Subgroups — C₅×#11081 #11933801

Order 1280.

938 conjugacy classes of subgroups.

The subgroup lattice has 634 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	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#410	C₂	1	1	yes	maximal, characteristic
4	C₅×#2285	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×H(3,ℤ/4)	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	C₂×C₅×#117	C₂²	1	1	yes	characteristic
12	C₂×C₅×#117	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₅×#421	—	2	2	no	—
16	C₅×#421	—	2	2	no	—
17	C₂×C₅×#104	—	2	1	no	—
18	C₂×C₅×#104	—	2	1	no	—
19	C₂×C₅×#104	—	2	2	no	—
20	C₂×C₅×#104	—	2	2	no	—
21	C₂×C₅×#104	C₄	1	4	yes	complemented
22	C₅×#410	—	2	2	no	—
23	C₅×#410	—	2	2	no	—
24	C₂×C₅×#99	—	2	2	no	—
25	C₅×#384	—	2	1	no	—
26	C₅×#382	—	2	1	no	—
27	C₅×#380	—	2	2	no	—
28	C₄×C₅×C₄⋊C₄	—	2	2	no	—
29	C₅×#344	—	2	2	no	—
30	C₅×#339	—	2	2	no	—
31	C₅×H(3,ℤ/4)	—	2	2	no	—
32	#11081	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
43	C₂×C₅×#41	C₂×C₄	1	2	yes	—
44	C₂×C₅×#41	D₄	1	2	yes	—
45	C₂²×C₅×Q₈	Q₈	1	1	yes	characteristic
46	C₂²×C₅×D₄	—	2	1	no	—
47	C₂²×C₅×D₄	Q₈	1	1	yes	characteristic
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₅×#117	—	2	1	no	—
66	C₅×#117	—	2	1	no	—
67	C₅×#117	—	2	1	no	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	—	2	1	no	—
70	C₅×#117	—	2	1	no	—
71	C₅×#117	—	2	1	no	—
72	C₅×#117	—	2	1	no	—
73	C₅×#117	—	2	1	no	—
74	C₅×#117	—	2	1	no	—
75	C₅×#117	—	2	1	no	—
76	C₅×#117	D₄	1	2	yes	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	4	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	2	1	no	—
81	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
84	C₂×C₄²×C₅	—	2	1	no	—
85	C₂×C₄²×C₅	—	2	1	no	—
86	C₂×C₄²×C₅	—	2	1	no	—
87	C₂×C₄²×C₅	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₅	D₄	1	2	yes	—
91	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	D₄	1	2	yes	—
94	C₅×#104	—	2	8	no	—
95	C₅×#104	—	2	4	no	—
96	C₅×#104	—	2	4	no	—
97	C₅×#99	—	2	8	no	—
98	C₅×#95	—	2	4	no	—
99	C₂×#421	C₂×C₅	1	1	yes	characteristic
100	C₂²×#104	C₂×C₅	1	1	yes	characteristic
101	C₂×#410	C₂×C₅	1	1	yes	characteristic
102	#2285	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×#344	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂⁴×C₅	—	2	1	no	—
107	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
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	—	2	2	no	—
115	C₅×#41	—	2	2	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	C₅×#41	—	4	1	no	—
123	C₅×#41	—	4	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	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	complemented
130	C₂×C₅×D₄	—	2	2	no	—
131	C₂×C₅×D₄	—	2	2	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	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	no	—
137	C₂×C₅×D₄	—	4	1	no	—
138	C₂×C₅×D₄	—	4	1	no	—
139	C₂×C₅×D₄	—	4	1	no	—
140	C₂×C₅×D₄	—	4	1	no	—
141	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	complemented
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	2	2	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	4	4	no	—
152	C₂²×C₄×C₅	—	4	1	no	—
153	C₂²×C₄×C₅	—	4	1	no	—
154	C₂²×C₄×C₅	—	4	1	no	—
155	C₂²×C₄×C₅	—	4	1	no	—
156	C₂²×C₄×C₅	—	4	1	no	—
157	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
165	C₂²×C₄×C₅	#41	1	1	yes	characteristic
166	C₂²×C₄×C₅	#41	1	1	yes	characteristic
167	C₂²×C₄×C₅	#41	1	1	yes	characteristic
168	C₂²×C₄×C₅	#41	1	1	yes	characteristic
169	C₂²×C₄×C₅	#41	1	1	yes	characteristic
170	C₂²×C₄×C₅	#41	1	1	yes	characteristic
171	C₅×M₁₆	—	2	2	no	—
172	C₅×M₁₆	—	2	2	no	—
173	C₅×M₁₆	—	2	2	no	—
174	C₅×M₁₆	—	2	2	no	—
175	C₅×M₁₆	—	4	1	no	—
176	C₅×M₁₆	—	4	1	no	—
177	C₅×M₁₆	—	4	1	no	—
178	C₅×M₁₆	—	4	1	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	4	1	no	—
182	C₂×C₅×C₈	—	4	1	no	—
183	C₂×C₅×C₈	—	4	1	no	—
184	C₂×C₅×C₈	—	4	1	no	—
185	C₅×C₄⋊C₄	—	2	2	no	—
186	C₅×C₄⋊C₄	—	4	8	no	—
187	C₅×C₄⋊C₄	—	4	1	no	—
188	C₅×C₄⋊C₄	—	4	1	no	—
189	C₅×C₄⋊C₄	—	4	1	no	—
190	C₅×C₄⋊C₄	—	4	1	no	—
191	C₅×C₄⋊C₄	—	4	1	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	—	4	1	no	—
196	C₅×C₂²⋊C₄	—	4	1	no	—
197	C₅×C₂²⋊C₄	—	4	1	no	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	—	2	2	no	—
200	C₄²×C₅	—	2	1	no	—
201	C₄²×C₅	—	2	1	no	—
202	C₄²×C₅	—	2	2	no	—
203	C₄²×C₅	—	2	2	no	—
204	C₄²×C₅	—	2	2	no	—
205	C₄²×C₅	—	4	1	no	—
206	C₄²×C₅	—	4	1	no	—
207	C₄²×C₅	—	4	1	no	—
208	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
209	C₄²×C₅	C₂²⋊C₄	1	2	yes	—
210	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
213	C₂×#117	C₂²×C₅	1	1	yes	characteristic
214	C₂×#117	C₂²×C₅	1	1	yes	characteristic
215	C₂×#117	C₂²×C₅	1	1	yes	characteristic
216	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
217	#421	—	2	2	no	—
218	#421	—	2	2	no	—
219	C₂×#104	—	2	2	no	—
220	C₂×#104	—	2	1	no	—
221	C₂×#104	—	2	1	no	—
222	C₂×#104	—	2	2	no	—
223	C₂×#104	C₄×C₅	1	4	yes	complemented
224	#410	—	2	2	no	—
225	#410	—	2	2	no	—
226	C₂×#99	—	2	2	no	—
227	#384	—	2	1	no	—
228	#382	—	2	1	no	—
229	#380	—	2	2	no	—
230	C₄×C₄⋊C₄	—	2	2	no	—
231	#344	—	2	2	no	—
232	#339	—	2	2	no	—
233	H(3,ℤ/4)	—	2	2	no	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	4	2	no	—
236	C₂³×C₅	—	4	1	no	—
237	C₂³×C₅	—	4	1	no	—
238	C₂³×C₅	—	8	2	no	—
239	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
240	C₂³×C₅	#120	1	1	yes	characteristic
241	C₂³×C₅	#120	1	1	yes	characteristic
242	C₂³×C₅	#121	1	1	yes	characteristic
243	C₂³×C₅	#121	1	1	yes	characteristic
244	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂³×C₅	#124	1	1	yes	characteristic
246	C₅×Q₈	—	2	2	no	—
247	C₅×Q₈	—	2	2	no	—
248	C₅×Q₈	—	4	1	no	—
249	C₅×Q₈	—	4	1	no	—
250	C₅×D₄	—	2	2	no	—
251	C₅×D₄	—	2	2	no	—
252	C₅×D₄	—	4	2	no	—
253	C₅×D₄	—	4	2	no	—
254	C₅×D₄	—	4	2	no	—
255	C₅×D₄	—	4	2	no	—
256	C₅×D₄	—	4	1	no	—
257	C₅×D₄	—	4	1	no	—
258	C₂×C₄×C₅	—	2	4	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	4	4	no	—
263	C₂×C₄×C₅	—	4	4	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	—	4	1	no	—
266	C₂×C₄×C₅	—	4	1	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	4	2	no	—
269	C₂×C₄×C₅	—	4	2	no	—
270	C₂×C₄×C₅	—	4	2	no	—
271	C₂×C₄×C₅	—	4	4	no	—
272	C₂×C₄×C₅	—	4	4	no	—
273	C₂×C₄×C₅	—	4	2	no	—
274	C₂×C₄×C₅	—	4	2	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	8	2	no	—
277	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
279	C₂×C₄×C₅	#117	1	1	yes	characteristic
280	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
283	C₂×C₄×C₅	#120	1	1	yes	characteristic
284	C₂×C₄×C₅	#121	1	1	yes	characteristic
285	C₂×C₄×C₅	#121	1	1	yes	characteristic
286	C₂×C₄×C₅	#121	1	1	yes	characteristic
287	C₂×C₄×C₅	#121	1	1	yes	characteristic
288	C₂×C₄×C₅	#121	1	1	yes	characteristic
289	C₂×C₄×C₅	#121	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
295	C₂×C₄×C₅	#123	1	1	yes	characteristic
296	C₂×C₄×C₅	#123	1	1	yes	characteristic
297	C₂×C₄×C₅	#123	1	1	yes	characteristic
298	C₂×C₄×C₅	#123	1	1	yes	characteristic
299	C₂×C₄×C₅	#123	1	1	yes	characteristic
300	C₂×C₄×C₅	#124	1	1	yes	characteristic
301	C₂×C₄×C₅	#124	1	1	yes	characteristic
302	C₂×C₄×C₅	#126	1	1	yes	characteristic
303	C₂×C₄×C₅	#126	1	1	yes	characteristic
304	C₂×C₄×C₅	#127	1	1	yes	characteristic
305	C₅×C₈	—	4	2	no	—
306	C₅×C₈	—	4	2	no	—
307	C₂×#41	—	2	1	no	—
308	C₂×#41	—	2	1	no	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	2	1	no	—
311	C₂×#41	—	2	1	no	—
312	C₂×#41	—	2	1	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	C₂×C₄×C₅	1	2	yes	—
318	C₂×#41	C₅×D₄	1	2	yes	—
319	C₂²×Q₈	C₅×Q₈	1	1	yes	characteristic
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	C₅×Q₈	1	1	yes	characteristic
322	C₂³×C₄	—	2	1	no	—
323	C₂³×C₄	—	2	1	no	—
324	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
336	C₂×M₁₆	C₅×D₄	1	2	yes	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	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	—	2	1	no	—
344	#117	—	2	1	no	—
345	#117	—	2	1	no	—
346	#117	—	2	1	no	—
347	#117	—	2	1	no	—
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	C₅×D₄	1	2	yes	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	4	no	—
353	C₂×C₄⋊C₄	—	2	1	no	—
354	C₂×C₄⋊C₄	—	2	1	no	—
355	C₂×C₂²⋊C₄	—	2	1	no	—
356	C₂×C₂²⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
358	C₂×C₄²	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	C₂×C₄²	—	2	1	no	—
362	C₂×C₄²	—	2	1	no	—
363	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
364	C₂×C₄²	C₅×D₄	1	2	yes	—
365	C₂×C₄²	C₅×D₄	1	2	yes	—
366	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
367	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
368	#104	—	2	8	no	—
369	#104	—	2	4	no	—
370	#104	—	2	4	no	—
371	#99	—	2	8	no	—
372	#95	—	2	4	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	1	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	2	no	—
381	C₂²×C₅	—	8	2	no	—
382	C₂²×C₅	—	8	2	no	—
383	C₂²×C₅	—	8	2	no	—
384	C₂²×C₅	#385	1	1	yes	characteristic
385	C₂²×C₅	#386	1	1	yes	characteristic
386	C₂²×C₅	#388	1	1	yes	characteristic
387	C₂²×C₅	#392	1	1	yes	characteristic
388	C₂²×C₅	#393	1	1	yes	characteristic
389	C₂²×C₅	#394	1	1	yes	characteristic
390	C₂²×C₅	#396	1	1	yes	characteristic
391	C₄×C₅	—	2	4	no	—
392	C₄×C₅	—	4	2	no	—
393	C₄×C₅	—	4	2	no	—
394	C₄×C₅	—	8	2	no	—
395	C₄×C₅	—	8	2	no	—
396	C₄×C₅	—	8	2	no	—
397	C₄×C₅	#380	1	1	yes	characteristic
398	C₄×C₅	#385	1	1	yes	characteristic
399	C₄×C₅	#388	1	1	yes	characteristic
400	C₄×C₅	#390	1	1	yes	characteristic
401	C₄×C₅	#394	1	1	yes	characteristic
402	C₄×C₅	#396	1	1	yes	characteristic
403	C₄×C₅	#397	1	1	yes	characteristic
404	C₄×C₅	#399	1	1	yes	characteristic
405	C₂⁴	—	2	1	no	—
406	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	4	1	no	—
416	#41	—	4	1	no	—
417	#41	—	4	1	no	—
418	#41	—	4	1	no	—
419	#41	—	4	1	no	—
420	#41	—	4	1	no	—
421	#41	—	4	1	no	—
422	#41	—	4	1	no	—
423	C₂×Q₈	—	2	1	no	—
424	C₂×Q₈	—	2	1	no	—
425	C₂×Q₈	—	2	1	no	—
426	C₂×Q₈	—	2	1	no	—
427	C₂×Q₈	—	2	1	no	—
428	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	complemented
429	C₂×D₄	—	2	2	no	—
430	C₂×D₄	—	2	2	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	—	2	1	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	1	no	—
436	C₂×D₄	—	4	1	no	—
437	C₂×D₄	—	4	1	no	—
438	C₂×D₄	—	4	1	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	complemented
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	2	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	4	1	no	—
455	C₂²×C₄	—	4	1	no	—
456	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
457	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂²×C₄	C₂×C₅×D₄	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×Q₈	1	1	yes	characteristic
464	C₂²×C₄	C₅×#41	1	1	yes	characteristic
465	C₂²×C₄	C₅×#41	1	1	yes	characteristic
466	C₂²×C₄	C₅×#41	1	1	yes	characteristic
467	C₂²×C₄	C₅×#41	1	1	yes	characteristic
468	C₂²×C₄	C₅×#41	1	1	yes	characteristic
469	C₂²×C₄	C₅×#41	1	1	yes	characteristic
470	M₁₆	—	2	2	no	—
471	M₁₆	—	2	2	no	—
472	M₁₆	—	2	2	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	4	1	no	—
475	M₁₆	—	4	1	no	—
476	M₁₆	—	4	1	no	—
477	M₁₆	—	4	1	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	2	2	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	—	4	1	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	4	8	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₄⋊C₄	—	4	1	no	—
489	C₄⋊C₄	—	4	1	no	—
490	C₄⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₂²⋊C₄	—	2	2	no	—
493	C₂²⋊C₄	—	2	2	no	—
494	C₂²⋊C₄	—	4	1	no	—
495	C₂²⋊C₄	—	4	1	no	—
496	C₂²⋊C₄	—	4	1	no	—
497	C₄²	—	2	2	no	—
498	C₄²	—	2	2	no	—
499	C₄²	—	2	1	no	—
500	C₄²	—	2	1	no	—
501	C₄²	—	2	2	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	2	no	—
504	C₄²	—	4	1	no	—
505	C₄²	—	4	1	no	—
506	C₄²	—	4	1	no	—
507	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
508	C₄²	C₅×C₂²⋊C₄	1	2	yes	—
509	C₂×C₅	—	2	1	no	—
510	C₂×C₅	—	2	1	no	—
511	C₂×C₅	—	2	1	no	—
512	C₂×C₅	—	2	1	no	—
513	C₂×C₅	—	2	1	no	—
514	C₂×C₅	—	2	1	no	—
515	C₂×C₅	—	8	2	no	—
516	C₂×C₅	#1439	1	1	yes	characteristic
517	C₂×C₅	#2031	1	2	yes	—
518	C₂³	—	2	2	no	—
519	C₂³	—	4	2	no	—
520	C₂³	—	4	1	no	—
521	C₂³	—	4	1	no	—
522	C₂³	—	8	2	no	—
523	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
524	C₂³	C₅×#120	1	1	yes	characteristic
525	C₂³	C₅×#120	1	1	yes	characteristic
526	C₂³	C₅×#121	1	1	yes	characteristic
527	C₂³	C₅×#121	1	1	yes	characteristic
528	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
529	C₂³	C₅×#124	1	1	yes	characteristic
530	Q₈	—	2	2	no	—
531	Q₈	—	2	2	no	—
532	Q₈	—	4	1	no	—
533	Q₈	—	4	1	no	—
534	D₄	—	2	2	no	—
535	D₄	—	2	2	no	—
536	D₄	—	4	2	no	—
537	D₄	—	4	2	no	—
538	D₄	—	4	2	no	—
539	D₄	—	4	2	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	4	no	—
556	C₂×C₄	—	4	4	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	8	2	no	—
561	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
563	C₂×C₄	C₅×#117	1	1	yes	characteristic
564	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
565	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
566	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
567	C₂×C₄	C₅×#120	1	1	yes	characteristic
568	C₂×C₄	C₅×#121	1	1	yes	characteristic
569	C₂×C₄	C₅×#121	1	1	yes	characteristic
570	C₂×C₄	C₅×#121	1	1	yes	characteristic
571	C₂×C₄	C₅×#121	1	1	yes	characteristic
572	C₂×C₄	C₅×#121	1	1	yes	characteristic
573	C₂×C₄	C₅×#121	1	1	yes	characteristic
574	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
575	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
576	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
577	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
578	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
579	C₂×C₄	C₅×#123	1	1	yes	characteristic
580	C₂×C₄	C₅×#123	1	1	yes	characteristic
581	C₂×C₄	C₅×#123	1	1	yes	characteristic
582	C₂×C₄	C₅×#123	1	1	yes	characteristic
583	C₂×C₄	C₅×#123	1	1	yes	characteristic
584	C₂×C₄	C₅×#124	1	1	yes	characteristic
585	C₂×C₄	C₅×#124	1	1	yes	characteristic
586	C₂×C₄	C₅×#126	1	1	yes	characteristic
587	C₂×C₄	C₅×#126	1	1	yes	characteristic
588	C₂×C₄	C₅×#127	1	1	yes	characteristic
589	C₈	—	4	2	no	—
590	C₈	—	4	2	no	—
591	C₅	#11081	1	1	yes	characteristic, direct product factor, Sylow
592	C₂²	—	2	2	no	—
593	C₂²	—	2	2	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	2	no	—
600	C₂²	—	8	2	no	—
601	C₂²	—	8	2	no	—
602	C₂²	—	8	2	no	—
603	C₂²	C₅×#385	1	1	yes	characteristic
604	C₂²	C₅×#386	1	1	yes	characteristic
605	C₂²	C₅×#388	1	1	yes	characteristic
606	C₂²	C₅×#392	1	1	yes	characteristic
607	C₂²	C₅×#393	1	1	yes	characteristic
608	C₂²	C₅×#394	1	1	yes	characteristic
609	C₂²	C₅×#396	1	1	yes	characteristic
610	C₄	—	2	4	no	—
611	C₄	—	4	2	no	—
612	C₄	—	4	2	no	—
613	C₄	—	8	2	no	—
614	C₄	—	8	2	no	—
615	C₄	—	8	2	no	—
616	C₄	C₅×#380	1	1	yes	characteristic
617	C₄	C₅×#385	1	1	yes	characteristic
618	C₄	C₅×#388	1	1	yes	characteristic
619	C₄	C₅×#390	1	1	yes	characteristic
620	C₄	C₅×#394	1	1	yes	characteristic
621	C₄	C₅×#396	1	1	yes	characteristic
622	C₄	C₅×#397	1	1	yes	characteristic
623	C₄	C₅×#399	1	1	yes	characteristic
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	8	2	no	—
631	C₂	C₅×#1439	1	1	yes	characteristic
632	C₂	C₅×#2031	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	#124
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	#393
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂²×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×#2285	C₂	semidirect
5. C₂×C₅×#344	C₂	semidirect
6. C₂×C₅×#339	C₂	semidirect
7. C₂×C₅×H(3,ℤ/4)	C₂	semidirect
21. C₂×C₅×#104	C₄	semidirect
32. #11081	C₅	direct (N × H)
102. #2285	C₂×C₅	semidirect
103. C₂×#344	C₂×C₅	semidirect
104. C₂×#339	C₂×C₅	semidirect
105. C₂×H(3,ℤ/4)	C₂×C₅	semidirect
129. C₂×C₅×Q₈	C₄⋊C₄	semidirect
141. C₂×C₅×D₄	C₄⋊C₄	semidirect
223. C₂×#104	C₄×C₅	semidirect
428. C₂×Q₈	C₅×C₄⋊C₄	semidirect
440. C₂×D₄	C₅×C₄⋊C₄	semidirect
591. C₅	#11081	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
C₂²×C₅×#104	2
C₂×C₅×#410	2
C₅×#2285	2
C₂×C₅×#344	2
C₂×C₅×#339	2
C₂×C₅×H(3,ℤ/4)	2
#11081	5

Subgroups — C5×#11081 #11933801

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11081 #11933801