Subgroups — C₅×#17533 #11940253

Order 1280.

1128 conjugacy classes of subgroups.

The subgroup lattice has 616 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×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1503	C₂	1	2	yes	maximal, complemented
5	C₅×#1502	C₂	1	2	yes	maximal, complemented
6	C₅×#1501	C₂	1	4	yes	maximal, complemented
7	C₅×#1500	C₂	1	4	yes	maximal, complemented
8	C₅×#533	C₄	1	1	yes	characteristic, complemented
9	C₅×#533	C₄	1	1	yes	characteristic, complemented
10	C₅×#533	C₂²	1	1	yes	characteristic
11	C₅×#532	C₄	1	1	yes	characteristic, complemented
12	C₅×#532	C₄	1	1	yes	characteristic, complemented
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₅×#529	—	2	1	no	—
15	C₅×#529	—	2	1	no	—
16	C₅×#529	—	2	1	no	—
17	C₅×#529	—	2	1	no	—
18	C₅×#529	C₄	1	2	yes	complemented
19	C₅×#529	C₂²	1	2	yes	—
20	C₅×#525	—	2	1	no	—
21	C₅×#525	—	2	1	no	—
22	C₅×#525	C₂²	1	2	yes	—
23	C₄×C₅×#41	—	2	1	no	—
24	C₄×C₅×#41	—	2	1	no	—
25	C₄×C₅×#41	C₄	1	2	yes	complemented
26	C₂×C₅×#117	—	2	1	no	—
27	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₅×#431	—	2	1	no	—
29	C₅×#431	—	2	1	no	—
30	C₅×#431	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	2	yes	—
32	C₂×C₅×C₄⋊C₈	—	2	1	no	—
33	C₂×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
34	C₂×C₄×C₅×C₈	—	2	1	no	—
35	C₄×C₅×C₄⋊C₄	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
37	C₄×C₅×C₂²⋊C₄	—	2	1	no	—
38	C₄×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
39	C₅×#376	C₂²	1	2	yes	—
40	C₄³×C₅	—	2	1	no	—
41	C₅×#328	C₂²	1	8	yes	—
42	C₅×#327	C₂²	1	8	yes	—
43	#17533	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	—	2	1	no	—
46	C₂×C₅×#41	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₅×C₈	—	2	2	no	—
51	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
52	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₅×#127	C₂×C₄	1	1	yes	characteristic
55	C₅×#126	—	2	2	no	—
56	C₅×#126	—	2	2	no	—
57	C₅×#125	—	2	1	no	—
58	C₅×#125	—	2	1	no	—
59	C₅×#125	C₂×C₄	1	2	yes	—
60	C₅×#124	—	2	1	no	—
61	C₅×#124	—	2	1	no	—
62	C₅×#124	C₂×C₄	1	2	yes	—
63	C₅×#123	—	2	2	no	—
64	C₅×#123	—	2	2	no	—
65	C₅×#123	—	2	2	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₅×C₂²⋊Q₈	—	2	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	1	no	—
70	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
71	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
72	C₅×#121	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₅×#121	C₂×C₄	1	2	yes	—
77	C₅×#121	C₂³	1	2	yes	—
78	C₅×#120	—	2	2	no	—
79	C₄×C₅×Q₈	—	2	1	no	—
80	C₄×C₅×Q₈	—	2	1	no	—
81	C₄×C₅×Q₈	—	2	1	no	—
82	C₄×C₅×Q₈	—	2	1	no	—
83	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
84	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₄×C₅×D₄	—	2	2	no	—
87	C₄×C₅×D₄	—	2	2	no	—
88	C₄×C₅×D₄	—	2	2	no	—
89	C₄×C₅×D₄	—	2	2	no	—
90	C₄×C₅×D₄	—	2	2	no	—
91	C₄×C₅×D₄	—	2	1	no	—
92	C₄×C₅×D₄	—	2	1	no	—
93	C₄×C₅×D₄	—	2	1	no	—
94	C₄×C₅×D₄	—	2	1	no	—
95	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
96	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
97	C₅×#117	—	2	8	no	—
98	C₅×#117	—	2	1	no	—
99	C₅×#117	—	2	1	no	—
100	C₅×#117	—	2	2	no	—
101	C₅×#117	—	2	2	no	—
102	C₅×#117	—	2	2	no	—
103	C₅×#117	C₂×C₄	1	2	yes	—
104	C₂×C₅×C₄⋊C₄	—	2	2	no	—
105	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
106	C₂×C₄²×C₅	—	2	2	no	—
107	C₂×C₄²×C₅	—	2	2	no	—
108	C₂×C₄²×C₅	—	2	2	no	—
109	C₂×C₄²×C₅	—	2	2	no	—
110	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂×C₄	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	D₄	1	1	yes	characteristic
119	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	—	2	2	no	—
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₂²⋊C₈	—	2	2	no	—
125	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
126	C₄×C₅×C₈	—	2	2	no	—
127	C₄×C₅×C₈	—	2	2	no	—
128	C₅×#95	—	2	2	no	—
129	C₅×#95	C₂³	1	4	yes	—
130	#3444	C₂×C₅	1	1	yes	characteristic
131	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
132	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
133	#1503	C₂×C₅	1	2	yes	complemented
134	#1502	C₂×C₅	1	2	yes	complemented
135	#1501	C₂×C₅	1	4	yes	complemented
136	#1500	C₂×C₅	1	4	yes	complemented
137	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
138	C₅×#41	—	4	4	no	—
139	C₅×#41	—	4	4	no	—
140	C₅×#41	—	4	4	no	—
141	C₂×C₅×Q₈	—	2	1	no	—
142	C₂×C₅×Q₈	—	2	1	no	—
143	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	2	2	no	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₅	—	2	4	no	—
151	C₂²×C₄×C₅	—	2	4	no	—
152	C₂²×C₄×C₅	—	2	4	no	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	4	2	no	—
157	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
175	C₂×C₅×C₈	—	2	4	no	—
176	C₂×C₅×C₈	—	4	4	no	—
177	C₅×C₄⋊C₄	—	2	8	no	—
178	C₅×C₄⋊C₄	—	2	1	no	—
179	C₅×C₄⋊C₄	—	2	1	no	—
180	C₅×C₄⋊C₄	—	2	1	no	—
181	C₅×C₄⋊C₄	—	2	1	no	—
182	C₅×C₄⋊C₄	—	2	2	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	C₂²×C₄	1	2	yes	—
189	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
190	C₅×C₂²⋊C₄	—	2	8	no	—
191	C₅×C₂²⋊C₄	—	2	2	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	2	2	no	—
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	C₄²×C₅	—	2	8	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	—	2	2	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	4	4	no	—
205	C₄²×C₅	—	4	4	no	—
206	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
217	C₄²×C₅	C₂²×C₄	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	#533	C₄×C₅	1	1	yes	characteristic, complemented
223	#533	C₄×C₅	1	1	yes	characteristic, complemented
224	#533	C₂²×C₅	1	1	yes	characteristic
225	#532	C₄×C₅	1	1	yes	characteristic, complemented
226	#532	C₄×C₅	1	1	yes	characteristic, complemented
227	#532	C₂²×C₅	1	1	yes	characteristic
228	#529	—	2	1	no	—
229	#529	—	2	1	no	—
230	#529	—	2	1	no	—
231	#529	—	2	1	no	—
232	#529	C₄×C₅	1	2	yes	complemented
233	#529	C₂²×C₅	1	2	yes	—
234	#525	—	2	1	no	—
235	#525	—	2	1	no	—
236	#525	C₂²×C₅	1	2	yes	—
237	C₄×#41	—	2	1	no	—
238	C₄×#41	—	2	1	no	—
239	C₄×#41	C₄×C₅	1	2	yes	complemented
240	C₂×#117	—	2	1	no	—
241	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
242	#431	—	2	1	no	—
243	#431	—	2	1	no	—
244	#431	C₂²×C₅	1	2	yes	—
245	#431	C₂²×C₅	1	2	yes	—
246	C₂×C₄⋊C₈	—	2	1	no	—
247	C₂×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
248	C₂×C₄×C₈	—	2	1	no	—
249	C₄×C₄⋊C₄	—	2	1	no	—
250	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
251	C₄×C₂²⋊C₄	—	2	1	no	—
252	C₄×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
253	#376	C₂²×C₅	1	2	yes	—
254	C₄³	—	2	1	no	—
255	#328	C₂²×C₅	1	8	yes	—
256	#327	C₂²×C₅	1	8	yes	—
257	C₂³×C₅	—	2	2	no	—
258	C₂³×C₅	—	2	2	no	—
259	C₂³×C₅	—	2	2	no	—
260	C₂³×C₅	—	4	1	no	—
261	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
262	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₅×Q₈	—	4	2	no	—
265	C₅×Q₈	—	4	2	no	—
266	C₅×Q₈	—	4	2	no	—
267	C₅×D₄	—	4	2	no	—
268	C₅×D₄	—	4	4	no	—
269	C₅×D₄	—	4	4	no	—
270	C₅×D₄	—	4	4	no	—
271	C₅×D₄	—	4	2	no	—
272	C₅×D₄	—	4	2	no	—
273	C₂×C₄×C₅	—	2	2	no	—
274	C₂×C₄×C₅	—	2	2	no	—
275	C₂×C₄×C₅	—	2	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	8	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	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	4	no	—
294	C₂×C₄×C₅	—	4	4	no	—
295	C₂×C₄×C₅	—	4	4	no	—
296	C₂×C₄×C₅	—	4	4	no	—
297	C₂×C₄×C₅	—	4	4	no	—
298	C₂×C₄×C₅	#104	1	4	yes	—
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	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₅	#135	1	4	yes	—
310	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
312	C₅×C₈	—	4	4	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	C₂×C₄×C₅	1	2	yes	—
316	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
317	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂²×C₈	—	2	2	no	—
320	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
321	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
322	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic
323	#127	C₂×C₄×C₅	1	1	yes	characteristic
324	#126	—	2	2	no	—
325	#126	—	2	2	no	—
326	#125	—	2	1	no	—
327	#125	—	2	1	no	—
328	#125	C₂×C₄×C₅	1	2	yes	—
329	#124	—	2	1	no	—
330	#124	—	2	1	no	—
331	#124	C₂×C₄×C₅	1	2	yes	—
332	#123	—	2	2	no	—
333	#123	—	2	2	no	—
334	#123	—	2	2	no	—
335	C₂²⋊Q₈	—	2	1	no	—
336	C₂²⋊Q₈	—	2	1	no	—
337	C₂²⋊Q₈	—	2	1	no	—
338	C₂²⋊Q₈	—	2	1	no	—
339	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
340	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
341	#121	—	2	1	no	—
342	#121	—	2	1	no	—
343	#121	—	2	1	no	—
344	#121	—	2	1	no	—
345	#121	C₂×C₄×C₅	1	2	yes	—
346	#121	C₂³×C₅	1	2	yes	—
347	#120	—	2	2	no	—
348	C₄×Q₈	—	2	1	no	—
349	C₄×Q₈	—	2	1	no	—
350	C₄×Q₈	—	2	1	no	—
351	C₄×Q₈	—	2	1	no	—
352	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
353	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
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	1	no	—
361	C₄×D₄	—	2	1	no	—
362	C₄×D₄	—	2	1	no	—
363	C₄×D₄	—	2	1	no	—
364	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
365	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
366	#117	—	2	8	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	2	no	—
370	#117	—	2	2	no	—
371	#117	—	2	2	no	—
372	#117	C₂×C₄×C₅	1	2	yes	—
373	C₂×C₄⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	2	no	—
375	C₂×C₄²	—	2	2	no	—
376	C₂×C₄²	—	2	2	no	—
377	C₂×C₄²	—	2	2	no	—
378	C₂×C₄²	—	2	2	no	—
379	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
380	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
381	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
382	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
383	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
384	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
385	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
386	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
387	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
388	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
391	C₄⋊C₈	—	2	2	no	—
392	C₄⋊C₈	—	2	2	no	—
393	C₂²⋊C₈	—	2	2	no	—
394	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
395	C₄×C₈	—	2	2	no	—
396	C₄×C₈	—	2	2	no	—
397	#95	—	2	2	no	—
398	#95	C₂³×C₅	1	4	yes	—
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	C₂×#104	1	2	yes	—
411	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
412	C₂²×C₅	C₂×#135	1	2	yes	—
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	—	4	8	no	—
421	C₄×C₅	—	4	2	no	—
422	C₄×C₅	—	4	2	no	—
423	C₄×C₅	—	4	2	no	—
424	C₄×C₅	#410	1	2	yes	—
425	C₄×C₅	#416	1	2	yes	—
426	C₄×C₅	#416	1	2	yes	—
427	C₄×C₅	C₂×#104	1	2	yes	—
428	C₄×C₅	C₂×#104	1	2	yes	—
429	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
430	#41	—	4	4	no	—
431	#41	—	4	4	no	—
432	#41	—	4	4	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
436	C₂×D₄	—	2	2	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	4	2	no	—
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	C₅×C₂²⋊C₄	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	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
467	C₂×C₈	—	2	4	no	—
468	C₂×C₈	—	4	4	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	2	no	—
478	C₄⋊C₄	—	2	2	no	—
479	C₄⋊C₄	—	2	2	no	—
480	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
481	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
482	C₂²⋊C₄	—	2	8	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	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₄²	—	2	8	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	4	4	no	—
497	C₄²	—	4	4	no	—
498	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
499	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
500	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
501	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
502	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
503	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
504	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
505	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
506	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
507	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
508	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
509	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
510	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
511	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
512	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
513	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
514	C₂×C₅	—	2	2	no	—
515	C₂×C₅	—	2	2	no	—
516	C₂×C₅	—	4	1	no	—
517	C₂×C₅	—	8	2	no	—
518	C₂×C₅	C₂×#410	1	1	yes	characteristic
519	C₂×C₅	C₂×#416	1	1	yes	characteristic
520	C₂×C₅	C₂²×#104	1	1	yes	characteristic
521	C₂³	—	2	2	no	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	4	1	no	—
525	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
526	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
527	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
528	Q₈	—	4	2	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	4	no	—
535	D₄	—	4	2	no	—
536	D₄	—	4	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	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	C₅×#104	1	4	yes	—
563	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
568	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
569	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
570	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
571	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
572	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
573	C₂×C₄	C₅×#135	1	4	yes	—
574	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
575	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
576	C₈	—	4	4	no	—
577	C₅	#17533	1	1	yes	characteristic, direct product factor, Sylow
578	C₂²	—	2	1	no	—
579	C₂²	—	2	1	no	—
580	C₂²	—	2	1	no	—
581	C₂²	—	2	1	no	—
582	C₂²	—	2	1	no	—
583	C₂²	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	C₂×C₅×#104	1	2	yes	—
590	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
591	C₂²	C₂×C₅×#135	1	2	yes	—
592	C₄	—	2	1	no	—
593	C₄	—	2	1	no	—
594	C₄	—	2	1	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	1	no	—
599	C₄	—	4	8	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	2	no	—
603	C₄	C₅×#410	1	2	yes	—
604	C₄	C₅×#416	1	2	yes	—
605	C₄	C₅×#416	1	2	yes	—
606	C₄	C₂×C₅×#104	1	2	yes	—
607	C₄	C₂×C₅×#104	1	2	yes	—
608	C₂	—	2	2	no	—
609	C₂	—	2	2	no	—
610	C₂	—	4	1	no	—
611	C₂	—	8	2	no	—
612	C₂	C₂×C₅×#410	1	1	yes	characteristic
613	C₂	C₂×C₅×#416	1	1	yes	characteristic
614	C₂	C₂²×C₅×#104	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#431	C₂	semidirect
3. C₄×C₅×#117	C₂	semidirect
4. C₅×#1503	C₂	semidirect
5. C₅×#1502	C₂	semidirect
6. C₅×#1501	C₂	semidirect
7. C₅×#1500	C₂	semidirect
8. C₅×#533	C₄	semidirect
9. C₅×#533	C₄	semidirect
11. C₅×#532	C₄	semidirect
12. C₅×#532	C₄	semidirect
18. C₅×#529	C₄	semidirect
25. C₄×C₅×#41	C₄	semidirect
43. #17533	C₅	direct (N × H)
131. C₂×#431	C₂×C₅	semidirect
132. C₄×#117	C₂×C₅	semidirect
133. #1503	C₂×C₅	semidirect
134. #1502	C₂×C₅	semidirect
135. #1501	C₂×C₅	semidirect
136. #1500	C₂×C₅	semidirect
222. #533	C₄×C₅	semidirect
223. #533	C₄×C₅	semidirect
225. #532	C₄×C₅	semidirect
226. #532	C₄×C₅	semidirect
232. #529	C₄×C₅	semidirect
239. C₄×#41	C₄×C₅	semidirect
577. C₅	#17533	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×#431	2
C₄×C₅×#117	2
C₅×#1503	2
C₅×#1502	2
C₅×#1501	2
C₅×#1500	2
#17533	5

Subgroups — C5×#17533 #11940253

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17533 #11940253