Subgroups — C₅×#17713 #11940433

Order 1280.

996 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3444	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1554	C₂	1	2	yes	maximal, complemented
5	C₅×#1553	C₂	1	2	yes	maximal, complemented
6	C₅×#1552	C₂	1	2	yes	maximal, complemented
7	C₅×#1551	C₂	1	2	yes	maximal, complemented
8	C₅×#1542	C₂	1	2	yes	maximal, complemented
9	C₅×#1540	C₂	1	2	yes	maximal, complemented
10	C₅×#533	C₂²	1	1	yes	characteristic
11	C₅×#533	C₂²	1	1	yes	characteristic
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₅×#532	C₂²	1	1	yes	characteristic
16	C₅×#529	—	2	1	no	—
17	C₅×#529	—	2	1	no	—
18	C₅×#529	—	2	1	no	—
19	C₅×#529	—	2	1	no	—
20	C₅×#529	C₄	1	2	yes	—
21	C₅×#529	C₄	1	2	yes	—
22	C₅×#525	—	2	1	no	—
23	C₅×#525	—	2	1	no	—
24	C₅×#525	C₄	1	2	yes	—
25	C₄×C₅×#41	—	2	1	no	—
26	C₄×C₅×#41	—	2	1	no	—
27	C₄×C₅×#41	C₄	1	2	yes	—
28	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₅×#432	—	2	1	no	—
30	C₅×#432	—	2	1	no	—
31	C₅×#432	C₂²	1	2	yes	—
32	C₅×#432	C₂²	1	2	yes	—
33	C₅×#431	—	2	1	no	—
34	C₅×#431	—	2	1	no	—
35	C₅×#431	C₂²	1	2	yes	—
36	C₅×#431	C₂²	1	2	yes	—
37	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
38	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	—
39	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
40	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
41	C₂×C₅×#97	—	2	1	no	—
42	C₂×C₄×C₅×C₈	—	2	1	no	—
43	C₅×#333	C₂²	1	4	yes	complemented
44	C₅×#332	C₂²	1	4	yes	complemented
45	C₅×#332	C₂²	1	4	yes	complemented
46	C₅×#331	C₂²	1	4	yes	complemented
47	#17713	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂×C₅×#41	—	2	1	no	—
50	C₂×C₅×#41	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
54	C₂²×C₅×C₈	—	2	2	no	—
55	C₂²×C₅×C₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
58	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
59	C₅×#127	C₂³	1	1	yes	characteristic
60	C₅×#126	—	2	2	no	—
61	C₅×#126	—	2	2	no	—
62	C₅×#125	—	2	1	no	—
63	C₅×#125	—	2	1	no	—
64	C₅×#125	C₂×C₄	1	2	yes	—
65	C₅×#124	—	2	1	no	—
66	C₅×#124	—	2	1	no	—
67	C₅×#124	C₂×C₄	1	2	yes	—
68	C₅×#123	—	2	2	no	—
69	C₅×#123	—	2	2	no	—
70	C₅×#123	—	2	2	no	—
71	C₅×C₂²⋊Q₈	—	2	1	no	—
72	C₅×C₂²⋊Q₈	—	2	1	no	—
73	C₅×C₂²⋊Q₈	—	2	1	no	—
74	C₅×C₂²⋊Q₈	—	2	1	no	—
75	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
76	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
77	C₅×#121	—	2	1	no	—
78	C₅×#121	—	2	1	no	—
79	C₅×#121	—	2	1	no	—
80	C₅×#121	—	2	1	no	—
81	C₅×#121	C₂×C₄	1	2	yes	—
82	C₅×#121	C₂×C₄	1	2	yes	—
83	C₅×#120	—	2	2	no	—
84	C₄×C₅×Q₈	—	2	1	no	—
85	C₄×C₅×Q₈	—	2	1	no	—
86	C₄×C₅×Q₈	—	2	1	no	—
87	C₄×C₅×Q₈	—	2	1	no	—
88	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
89	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
90	C₄×C₅×D₄	—	2	2	no	—
91	C₄×C₅×D₄	—	2	2	no	—
92	C₄×C₅×D₄	—	2	2	no	—
93	C₄×C₅×D₄	—	2	2	no	—
94	C₄×C₅×D₄	—	2	2	no	—
95	C₄×C₅×D₄	—	2	2	no	—
96	C₄×C₅×D₄	—	2	1	no	—
97	C₄×C₅×D₄	—	2	1	no	—
98	C₄×C₅×D₄	—	2	1	no	—
99	C₄×C₅×D₄	—	2	1	no	—
100	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
101	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
102	C₅×#117	—	2	1	no	—
103	C₅×#117	—	2	1	no	—
104	C₅×#117	—	2	2	no	—
105	C₅×#117	—	2	2	no	—
106	C₅×#117	—	2	2	no	—
107	C₅×#117	C₂×C₄	1	2	yes	—
108	C₂×C₄²×C₅	—	2	2	no	—
109	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
113	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
114	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
115	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
116	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
117	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₅×C₄⋊C₈	—	2	2	no	—
122	C₅×C₄⋊C₈	—	2	2	no	—
123	C₅×C₄⋊C₈	C₂³	1	4	yes	—
124	C₅×C₄⋊C₈	C₂³	1	4	yes	—
125	C₅×C₂²⋊C₈	—	2	2	no	—
126	C₅×C₂²⋊C₈	—	2	2	no	—
127	C₅×C₂²⋊C₈	—	2	2	no	—
128	C₅×C₂²⋊C₈	—	2	2	no	—
129	C₅×#97	—	2	2	no	—
130	C₅×#97	—	2	2	no	—
131	C₄×C₅×C₈	—	2	2	no	—
132	C₄×C₅×C₈	—	2	2	no	—
133	#3444	C₂×C₅	1	1	yes	characteristic
134	C₂×#432	C₂×C₅	1	1	yes	characteristic, complemented
135	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
136	#1554	C₂×C₅	1	2	yes	complemented
137	#1553	C₂×C₅	1	2	yes	complemented
138	#1552	C₂×C₅	1	2	yes	complemented
139	#1551	C₂×C₅	1	2	yes	complemented
140	#1542	C₂×C₅	1	2	yes	complemented
141	#1540	C₂×C₅	1	2	yes	complemented
142	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
143	C₅×#41	—	4	4	no	—
144	C₅×#41	—	4	4	no	—
145	C₅×#41	—	4	4	no	—
146	C₂×C₅×Q₈	—	2	1	no	—
147	C₂×C₅×Q₈	—	2	1	no	—
148	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	—	2	2	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	—	2	1	no	—
154	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₅	—	2	4	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	4	2	no	—
160	C₂²×C₄×C₅	—	4	2	no	—
161	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
179	C₂×C₅×C₈	—	2	4	no	—
180	C₂×C₅×C₈	—	2	4	no	—
181	C₂×C₅×C₈	—	4	4	no	—
182	C₂×C₅×C₈	—	4	4	no	—
183	C₅×C₄⋊C₄	—	2	2	no	—
184	C₅×C₄⋊C₄	—	2	2	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	2	2	no	—
187	C₅×C₄⋊C₄	—	2	2	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	—	2	1	no	—
190	C₅×C₄⋊C₄	—	2	1	no	—
191	C₅×C₄⋊C₄	—	2	1	no	—
192	C₅×C₄⋊C₄	—	2	1	no	—
193	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
194	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
195	C₅×C₂²⋊C₄	—	2	2	no	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₅×C₂²⋊C₄	—	2	2	no	—
199	C₅×C₂²⋊C₄	—	2	2	no	—
200	C₅×C₂²⋊C₄	—	2	2	no	—
201	C₅×C₂²⋊C₄	—	2	2	no	—
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₄²×C₅	—	2	2	no	—
205	C₄²×C₅	—	2	2	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
208	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
209	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
210	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
211	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
212	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
213	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
214	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
215	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
216	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
217	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
218	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
222	C₄²×C₅	C₂⁴	1	1	yes	characteristic
223	#533	C₂²×C₅	1	1	yes	characteristic
224	#533	C₂²×C₅	1	1	yes	characteristic
225	#533	C₂²×C₅	1	1	yes	characteristic
226	#532	C₂²×C₅	1	1	yes	characteristic
227	#532	C₂²×C₅	1	1	yes	characteristic
228	#532	C₂²×C₅	1	1	yes	characteristic
229	#529	—	2	1	no	—
230	#529	—	2	1	no	—
231	#529	—	2	1	no	—
232	#529	—	2	1	no	—
233	#529	C₄×C₅	1	2	yes	—
234	#529	C₄×C₅	1	2	yes	—
235	#525	—	2	1	no	—
236	#525	—	2	1	no	—
237	#525	C₄×C₅	1	2	yes	—
238	C₄×#41	—	2	1	no	—
239	C₄×#41	—	2	1	no	—
240	C₄×#41	C₄×C₅	1	2	yes	—
241	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
242	#432	—	2	1	no	—
243	#432	—	2	1	no	—
244	#432	C₂²×C₅	1	2	yes	—
245	#432	C₂²×C₅	1	2	yes	—
246	#431	—	2	1	no	—
247	#431	—	2	1	no	—
248	#431	C₂²×C₅	1	2	yes	—
249	#431	C₂²×C₅	1	2	yes	—
250	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
251	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	—
252	C₂×C₂²⋊C₈	—	2	1	no	—
253	C₂×C₂²⋊C₈	—	2	1	no	—
254	C₂×#97	—	2	1	no	—
255	C₂×C₄×C₈	—	2	1	no	—
256	#333	C₂²×C₅	1	4	yes	complemented
257	#332	C₂²×C₅	1	4	yes	complemented
258	#332	C₂²×C₅	1	4	yes	complemented
259	#331	C₂²×C₅	1	4	yes	complemented
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	4	1	no	—
264	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
266	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₅×Q₈	—	4	2	no	—
268	C₅×Q₈	—	4	2	no	—
269	C₅×Q₈	—	4	2	no	—
270	C₅×D₄	—	4	2	no	—
271	C₅×D₄	—	4	4	no	—
272	C₅×D₄	—	4	4	no	—
273	C₅×D₄	—	4	4	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	4	1	no	—
290	C₂×C₄×C₅	—	4	1	no	—
291	C₂×C₄×C₅	—	4	1	no	—
292	C₂×C₄×C₅	—	4	1	no	—
293	C₂×C₄×C₅	—	4	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	4	no	—
297	C₂×C₄×C₅	—	4	4	no	—
298	C₂×C₄×C₅	—	4	4	no	—
299	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
308	C₂×C₄×C₅	#135	1	4	yes	—
309	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₅×C₈	—	4	4	no	—
313	C₅×C₈	—	4	4	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	C₂×C₄×C₅	1	2	yes	—
317	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
318	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
319	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
320	C₂²×C₈	—	2	2	no	—
321	C₂²×C₈	—	2	2	no	—
322	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
323	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
324	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
325	#127	C₂³×C₅	1	1	yes	characteristic
326	#126	—	2	2	no	—
327	#126	—	2	2	no	—
328	#125	—	2	1	no	—
329	#125	—	2	1	no	—
330	#125	C₂×C₄×C₅	1	2	yes	—
331	#124	—	2	1	no	—
332	#124	—	2	1	no	—
333	#124	C₂×C₄×C₅	1	2	yes	—
334	#123	—	2	2	no	—
335	#123	—	2	2	no	—
336	#123	—	2	2	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	—	2	1	no	—
340	C₂²⋊Q₈	—	2	1	no	—
341	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
342	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
343	#121	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	—	2	1	no	—
346	#121	—	2	1	no	—
347	#121	C₂×C₄×C₅	1	2	yes	—
348	#121	C₂×C₄×C₅	1	2	yes	—
349	#120	—	2	2	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
355	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
356	C₄×D₄	—	2	2	no	—
357	C₄×D₄	—	2	2	no	—
358	C₄×D₄	—	2	2	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	—	2	2	no	—
361	C₄×D₄	—	2	2	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
367	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	—	2	2	no	—
373	#117	C₂×C₄×C₅	1	2	yes	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
376	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
377	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
378	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
379	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
380	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
381	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
382	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
383	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
384	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
385	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
386	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
387	C₄⋊C₈	—	2	2	no	—
388	C₄⋊C₈	—	2	2	no	—
389	C₄⋊C₈	C₂³×C₅	1	4	yes	—
390	C₄⋊C₈	C₂³×C₅	1	4	yes	—
391	C₂²⋊C₈	—	2	2	no	—
392	C₂²⋊C₈	—	2	2	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	—	2	2	no	—
395	#97	—	2	2	no	—
396	#97	—	2	2	no	—
397	C₄×C₈	—	2	2	no	—
398	C₄×C₈	—	2	2	no	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	2	1	no	—
405	C₂²×C₅	—	2	1	no	—
406	C₂²×C₅	—	4	4	no	—
407	C₂²×C₅	—	4	2	no	—
408	C₂²×C₅	—	4	2	no	—
409	C₂²×C₅	—	4	2	no	—
410	C₂²×C₅	#413	1	2	yes	—
411	C₂²×C₅	#416	1	2	yes	—
412	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
413	C₄×C₅	—	2	1	no	—
414	C₄×C₅	—	2	1	no	—
415	C₄×C₅	—	2	1	no	—
416	C₄×C₅	—	2	1	no	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	—	2	1	no	—
420	C₄×C₅	—	2	1	no	—
421	C₄×C₅	—	2	1	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	2	no	—
424	C₄×C₅	—	4	2	no	—
425	C₄×C₅	#416	1	2	yes	—
426	C₄×C₅	C₂×#135	1	2	yes	—
427	C₄×C₅	#575	1	2	yes	—
428	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
429	#41	—	4	4	no	—
430	#41	—	4	4	no	—
431	#41	—	4	4	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	4	2	no	—
446	C₂²×C₄	—	4	2	no	—
447	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
448	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
449	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
450	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
451	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
452	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
453	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
454	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
455	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
456	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
458	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂×C₈	—	2	4	no	—
466	C₂×C₈	—	2	4	no	—
467	C₂×C₈	—	4	4	no	—
468	C₂×C₈	—	4	4	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	2	2	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
480	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
481	C₂²⋊C₄	—	2	2	no	—
482	C₂²⋊C₄	—	2	2	no	—
483	C₂²⋊C₄	—	2	2	no	—
484	C₂²⋊C₄	—	2	2	no	—
485	C₂²⋊C₄	—	2	2	no	—
486	C₂²⋊C₄	—	2	2	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₄²	—	2	2	no	—
491	C₄²	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
494	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
495	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
496	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
497	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
498	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
499	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
500	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
501	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
502	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
503	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
504	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
505	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
506	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
507	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
508	C₄²	C₂⁴×C₅	1	1	yes	characteristic
509	C₂×C₅	—	2	2	no	—
510	C₂×C₅	—	2	2	no	—
511	C₂×C₅	—	4	1	no	—
512	C₂×C₅	—	8	2	no	—
513	C₂×C₅	C₂×#413	1	1	yes	characteristic
514	C₂×C₅	C₂×#416	1	1	yes	characteristic
515	C₂×C₅	#2896	1	1	yes	characteristic
516	C₂³	—	2	2	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	2	no	—
519	C₂³	—	4	1	no	—
520	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
521	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
522	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
523	Q₈	—	4	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	4	no	—
528	D₄	—	4	4	no	—
529	D₄	—	4	4	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	2	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	4	no	—
553	C₂×C₄	—	4	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
556	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
557	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
558	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₅×#135	1	4	yes	—
565	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
566	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
567	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
568	C₈	—	4	4	no	—
569	C₈	—	4	4	no	—
570	C₅	#17713	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	2	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	2	1	no	—
577	C₂²	—	2	1	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	C₅×#413	1	2	yes	—
583	C₂²	C₅×#416	1	2	yes	—
584	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	1	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	2	1	no	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	4	2	no	—
595	C₄	—	4	2	no	—
596	C₄	—	4	2	no	—
597	C₄	C₅×#416	1	2	yes	—
598	C₄	C₂×C₅×#135	1	2	yes	—
599	C₄	C₅×#575	1	2	yes	—
600	C₂	—	2	2	no	—
601	C₂	—	2	2	no	—
602	C₂	—	4	1	no	—
603	C₂	—	8	2	no	—
604	C₂	C₂×C₅×#413	1	1	yes	characteristic
605	C₂	C₂×C₅×#416	1	1	yes	characteristic
606	C₂	C₅×#2896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₅×#3444	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#432	C₂	semidirect
3. C₂×C₅×#431	C₂	semidirect
4. C₅×#1554	C₂	semidirect
5. C₅×#1553	C₂	semidirect
6. C₅×#1552	C₂	semidirect
7. C₅×#1551	C₂	semidirect
8. C₅×#1542	C₂	semidirect
9. C₅×#1540	C₂	semidirect
43. C₅×#333	C₂²	semidirect
44. C₅×#332	C₂²	semidirect
45. C₅×#332	C₂²	semidirect
46. C₅×#331	C₂²	semidirect
47. #17713	C₅	direct (N × H)
134. C₂×#432	C₂×C₅	semidirect
135. C₂×#431	C₂×C₅	semidirect
136. #1554	C₂×C₅	semidirect
137. #1553	C₂×C₅	semidirect
138. #1552	C₂×C₅	semidirect
139. #1551	C₂×C₅	semidirect
140. #1542	C₂×C₅	semidirect
141. #1540	C₂×C₅	semidirect
256. #333	C₂²×C₅	semidirect
257. #332	C₂²×C₅	semidirect
258. #332	C₂²×C₅	semidirect
259. #331	C₂²×C₅	semidirect
570. C₅	#17713	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×#3444	2
C₂×C₅×#432	2
C₂×C₅×#431	2
C₅×#1554	2
C₅×#1553	2
C₅×#1552	2
C₅×#1551	2
C₅×#1542	2
C₅×#1540	2
#17713	5

Subgroups — C5×#17713 #11940433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17713 #11940433