Subgroups — C₅×#11068 #11933788

Order 1280.

934 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#336	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	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	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×#424	—	2	2	no	—
16	C₅×#424	—	2	2	no	—
17	C₂×C₅×C₄⋊C₈	—	2	2	no	—
18	C₂×C₅×#104	—	2	2	no	—
19	C₂×C₅×#104	—	2	2	no	—
20	C₂×C₅×#104	—	2	2	no	—
21	C₅×#416	—	2	2	no	—
22	C₅×#416	—	2	2	no	—
23	C₂×C₅×#103	C₄	1	2	yes	complemented
24	C₂×C₅×#102	C₄	1	2	yes	complemented
25	C₅×#408	—	2	2	no	—
26	C₅×#408	—	2	2	no	—
27	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
28	C₅×#341	—	2	2	no	—
29	C₅×#339	—	2	2	no	—
30	C₅×#336	—	2	2	no	—
31	#11068	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	D₄	1	2	yes	—
43	C₂×C₅×#41	Q₈	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	—	2	1	no	—
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
61	C₂×C₅×M₁₆	D₄	1	2	yes	—
62	C₂²×C₅×C₈	—	2	1	no	—
63	C₂²×C₅×C₈	—	2	1	no	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	—	2	1	no	—
66	C₂²×C₅×C₈	—	2	1	no	—
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	—	2	1	no	—
76	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
77	C₂²×C₅×C₈	D₄	1	2	yes	—
78	C₅×#117	—	2	1	no	—
79	C₅×#117	—	2	1	no	—
80	C₅×#117	D₄	1	2	yes	—
81	C₅×#117	D₄	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
83	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
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	—	2	1	no	—
90	C₂×C₄²×C₅	D₄	1	2	yes	—
91	C₅×C₄⋊C₈	—	2	8	no	—
92	C₅×#104	—	2	8	no	—
93	C₅×#103	—	2	4	no	—
94	C₅×#102	—	2	4	no	—
95	C₅×C₂²⋊C₈	—	2	8	no	—
96	C₂×#424	C₂×C₅	1	1	yes	characteristic, complemented
97	C₂²×#104	C₂×C₅	1	1	yes	characteristic
98	C₂×#416	C₂×C₅	1	1	yes	characteristic
99	C₂×#408	C₂×C₅	1	1	yes	characteristic
100	C₂×#341	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×#336	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂⁴×C₅	—	2	1	no	—
104	C₂⁴×C₅	#41	1	1	yes	characteristic
105	C₅×#41	—	2	2	no	—
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	—	4	1	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	C₂×C₅×Q₈	—	2	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	C₄⋊C₄	1	2	yes	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	—	2	2	no	—
129	C₂×C₅×D₄	—	2	1	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	—	4	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	C₄⋊C₄	1	2	yes	—
139	C₂²×C₄×C₅	—	2	4	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	2	2	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	4	2	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	—	4	1	no	—
150	C₂²×C₄×C₅	—	4	1	no	—
151	C₂²×C₄×C₅	—	4	1	no	—
152	C₂²×C₄×C₅	C₂²×C₄	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	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
161	C₂²×C₄×C₅	#41	1	1	yes	characteristic
162	C₂²×C₄×C₅	#41	1	1	yes	characteristic
163	C₂²×C₄×C₅	#41	1	1	yes	characteristic
164	C₂²×C₄×C₅	#41	1	1	yes	characteristic
165	C₂²×C₄×C₅	#41	1	1	yes	characteristic
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	—	4	1	no	—
171	C₅×M₁₆	—	4	1	no	—
172	C₅×M₁₆	—	4	1	no	—
173	C₅×M₁₆	—	4	1	no	—
174	C₂×C₅×C₈	—	2	2	no	—
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	—	4	1	no	—
183	C₂×C₅×C₈	—	4	1	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	—	4	1	no	—
191	C₂×C₅×C₈	—	4	1	no	—
192	C₂×C₅×C₈	—	4	1	no	—
193	C₂×C₅×C₈	—	4	1	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	C₂²⋊C₄	1	4	yes	—
196	C₅×C₂²⋊C₄	—	2	2	no	—
197	C₅×C₂²⋊C₄	—	2	2	no	—
198	C₄²×C₅	—	2	2	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	C₄²×C₅	—	4	1	no	—
204	C₂²×#41	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	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
209	C₂×#117	C₂²×C₅	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
211	#424	—	2	2	no	—
212	#424	—	2	2	no	—
213	C₂×C₄⋊C₈	—	2	2	no	—
214	C₂×#104	—	2	2	no	—
215	C₂×#104	—	2	2	no	—
216	C₂×#104	—	2	2	no	—
217	#416	—	2	2	no	—
218	#416	—	2	2	no	—
219	C₂×#103	C₄×C₅	1	2	yes	complemented
220	C₂×#102	C₄×C₅	1	2	yes	complemented
221	#408	—	2	2	no	—
222	#408	—	2	2	no	—
223	C₂×C₂²⋊C₈	—	2	2	no	—
224	#341	—	2	2	no	—
225	#339	—	2	2	no	—
226	#336	—	2	2	no	—
227	C₂³×C₅	—	2	2	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	2	no	—
230	C₂³×C₅	—	4	1	no	—
231	C₂³×C₅	—	4	1	no	—
232	C₂³×C₅	—	4	2	no	—
233	C₂³×C₅	—	4	2	no	—
234	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂³×C₅	#121	1	1	yes	characteristic
236	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
237	C₂³×C₅	#123	1	1	yes	characteristic
238	C₂³×C₅	#123	1	1	yes	characteristic
239	C₂³×C₅	#123	1	1	yes	characteristic
240	C₂³×C₅	#126	1	1	yes	characteristic
241	C₅×Q₈	—	2	2	no	—
242	C₅×Q₈	—	2	2	no	—
243	C₅×Q₈	—	4	1	no	—
244	C₅×Q₈	—	4	1	no	—
245	C₅×D₄	—	2	2	no	—
246	C₅×D₄	—	2	2	no	—
247	C₅×D₄	—	4	2	no	—
248	C₅×D₄	—	4	2	no	—
249	C₅×D₄	—	4	2	no	—
250	C₅×D₄	—	4	2	no	—
251	C₅×D₄	—	4	1	no	—
252	C₅×D₄	—	4	1	no	—
253	C₂×C₄×C₅	—	2	4	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	4	no	—
256	C₂×C₄×C₅	—	4	4	no	—
257	C₂×C₄×C₅	—	4	4	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	—	4	1	no	—
261	C₂×C₄×C₅	—	4	2	no	—
262	C₂×C₄×C₅	—	4	2	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	—	4	2	no	—
266	C₂×C₄×C₅	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	#117	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	#120	1	1	yes	characteristic
275	C₂×C₄×C₅	#120	1	1	yes	characteristic
276	C₂×C₄×C₅	#120	1	1	yes	characteristic
277	C₂×C₄×C₅	#121	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	#121	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄×C₅	#123	1	1	yes	characteristic
290	C₂×C₄×C₅	#123	1	1	yes	characteristic
291	C₂×C₄×C₅	#124	1	1	yes	characteristic
292	C₂×C₄×C₅	#124	1	1	yes	characteristic
293	C₂×C₄×C₅	#124	1	1	yes	characteristic
294	C₂×C₄×C₅	#126	1	1	yes	characteristic
295	C₂×C₄×C₅	#127	1	1	yes	characteristic
296	C₅×C₈	—	4	2	no	—
297	C₅×C₈	—	4	2	no	—
298	C₅×C₈	—	4	2	no	—
299	C₅×C₈	—	4	2	no	—
300	C₂×#41	—	2	1	no	—
301	C₂×#41	—	2	1	no	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	2	1	no	—
308	C₂×#41	—	2	1	no	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	C₅×D₄	1	2	yes	—
311	C₂×#41	C₅×Q₈	1	2	yes	—
312	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	C₅×D₄	1	2	yes	—
329	C₂×M₁₆	C₅×D₄	1	2	yes	—
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	—	2	1	no	—
337	C₂²×C₈	—	2	1	no	—
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	2	1	no	—
340	C₂²×C₈	—	2	1	no	—
341	C₂²×C₈	—	2	1	no	—
342	C₂²×C₈	—	2	1	no	—
343	C₂²×C₈	—	2	1	no	—
344	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
345	C₂²×C₈	C₅×D₄	1	2	yes	—
346	#117	—	2	1	no	—
347	#117	—	2	1	no	—
348	#117	C₅×D₄	1	2	yes	—
349	#117	C₅×D₄	1	2	yes	—
350	C₂×C₄⋊C₄	C₂×C₄×C₅	1	2	yes	—
351	C₂×C₂²⋊C₄	—	2	1	no	—
352	C₂×C₄²	—	2	1	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	—	2	1	no	—
356	C₂×C₄²	—	2	1	no	—
357	C₂×C₄²	—	2	1	no	—
358	C₂×C₄²	C₅×D₄	1	2	yes	—
359	C₄⋊C₈	—	2	8	no	—
360	#104	—	2	8	no	—
361	#103	—	2	4	no	—
362	#102	—	2	4	no	—
363	C₂²⋊C₈	—	2	8	no	—
364	C₂²×C₅	—	2	2	no	—
365	C₂²×C₅	—	2	2	no	—
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	2	no	—
368	C₂²×C₅	—	2	1	no	—
369	C₂²×C₅	—	2	1	no	—
370	C₂²×C₅	—	2	1	no	—
371	C₂²×C₅	—	2	1	no	—
372	C₂²×C₅	—	4	4	no	—
373	C₂²×C₅	—	4	2	no	—
374	C₂²×C₅	—	8	2	no	—
375	C₂²×C₅	—	8	1	no	—
376	C₂²×C₅	—	8	1	no	—
377	C₂²×C₅	#385	1	1	yes	characteristic
378	C₂²×C₅	#386	1	1	yes	characteristic
379	C₂²×C₅	#388	1	1	yes	characteristic
380	C₂²×C₅	#394	1	1	yes	characteristic
381	C₂²×C₅	#396	1	1	yes	characteristic
382	C₂²×C₅	#397	1	1	yes	characteristic
383	C₂²×C₅	#399	1	1	yes	characteristic
384	C₂²×C₅	#443	1	2	yes	—
385	C₂²×C₅	#444	1	2	yes	—
386	C₄×C₅	—	4	4	no	—
387	C₄×C₅	—	4	4	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	#380	1	1	yes	characteristic
390	C₄×C₅	#385	1	1	yes	characteristic
391	C₄×C₅	#388	1	1	yes	characteristic
392	C₄×C₅	#390	1	1	yes	characteristic
393	C₄×C₅	#392	1	1	yes	characteristic
394	C₄×C₅	#393	1	1	yes	characteristic
395	C₄×C₅	#394	1	1	yes	characteristic
396	C₄×C₅	#396	1	1	yes	characteristic
397	C₂⁴	—	2	1	no	—
398	C₂⁴	C₅×#41	1	1	yes	characteristic
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	4	1	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	4	2	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	—	4	1	no	—
443	C₂²×C₄	—	4	1	no	—
444	C₂²×C₄	—	4	1	no	—
445	C₂²×C₄	—	4	1	no	—
446	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
453	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
455	C₂²×C₄	C₅×#41	1	1	yes	characteristic
456	C₂²×C₄	C₅×#41	1	1	yes	characteristic
457	C₂²×C₄	C₅×#41	1	1	yes	characteristic
458	C₂²×C₄	C₅×#41	1	1	yes	characteristic
459	C₂²×C₄	C₅×#41	1	1	yes	characteristic
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	4	1	no	—
465	M₁₆	—	4	1	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	2	no	—
471	C₂×C₈	—	2	2	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	4	1	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	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	C₂×C₈	—	4	1	no	—
485	C₂×C₈	—	4	1	no	—
486	C₂×C₈	—	4	1	no	—
487	C₂×C₈	—	4	1	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	C₅×C₂²⋊C₄	1	4	yes	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	—	2	2	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	2	2	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	4	1	no	—
497	C₄²	—	4	1	no	—
498	C₂×C₅	—	2	1	no	—
499	C₂×C₅	—	2	1	no	—
500	C₂×C₅	—	2	1	no	—
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	8	2	no	—
503	C₂×C₅	#1439	1	1	yes	characteristic
504	C₂×C₅	#1866	1	2	yes	—
505	C₂×C₅	#1876	1	2	yes	—
506	C₂×C₅	#1937	1	1	yes	characteristic
507	C₂×C₅	#1938	1	1	yes	characteristic
508	C₂³	—	2	2	no	—
509	C₂³	—	2	2	no	—
510	C₂³	—	2	2	no	—
511	C₂³	—	4	1	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	2	no	—
514	C₂³	—	4	2	no	—
515	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
516	C₂³	C₅×#121	1	1	yes	characteristic
517	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
518	C₂³	C₅×#123	1	1	yes	characteristic
519	C₂³	C₅×#123	1	1	yes	characteristic
520	C₂³	C₅×#123	1	1	yes	characteristic
521	C₂³	C₅×#126	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	4	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	2	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	4	4	no	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	2	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	2	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
550	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
551	C₂×C₄	C₅×#117	1	1	yes	characteristic
552	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
553	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
554	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
555	C₂×C₄	C₅×#120	1	1	yes	characteristic
556	C₂×C₄	C₅×#120	1	1	yes	characteristic
557	C₂×C₄	C₅×#120	1	1	yes	characteristic
558	C₂×C₄	C₅×#121	1	1	yes	characteristic
559	C₂×C₄	C₅×#121	1	1	yes	characteristic
560	C₂×C₄	C₅×#121	1	1	yes	characteristic
561	C₂×C₄	C₅×#121	1	1	yes	characteristic
562	C₂×C₄	C₅×#121	1	1	yes	characteristic
563	C₂×C₄	C₅×#121	1	1	yes	characteristic
564	C₂×C₄	C₅×#121	1	1	yes	characteristic
565	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
566	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
567	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
568	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
569	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
570	C₂×C₄	C₅×#123	1	1	yes	characteristic
571	C₂×C₄	C₅×#123	1	1	yes	characteristic
572	C₂×C₄	C₅×#124	1	1	yes	characteristic
573	C₂×C₄	C₅×#124	1	1	yes	characteristic
574	C₂×C₄	C₅×#124	1	1	yes	characteristic
575	C₂×C₄	C₅×#126	1	1	yes	characteristic
576	C₂×C₄	C₅×#127	1	1	yes	characteristic
577	C₈	—	4	2	no	—
578	C₈	—	4	2	no	—
579	C₈	—	4	2	no	—
580	C₈	—	4	2	no	—
581	C₅	#11068	1	1	yes	characteristic, direct product factor, Sylow
582	C₂²	—	2	2	no	—
583	C₂²	—	2	2	no	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	2	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	8	2	no	—
593	C₂²	—	8	1	no	—
594	C₂²	—	8	1	no	—
595	C₂²	C₅×#385	1	1	yes	characteristic
596	C₂²	C₅×#386	1	1	yes	characteristic
597	C₂²	C₅×#388	1	1	yes	characteristic
598	C₂²	C₅×#394	1	1	yes	characteristic
599	C₂²	C₅×#396	1	1	yes	characteristic
600	C₂²	C₅×#397	1	1	yes	characteristic
601	C₂²	C₅×#399	1	1	yes	characteristic
602	C₂²	C₅×#443	1	2	yes	—
603	C₂²	C₅×#444	1	2	yes	—
604	C₄	—	4	4	no	—
605	C₄	—	4	4	no	—
606	C₄	—	4	2	no	—
607	C₄	C₅×#380	1	1	yes	characteristic
608	C₄	C₅×#385	1	1	yes	characteristic
609	C₄	C₅×#388	1	1	yes	characteristic
610	C₄	C₅×#390	1	1	yes	characteristic
611	C₄	C₅×#392	1	1	yes	characteristic
612	C₄	C₅×#393	1	1	yes	characteristic
613	C₄	C₅×#394	1	1	yes	characteristic
614	C₄	C₅×#396	1	1	yes	characteristic
615	C₂	—	2	1	no	—
616	C₂	—	2	1	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	1	no	—
619	C₂	—	8	2	no	—
620	C₂	C₅×#1439	1	1	yes	characteristic
621	C₂	C₅×#1866	1	2	yes	—
622	C₂	C₅×#1876	1	2	yes	—
623	C₂	C₅×#1937	1	1	yes	characteristic
624	C₂	C₅×#1938	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂³×C₅	C₄×D₄
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#424	C₂	semidirect
5. C₂×C₅×#341	C₂	semidirect
6. C₂×C₅×#339	C₂	semidirect
7. C₂×C₅×#336	C₂	semidirect
23. C₂×C₅×#103	C₄	semidirect
24. C₂×C₅×#102	C₄	semidirect
31. #11068	C₅	direct (N × H)
96. C₂×#424	C₂×C₅	semidirect
100. C₂×#341	C₂×C₅	semidirect
101. C₂×#339	C₂×C₅	semidirect
102. C₂×#336	C₂×C₅	semidirect
219. C₂×#103	C₄×C₅	semidirect
220. C₂×#102	C₄×C₅	semidirect
581. C₅	#11068	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×#424	2
C₂²×C₅×#104	2
C₂×C₅×#416	2
C₂×C₅×#408	2
C₂×C₅×#341	2
C₂×C₅×#339	2
C₂×C₅×#336	2
#11068	5

Subgroups — C5×#11068 #11933788

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11068 #11933788