Subgroups — C₅×#60618 #11983338

Order 1280.

2170 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic
3	C₅×#3142	C₂	1	4	yes	maximal, complemented
4	C₅×#3141	C₂	1	4	yes	maximal, complemented
5	C₅×#3140	C₂	1	4	yes	maximal, complemented
6	C₅×#3139	C₂	1	2	yes	maximal, complemented
7	C₅×#3138	C₂	1	2	yes	maximal, complemented
8	C₅×#3135	C₂	1	4	yes	maximal, complemented
9	C₅×#3131	C₂	1	4	yes	maximal, complemented
10	C₅×#2896	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×#41	C₂²	1	2	yes	—
13	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
14	C₅×#533	—	2	2	no	—
15	C₅×#533	—	2	2	no	—
16	C₅×#533	C₂²	1	2	yes	—
17	C₅×#533	C₂²	1	2	yes	—
18	C₅×#533	C₂²	1	2	yes	complemented
19	C₅×#533	C₂²	1	2	yes	complemented
20	C₅×#532	—	2	2	no	—
21	C₅×#532	—	2	2	no	—
22	C₅×#532	C₂²	1	2	yes	—
23	C₅×#532	C₂²	1	2	yes	—
24	C₅×#532	C₂²	1	2	yes	—
25	C₅×#532	C₂²	1	2	yes	—
26	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
28	C₂×C₅×#127	C₂²	1	1	yes	characteristic
29	C₂×C₅×#125	C₂²	1	2	yes	complemented
30	C₂×C₅×#124	C₂²	1	2	yes	—
31	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
32	C₂×C₅×#121	—	2	2	no	—
33	C₂×C₄×C₅×Q₈	—	2	2	no	—
34	C₂×C₄×C₅×D₄	—	2	2	no	—
35	C₂×C₅×#117	C₂²	1	2	yes	—
36	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
37	C₅×#491	C₂²	1	8	yes	complemented
38	C₅×#490	C₂²	1	8	yes	complemented
39	C₅×#489	C₂²	1	16	yes	complemented
40	C₅×#488	C₂²	1	16	yes	complemented
41	C₅×#487	C₂²	1	8	yes	complemented
42	C₅×#486	C₂²	1	8	yes	complemented
43	C₅×#419	C₂²	1	8	yes	—
44	C₅×#418	C₂²	1	8	yes	—
45	C₅×#417	C₂²	1	16	yes	complemented
46	C₅×#416	C₂²	1	16	yes	complemented
47	C₄×C₅×M₁₆	C₂²	1	2	yes	—
48	C₄×C₅×M₁₆	C₂²	1	2	yes	—
49	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
50	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
51	C₂×C₅×#97	C₂²	1	2	yes	complemented
52	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
53	#60618	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
54	C₂×C₅×#41	—	2	2	no	—
55	C₂×C₅×#41	—	2	2	no	—
56	C₂×C₅×#41	—	2	16	no	—
57	C₂×C₅×#41	C₂³	1	4	yes	—
58	C₂×C₅×#41	C₂³	1	4	yes	—
59	C₂²×C₅×Q₈	—	2	2	no	—
60	C₂²×C₅×Q₈	C₂³	1	2	yes	—
61	C₂²×C₅×D₄	—	2	2	no	—
62	C₂²×C₅×D₄	—	2	2	no	—
63	C₂²×C₅×D₄	C₂³	1	2	yes	—
64	C₂³×C₄×C₅	—	2	2	no	—
65	C₂³×C₄×C₅	D₄	1	2	yes	—
66	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂×C₅×M₁₆	—	2	8	no	—
68	C₂×C₅×M₁₆	C₂³	1	4	yes	—
69	C₂×C₅×M₁₆	C₂³	1	4	yes	—
70	C₂²×C₅×C₈	C₂³	1	4	yes	—
71	C₅×C₄⋊Q₈	—	2	2	no	—
72	C₅×C₄⋊Q₈	—	2	2	no	—
73	C₅×C₄⋊Q₈	—	2	2	no	—
74	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
75	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
76	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
77	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
78	C₅×#127	—	2	2	no	—
79	C₅×#127	C₂³	1	2	yes	—
80	C₅×#127	C₂³	1	2	yes	—
81	C₅×#125	—	2	4	no	—
82	C₅×#125	C₂³	1	4	yes	—
83	C₅×#125	C₂³	1	4	yes	—
84	C₅×#124	—	2	4	no	—
85	C₅×#124	C₂³	1	4	yes	—
86	C₅×#124	C₂³	1	4	yes	—
87	C₅×C₂²⋊Q₈	—	2	4	no	—
88	C₅×C₂²⋊Q₈	—	2	4	no	—
89	C₅×C₂²⋊Q₈	—	2	4	no	—
90	C₅×C₂²⋊Q₈	—	2	4	no	—
91	C₅×#121	—	2	4	no	—
92	C₅×#121	—	2	4	no	—
93	C₅×#121	—	2	4	no	—
94	C₅×#121	—	2	4	no	—
95	C₄×C₅×Q₈	—	2	4	no	—
96	C₄×C₅×Q₈	—	2	4	no	—
97	C₄×C₅×Q₈	—	2	4	no	—
98	C₄×C₅×Q₈	—	2	4	no	—
99	C₄×C₅×D₄	—	2	4	no	—
100	C₄×C₅×D₄	—	2	4	no	—
101	C₄×C₅×D₄	—	2	4	no	—
102	C₄×C₅×D₄	—	2	4	no	—
103	C₅×#117	—	2	2	no	—
104	C₅×#117	—	2	2	no	—
105	C₅×#117	C₂³	1	4	yes	—
106	C₅×#117	C₂³	1	4	yes	—
107	C₂×C₅×C₄⋊C₄	—	2	2	no	—
108	C₂×C₅×C₄⋊C₄	—	2	4	no	—
109	C₂×C₅×C₄⋊C₄	—	2	2	no	—
110	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
111	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
113	C₂×C₄²×C₅	—	2	2	no	—
114	C₂×C₄²×C₅	D₄	1	2	yes	—
115	C₂×C₄²×C₅	D₄	1	2	yes	—
116	C₂×C₄²×C₅	D₄	1	2	yes	—
117	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
123	C₅×#103	C₂³	1	32	yes	—
124	C₅×#102	C₂³	1	32	yes	—
125	C₅×#97	C₂³	1	4	yes	—
126	C₅×#97	C₂³	1	4	yes	—
127	C₄×C₅×C₈	C₂³	1	4	yes	—
128	C₄×C₅×C₈	C₂³	1	4	yes	—
129	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
130	C₂×#532	C₂×C₅	1	1	yes	characteristic
131	#3142	C₂×C₅	1	4	yes	complemented
132	#3141	C₂×C₅	1	4	yes	complemented
133	#3140	C₂×C₅	1	4	yes	complemented
134	#3139	C₂×C₅	1	2	yes	complemented
135	#3138	C₂×C₅	1	2	yes	complemented
136	#3135	C₂×C₅	1	4	yes	complemented
137	#3131	C₂×C₅	1	4	yes	complemented
138	#2896	C₂×C₅	1	4	yes	complemented
139	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂⁴×C₅	—	2	2	no	—
141	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
142	C₅×#41	—	2	16	no	—
143	C₅×#41	—	2	16	no	—
144	C₅×#41	—	4	8	no	—
145	C₅×#41	—	4	8	no	—
146	C₂×C₅×Q₈	—	2	4	no	—
147	C₂×C₅×Q₈	—	2	4	no	—
148	C₂×C₅×Q₈	—	2	2	no	—
149	C₂×C₅×Q₈	—	2	8	no	—
150	C₂×C₅×Q₈	—	4	8	no	—
151	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
152	C₂×C₅×D₄	—	2	4	no	—
153	C₂×C₅×D₄	—	2	4	no	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	—	2	4	no	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	2	8	no	—
158	C₂×C₅×D₄	—	4	8	no	—
159	C₂×C₅×D₄	—	4	8	no	—
160	C₂×C₅×D₄	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₅	—	2	4	no	—
162	C₂²×C₄×C₅	—	2	2	no	—
163	C₂²×C₄×C₅	—	2	4	no	—
164	C₂²×C₄×C₅	—	2	4	no	—
165	C₂²×C₄×C₅	—	4	4	no	—
166	C₂²×C₄×C₅	—	4	8	no	—
167	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
168	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
169	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
170	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
171	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
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	#41	1	8	yes	—
177	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
180	C₅×M₁₆	—	2	8	no	—
181	C₅×M₁₆	—	2	8	no	—
182	C₂×C₅×C₈	—	2	8	no	—
183	C₂×C₅×C₈	C₂⁴	1	8	yes	—
184	C₅×C₄⋊C₄	—	2	4	no	—
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₄⋊C₄	—	2	8	no	—
187	C₅×C₄⋊C₄	—	2	8	no	—
188	C₅×C₄⋊C₄	—	2	4	no	—
189	C₅×C₄⋊C₄	—	2	4	no	—
190	C₅×C₄⋊C₄	—	2	4	no	—
191	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
192	C₅×C₂²⋊C₄	—	2	4	no	—
193	C₅×C₂²⋊C₄	—	2	4	no	—
194	C₅×C₂²⋊C₄	—	2	8	no	—
195	C₅×C₂²⋊C₄	—	2	8	no	—
196	C₄²×C₅	—	2	4	no	—
197	C₄²×C₅	—	2	4	no	—
198	C₄²×C₅	C₂×D₄	1	2	yes	—
199	C₄²×C₅	C₂×D₄	1	2	yes	—
200	C₄²×C₅	C₂×D₄	1	2	yes	—
201	C₄²×C₅	C₂×D₄	1	2	yes	—
202	C₄²×C₅	C₂×D₄	1	2	yes	—
203	C₄²×C₅	C₂×D₄	1	2	yes	—
204	C₄²×C₅	C₂⁴	1	1	yes	characteristic
205	C₄²×C₅	C₂⁴	1	1	yes	characteristic
206	C₄²×C₅	C₂⁴	1	1	yes	characteristic
207	C₄²×C₅	C₂⁴	1	1	yes	characteristic
208	C₂²×#41	C₂²×C₅	1	2	yes	—
209	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
210	#533	—	2	2	no	—
211	#533	—	2	2	no	—
212	#533	C₂²×C₅	1	2	yes	—
213	#533	C₂²×C₅	1	2	yes	—
214	#533	C₂²×C₅	1	2	yes	complemented
215	#533	C₂²×C₅	1	2	yes	complemented
216	#532	—	2	2	no	—
217	#532	—	2	2	no	—
218	#532	C₂²×C₅	1	2	yes	—
219	#532	C₂²×C₅	1	2	yes	—
220	#532	C₂²×C₅	1	2	yes	—
221	#532	C₂²×C₅	1	2	yes	—
222	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
223	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
224	C₂×#127	C₂²×C₅	1	1	yes	characteristic
225	C₂×#125	C₂²×C₅	1	2	yes	complemented
226	C₂×#124	C₂²×C₅	1	2	yes	—
227	C₂×C₂²⋊Q₈	—	2	2	no	—
228	C₂×#121	—	2	2	no	—
229	C₂×C₄×Q₈	—	2	2	no	—
230	C₂×C₄×D₄	—	2	2	no	—
231	C₂×#117	C₂²×C₅	1	2	yes	—
232	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
233	#491	C₂²×C₅	1	8	yes	complemented
234	#490	C₂²×C₅	1	8	yes	complemented
235	#489	C₂²×C₅	1	16	yes	complemented
236	#488	C₂²×C₅	1	16	yes	complemented
237	#487	C₂²×C₅	1	8	yes	complemented
238	#486	C₂²×C₅	1	8	yes	complemented
239	#419	C₂²×C₅	1	8	yes	—
240	#418	C₂²×C₅	1	8	yes	—
241	#417	C₂²×C₅	1	16	yes	complemented
242	#416	C₂²×C₅	1	16	yes	complemented
243	C₄×M₁₆	C₂²×C₅	1	2	yes	—
244	C₄×M₁₆	C₂²×C₅	1	2	yes	—
245	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
246	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
247	C₂×#97	C₂²×C₅	1	2	yes	complemented
248	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
249	C₂³×C₅	—	2	4	no	—
250	C₂³×C₅	—	4	2	no	—
251	C₂³×C₅	—	4	8	no	—
252	C₂³×C₅	—	4	4	no	—
253	C₂³×C₅	#124	1	4	yes	—
254	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
256	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₅×Q₈	—	2	8	no	—
258	C₅×Q₈	—	4	8	no	—
259	C₅×Q₈	—	4	4	no	—
260	C₅×Q₈	—	4	8	no	—
261	C₅×D₄	—	2	8	no	—
262	C₅×D₄	—	4	8	no	—
263	C₅×D₄	—	4	8	no	—
264	C₅×D₄	—	4	8	no	—
265	C₅×D₄	—	4	4	no	—
266	C₅×D₄	—	4	8	no	—
267	C₂×C₄×C₅	—	2	4	no	—
268	C₂×C₄×C₅	—	2	4	no	—
269	C₂×C₄×C₅	—	2	4	no	—
270	C₂×C₄×C₅	—	2	8	no	—
271	C₂×C₄×C₅	—	2	4	no	—
272	C₂×C₄×C₅	—	4	2	no	—
273	C₂×C₄×C₅	—	4	2	no	—
274	C₂×C₄×C₅	—	4	2	no	—
275	C₂×C₄×C₅	—	4	8	no	—
276	C₂×C₄×C₅	—	4	4	no	—
277	C₂×C₄×C₅	—	4	8	no	—
278	C₂×C₄×C₅	—	4	8	no	—
279	C₂×C₄×C₅	#124	1	4	yes	—
280	C₂×C₄×C₅	#124	1	4	yes	—
281	C₂×C₄×C₅	#124	1	4	yes	—
282	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
284	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
285	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
288	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂×#41	1	4	yes	—
290	C₂×C₄×C₅	C₂×#41	1	4	yes	—
291	C₂×C₄×C₅	C₂×#41	1	4	yes	—
292	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
293	C₅×C₈	—	2	8	no	—
294	C₂×#41	—	2	2	no	—
295	C₂×#41	—	2	2	no	—
296	C₂×#41	—	2	16	no	—
297	C₂×#41	C₂³×C₅	1	4	yes	—
298	C₂×#41	C₂³×C₅	1	4	yes	—
299	C₂²×Q₈	—	2	2	no	—
300	C₂²×Q₈	C₂³×C₅	1	2	yes	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	2	no	—
303	C₂²×D₄	C₂³×C₅	1	2	yes	—
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	C₅×D₄	1	2	yes	—
306	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
307	C₂×M₁₆	—	2	8	no	—
308	C₂×M₁₆	C₂³×C₅	1	4	yes	—
309	C₂×M₁₆	C₂³×C₅	1	4	yes	—
310	C₂²×C₈	C₂³×C₅	1	4	yes	—
311	C₄⋊Q₈	—	2	2	no	—
312	C₄⋊Q₈	—	2	2	no	—
313	C₄⋊Q₈	—	2	2	no	—
314	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
315	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
316	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
317	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
318	#127	—	2	2	no	—
319	#127	C₂³×C₅	1	2	yes	—
320	#127	C₂³×C₅	1	2	yes	—
321	#125	—	2	4	no	—
322	#125	C₂³×C₅	1	4	yes	—
323	#125	C₂³×C₅	1	4	yes	—
324	#124	—	2	4	no	—
325	#124	C₂³×C₅	1	4	yes	—
326	#124	C₂³×C₅	1	4	yes	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	4	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	#121	—	2	4	no	—
332	#121	—	2	4	no	—
333	#121	—	2	4	no	—
334	#121	—	2	4	no	—
335	C₄×Q₈	—	2	4	no	—
336	C₄×Q₈	—	2	4	no	—
337	C₄×Q₈	—	2	4	no	—
338	C₄×Q₈	—	2	4	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	4	no	—
341	C₄×D₄	—	2	4	no	—
342	C₄×D₄	—	2	4	no	—
343	#117	—	2	2	no	—
344	#117	—	2	2	no	—
345	#117	C₂³×C₅	1	4	yes	—
346	#117	C₂³×C₅	1	4	yes	—
347	C₂×C₄⋊C₄	—	2	2	no	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	4	no	—
353	C₂×C₄²	—	2	2	no	—
354	C₂×C₄²	C₅×D₄	1	2	yes	—
355	C₂×C₄²	C₅×D₄	1	2	yes	—
356	C₂×C₄²	C₅×D₄	1	2	yes	—
357	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
361	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
363	#103	C₂³×C₅	1	32	yes	—
364	#102	C₂³×C₅	1	32	yes	—
365	#97	C₂³×C₅	1	4	yes	—
366	#97	C₂³×C₅	1	4	yes	—
367	C₄×C₈	C₂³×C₅	1	4	yes	—
368	C₄×C₈	C₂³×C₅	1	4	yes	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	—	2	2	no	—
372	C₂²×C₅	—	4	4	no	—
373	C₂²×C₅	—	4	4	no	—
374	C₂²×C₅	—	4	8	no	—
375	C₂²×C₅	—	8	8	no	—
376	C₂²×C₅	C₂×#124	1	2	yes	—
377	C₂²×C₅	C₂×#124	1	2	yes	—
378	C₂²×C₅	C₂×#124	1	2	yes	—
379	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
380	C₄×C₅	—	2	2	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	4	4	no	—
384	C₄×C₅	—	4	8	no	—
385	C₄×C₅	C₂×#124	1	2	yes	—
386	C₄×C₅	C₂×#124	1	2	yes	—
387	C₄×C₅	C₂×#124	1	2	yes	—
388	C₄×C₅	#575	1	4	yes	—
389	C₄×C₅	C₂²×#41	1	2	yes	—
390	C₂⁴	—	2	2	no	—
391	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
392	#41	—	2	16	no	—
393	#41	—	2	16	no	—
394	#41	—	4	8	no	—
395	#41	—	4	8	no	—
396	C₂×Q₈	—	2	4	no	—
397	C₂×Q₈	—	2	4	no	—
398	C₂×Q₈	—	2	2	no	—
399	C₂×Q₈	—	2	8	no	—
400	C₂×Q₈	—	4	8	no	—
401	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	4	8	no	—
409	C₂×D₄	—	4	8	no	—
410	C₂×D₄	C₂⁴×C₅	1	4	yes	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	8	no	—
417	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
418	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
419	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
420	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
421	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
422	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
423	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂²×C₄	C₅×#41	1	8	yes	—
427	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
428	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
430	M₁₆	—	2	8	no	—
431	M₁₆	—	2	8	no	—
432	C₂×C₈	—	2	8	no	—
433	C₂×C₈	C₂⁴×C₅	1	8	yes	—
434	C₄⋊C₄	—	2	4	no	—
435	C₄⋊C₄	—	2	4	no	—
436	C₄⋊C₄	—	2	8	no	—
437	C₄⋊C₄	—	2	8	no	—
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
442	C₂²⋊C₄	—	2	4	no	—
443	C₂²⋊C₄	—	2	4	no	—
444	C₂²⋊C₄	—	2	8	no	—
445	C₂²⋊C₄	—	2	8	no	—
446	C₄²	—	2	4	no	—
447	C₄²	—	2	4	no	—
448	C₄²	C₂×C₅×D₄	1	2	yes	—
449	C₄²	C₂×C₅×D₄	1	2	yes	—
450	C₄²	C₂×C₅×D₄	1	2	yes	—
451	C₄²	C₂×C₅×D₄	1	2	yes	—
452	C₄²	C₂×C₅×D₄	1	2	yes	—
453	C₄²	C₂×C₅×D₄	1	2	yes	—
454	C₄²	C₂⁴×C₅	1	1	yes	characteristic
455	C₄²	C₂⁴×C₅	1	1	yes	characteristic
456	C₄²	C₂⁴×C₅	1	1	yes	characteristic
457	C₄²	C₂⁴×C₅	1	1	yes	characteristic
458	C₂×C₅	—	2	2	no	—
459	C₂×C₅	—	2	2	no	—
460	C₂×C₅	—	2	2	no	—
461	C₂×C₅	—	8	4	no	—
462	C₂×C₅	C₂²×#124	1	1	yes	characteristic
463	C₂×C₅	C₂×#575	1	2	yes	—
464	C₂³	—	2	4	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	8	no	—
467	C₂³	—	4	4	no	—
468	C₂³	C₅×#124	1	4	yes	—
469	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
470	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
471	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
472	Q₈	—	2	8	no	—
473	Q₈	—	4	8	no	—
474	Q₈	—	4	4	no	—
475	Q₈	—	4	8	no	—
476	D₄	—	2	8	no	—
477	D₄	—	4	8	no	—
478	D₄	—	4	8	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	4	no	—
481	D₄	—	4	8	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	4	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	8	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	8	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	C₅×#124	1	4	yes	—
495	C₂×C₄	C₅×#124	1	4	yes	—
496	C₂×C₄	C₅×#124	1	4	yes	—
497	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
498	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
499	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
500	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
501	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
502	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
503	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
504	C₂×C₄	C₂×C₅×#41	1	4	yes	—
505	C₂×C₄	C₂×C₅×#41	1	4	yes	—
506	C₂×C₄	C₂×C₅×#41	1	4	yes	—
507	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
508	C₈	—	2	8	no	—
509	C₅	#60618	1	1	yes	characteristic, direct product factor, Sylow
510	C₂²	—	2	2	no	—
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	4	4	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	8	8	no	—
517	C₂²	C₂×C₅×#124	1	2	yes	—
518	C₂²	C₂×C₅×#124	1	2	yes	—
519	C₂²	C₂×C₅×#124	1	2	yes	—
520	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	4	4	no	—
525	C₄	—	4	8	no	—
526	C₄	C₂×C₅×#124	1	2	yes	—
527	C₄	C₂×C₅×#124	1	2	yes	—
528	C₄	C₂×C₅×#124	1	2	yes	—
529	C₄	C₅×#575	1	4	yes	—
530	C₄	C₂²×C₅×#41	1	2	yes	—
531	C₂	—	2	2	no	—
532	C₂	—	2	2	no	—
533	C₂	—	2	2	no	—
534	C₂	—	8	4	no	—
535	C₂	C₂²×C₅×#124	1	1	yes	characteristic
536	C₂	C₂×C₅×#575	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
prime radical	C₂×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ 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
1. C₂×C₅×#533	C₂	semidirect
3. C₅×#3142	C₂	semidirect
4. C₅×#3141	C₂	semidirect
5. C₅×#3140	C₂	semidirect
6. C₅×#3139	C₂	semidirect
7. C₅×#3138	C₂	semidirect
8. C₅×#3135	C₂	semidirect
9. C₅×#3131	C₂	semidirect
10. C₅×#2896	C₂	semidirect
11. C₂×C₄×C₅×M₁₆	C₂	semidirect
18. C₅×#533	C₂²	semidirect
19. C₅×#533	C₂²	semidirect
27. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
29. C₂×C₅×#125	C₂²	semidirect
37. C₅×#491	C₂²	semidirect
38. C₅×#490	C₂²	semidirect
39. C₅×#489	C₂²	semidirect
40. C₅×#488	C₂²	semidirect
41. C₅×#487	C₂²	semidirect
42. C₅×#486	C₂²	semidirect
45. C₅×#417	C₂²	semidirect
46. C₅×#416	C₂²	semidirect
49. C₄×C₅×M₁₆	C₂²	semidirect
50. C₄×C₅×M₁₆	C₂²	semidirect
51. C₂×C₅×#97	C₂²	semidirect
52. C₂×C₄×C₅×C₈	C₂²	semidirect
53. #60618	C₅	direct (N × H)
129. C₂×#533	C₂×C₅	semidirect
131. #3142	C₂×C₅	semidirect
132. #3141	C₂×C₅	semidirect
133. #3140	C₂×C₅	semidirect
134. #3139	C₂×C₅	semidirect
135. #3138	C₂×C₅	semidirect
136. #3135	C₂×C₅	semidirect
137. #3131	C₂×C₅	semidirect
138. #2896	C₂×C₅	semidirect
139. C₂×C₄×M₁₆	C₂×C₅	semidirect
214. #533	C₂²×C₅	semidirect
215. #533	C₂²×C₅	semidirect
223. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
225. C₂×#125	C₂²×C₅	semidirect
233. #491	C₂²×C₅	semidirect
234. #490	C₂²×C₅	semidirect
235. #489	C₂²×C₅	semidirect
236. #488	C₂²×C₅	semidirect
237. #487	C₂²×C₅	semidirect
238. #486	C₂²×C₅	semidirect
241. #417	C₂²×C₅	semidirect
242. #416	C₂²×C₅	semidirect
245. C₄×M₁₆	C₂²×C₅	semidirect
246. C₄×M₁₆	C₂²×C₅	semidirect
247. C₂×#97	C₂²×C₅	semidirect
248. C₂×C₄×C₈	C₂²×C₅	semidirect
509. C₅	#60618	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×#533	2
C₂×C₅×#532	2
C₅×#3142	2
C₅×#3141	2
C₅×#3140	2
C₅×#3139	2
C₅×#3138	2
C₅×#3135	2
C₅×#3131	2
C₅×#2896	2
C₂×C₄×C₅×M₁₆	2
#60618	5

Subgroups — C5×#60618 #11983338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60618 #11983338