Subgroups — C₅×#17546 #11940266

Order 1280.

1194 conjugacy classes of subgroups.

The subgroup lattice has 642 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	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1509	C₂	1	4	yes	maximal, complemented
5	C₅×#1504	C₂	1	4	yes	maximal, complemented
6	C₅×#1503	C₂	1	2	yes	maximal, complemented
7	C₅×#1502	C₂	1	2	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	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
27	C₂²×C₄²×C₅	—	2	1	no	—
28	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₅×#432	—	2	1	no	—
30	C₅×#432	C₂²	1	2	yes	—
31	C₅×#431	—	2	1	no	—
32	C₅×#431	C₂²	1	2	yes	—
33	C₅×#423	—	2	1	no	—
34	C₅×#407	C₂²	1	2	yes	—
35	C₄×C₅×M₁₆	—	2	1	no	—
36	C₄×C₅×C₄⋊C₄	—	2	1	no	—
37	C₄×C₅×C₄⋊C₄	—	2	1	no	—
38	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
40	C₂×C₅×#95	C₂²	1	2	yes	—
41	C₅×#328	C₂²	1	8	yes	—
42	C₅×#327	C₂²	1	8	yes	—
43	#17546	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	—	2	2	no	—
48	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	2	no	—
52	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
53	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
54	C₅×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
55	C₅×#127	C₂×C₄	1	1	yes	characteristic, complemented
56	C₅×#126	—	2	2	no	—
57	C₅×#126	—	2	2	no	—
58	C₅×#125	—	2	1	no	—
59	C₅×#125	—	2	1	no	—
60	C₅×#125	C₂×C₄	1	2	yes	complemented
61	C₅×#124	—	2	1	no	—
62	C₅×#124	—	2	1	no	—
63	C₅×#124	C₂×C₄	1	2	yes	complemented
64	C₅×#123	—	2	2	no	—
65	C₅×#123	—	2	2	no	—
66	C₅×#123	—	2	2	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	—	2	1	no	—
71	C₅×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
72	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₅×#121	—	2	1	no	—
77	C₅×#121	C₂×C₄	1	2	yes	—
78	C₅×#121	C₂³	1	2	yes	—
79	C₅×#120	—	2	2	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	—	2	1	no	—
84	C₄×C₅×Q₈	C₂×C₄	1	2	yes	complemented
85	C₄×C₅×Q₈	C₂×C₄	1	2	yes	complemented
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	2	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	—	2	1	no	—
96	C₄×C₅×D₄	C₂×C₄	1	2	yes	complemented
97	C₄×C₅×D₄	C₂×C₄	1	2	yes	complemented
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	8	no	—
105	C₂×C₅×C₄⋊C₄	—	2	2	no	—
106	C₂×C₅×C₄⋊C₄	—	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	—	4	4	no	—
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	C₂×C₄	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	D₄	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
123	C₅×C₄⋊C₈	—	2	2	no	—
124	C₅×C₄⋊C₈	—	2	2	no	—
125	C₅×C₂²⋊C₈	—	2	2	no	—
126	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
127	C₅×#97	—	2	2	no	—
128	C₄×C₅×C₈	—	2	2	no	—
129	C₅×#95	—	2	2	no	—
130	C₅×#95	C₂³	1	4	yes	—
131	#3444	C₂×C₅	1	1	yes	characteristic
132	#2920	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
134	#1509	C₂×C₅	1	4	yes	complemented
135	#1504	C₂×C₅	1	4	yes	complemented
136	#1503	C₂×C₅	1	2	yes	complemented
137	#1502	C₂×C₅	1	2	yes	complemented
138	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
139	C₅×#41	—	4	4	no	—
140	C₅×#41	—	4	4	no	—
141	C₅×#41	—	4	2	no	—
142	C₅×#41	—	4	2	no	—
143	C₂×C₅×Q₈	—	2	1	no	—
144	C₂×C₅×Q₈	—	2	1	no	—
145	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
146	C₂×C₅×D₄	—	2	2	no	—
147	C₂×C₅×D₄	—	2	2	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
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	8	no	—
156	C₂²×C₄×C₅	—	2	4	no	—
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	2	2	no	—
160	C₂²×C₄×C₅	—	4	2	no	—
161	C₂²×C₄×C₅	—	4	4	no	—
162	C₂²×C₄×C₅	—	4	4	no	—
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	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
181	C₅×M₁₆	—	4	4	no	—
182	C₂×C₅×C₈	—	2	4	no	—
183	C₅×C₄⋊C₄	—	2	8	no	—
184	C₅×C₄⋊C₄	—	2	8	no	—
185	C₅×C₄⋊C₄	—	2	1	no	—
186	C₅×C₄⋊C₄	—	2	1	no	—
187	C₅×C₄⋊C₄	—	2	1	no	—
188	C₅×C₄⋊C₄	—	2	1	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	2	2	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
196	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
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	C₅×C₂²⋊C₄	—	2	2	no	—
205	C₅×C₂²⋊C₄	—	2	2	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	—	2	2	no	—
208	C₄²×C₅	—	2	2	no	—
209	C₄²×C₅	—	4	4	no	—
210	C₄²×C₅	—	4	4	no	—
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	C₂²⋊C₄	1	1	yes	characteristic
219	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
220	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
223	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
224	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
225	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
226	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
227	#533	C₄×C₅	1	1	yes	characteristic, complemented
228	#533	C₄×C₅	1	1	yes	characteristic, complemented
229	#533	C₂²×C₅	1	1	yes	characteristic
230	#532	C₄×C₅	1	1	yes	characteristic, complemented
231	#532	C₄×C₅	1	1	yes	characteristic, complemented
232	#532	C₂²×C₅	1	1	yes	characteristic
233	#529	—	2	1	no	—
234	#529	—	2	1	no	—
235	#529	—	2	1	no	—
236	#529	—	2	1	no	—
237	#529	C₄×C₅	1	2	yes	complemented
238	#529	C₂²×C₅	1	2	yes	—
239	#525	—	2	1	no	—
240	#525	—	2	1	no	—
241	#525	C₂²×C₅	1	2	yes	—
242	C₄×#41	—	2	1	no	—
243	C₄×#41	—	2	1	no	—
244	C₄×#41	C₄×C₅	1	2	yes	complemented
245	C₂²×C₄⋊C₄	—	2	1	no	—
246	C₂²×C₄²	—	2	1	no	—
247	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
248	#432	—	2	1	no	—
249	#432	C₂²×C₅	1	2	yes	—
250	#431	—	2	1	no	—
251	#431	C₂²×C₅	1	2	yes	—
252	#423	—	2	1	no	—
253	#407	C₂²×C₅	1	2	yes	—
254	C₄×M₁₆	—	2	1	no	—
255	C₄×C₄⋊C₄	—	2	1	no	—
256	C₄×C₄⋊C₄	—	2	1	no	—
257	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
258	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
259	C₂×#95	C₂²×C₅	1	2	yes	—
260	#328	C₂²×C₅	1	8	yes	—
261	#327	C₂²×C₅	1	8	yes	—
262	C₂³×C₅	—	2	1	no	—
263	C₂³×C₅	—	2	1	no	—
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	2	2	no	—
267	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₅×Q₈	—	4	2	no	—
271	C₅×Q₈	—	4	2	no	—
272	C₅×Q₈	—	4	2	no	—
273	C₅×D₄	—	4	2	no	—
274	C₅×D₄	—	4	2	no	—
275	C₅×D₄	—	4	2	no	—
276	C₅×D₄	—	4	4	no	—
277	C₅×D₄	—	4	4	no	—
278	C₅×D₄	—	4	2	no	—
279	C₅×D₄	—	4	2	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	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	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	8	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	4	4	no	—
302	C₂×C₄×C₅	—	4	16	no	—
303	C₂×C₄×C₅	—	4	4	no	—
304	C₂×C₄×C₅	—	4	4	no	—
305	C₂×C₄×C₅	—	4	4	no	—
306	C₂×C₄×C₅	—	4	4	no	—
307	C₂×C₄×C₅	#104	1	4	yes	—
308	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
318	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
319	C₂×C₄×C₅	#137	1	2	yes	—
320	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
321	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
322	C₅×C₈	—	4	4	no	—
323	C₂×#41	—	2	1	no	—
324	C₂×#41	—	2	1	no	—
325	C₂×#41	C₂×C₄×C₅	1	2	yes	—
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
328	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
330	C₂×M₁₆	—	2	2	no	—
331	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
332	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
333	C₄⋊Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
334	#127	C₂×C₄×C₅	1	1	yes	characteristic, complemented
335	#126	—	2	2	no	—
336	#126	—	2	2	no	—
337	#125	—	2	1	no	—
338	#125	—	2	1	no	—
339	#125	C₂×C₄×C₅	1	2	yes	complemented
340	#124	—	2	1	no	—
341	#124	—	2	1	no	—
342	#124	C₂×C₄×C₅	1	2	yes	complemented
343	#123	—	2	2	no	—
344	#123	—	2	2	no	—
345	#123	—	2	2	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	2	1	no	—
349	C₂²⋊Q₈	—	2	1	no	—
350	C₂²⋊Q₈	C₂×C₄×C₅	1	2	yes	—
351	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
352	#121	—	2	1	no	—
353	#121	—	2	1	no	—
354	#121	—	2	1	no	—
355	#121	—	2	1	no	—
356	#121	C₂×C₄×C₅	1	2	yes	—
357	#121	C₂³×C₅	1	2	yes	—
358	#120	—	2	2	no	—
359	C₄×Q₈	—	2	1	no	—
360	C₄×Q₈	—	2	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	C₂×C₄×C₅	1	2	yes	complemented
364	C₄×Q₈	C₂×C₄×C₅	1	2	yes	complemented
365	C₄×D₄	—	2	2	no	—
366	C₄×D₄	—	2	2	no	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	C₂×C₄×C₅	1	2	yes	complemented
376	C₄×D₄	C₂×C₄×C₅	1	2	yes	complemented
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	#117	—	2	2	no	—
380	#117	—	2	2	no	—
381	#117	—	2	2	no	—
382	#117	C₂×C₄×C₅	1	2	yes	—
383	C₂×C₄⋊C₄	—	2	8	no	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	—	2	2	no	—
386	C₂×C₄²	—	2	2	no	—
387	C₂×C₄²	—	2	2	no	—
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	—	4	4	no	—
390	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
391	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
392	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
393	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
394	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
395	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
396	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
397	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
398	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
399	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
400	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
401	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
402	C₄⋊C₈	—	2	2	no	—
403	C₄⋊C₈	—	2	2	no	—
404	C₂²⋊C₈	—	2	2	no	—
405	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
406	#97	—	2	2	no	—
407	C₄×C₈	—	2	2	no	—
408	#95	—	2	2	no	—
409	#95	C₂³×C₅	1	4	yes	—
410	C₂²×C₅	—	2	4	no	—
411	C₂²×C₅	—	2	4	no	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	1	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	#410	1	2	yes	—
422	C₂²×C₅	C₂×#104	1	2	yes	—
423	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
424	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
425	C₂²×C₅	C₂×#137	1	1	yes	characteristic
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	2	1	no	—
431	C₄×C₅	—	2	1	no	—
432	C₄×C₅	—	2	1	no	—
433	C₄×C₅	—	2	1	no	—
434	C₄×C₅	—	4	8	no	—
435	C₄×C₅	—	4	2	no	—
436	C₄×C₅	—	4	2	no	—
437	C₄×C₅	—	4	2	no	—
438	C₄×C₅	#417	1	2	yes	—
439	C₄×C₅	#417	1	2	yes	—
440	C₄×C₅	C₂×#104	1	2	yes	—
441	C₄×C₅	C₂×#104	1	2	yes	—
442	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
443	#41	—	4	4	no	—
444	#41	—	4	2	no	—
445	#41	—	4	2	no	—
446	#41	—	4	4	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
450	C₂×D₄	—	2	2	no	—
451	C₂×D₄	—	2	2	no	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	8	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	2	2	no	—
464	C₂²×C₄	—	4	2	no	—
465	C₂²×C₄	—	4	4	no	—
466	C₂²×C₄	—	4	4	no	—
467	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
468	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
469	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
470	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
471	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
472	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
473	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
474	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
475	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
476	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
485	M₁₆	—	4	4	no	—
486	C₂×C₈	—	2	4	no	—
487	C₄⋊C₄	—	2	8	no	—
488	C₄⋊C₄	—	2	8	no	—
489	C₄⋊C₄	—	2	1	no	—
490	C₄⋊C₄	—	2	1	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	2	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
500	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
501	C₂²⋊C₄	—	2	2	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	2	2	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	2	2	no	—
513	C₄²	—	4	4	no	—
514	C₄²	—	4	4	no	—
515	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
516	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
517	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
518	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
519	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
520	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
521	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
522	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
523	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
524	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
525	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
526	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
527	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
528	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
529	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
530	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
531	C₂×C₅	—	2	1	no	—
532	C₂×C₅	—	2	1	no	—
533	C₂×C₅	—	2	2	no	—
534	C₂×C₅	—	2	2	no	—
535	C₂×C₅	—	8	2	no	—
536	C₂×C₅	C₂×#410	1	1	yes	characteristic
537	C₂×C₅	C₂×#417	1	1	yes	characteristic
538	C₂×C₅	C₂²×#104	1	1	yes	characteristic
539	C₂³	—	2	2	no	—
540	C₂³	—	2	2	no	—
541	C₂³	—	2	1	no	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	2	no	—
544	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
545	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
546	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
547	Q₈	—	4	2	no	—
548	Q₈	—	4	2	no	—
549	Q₈	—	4	2	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	4	no	—
552	D₄	—	4	4	no	—
553	D₄	—	4	2	no	—
554	D₄	—	4	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	2	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	8	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	1	no	—
576	C₂×C₄	—	4	1	no	—
577	C₂×C₄	—	4	1	no	—
578	C₂×C₄	—	4	4	no	—
579	C₂×C₄	—	4	16	no	—
580	C₂×C₄	—	4	4	no	—
581	C₂×C₄	—	4	4	no	—
582	C₂×C₄	—	4	4	no	—
583	C₂×C₄	—	4	4	no	—
584	C₂×C₄	C₅×#104	1	4	yes	—
585	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
586	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
587	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
588	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
589	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
590	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
591	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
592	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
593	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
594	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
595	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
596	C₂×C₄	C₅×#137	1	2	yes	—
597	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
598	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
599	C₈	—	4	4	no	—
600	C₅	#17546	1	1	yes	characteristic, direct product factor, Sylow
601	C₂²	—	2	4	no	—
602	C₂²	—	2	4	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	2	1	no	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	4	2	no	—
610	C₂²	—	4	2	no	—
611	C₂²	—	4	2	no	—
612	C₂²	C₅×#410	1	2	yes	—
613	C₂²	C₂×C₅×#104	1	2	yes	—
614	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
615	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
616	C₂²	C₂×C₅×#137	1	1	yes	characteristic
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	1	no	—
621	C₄	—	2	1	no	—
622	C₄	—	2	1	no	—
623	C₄	—	2	1	no	—
624	C₄	—	2	1	no	—
625	C₄	—	4	8	no	—
626	C₄	—	4	2	no	—
627	C₄	—	4	2	no	—
628	C₄	—	4	2	no	—
629	C₄	C₅×#417	1	2	yes	—
630	C₄	C₅×#417	1	2	yes	—
631	C₄	C₂×C₅×#104	1	2	yes	—
632	C₄	C₂×C₅×#104	1	2	yes	—
633	C₂	—	2	1	no	—
634	C₂	—	2	2	no	—
635	C₂	—	2	2	no	—
636	C₂	—	2	1	no	—
637	C₂	—	8	2	no	—
638	C₂	C₂×C₅×#410	1	1	yes	characteristic
639	C₂	C₂×C₅×#417	1	1	yes	characteristic
640	C₂	C₂²×C₅×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×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 ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2920	C₂	semidirect
3. C₂×C₄×C₅×C₄⋊C₄	C₂	semidirect
4. C₅×#1509	C₂	semidirect
5. C₅×#1504	C₂	semidirect
6. C₅×#1503	C₂	semidirect
7. C₅×#1502	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. #17546	C₅	direct (N × H)
52. C₅×C₄⋊Q₈	C₂×C₄	semidirect
53. C₅×C₄⋊Q₈	C₂×C₄	semidirect
54. C₅×C₄⋊Q₈	C₂×C₄	semidirect
55. C₅×#127	C₂×C₄	semidirect
60. C₅×#125	C₂×C₄	semidirect
63. C₅×#124	C₂×C₄	semidirect
84. C₄×C₅×Q₈	C₂×C₄	semidirect
85. C₄×C₅×Q₈	C₂×C₄	semidirect
96. C₄×C₅×D₄	C₂×C₄	semidirect
97. C₄×C₅×D₄	C₂×C₄	semidirect
132. #2920	C₂×C₅	semidirect
133. C₂×C₄×C₄⋊C₄	C₂×C₅	semidirect
134. #1509	C₂×C₅	semidirect
135. #1504	C₂×C₅	semidirect
136. #1503	C₂×C₅	semidirect
137. #1502	C₂×C₅	semidirect
227. #533	C₄×C₅	semidirect
228. #533	C₄×C₅	semidirect
230. #532	C₄×C₅	semidirect
231. #532	C₄×C₅	semidirect
237. #529	C₄×C₅	semidirect
244. C₄×#41	C₄×C₅	semidirect
331. C₄⋊Q₈	C₂×C₄×C₅	semidirect
332. C₄⋊Q₈	C₂×C₄×C₅	semidirect
333. C₄⋊Q₈	C₂×C₄×C₅	semidirect
334. #127	C₂×C₄×C₅	semidirect
339. #125	C₂×C₄×C₅	semidirect
342. #124	C₂×C₄×C₅	semidirect
363. C₄×Q₈	C₂×C₄×C₅	semidirect
364. C₄×Q₈	C₂×C₄×C₅	semidirect
375. C₄×D₄	C₂×C₄×C₅	semidirect
376. C₄×D₄	C₂×C₄×C₅	semidirect
600. C₅	#17546	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
C₅×#2920	2
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1509	2
C₅×#1504	2
C₅×#1503	2
C₅×#1502	2
#17546	5

Subgroups — C5×#17546 #11940266

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17546 #11940266