	—	2	1	no	—
49	C₅×#460	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×#448	—	2	1	no	—
54	C₅×#440	—	2	1	no	—
55	C₅×#440	—	2	1	no	—
56	C₅×#432	C₂²	1	1	yes	characteristic
57	C₂×C₅×C₄⋊C₈	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×#331	C₂²	1	1	yes	characteristic
62	C₅×#331	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	#18619	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
72	C₂×C₅×#41	—	2	2	no	—
73	C₂×C₅×#41	—	2	1	no	—
74	C₂×C₅×#41	—	2	1	no	—
75	C₂×C₅×#41	D₄	1	2	yes	—
76	C₂²×C₅×Q₈	D₄	1	1	yes	characteristic
77	C₅×#135	—	4	8	no	—
78	C₂×C₅×Q₁₆	—	2	2	no	—
79	C₂×C₅×SD₁₆	—	2	1	no	—
80	C₂×C₅×SD₁₆	—	2	1	no	—
81	C₂×C₅×SD₁₆	—	2	2	no	—
82	C₂×C₅×SD₁₆	—	2	2	no	—
83	C₂×C₅×SD₁₆	—	2	1	no	—
84	C₂×C₅×D₈	—	2	2	no	—
85	C₂×C₅×D₈	—	2	1	no	—
86	C₂²×C₅×C₈	—	2	1	no	—
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₅×C₄⋊Q₈	—	2	2	no	—
89	C₅×C₄⋊Q₈	—	2	1	no	—
90	C₅×C₄⋊Q₈	—	2	1	no	—
91	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
92	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
93	C₅×#127	—	2	1	no	—
94	C₅×#127	C₂³	1	1	yes	characteristic
95	C₅×#127	C₂³	1	1	yes	characteristic
96	C₅×#126	—	2	2	no	—
97	C₅×#126	—	2	1	no	—
98	C₅×#125	—	2	1	no	—
99	C₅×#125	D₄	1	1	yes	characteristic
100	C₅×#124	—	2	2	no	—
101	C₅×#124	—	2	2	no	—
102	C₅×#124	—	2	1	no	—
103	C₅×#124	—	2	1	no	—
104	C₅×#124	—	2	1	no	—
105	C₅×#124	D₄	1	1	yes	characteristic
106	C₅×#124	D₄	1	2	yes	—
107	C₅×#123	—	2	2	no	—
108	C₅×#123	—	2	2	no	—
109	C₅×#123	—	2	2	no	—
110	C₅×#123	—	2	2	no	—
111	C₅×#123	—	2	1	no	—
112	C₅×C₂²⋊Q₈	—	2	2	no	—
113	C₅×C₂²⋊Q₈	—	2	2	no	—
114	C₅×C₂²⋊Q₈	—	2	2	no	—
115	C₅×C₂²⋊Q₈	—	2	2	no	—
116	C₅×C₂²⋊Q₈	—	2	1	no	—
117	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
118	C₅×#121	—	2	2	no	—
119	C₅×#121	—	2	2	no	—
120	C₅×#121	—	2	1	no	—
121	C₅×#121	—	2	1	no	—
122	C₅×#121	—	2	1	no	—
123	C₅×#121	—	2	1	no	—
124	C₅×#121	—	2	1	no	—
125	C₅×#121	D₄	1	1	yes	characteristic
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	2	no	—
137	C₄×C₅×D₄	—	2	2	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	—	2	1	no	—
143	C₄×C₅×D₄	—	2	1	no	—
144	C₄×C₅×D₄	—	2	1	no	—
145	C₄×C₅×D₄	—	2	1	no	—
146	C₄×C₅×D₄	—	2	1	no	—
147	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
148	C₅×#117	—	2	2	no	—
149	C₅×#117	—	2	1	no	—
150	C₂×C₅×C₄⋊C₄	—	2	2	no	—
151	C₂×C₅×C₄⋊C₄	—	2	1	no	—
152	C₂×C₅×C₄⋊C₄	—	2	1	no	—
153	C₂×C₅×C₄⋊C₄	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	1	no	—
157	C₅×#107	—	2	1	no	—
158	C₅×#107	—	2	1	no	—
159	C₅×#106	—	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	1	no	—
166	C₅×#103	—	2	1	no	—
167	C₅×#103	—	2	1	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×#102	—	2	1	no	—
173	C₅×C₂²⋊C₈	—	2	1	no	—
174	C₅×#97	—	2	1	no	—
175	C₄×C₅×C₈	—	2	1	no	—
176	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
177	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
178	#3522	C₂×C₅	1	1	yes	characteristic, complemented
179	#3247	C₂×C₅	1	1	yes	characteristic, complemented
180	#3147	C₂×C₅	1	1	yes	characteristic, complemented
181	#3112	C₂×C₅	1	1	yes	characteristic, complemented
182	#1633	C₂×C₅	1	1	yes	characteristic, complemented
183	#1632	C₂×C₅	1	1	yes	characteristic, complemented
184	#1631	C₂×C₅	1	1	yes	characteristic, complemented
185	#1630	C₂×C₅	1	1	yes	characteristic, complemented
186	#1623	C₂×C₅	1	1	yes	characteristic, complemented
187	#1622	C₂×C₅	1	1	yes	characteristic, complemented
188	#1621	C₂×C₅	1	1	yes	characteristic, complemented
189	#1620	C₂×C₅	1	1	yes	characteristic, complemented
190	#1551	C₂×C₅	1	1	yes	characteristic, complemented
191	#1494	C₂×C₅	1	1	yes	characteristic, complemented
192	C₂×Q₈⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
193	C₅×#41	—	4	4	no	—
194	C₅×#41	—	4	4	no	—
195	C₅×#41	—	4	2	no	—
196	C₅×#41	—	4	2	no	—
197	C₅×#41	—	8	4	no	—
198	C₂×C₅×Q₈	—	2	2	no	—
199	C₂×C₅×Q₈	—	2	1	no	—
200	C₂×C₅×Q₈	—	2	2	no	—
201	C₂×C₅×Q₈	—	2	1	no	—
202	C₂×C₅×Q₈	—	4	1	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	1	yes	characteristic
206	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
207	C₂×C₅×D₄	—	2	2	no	—
208	C₂×C₅×D₄	—	2	2	no	—
209	C₂×C₅×D₄	—	2	1	no	—
210	C₂×C₅×D₄	—	2	2	no	—
211	C₂×C₅×D₄	—	2	1	no	—
212	C₂×C₅×D₄	—	2	1	no	—
213	C₂×C₅×D₄	—	2	1	no	—
214	C₂×C₅×D₄	—	2	1	no	—
215	C₂×C₅×D₄	—	2	1	no	—
216	C₂×C₅×D₄	—	4	1	no	—
217	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
218	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
219	C₂²×C₄×C₅	—	2	2	no	—
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	—	2	1	no	—
222	C₂²×C₄×C₅	—	2	2	no	—
223	C₂²×C₄×C₅	—	2	2	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	2	2	no	—
226	C₂²×C₄×C₅	—	4	1	no	—
227	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
230	C₅×Q₁₆	—	4	4	no	—
231	C₅×SD₁₆	—	4	4	no	—
232	C₅×SD₁₆	—	4	4	no	—
233	C₅×SD₁₆	—	4	2	no	—
234	C₅×SD₁₆	—	4	2	no	—
235	C₅×SD₁₆	—	8	1	no	—
236	C₅×D₈	—	4	4	no	—
237	C₅×D₈	—	8	1	no	—
238	C₂×C₅×C₈	—	2	4	no	—
239	C₂×C₅×C₈	—	2	1	no	—
240	C₂×C₅×C₈	—	2	1	no	—
241	C₂×C₅×C₈	—	2	1	no	—
242	C₂×C₅×C₈	—	2	1	no	—
243	C₂×C₅×C₈	—	2	1	no	—
244	C₂×C₅×C₈	—	2	1	no	—
245	C₂×C₅×C₈	—	8	1	no	—
246	C₅×C₄⋊C₄	—	2	2	no	—
247	C₅×C₄⋊C₄	—	2	2	no	—
248	C₅×C₄⋊C₄	—	2	2	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	—	2	1	no	—
258	C₅×C₄⋊C₄	—	2	1	no	—
259	C₅×C₄⋊C₄	—	2	1	no	—
260	C₅×C₄⋊C₄	—	2	1	no	—
261	C₅×C₄⋊C₄	—	2	1	no	—
262	C₅×C₄⋊C₄	—	2	1	no	—
263	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
264	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
265	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
266	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
267	C₅×C₂²⋊C₄	—	2	2	no	—
268	C₅×C₂²⋊C₄	—	2	2	no	—
269	C₅×C₂²⋊C₄	—	2	2	no	—
270	C₅×C₂²⋊C₄	—	2	2	no	—
271	C₅×C₂²⋊C₄	—	2	2	no	—
272	C₅×C₂²⋊C₄	—	2	1	no	—
273	C₅×C₂²⋊C₄	—	2	2	no	—
274	C₅×C₂²⋊C₄	—	2	1	no	—
275	C₅×C₂²⋊C₄	—	2	1	no	—
276	C₅×C₂²⋊C₄	—	2	2	no	—
277	C₅×C₂²⋊C₄	—	2	1	no	—
278	C₅×C₂²⋊C₄	—	2	1	no	—
279	C₅×C₂²⋊C₄	—	4	1	no	—
280	C₅×C₂²⋊C₄	—	4	1	no	—
281	C₄²×C₅	—	2	2	no	—
282	C₄²×C₅	—	2	1	no	—
283	C₄²×C₅	—	2	1	no	—
284	C₄²×C₅	—	2	1	no	—
285	C₄²×C₅	—	2	1	no	—
286	C₄²×C₅	—	2	1	no	—
287	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
288	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
289	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
290	C₄²×C₅	C₂⁴	1	1	yes	characteristic
291	C₂×#135	—	2	2	no	—
292	#559	—	2	1	no	—
293	#559	C₂²×C₅	1	1	yes	characteristic
294	Q₈²	C₂²×C₅	1	1	yes	characteristic
295	#554	—	2	1	no	—
296	#554	C₂²×C₅	1	1	yes	characteristic
297	#550	C₂²×C₅	1	1	yes	characteristic
298	#548	—	2	1	no	—
299	#547	—	2	2	no	—
300	#547	—	2	1	no	—
301	#542	—	2	2	no	—
302	#542	—	2	1	no	—
303	#532	—	2	1	no	—
304	#532	C₂²×C₅	1	1	yes	characteristic
305	#532	C₂²×C₅	1	1	yes	characteristic
306	#529	—	2	1	no	—
307	#529	C₂²×C₅	1	1	yes	characteristic
308	#520	—	2	1	no	—
309	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
310	#495	—	2	2	no	—
311	#494	C₂²×C₅	1	1	yes	characteristic
312	#493	C₂²×C₅	1	1	yes	characteristic
313	#492	C₂²×C₅	1	1	yes	characteristic
314	#492	C₂²×C₅	1	1	yes	characteristic
315	#480	—	2	1	no	—
316	#478	—	2	1	no	—
317	#477	C₂²×C₅	1	1	yes	characteristic
318	#477	C₂²×C₅	1	1	yes	characteristic
319	#477	C₂²×C₅	1	1	yes	characteristic
320	#476	C₂²×C₅	1	1	yes	characteristic
321	#466	—	2	1	no	—
322	#465	—	2	1	no	—
323	#463	—	2	1	no	—
324	#460	C₂²×C₅	1	1	yes	characteristic
325	#460	C₂²×C₅	1	1	yes	characteristic
326	#460	C₂²×C₅	1	1	yes	characteristic
327	#459	C₂²×C₅	1	1	yes	characteristic
328	#448	—	2	1	no	—
329	#440	—	2	1	no	—
330	#440	—	2	1	no	—
331	#432	C₂²×C₅	1	1	yes	characteristic
332	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
333	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
334	#333	C₂²×C₅	1	1	yes	characteristic
335	#333	C₂²×C₅	1	1	yes	characteristic
336	#331	C₂²×C₅	1	1	yes	characteristic
337	#331	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	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
343	Q₈⋊C₈	C₂²×C₅	1	1	yes	characteristic
344	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
345	D₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
346	C₂³×C₅	—	2	1	no	—
347	C₂³×C₅	—	2	2	no	—
348	C₂³×C₅	—	4	1	no	—
349	C₂³×C₅	#120	1	1	yes	characteristic
350	C₅×Q₈	—	2	1	no	—
351	C₅×Q₈	—	2	1	no	—
352	C₅×Q₈	—	2	1	no	—
353	C₅×Q₈	—	2	1	no	—
354	C₅×Q₈	—	2	1	no	—
355	C₅×Q₈	—	4	2	no	—
356	C₅×Q₈	—	4	2	no	—
357	C₅×Q₈	—	4	2	no	—
358	C₅×Q₈	—	8	2	no	—
359	C₅×Q₈	#135	1	2	yes	complemented
360	C₅×D₄	—	2	1	no	—
361	C₅×D₄	—	2	1	no	—
362	C₅×D₄	—	4	2	no	—
363	C₅×D₄	—	4	4	no	—
364	C₅×D₄	—	4	2	no	—
365	C₅×D₄	—	4	4	no	—
366	C₅×D₄	—	4	2	no	—
367	C₅×D₄	—	4	1	no	—
368	C₅×D₄	—	4	1	no	—
369	C₅×D₄	—	4	1	no	—
370	C₅×D₄	—	4	1	no	—
371	C₅×D₄	—	4	1	no	—
372	C₅×D₄	—	4	1	no	—
373	C₅×D₄	—	4	1	no	—
374	C₅×D₄	—	4	1	no	—
375	C₅×D₄	—	8	2	no	—
376	C₅×D₄	—	8	2	no	—
377	C₂×C₄×C₅	—	2	1	no	—
378	C₂×C₄×C₅	—	2	2	no	—
379	C₂×C₄×C₅	—	2	1	no	—
380	C₂×C₄×C₅	—	2	1	no	—
381	C₂×C₄×C₅	—	2	1	no	—
382	C₂×C₄×C₅	—	2	1	no	—
383	C₂×C₄×C₅	—	2	1	no	—
384	C₂×C₄×C₅	—	2	1	no	—
385	C₂×C₄×C₅	—	2	1	no	—
386	C₂×C₄×C₅	—	2	1	no	—
387	C₂×C₄×C₅	—	2	2	no	—
388	C₂×C₄×C₅	—	2	1	no	—
389	C₂×C₄×C₅	—	2	1	no	—
390	C₂×C₄×C₅	—	4	2	no	—
391	C₂×C₄×C₅	—	4	4	no	—
392	C₂×C₄×C₅	—	4	2	no	—
393	C₂×C₄×C₅	—	4	1	no	—
394	C₂×C₄×C₅	—	4	1	no	—
395	C₂×C₄×C₅	—	4	1	no	—
396	C₂×C₄×C₅	—	8	2	no	—
397	C₂×C₄×C₅	—	8	2	no	—
398	C₂×C₄×C₅	—	8	2	no	—
399	C₂×C₄×C₅	—	8	2	no	—
400	C₂×C₄×C₅	#120	1	1	yes	characteristic
401	C₂×C₄×C₅	#120	1	1	yes	characteristic
402	C₂×C₄×C₅	#120	1	1	yes	characteristic
403	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
404	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
406	C₅×C₈	—	2	2	no	—
407	C₅×C₈	—	2	2	no	—
408	C₅×C₈	—	4	1	no	—
409	C₅×C₈	—	4	1	no	—
410	C₅×C₈	—	4	1	no	—
411	C₅×C₈	—	4	1	no	—
412	C₂×#41	—	2	2	no	—
413	C₂×#41	—	2	1	no	—
414	C₂×#41	—	2	1	no	—
415	C₂×#41	C₅×D₄	1	2	yes	—
416	C₂²×Q₈	C₅×D₄	1	1	yes	characteristic
417	#135	—	4	8	no	—
418	C₂×Q₁₆	—	2	2	no	—
419	C₂×SD₁₆	—	2	2	no	—
420	C₂×SD₁₆	—	2	1	no	—
421	C₂×SD₁₆	—	2	1	no	—
422	C₂×SD₁₆	—	2	2	no	—
423	C₂×SD₁₆	—	2	1	no	—
424	C₂×D₈	—	2	2	no	—
425	C₂×D₈	—	2	1	no	—
426	C₂²×C₈	—	2	1	no	—
427	C₂²×C₈	—	2	1	no	—
428	C₄⋊Q₈	—	2	2	no	—
429	C₄⋊Q₈	—	2	1	no	—
430	C₄⋊Q₈	—	2	1	no	—
431	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
432	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
433	#127	—	2	1	no	—
434	#127	C₂³×C₅	1	1	yes	characteristic
435	#127	C₂³×C₅	1	1	yes	characteristic
436	#126	—	2	2	no	—
437	#126	—	2	1	no	—
438	#125	—	2	1	no	—
439	#125	C₅×D₄	1	1	yes	characteristic
440	#124	—	2	2	no	—
441	#124	—	2	2	no	—
442	#124	—	2	1	no	—
443	#124	—	2	1	no	—
444	#124	—	2	1	no	—
445	#124	C₅×D₄	1	1	yes	characteristic
446	#124	C₅×D₄	1	2	yes	—
447	#123	—	2	2	no	—
448	#123	—	2	2	no	—
449	#123	—	2	2	no	—
450	#123	—	2	2	no	—
451	#123	—	2	1	no	—
452	C₂²⋊Q₈	—	2	2	no	—
453	C₂²⋊Q₈	—	2	2	no	—
454	C₂²⋊Q₈	—	2	2	no	—
455	C₂²⋊Q₈	—	2	2	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
458	#121	—	2	2	no	—
459	#121	—	2	2	no	—
460	#121	—	2	1	no	—
461	#121	—	2	1	no	—
462	#121	—	2	1	no	—
463	#121	—	2	1	no	—
464	#121	—	2	1	no	—
465	#121	C₅×D₄	1	1	yes	characteristic
466	C₄×Q₈	—	2	1	no	—
467	C₄×Q₈	—	2	1	no	—
468	C₄×Q₈	—	2	1	no	—
469	C₄×Q₈	—	2	1	no	—
470	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
471	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
472	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
473	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
474	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
475	C₄×D₄	—	2	2	no	—
476	C₄×D₄	—	2	2	no	—
477	C₄×D₄	—	2	2	no	—
478	C₄×D₄	—	2	1	no	—
479	C₄×D₄	—	2	1	no	—
480	C₄×D₄	—	2	1	no	—
481	C₄×D₄	—	2	1	no	—
482	C₄×D₄	—	2	1	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	1	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
488	#117	—	2	2	no	—
489	#117	—	2	1	no	—
490	C₂×C₄⋊C₄	—	2	2	no	—
491	C₂×C₄⋊C₄	—	2	1	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
494	C₂×C₄²	—	2	1	no	—
495	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
496	#107	—	2	1	no	—
497	#107	—	2	1	no	—
498	#107	—	2	1	no	—
499	#106	—	2	1	no	—
500	C₄⋊C₈	—	2	1	no	—
501	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
502	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
503	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
504	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
505	#103	—	2	1	no	—
506	#103	—	2	1	no	—
507	#103	—	2	1	no	—
508	#102	—	2	1	no	—
509	#102	—	2	1	no	—
510	#102	—	2	1	no	—
511	#102	—	2	1	no	—
512	#102	—	2	1	no	—
513	C₂²⋊C₈	—	2	1	no	—
514	#97	—	2	1	no	—
515	C₄×C₈	—	2	1	no	—
516	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
517	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
518	C₂²×C₅	—	2	1	no	—
519	C₂²×C₅	—	2	1	no	—
520	C₂²×C₅	—	4	2	no	—
521	C₂²×C₅	—	4	1	no	—
522	C₂²×C₅	—	4	1	no	—
523	C₂²×C₅	—	4	2	no	—
524	C₂²×C₅	—	4	2	no	—
525	C₂²×C₅	—	4	1	no	—
526	C₂²×C₅	—	8	1	no	—
527	C₂²×C₅	—	8	1	no	—
528	C₂²×C₅	—	8	1	no	—
529	C₂²×C₅	#453	1	2	yes	—
530	C₂²×C₅	C₂×#120	1	1	yes	characteristic
531	C₄×C₅	—	2	1	no	—
532	C₄×C₅	—	2	2	no	—
533	C₄×C₅	—	2	1	no	—
534	C₄×C₅	—	2	1	no	—
535	C₄×C₅	—	2	1	no	—
536	C₄×C₅	—	4	1	no	—
537	C₄×C₅	—	4	1	no	—
538	C₄×C₅	—	4	1	no	—
539	C₄×C₅	—	4	1	no	—
540	C₄×C₅	—	4	1	no	—
541	C₄×C₅	—	4	2	no	—
542	C₄×C₅	—	4	1	no	—
543	C₄×C₅	—	8	1	no	—
544	C₄×C₅	C₂×#135	1	1	yes	characteristic
545	C₄×C₅	#575	1	1	yes	characteristic
546	C₄×C₅	#577	1	1	yes	characteristic
547	C₄×C₅	#578	1	1	yes	characteristic
548	#41	—	4	4	no	—
549	#41	—	4	4	no	—
550	#41	—	4	2	no	—
551	#41	—	4	2	no	—
552	#41	—	8	4	no	—
553	C₂×Q₈	—	2	2	no	—
554	C₂×Q₈	—	2	1	no	—
555	C₂×Q₈	—	2	2	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	4	1	no	—
558	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
559	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
560	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
561	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	2	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	—	2	1	no	—
570	C₂×D₄	—	2	1	no	—
571	C₂×D₄	—	4	1	no	—
572	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
573	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
574	C₂²×C₄	—	2	2	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	—	2	2	no	—
578	C₂²×C₄	—	2	2	no	—
579	C₂²×C₄	—	2	1	no	—
580	C₂²×C₄	—	2	2	no	—
581	C₂²×C₄	—	4	1	no	—
582	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
583	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
584	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
585	Q₁₆	—	4	4	no	—
586	SD₁₆	—	4	4	no	—
587	SD₁₆	—	4	4	no	—
588	SD₁₆	—	4	2	no	—
589	SD₁₆	—	4	2	no	—
590	SD₁₆	—	8	1	no	—
591	D₈	—	4	4	no	—
592	D₈	—	8	1	no	—
593	C₂×C₈	—	2	4	no	—
594	C₂×C₈	—	2	1	no	—
595	C₂×C₈	—	2	1	no	—
596	C₂×C₈	—	2	1	no	—
597	C₂×C₈	—	2	1	no	—
598	C₂×C₈	—	2	1	no	—
599	C₂×C₈	—	2	1	no	—
600	C₂×C₈	—	8	1	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₄⋊C₄	—	2	2	no	—
604	C₄⋊C₄	—	2	2	no	—
605	C₄⋊C₄	—	2	1	no	—
606	C₄⋊C₄	—	2	1	no	—
607	C₄⋊C₄	—	2	1	no	—
608	C₄⋊C₄	—	2	1	no	—
609	C₄⋊C₄	—	2	1	no	—
610	C₄⋊C₄	—	2	1	no	—
611	C₄⋊C₄	—	2	1	no	—
612	C₄⋊C₄	—	2	1	no	—
613	C₄⋊C₄	—	2	1	no	—
614	C₄⋊C₄	—	2	1	no	—
615	C₄⋊C₄	—	2	1	no	—
616	C₄⋊C₄	—	2	1	no	—
617	C₄⋊C₄	—	2	1	no	—
618	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
619	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
620	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
621	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
622	C₂²⋊C₄	—	2	2	no	—
623	C₂²⋊C₄	—	2	2	no	—
624	C₂²⋊C₄	—	2	2	no	—
625	C₂²⋊C₄	—	2	2	no	—
626	C₂²⋊C₄	—	2	2	no	—
627	C₂²⋊C₄	—	2	1	no	—
628	C₂²⋊C₄	—	2	2	no	—
629	C₂²⋊C₄	—	2	1	no	—
630	C₂²⋊C₄	—	2	1	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	1	no	—
633	C₂²⋊C₄	—	2	1	no	—
634	C₂²⋊C₄	—	4	1	no	—
635	C₂²⋊C₄	—	4	1	no	—
636	C₄²	—	2	2	no	—
637	C₄²	—	2	1	no	—
638	C₄²	—	2	1	no	—
639	C₄²	—	2	1	no	—
640	C₄²	—	2	1	no	—
641	C₄²	—	2	1	no	—
642	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
643	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
644	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
645	C₄²	C₂⁴×C₅	1	1	yes	characteristic
646	C₂×C₅	—	2	2	no	—
647	C₂×C₅	—	8	1	no	—
648	C₂×C₅	—	8	2	no	—
649	C₂×C₅	—	16	1	no	—
650	C₂×C₅	#3002	1	1	yes	characteristic
651	C₂×C₅	#3013	1	1	yes	characteristic
652	C₂×C₅	C₂×#453	1	1	yes	characteristic
653	C₂³	—	2	1	no	—
654	C₂³	—	2	2	no	—
655	C₂³	—	4	1	no	—
656	C₂³	C₅×#120	1	1	yes	characteristic
657	Q₈	—	2	1	no	—
658	Q₈	—	2	1	no	—
659	Q₈	—	2	1	no	—
660	Q₈	—	2	1	no	—
661	Q₈	—	2	1	no	—
662	Q₈	—	4	2	no	—
663	Q₈	—	4	2	no	—
664	Q₈	—	4	2	no	—
665	Q₈	—	8	2	no	—
666	Q₈	C₅×#135	1	2	yes	complemented
667	D₄	—	2	1	no	—
668	D₄	—	2	1	no	—
669	D₄	—	4	2	no	—
670	D₄	—	4	4	no	—
671	D₄	—	4	2	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	2	no	—
674	D₄	—	4	1	no	—
675	D₄	—	4	1	no	—
676	D₄	—	4	1	no	—
677	D₄	—	4	1	no	—
678	D₄	—	4	1	no	—
679	D₄	—	4	1	no	—
680	D₄	—	4	1	no	—
681	D₄	—	4	1	no	—
682	D₄	—	8	2	no	—
683	D₄	—	8	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	2	1	no	—
688	C₂×C₄	—	2	1	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	1	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	2	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	4	2	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	4	2	no	—
700	C₂×C₄	—	4	1	no	—
701	C₂×C₄	—	4	1	no	—
702	C₂×C₄	—	4	1	no	—
703	C₂×C₄	—	8	2	no	—
704	C₂×C₄	—	8	2	no	—
705	C₂×C₄	—	8	2	no	—
706	C₂×C₄	—	8	2	no	—
707	C₂×C₄	C₅×#120	1	1	yes	characteristic
708	C₂×C₄	C₅×#120	1	1	yes	characteristic
709	C₂×C₄	C₅×#120	1	1	yes	characteristic
710	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
711	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
712	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
713	C₈	—	2	2	no	—
714	C₈	—	2	2	no	—
715	C₈	—	4	1	no	—
716	C₈	—	4	1	no	—
717	C₈	—	4	1	no	—
718	C₈	—	4	1	no	—
719	C₅	#18619	1	1	yes	characteristic, direct product factor, Sylow
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	8	1	no	—
729	C₂²	—	8	1	no	—
730	C₂²	—	8	1	no	—
731	C₂²	C₅×#453	1	2	yes	—
732	C₂²	C₂×C₅×#120	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	4	1	no	—
739	C₄	—	4	1	no	—
740	C₄	—	4	1	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	2	no	—
744	C₄	—	4	1	no	—
745	C₄	—	8	1	no	—
746	C₄	C₂×C₅×#135	1	1	yes	characteristic
747	C₄	C₅×#575	1	1	yes	characteristic
748	C₄	C₅×#577	1	1	yes	characteristic
749	C₄	C₅×#578	1	1	yes	characteristic
750	C₂	—	2	2	no	—
751	C₂	—	8	1	no	—
752	C₂	—	8	2	no	—
753	C₂	—	16	1	no	—
754	C₂	C₅×#3002	1	1	yes	characteristic
755	C₂	C₅×#3013	1	1	yes	characteristic
756	C₂	C₂×C₅×#453	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×#3522	C₂	semidirect
2. C₅×#3247	C₂	semidirect
3. C₅×#3147	C₂	semidirect
4. C₅×#3112	C₂	semidirect
5. C₅×#1633	C₂	semidirect
6. C₅×#1632	C₂	semidirect
7. C₅×#1631	C₂	semidirect
8. C₅×#1630	C₂	semidirect
9. C₅×#1623	C₂	semidirect
10. C₅×#1622	C₂	semidirect
11. C₅×#1621	C₂	semidirect
12. C₅×#1620	C₂	semidirect
13. C₅×#1551	C₂	semidirect
14. C₅×#1494	C₂	semidirect
15. C₂×C₅×Q₈⋊C₈	C₂	semidirect
71. #18619	C₅	direct (N × H)
178. #3522	C₂×C₅	semidirect
179. #3247	C₂×C₅	semidirect
180. #3147	C₂×C₅	semidirect
181. #3112	C₂×C₅	semidirect
182. #1633	C₂×C₅	semidirect
183. #1632	C₂×C₅	semidirect
184. #1631	C₂×C₅	semidirect
185. #1630	C₂×C₅	semidirect
186. #1623	C₂×C₅	semidirect
187. #1622	C₂×C₅	semidirect
188. #1621	C₂×C₅	semidirect
189. #1620	C₂×C₅	semidirect
190. #1551	C₂×C₅	semidirect
191. #1494	C₂×C₅	semidirect
192. C₂×Q₈⋊C₈	C₂×C₅	semidirect
359. C₅×Q₈	#135	semidirect
666. Q₈	C₅×#135	semidirect
719. C₅	#18619	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×#3522	2
C₅×#3247	2
C₅×#3147	2
C₅×#3112	2
C₅×#1633	2
C₅×#1632	2
C₅×#1631	2
C₅×#1630	2
C₅×#1623	2
C₅×#1622	2
C₅×#1621	2
C₅×#1620	2
C₅×#1551	2
C₅×#1494	2
C₂×C₅×Q₈⋊C₈	2
#18619	5

Subgroups — C5×#18619 #11941339

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#18619 #11941339