Subgroups — C₅×#10956 #11933676

Order 1280.

918 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
2	C₅×#2896	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#408	C₂	1	1	yes	maximal, characteristic
4	C₅×#2873	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1735	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₅×#421	—	2	2	no	—
16	C₅×#421	C₄	1	4	yes	complemented
17	C₂×C₅×#104	—	2	2	no	—
18	C₅×#419	C₄	1	2	yes	complemented
19	C₅×#418	C₄	1	2	yes	complemented
20	C₅×#417	—	2	2	no	—
21	C₅×#416	—	2	2	no	—
22	C₅×#408	—	2	2	no	—
23	C₅×#408	C₄	1	4	yes	complemented
24	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
25	C₅×#405	—	2	2	no	—
26	C₅×#405	—	2	2	no	—
27	C₄×C₅×M₁₆	—	2	2	no	—
28	C₅×#344	—	2	2	no	—
29	C₅×#341	—	2	2	no	—
30	C₅×#340	—	2	2	no	—
31	#10956	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂×C₅×#41	—	2	1	no	—
33	C₂×C₅×#41	—	2	1	no	—
34	C₂×C₅×#41	—	2	1	no	—
35	C₂×C₅×#41	—	2	1	no	—
36	C₂×C₅×#41	—	2	1	no	—
37	C₂×C₅×#41	—	2	1	no	—
38	C₂×C₅×#41	—	2	1	no	—
39	C₂×C₅×#41	—	2	1	no	—
40	C₂×C₅×#41	—	2	1	no	—
41	C₂×C₅×#41	—	2	1	no	—
42	C₂×C₅×#41	C₂×C₄	1	2	yes	—
43	C₂×C₅×#41	C₂×C₄	1	2	yes	—
44	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
47	C₂³×C₄×C₅	—	2	1	no	—
48	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	—	2	1	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	1	no	—
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
62	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
63	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
64	C₂×C₅×M₁₆	D₄	1	2	yes	—
65	C₂×C₅×M₁₆	D₄	1	2	yes	—
66	C₂×C₅×M₁₆	D₄	1	2	yes	—
67	C₂²×C₅×C₈	—	2	1	no	—
68	C₂²×C₅×C₈	—	2	1	no	—
69	C₂²×C₅×C₈	—	2	1	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₂²×C₅×C₈	—	2	1	no	—
73	C₂²×C₅×C₈	—	2	1	no	—
74	C₂²×C₅×C₈	—	2	1	no	—
75	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
76	C₂²×C₅×C₈	D₄	1	2	yes	—
77	C₅×#117	—	2	1	no	—
78	C₅×#117	—	2	1	no	—
79	C₅×#117	—	2	1	no	—
80	C₅×#117	—	2	1	no	—
81	C₅×#117	—	2	1	no	—
82	C₅×#117	C₂×C₄	1	2	yes	—
83	C₅×#117	C₂×C₄	1	2	yes	—
84	C₅×#117	D₄	1	2	yes	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
89	C₂×C₄²×C₅	—	2	1	no	—
90	C₂×C₄²×C₅	—	2	1	no	—
91	C₅×#104	—	2	8	no	—
92	C₅×#103	—	2	4	no	—
93	C₅×#102	—	2	4	no	—
94	C₅×C₂²⋊C₈	—	2	8	no	—
95	C₅×#97	—	2	4	no	—
96	C₄×C₅×C₈	—	2	4	no	—
97	C₂×#421	C₂×C₅	1	1	yes	characteristic
98	#2896	C₂×C₅	1	1	yes	characteristic
99	C₂×#408	C₂×C₅	1	1	yes	characteristic
100	#2873	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#344	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#341	C₂×C₅	1	1	yes	characteristic, complemented
103	#1735	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	2	1	no	—
105	C₂⁴×C₅	#41	1	1	yes	characteristic
106	C₅×#41	—	2	2	no	—
107	C₅×#41	—	2	2	no	—
108	C₅×#41	—	2	2	no	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	4	1	no	—
115	C₅×#41	—	4	1	no	—
116	C₅×#41	—	4	1	no	—
117	C₅×#41	—	4	1	no	—
118	C₅×#41	—	4	1	no	—
119	C₅×#41	—	4	1	no	—
120	C₅×#41	—	4	1	no	—
121	C₅×#41	—	4	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	1	no	—
125	C₂×C₅×Q₈	—	2	1	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	C₄²	1	2	yes	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	2	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	—	4	1	no	—
137	C₂×C₅×D₄	—	4	1	no	—
138	C₂×C₅×D₄	—	4	1	no	—
139	C₂×C₅×D₄	C₄²	1	2	yes	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	4	1	no	—
145	C₂²×C₄×C₅	—	4	1	no	—
146	C₂²×C₄×C₅	—	4	1	no	—
147	C₂²×C₄×C₅	—	4	1	no	—
148	C₂²×C₄×C₅	—	4	1	no	—
149	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	#41	1	1	yes	characteristic
159	C₂²×C₄×C₅	#41	1	1	yes	characteristic
160	C₂²×C₄×C₅	#41	1	1	yes	characteristic
161	C₂²×C₄×C₅	#41	1	1	yes	characteristic
162	C₂²×C₄×C₅	#41	1	1	yes	characteristic
163	C₅×M₁₆	—	2	2	no	—
164	C₅×M₁₆	—	2	2	no	—
165	C₅×M₁₆	—	2	2	no	—
166	C₅×M₁₆	—	2	2	no	—
167	C₅×M₁₆	—	2	2	no	—
168	C₅×M₁₆	—	2	2	no	—
169	C₅×M₁₆	—	2	2	no	—
170	C₅×M₁₆	—	2	2	no	—
171	C₅×M₁₆	—	2	2	no	—
172	C₅×M₁₆	—	4	1	no	—
173	C₅×M₁₆	—	4	1	no	—
174	C₅×M₁₆	C₂²⋊C₄	1	4	yes	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	2	2	no	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	2	2	no	—
182	C₂×C₅×C₈	—	2	2	no	—
183	C₂×C₅×C₈	—	2	2	no	—
184	C₂×C₅×C₈	—	4	1	no	—
185	C₂×C₅×C₈	—	4	1	no	—
186	C₂×C₅×C₈	—	4	1	no	—
187	C₂×C₅×C₈	—	4	1	no	—
188	C₂×C₅×C₈	—	4	1	no	—
189	C₂×C₅×C₈	—	4	1	no	—
190	C₂×C₅×C₈	C₂²⋊C₄	1	4	yes	—
191	C₅×C₄⋊C₄	—	2	2	no	—
192	C₅×C₄⋊C₄	—	2	2	no	—
193	C₅×C₄⋊C₄	—	4	1	no	—
194	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	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	—	4	1	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	2	no	—
201	C₄²×C₅	—	2	2	no	—
202	C₄²×C₅	—	4	1	no	—
203	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
204	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
205	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
206	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
207	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
208	C₂×#117	C₂²×C₅	1	1	yes	characteristic
209	C₂×#117	C₂²×C₅	1	1	yes	characteristic
210	#421	—	2	2	no	—
211	#421	C₄×C₅	1	4	yes	complemented
212	C₂×#104	—	2	2	no	—
213	#419	C₄×C₅	1	2	yes	complemented
214	#418	C₄×C₅	1	2	yes	complemented
215	#417	—	2	2	no	—
216	#416	—	2	2	no	—
217	#408	—	2	2	no	—
218	#408	C₄×C₅	1	4	yes	complemented
219	C₂×C₂²⋊C₈	—	2	2	no	—
220	#405	—	2	2	no	—
221	#405	—	2	2	no	—
222	C₄×M₁₆	—	2	2	no	—
223	#344	—	2	2	no	—
224	#341	—	2	2	no	—
225	#340	—	2	2	no	—
226	C₂³×C₅	—	2	2	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	—	4	4	no	—
229	C₂³×C₅	—	4	1	no	—
230	C₂³×C₅	—	4	1	no	—
231	C₂³×C₅	#117	1	1	yes	characteristic
232	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
233	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂³×C₅	#121	1	1	yes	characteristic
235	C₂³×C₅	#123	1	1	yes	characteristic
236	C₂³×C₅	#124	1	1	yes	characteristic
237	C₂³×C₅	#126	1	1	yes	characteristic
238	C₅×Q₈	—	2	2	no	—
239	C₅×Q₈	—	2	2	no	—
240	C₅×Q₈	—	4	1	no	—
241	C₅×Q₈	—	4	1	no	—
242	C₅×D₄	—	2	2	no	—
243	C₅×D₄	—	2	2	no	—
244	C₅×D₄	—	4	2	no	—
245	C₅×D₄	—	4	2	no	—
246	C₅×D₄	—	4	2	no	—
247	C₅×D₄	—	4	2	no	—
248	C₅×D₄	—	4	1	no	—
249	C₅×D₄	—	4	1	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	4	1	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	2	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	8	2	no	—
260	C₂×C₄×C₅	—	8	2	no	—
261	C₂×C₄×C₅	C₂×C₄²	1	1	yes	characteristic
262	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
263	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
265	C₂×C₄×C₅	#117	1	1	yes	characteristic
266	C₂×C₄×C₅	#117	1	1	yes	characteristic
267	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
268	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
277	C₂×C₄×C₅	#120	1	1	yes	characteristic
278	C₂×C₄×C₅	#121	1	1	yes	characteristic
279	C₂×C₄×C₅	#121	1	1	yes	characteristic
280	C₂×C₄×C₅	#121	1	1	yes	characteristic
281	C₂×C₄×C₅	#121	1	1	yes	characteristic
282	C₂×C₄×C₅	#121	1	1	yes	characteristic
283	C₂×C₄×C₅	#123	1	1	yes	characteristic
284	C₂×C₄×C₅	#123	1	1	yes	characteristic
285	C₂×C₄×C₅	#124	1	1	yes	characteristic
286	C₂×C₄×C₅	#124	1	1	yes	characteristic
287	C₂×C₄×C₅	#126	1	1	yes	characteristic
288	C₂×C₄×C₅	#127	1	1	yes	characteristic
289	C₅×C₈	—	2	4	no	—
290	C₅×C₈	—	2	4	no	—
291	C₅×C₈	—	4	2	no	—
292	C₅×C₈	—	4	2	no	—
293	C₂×#41	—	2	1	no	—
294	C₂×#41	—	2	1	no	—
295	C₂×#41	—	2	1	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	2	1	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	2	1	no	—
300	C₂×#41	—	2	1	no	—
301	C₂×#41	—	2	1	no	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	C₂×C₄×C₅	1	2	yes	—
304	C₂×#41	C₂×C₄×C₅	1	2	yes	—
305	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
306	C₂²×D₄	—	2	1	no	—
307	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
323	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
324	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
325	C₂×M₁₆	C₅×D₄	1	2	yes	—
326	C₂×M₁₆	C₅×D₄	1	2	yes	—
327	C₂×M₁₆	C₅×D₄	1	2	yes	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	—	2	1	no	—
333	C₂²×C₈	—	2	1	no	—
334	C₂²×C₈	—	2	1	no	—
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
337	C₂²×C₈	C₅×D₄	1	2	yes	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	—	2	1	no	—
341	#117	—	2	1	no	—
342	#117	—	2	1	no	—
343	#117	C₂×C₄×C₅	1	2	yes	—
344	#117	C₂×C₄×C₅	1	2	yes	—
345	#117	C₅×D₄	1	2	yes	—
346	C₂×C₄⋊C₄	—	2	1	no	—
347	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₂²⋊C₄	—	2	1	no	—
350	C₂×C₄²	—	2	1	no	—
351	C₂×C₄²	—	2	1	no	—
352	#104	—	2	8	no	—
353	#103	—	2	4	no	—
354	#102	—	2	4	no	—
355	C₂²⋊C₈	—	2	8	no	—
356	#97	—	2	4	no	—
357	C₄×C₈	—	2	4	no	—
358	C₂²×C₅	—	2	2	no	—
359	C₂²×C₅	—	2	2	no	—
360	C₂²×C₅	—	2	2	no	—
361	C₂²×C₅	—	4	1	no	—
362	C₂²×C₅	—	4	1	no	—
363	C₂²×C₅	—	4	1	no	—
364	C₂²×C₅	—	4	1	no	—
365	C₂²×C₅	—	4	4	no	—
366	C₂²×C₅	—	4	2	no	—
367	C₂²×C₅	—	8	2	no	—
368	C₂²×C₅	—	8	2	no	—
369	C₂²×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
370	C₂²×C₅	#386	1	1	yes	characteristic
371	C₂²×C₅	#388	1	1	yes	characteristic
372	C₂²×C₅	#388	1	1	yes	characteristic
373	C₂²×C₅	#388	1	1	yes	characteristic
374	C₂²×C₅	#388	1	1	yes	characteristic
375	C₂²×C₅	#390	1	1	yes	characteristic
376	C₄×C₅	—	4	4	no	—
377	C₄×C₅	—	4	2	no	—
378	C₄×C₅	—	8	2	no	—
379	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
380	C₄×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
381	C₄×C₅	#386	1	1	yes	characteristic
382	C₄×C₅	#386	1	1	yes	characteristic
383	C₄×C₅	#388	1	1	yes	characteristic
384	C₄×C₅	#388	1	1	yes	characteristic
385	C₄×C₅	#390	1	1	yes	characteristic
386	C₄×C₅	#390	1	1	yes	characteristic
387	C₂⁴	—	2	1	no	—
388	C₂⁴	C₅×#41	1	1	yes	characteristic
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	2	2	no	—
392	#41	—	2	2	no	—
393	#41	—	2	2	no	—
394	#41	—	2	2	no	—
395	#41	—	2	2	no	—
396	#41	—	2	2	no	—
397	#41	—	4	1	no	—
398	#41	—	4	1	no	—
399	#41	—	4	1	no	—
400	#41	—	4	1	no	—
401	#41	—	4	1	no	—
402	#41	—	4	1	no	—
403	#41	—	4	1	no	—
404	#41	—	4	1	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	2	1	no	—
409	C₂×Q₈	—	2	1	no	—
410	C₂×Q₈	C₄²×C₅	1	2	yes	—
411	C₂×D₄	—	2	2	no	—
412	C₂×D₄	—	2	2	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	2	1	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	—	4	1	no	—
420	C₂×D₄	—	4	1	no	—
421	C₂×D₄	—	4	1	no	—
422	C₂×D₄	C₄²×C₅	1	2	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	4	1	no	—
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
433	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
435	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
436	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
437	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
438	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
439	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
440	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
441	C₂²×C₄	C₅×#41	1	1	yes	characteristic
442	C₂²×C₄	C₅×#41	1	1	yes	characteristic
443	C₂²×C₄	C₅×#41	1	1	yes	characteristic
444	C₂²×C₄	C₅×#41	1	1	yes	characteristic
445	C₂²×C₄	C₅×#41	1	1	yes	characteristic
446	M₁₆	—	2	2	no	—
447	M₁₆	—	2	2	no	—
448	M₁₆	—	2	2	no	—
449	M₁₆	—	2	2	no	—
450	M₁₆	—	2	2	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	4	1	no	—
456	M₁₆	—	4	1	no	—
457	M₁₆	C₅×C₂²⋊C₄	1	4	yes	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	2	no	—
462	C₂×C₈	—	2	2	no	—
463	C₂×C₈	—	2	2	no	—
464	C₂×C₈	—	2	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	4	1	no	—
468	C₂×C₈	—	4	1	no	—
469	C₂×C₈	—	4	1	no	—
470	C₂×C₈	—	4	1	no	—
471	C₂×C₈	—	4	1	no	—
472	C₂×C₈	—	4	1	no	—
473	C₂×C₈	C₅×C₂²⋊C₄	1	4	yes	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	4	1	no	—
477	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	2	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₄²	—	2	2	no	—
483	C₄²	—	2	2	no	—
484	C₄²	—	2	2	no	—
485	C₄²	—	4	1	no	—
486	C₂×C₅	—	2	1	no	—
487	C₂×C₅	—	2	1	no	—
488	C₂×C₅	—	2	1	no	—
489	C₂×C₅	—	2	1	no	—
490	C₂×C₅	—	2	1	no	—
491	C₂×C₅	—	2	1	no	—
492	C₂×C₅	—	8	2	no	—
493	C₂×C₅	#1437	1	1	yes	characteristic
494	C₂×C₅	#1881	1	2	yes	—
495	C₂³	—	2	2	no	—
496	C₂³	—	4	2	no	—
497	C₂³	—	4	4	no	—
498	C₂³	—	4	1	no	—
499	C₂³	—	4	1	no	—
500	C₂³	C₅×#117	1	1	yes	characteristic
501	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
502	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
503	C₂³	C₅×#121	1	1	yes	characteristic
504	C₂³	C₅×#123	1	1	yes	characteristic
505	C₂³	C₅×#124	1	1	yes	characteristic
506	C₂³	C₅×#126	1	1	yes	characteristic
507	Q₈	—	2	2	no	—
508	Q₈	—	2	2	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	D₄	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	4	2	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	2	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	1	no	—
518	D₄	—	4	1	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	2	no	—
527	C₂×C₄	—	4	2	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	—	8	2	no	—
530	C₂×C₄	C₂×C₄²×C₅	1	1	yes	characteristic
531	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
532	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
533	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
534	C₂×C₄	C₅×#117	1	1	yes	characteristic
535	C₂×C₄	C₅×#117	1	1	yes	characteristic
536	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
537	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
538	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
539	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
540	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
541	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
542	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
543	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
544	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
545	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
546	C₂×C₄	C₅×#120	1	1	yes	characteristic
547	C₂×C₄	C₅×#121	1	1	yes	characteristic
548	C₂×C₄	C₅×#121	1	1	yes	characteristic
549	C₂×C₄	C₅×#121	1	1	yes	characteristic
550	C₂×C₄	C₅×#121	1	1	yes	characteristic
551	C₂×C₄	C₅×#121	1	1	yes	characteristic
552	C₂×C₄	C₅×#123	1	1	yes	characteristic
553	C₂×C₄	C₅×#123	1	1	yes	characteristic
554	C₂×C₄	C₅×#124	1	1	yes	characteristic
555	C₂×C₄	C₅×#124	1	1	yes	characteristic
556	C₂×C₄	C₅×#126	1	1	yes	characteristic
557	C₂×C₄	C₅×#127	1	1	yes	characteristic
558	C₈	—	2	4	no	—
559	C₈	—	2	4	no	—
560	C₈	—	4	2	no	—
561	C₈	—	4	2	no	—
562	C₅	#10956	1	1	yes	characteristic, direct product factor, Sylow
563	C₂²	—	2	2	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	4	no	—
571	C₂²	—	4	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	—	8	2	no	—
574	C₂²	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
575	C₂²	C₅×#386	1	1	yes	characteristic
576	C₂²	C₅×#388	1	1	yes	characteristic
577	C₂²	C₅×#388	1	1	yes	characteristic
578	C₂²	C₅×#388	1	1	yes	characteristic
579	C₂²	C₅×#388	1	1	yes	characteristic
580	C₂²	C₅×#390	1	1	yes	characteristic
581	C₄	—	4	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	8	2	no	—
584	C₄	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
585	C₄	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
586	C₄	C₅×#386	1	1	yes	characteristic
587	C₄	C₅×#386	1	1	yes	characteristic
588	C₄	C₅×#388	1	1	yes	characteristic
589	C₄	C₅×#388	1	1	yes	characteristic
590	C₄	C₅×#390	1	1	yes	characteristic
591	C₄	C₅×#390	1	1	yes	characteristic
592	C₂	—	2	1	no	—
593	C₂	—	2	1	no	—
594	C₂	—	2	1	no	—
595	C₂	—	2	1	no	—
596	C₂	—	2	1	no	—
597	C₂	—	2	1	no	—
598	C₂	—	8	2	no	—
599	C₂	C₅×#1437	1	1	yes	characteristic
600	C₂	C₅×#1881	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	#120
commutator	C₂×C₄	C₂×C₄²×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	#386
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#2873	C₂	semidirect
5. C₂×C₅×#344	C₂	semidirect
6. C₂×C₅×#341	C₂	semidirect
7. C₅×#1735	C₂	semidirect
16. C₅×#421	C₄	semidirect
18. C₅×#419	C₄	semidirect
19. C₅×#418	C₄	semidirect
23. C₅×#408	C₄	semidirect
31. #10956	C₅	direct (N × H)
100. #2873	C₂×C₅	semidirect
101. C₂×#344	C₂×C₅	semidirect
102. C₂×#341	C₂×C₅	semidirect
103. #1735	C₂×C₅	semidirect
211. #421	C₄×C₅	semidirect
213. #419	C₄×C₅	semidirect
214. #418	C₄×C₅	semidirect
218. #408	C₄×C₅	semidirect
562. C₅	#10956	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#421	2
C₅×#2896	2
C₂×C₅×#408	2
C₅×#2873	2
C₂×C₅×#344	2
C₂×C₅×#341	2
C₅×#1735	2
#10956	5

Subgroups — C5×#10956 #11933676

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#10956 #11933676