Subgroups — C₅×#20405 #11943125

Order 1280.

1562 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3428	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
4	C₅×#2873	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1759	C₂	1	4	yes	maximal, complemented
7	C₄×C₅×#104	C₂	1	4	yes	maximal, complemented
8	C₅×#1733	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₅×#520	—	2	2	no	—
14	C₅×#520	C₄	1	4	yes	complemented
15	C₅×#519	C₄	1	2	yes	complemented
16	C₅×#518	—	2	2	no	—
17	C₅×#518	C₄	1	2	yes	complemented
18	C₄×C₅×#41	—	2	2	no	—
19	C₄×C₅×#41	C₂²	1	4	yes	—
20	C₂×C₅×#117	—	2	2	no	—
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂×C₅×#117	C₂²	1	1	yes	characteristic
23	C₂×C₅×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#421	C₄	1	8	yes	complemented
26	C₂×C₅×#104	C₄	1	8	yes	complemented
27	C₂×C₅×#104	C₂²	1	2	yes	—
28	C₂×C₅×#104	C₂²	1	4	yes	—
29	C₂×C₅×#104	C₂²	1	2	yes	—
30	C₅×#405	—	2	2	no	—
31	C₅×#405	—	2	2	no	—
32	C₄×C₅×M₁₆	C₂²	1	4	yes	complemented
33	C₄×C₅×C₄⋊C₄	—	2	2	no	—
34	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
35	C₅×#376	C₂²	1	2	yes	complemented
36	C₄³×C₅	C₂²	1	2	yes	complemented
37	C₅×#339	C₂²	1	2	yes	complemented
38	C₅×#339	C₂²	1	4	yes	complemented
39	C₅×#339	C₂²	1	2	yes	complemented
40	#20405	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×C₅×#41	—	2	1	no	—
42	C₂×C₅×#41	—	2	1	no	—
43	C₂×C₅×#41	—	2	2	no	—
44	C₂×C₅×#41	—	2	2	no	—
45	C₂×C₅×#41	C₂×C₄	1	4	yes	—
46	C₂×C₅×#41	C₂×C₄	1	4	yes	—
47	C₂×C₅×#41	C₂×C₄	1	2	yes	—
48	C₂×C₅×#41	C₂³	1	2	yes	—
49	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₅×D₄	—	2	1	no	—
51	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₂³×C₄×C₅	—	2	1	no	—
54	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂×C₅×M₁₆	—	2	2	no	—
59	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
60	C₂×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
61	C₂×C₅×M₁₆	C₂³	1	2	yes	—
62	C₂×C₅×M₁₆	C₂³	1	2	yes	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₄×C₅×Q₈	—	2	4	no	—
66	C₄×C₅×Q₈	C₂×C₄	1	8	yes	complemented
67	C₄×C₅×D₄	—	2	8	no	—
68	C₄×C₅×D₄	—	2	4	no	—
69	C₄×C₅×D₄	—	2	8	no	—
70	C₄×C₅×D₄	C₂×C₄	1	8	yes	complemented
71	C₅×#117	—	2	1	no	—
72	C₅×#117	—	2	1	no	—
73	C₅×#117	—	2	2	no	—
74	C₅×#117	—	2	4	no	—
75	C₅×#117	—	2	4	no	—
76	C₅×#117	—	2	4	no	—
77	C₅×#117	C₂×C₄	1	2	yes	—
78	C₅×#117	C₂×C₄	1	2	yes	—
79	C₅×#117	C₂×C₄	1	2	yes	—
80	C₅×#117	C₂×C₄	1	4	yes	complemented
81	C₅×#117	D₄	1	2	yes	—
82	C₅×#117	D₄	1	2	yes	—
83	C₅×#117	C₂³	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	4	no	—
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
87	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
90	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
91	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
92	C₂×C₄²×C₅	—	2	1	no	—
93	C₂×C₄²×C₅	—	2	1	no	—
94	C₂×C₄²×C₅	—	2	2	no	—
95	C₂×C₄²×C₅	—	2	4	no	—
96	C₂×C₄²×C₅	—	2	4	no	—
97	C₂×C₄²×C₅	C₂×C₄	1	4	yes	complemented
98	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	2	yes	—
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	2	yes	—
102	C₅×#104	C₂×C₄	1	8	yes	complemented
103	C₅×#104	C₂×C₄	1	8	yes	complemented
104	C₅×#104	C₂×C₄	1	16	yes	complemented
105	C₅×#97	—	2	4	no	—
106	C₄×C₅×C₈	—	2	4	no	—
107	C₅×#95	—	2	4	no	—
108	#3428	C₂×C₅	1	1	yes	characteristic
109	C₂×#421	C₂×C₅	1	1	yes	characteristic
110	C₂²×#104	C₂×C₅	1	1	yes	characteristic
111	#2873	C₂×C₅	1	1	yes	characteristic, complemented
112	C₄×#117	C₂×C₅	1	1	yes	characteristic, complemented
113	#1759	C₂×C₅	1	4	yes	complemented
114	C₄×#104	C₂×C₅	1	4	yes	complemented
115	#1733	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂⁴×C₅	—	2	1	no	—
118	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
119	C₅×#41	—	2	4	no	—
120	C₅×#41	—	2	4	no	—
121	C₅×#41	—	2	4	no	—
122	C₅×#41	—	2	4	no	—
123	C₅×#41	—	2	4	no	—
124	C₅×#41	—	2	2	no	—
125	C₅×#41	—	2	2	no	—
126	C₅×#41	C₄²	1	8	yes	complemented
127	C₅×#41	C₂²×C₄	1	4	yes	—
128	C₅×#41	C₂²×C₄	1	4	yes	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	2	2	no	—
131	C₂×C₅×Q₈	C₄²	1	4	yes	complemented
132	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	4	no	—
135	C₂×C₅×D₄	—	2	4	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	C₄²	1	4	yes	complemented
140	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	4	no	—
145	C₂²×C₄×C₅	—	2	4	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	4	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	1	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	8	no	—
152	C₂²×C₄×C₅	—	4	4	no	—
153	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
156	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
157	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	#41	1	2	yes	—
162	C₂²×C₄×C₅	#41	1	2	yes	—
163	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₅×M₁₆	—	2	4	no	—
165	C₅×M₁₆	—	2	4	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	2	2	no	—
168	C₅×M₁₆	C₂²×C₄	1	4	yes	—
169	C₅×M₁₆	C₂²×C₄	1	4	yes	—
170	C₂×C₅×C₈	—	2	4	no	—
171	C₂×C₅×C₈	—	2	4	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₄⋊C₄	—	2	8	no	—
176	C₅×C₄⋊C₄	—	2	4	no	—
177	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
178	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
179	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
180	C₅×C₂²⋊C₄	—	2	2	no	—
181	C₅×C₂²⋊C₄	—	2	4	no	—
182	C₅×C₂²⋊C₄	—	2	2	no	—
183	C₅×C₂²⋊C₄	—	2	8	no	—
184	C₅×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
185	C₅×C₂²⋊C₄	C₂²⋊C₄	1	4	yes	—
186	C₄²×C₅	—	2	8	no	—
187	C₄²×C₅	—	2	2	no	—
188	C₄²×C₅	—	2	4	no	—
189	C₄²×C₅	—	2	2	no	—
190	C₄²×C₅	—	2	1	no	—
191	C₄²×C₅	—	2	1	no	—
192	C₄²×C₅	—	2	2	no	—
193	C₄²×C₅	—	4	8	no	—
194	C₄²×C₅	C₂²×C₄	1	2	yes	—
195	C₄²×C₅	C₂²×C₄	1	2	yes	—
196	C₄²×C₅	C₂²×C₄	1	4	yes	—
197	C₄²×C₅	C₂²×C₄	1	4	yes	—
198	C₄²×C₅	C₂×D₄	1	4	yes	—
199	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
200	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
201	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
202	#520	—	2	2	no	—
203	#520	C₄×C₅	1	4	yes	complemented
204	#519	C₄×C₅	1	2	yes	complemented
205	#518	—	2	2	no	—
206	#518	C₄×C₅	1	2	yes	complemented
207	C₄×#41	—	2	2	no	—
208	C₄×#41	C₂²×C₅	1	4	yes	—
209	C₂×#117	—	2	2	no	—
210	C₂×#117	C₂²×C₅	1	1	yes	characteristic
211	C₂×#117	C₂²×C₅	1	1	yes	characteristic
212	C₂×#117	C₂²×C₅	1	1	yes	characteristic
213	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
214	#421	C₄×C₅	1	8	yes	complemented
215	C₂×#104	C₄×C₅	1	8	yes	complemented
216	C₂×#104	C₂²×C₅	1	2	yes	—
217	C₂×#104	C₂²×C₅	1	2	yes	—
218	C₂×#104	C₂²×C₅	1	4	yes	—
219	#405	—	2	2	no	—
220	#405	—	2	2	no	—
221	C₄×M₁₆	C₂²×C₅	1	4	yes	complemented
222	C₄×C₄⋊C₄	—	2	2	no	—
223	C₄×C₂²⋊C₄	—	2	2	no	—
224	#376	C₂²×C₅	1	2	yes	complemented
225	C₄³	C₂²×C₅	1	2	yes	complemented
226	#339	C₂²×C₅	1	2	yes	complemented
227	#339	C₂²×C₅	1	2	yes	complemented
228	#339	C₂²×C₅	1	4	yes	complemented
229	C₂³×C₅	—	2	2	no	—
230	C₂³×C₅	—	2	4	no	—
231	C₂³×C₅	—	4	2	no	—
232	C₂³×C₅	—	8	2	no	—
233	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
234	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
235	C₂³×C₅	C₄×D₄	1	2	yes	—
236	C₂³×C₅	C₄×D₄	1	2	yes	—
237	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₅×Q₈	—	2	2	no	—
239	C₅×Q₈	—	2	4	no	—
240	C₅×Q₈	C₂×C₄²	1	4	yes	—
241	C₅×D₄	—	2	4	no	—
242	C₅×D₄	—	2	4	no	—
243	C₅×D₄	—	2	8	no	—
244	C₅×D₄	—	2	2	no	—
245	C₅×D₄	—	2	4	no	—
246	C₅×D₄	C₂×C₄²	1	4	yes	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	4	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	2	8	no	—
254	C₂×C₄×C₅	—	2	4	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	4	4	no	—
258	C₂×C₄×C₅	—	4	8	no	—
259	C₂×C₄×C₅	—	4	4	no	—
260	C₂×C₄×C₅	—	4	2	no	—
261	C₂×C₄×C₅	—	8	8	no	—
262	C₂×C₄×C₅	—	8	2	no	—
263	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
264	C₂×C₄×C₅	C₂×C₄²	1	2	yes	—
265	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	8	yes	—
266	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
267	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
268	C₂×C₄×C₅	#117	1	2	yes	—
269	C₂×C₄×C₅	#117	1	2	yes	—
270	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
271	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
272	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
273	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
274	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
275	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
276	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
279	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
282	C₅×C₈	—	2	4	no	—
283	C₅×C₈	—	2	4	no	—
284	C₂×#41	—	2	1	no	—
285	C₂×#41	—	2	1	no	—
286	C₂×#41	—	2	2	no	—
287	C₂×#41	—	2	2	no	—
288	C₂×#41	C₂×C₄×C₅	1	4	yes	—
289	C₂×#41	C₂×C₄×C₅	1	4	yes	—
290	C₂×#41	C₂×C₄×C₅	1	2	yes	—
291	C₂×#41	C₂³×C₅	1	2	yes	—
292	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
293	C₂²×D₄	—	2	1	no	—
294	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
295	C₂³×C₄	—	2	1	no	—
296	C₂³×C₄	—	2	1	no	—
297	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	2	no	—
301	C₂×M₁₆	—	2	2	no	—
302	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
303	C₂×M₁₆	C₂×C₄×C₅	1	4	yes	complemented
304	C₂×M₁₆	C₂³×C₅	1	2	yes	—
305	C₂×M₁₆	C₂³×C₅	1	2	yes	—
306	C₂²×C₈	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₄×Q₈	—	2	4	no	—
309	C₄×Q₈	C₂×C₄×C₅	1	8	yes	complemented
310	C₄×D₄	—	2	8	no	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	8	no	—
313	C₄×D₄	C₂×C₄×C₅	1	8	yes	complemented
314	#117	—	2	1	no	—
315	#117	—	2	1	no	—
316	#117	—	2	2	no	—
317	#117	—	2	4	no	—
318	#117	—	2	4	no	—
319	#117	—	2	4	no	—
320	#117	C₂×C₄×C₅	1	2	yes	—
321	#117	C₂×C₄×C₅	1	2	yes	—
322	#117	C₂×C₄×C₅	1	2	yes	—
323	#117	C₂×C₄×C₅	1	4	yes	complemented
324	#117	C₅×D₄	1	2	yes	—
325	#117	C₅×D₄	1	2	yes	—
326	#117	C₂³×C₅	1	2	yes	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	—	2	4	no	—
329	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
330	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	2	4	no	—
334	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	—	2	2	no	—
338	C₂×C₄²	—	2	4	no	—
339	C₂×C₄²	—	2	4	no	—
340	C₂×C₄²	C₂×C₄×C₅	1	4	yes	complemented
341	C₂×C₄²	C₂³×C₅	1	2	yes	—
342	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₅	1	2	yes	—
345	#104	C₂×C₄×C₅	1	8	yes	complemented
346	#104	C₂×C₄×C₅	1	8	yes	complemented
347	#104	C₂×C₄×C₅	1	16	yes	complemented
348	#97	—	2	4	no	—
349	C₄×C₈	—	2	4	no	—
350	#95	—	2	4	no	—
351	C₂²×C₅	—	2	2	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	4	no	—
355	C₂²×C₅	—	4	2	no	—
356	C₂²×C₅	—	4	2	no	—
357	C₂²×C₅	—	4	4	no	—
358	C₂²×C₅	—	8	4	no	—
359	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
360	C₂²×C₅	C₄×C₂²⋊C₄	1	2	yes	—
361	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
362	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
363	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
364	C₄×C₅	—	2	4	no	—
365	C₄×C₅	—	2	8	no	—
366	C₄×C₅	—	2	4	no	—
367	C₄×C₅	—	4	4	no	—
368	C₄×C₅	—	4	2	no	—
369	C₄×C₅	—	4	4	no	—
370	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
371	C₄×C₅	C₄×C₂²⋊C₄	1	2	yes	—
372	C₄×C₅	C₂²×C₄²	1	1	yes	characteristic
373	C₄×C₅	C₂×#117	1	1	yes	characteristic
374	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
375	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
376	C₂⁴	—	2	1	no	—
377	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
378	#41	—	2	4	no	—
379	#41	—	2	4	no	—
380	#41	—	2	4	no	—
381	#41	—	2	4	no	—
382	#41	—	2	4	no	—
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	C₄²×C₅	1	8	yes	complemented
386	#41	C₂²×C₄×C₅	1	4	yes	—
387	#41	C₂²×C₄×C₅	1	4	yes	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	C₄²×C₅	1	4	yes	complemented
391	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	1	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₄²×C₅	1	4	yes	complemented
399	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	4	4	no	—
412	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
413	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
414	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
415	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
416	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
417	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
420	C₂²×C₄	C₅×#41	1	2	yes	—
421	C₂²×C₄	C₅×#41	1	2	yes	—
422	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
423	M₁₆	—	2	4	no	—
424	M₁₆	—	2	4	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	2	no	—
427	M₁₆	C₂²×C₄×C₅	1	4	yes	—
428	M₁₆	C₂²×C₄×C₅	1	4	yes	—
429	C₂×C₈	—	2	4	no	—
430	C₂×C₈	—	2	4	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₄⋊C₄	—	2	2	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
437	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
438	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	2	no	—
442	C₂²⋊C₄	—	2	8	no	—
443	C₂²⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
444	C₂²⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
445	C₄²	—	2	8	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	4	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	2	no	—
452	C₄²	—	4	8	no	—
453	C₄²	C₂²×C₄×C₅	1	2	yes	—
454	C₄²	C₂²×C₄×C₅	1	2	yes	—
455	C₄²	C₂²×C₄×C₅	1	4	yes	—
456	C₄²	C₂²×C₄×C₅	1	4	yes	—
457	C₄²	C₂×C₅×D₄	1	4	yes	—
458	C₂×C₅	—	2	1	no	—
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	2	2	no	—
461	C₂×C₅	—	2	2	no	—
462	C₂×C₅	—	4	4	no	—
463	C₂×C₅	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic
464	C₂×C₅	#2901	1	2	yes	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	4	2	no	—
468	C₂³	—	8	2	no	—
469	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
470	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
471	C₂³	C₄×C₅×D₄	1	2	yes	—
472	C₂³	C₄×C₅×D₄	1	2	yes	—
473	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
474	Q₈	—	2	4	no	—
475	Q₈	—	2	2	no	—
476	Q₈	C₂×C₄²×C₅	1	4	yes	—
477	D₄	—	2	8	no	—
478	D₄	—	2	4	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	4	no	—
481	D₄	—	2	2	no	—
482	D₄	C₂×C₄²×C₅	1	4	yes	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	8	8	no	—
498	C₂×C₄	—	8	2	no	—
499	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
500	C₂×C₄	C₂×C₄²×C₅	1	2	yes	—
501	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	8	yes	—
502	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
504	C₂×C₄	C₅×#117	1	2	yes	—
505	C₂×C₄	C₅×#117	1	2	yes	—
506	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
507	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
508	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
509	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
510	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
511	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
512	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
513	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
514	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
515	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
516	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
517	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
518	C₈	—	2	4	no	—
519	C₈	—	2	4	no	—
520	C₅	#20405	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²	—	2	2	no	—
522	C₂²	—	2	2	no	—
523	C₂²	—	2	2	no	—
524	C₂²	—	2	4	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	4	no	—
528	C₂²	—	8	4	no	—
529	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
530	C₂²	C₄×C₅×C₂²⋊C₄	1	2	yes	—
531	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
532	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
533	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
534	C₄	—	2	4	no	—
535	C₄	—	2	4	no	—
536	C₄	—	2	8	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	4	no	—
540	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
541	C₄	C₄×C₅×C₂²⋊C₄	1	2	yes	—
542	C₄	C₂²×C₄²×C₅	1	1	yes	characteristic
543	C₄	C₂×C₅×#117	1	1	yes	characteristic
544	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
545	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
546	C₂	—	2	1	no	—
547	C₂	—	2	1	no	—
548	C₂	—	2	2	no	—
549	C₂	—	2	2	no	—
550	C₂	—	4	4	no	—
551	C₂	C₂×C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
552	C₂	C₅×#2901	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₄	C₂²×C₄²×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#2873	C₂	semidirect
5. C₄×C₅×#117	C₂	semidirect
6. C₅×#1759	C₂	semidirect
7. C₄×C₅×#104	C₂	semidirect
8. C₅×#1733	C₂	semidirect
9. C₂×C₅×#339	C₂	semidirect
14. C₅×#520	C₄	semidirect
15. C₅×#519	C₄	semidirect
17. C₅×#518	C₄	semidirect
25. C₅×#421	C₄	semidirect
26. C₂×C₅×#104	C₄	semidirect
32. C₄×C₅×M₁₆	C₂²	semidirect
35. C₅×#376	C₂²	semidirect
36. C₄³×C₅	C₂²	semidirect
37. C₅×#339	C₂²	semidirect
38. C₅×#339	C₂²	semidirect
39. C₅×#339	C₂²	semidirect
40. #20405	C₅	direct (N × H)
59. C₂×C₅×M₁₆	C₂×C₄	semidirect
60. C₂×C₅×M₁₆	C₂×C₄	semidirect
66. C₄×C₅×Q₈	C₂×C₄	semidirect
70. C₄×C₅×D₄	C₂×C₄	semidirect
80. C₅×#117	C₂×C₄	semidirect
97. C₂×C₄²×C₅	C₂×C₄	semidirect
102. C₅×#104	C₂×C₄	semidirect
103. C₅×#104	C₂×C₄	semidirect
104. C₅×#104	C₂×C₄	semidirect
111. #2873	C₂×C₅	semidirect
112. C₄×#117	C₂×C₅	semidirect
113. #1759	C₂×C₅	semidirect
114. C₄×#104	C₂×C₅	semidirect
115. #1733	C₂×C₅	semidirect
116. C₂×#339	C₂×C₅	semidirect
126. C₅×#41	C₄²	semidirect
131. C₂×C₅×Q₈	C₄²	semidirect
139. C₂×C₅×D₄	C₄²	semidirect
203. #520	C₄×C₅	semidirect
204. #519	C₄×C₅	semidirect
206. #518	C₄×C₅	semidirect
214. #421	C₄×C₅	semidirect
215. C₂×#104	C₄×C₅	semidirect
221. C₄×M₁₆	C₂²×C₅	semidirect
224. #376	C₂²×C₅	semidirect
225. C₄³	C₂²×C₅	semidirect
226. #339	C₂²×C₅	semidirect
227. #339	C₂²×C₅	semidirect
228. #339	C₂²×C₅	semidirect
302. C₂×M₁₆	C₂×C₄×C₅	semidirect
303. C₂×M₁₆	C₂×C₄×C₅	semidirect
309. C₄×Q₈	C₂×C₄×C₅	semidirect
313. C₄×D₄	C₂×C₄×C₅	semidirect
323. #117	C₂×C₄×C₅	semidirect
340. C₂×C₄²	C₂×C₄×C₅	semidirect
345. #104	C₂×C₄×C₅	semidirect
346. #104	C₂×C₄×C₅	semidirect
347. #104	C₂×C₄×C₅	semidirect
385. #41	C₄²×C₅	semidirect
390. C₂×Q₈	C₄²×C₅	semidirect
398. C₂×D₄	C₄²×C₅	semidirect
520. C₅	#20405	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×#3428	2
C₂×C₅×#421	2
C₂²×C₅×#104	2
C₅×#2873	2
C₄×C₅×#117	2
C₅×#1759	2
C₄×C₅×#104	2
C₅×#1733	2
C₂×C₅×#339	2
#20405	5

Subgroups — C5×#20405 #11943125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20405 #11943125