Subgroups — C₅×#62811 #11985531

Order 1280.

11534 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#585	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3489	C₂	1	8	yes	maximal, complemented
4	C₅×#3488	C₂	1	8	yes	maximal, complemented
5	C₅×#3487	C₂	1	2	yes	maximal, complemented
6	C₅×#3486	C₂	1	2	yes	maximal, complemented
7	C₅×#3485	C₂	1	6	yes	maximal, complemented
8	C₅×#3484	C₂	1	6	yes	maximal, complemented
9	C₅×D₄×#41	C₂	1	16	yes	maximal, complemented
10	C₅×#3449	C₂	1	6	yes	maximal, complemented
11	C₂×C₅×#525	C₂	1	6	yes	maximal, complemented
12	C₅×#3428	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#585	—	2	16	no	—
14	C₂×C₅×2₋¹⁺⁴	C₂²	1	2	yes	complemented
15	C₂×C₅×2₋¹⁺⁴	C₂²	1	4	yes	complemented
16	C₂×C₅×H(5,𝔽₂)	C₂²	1	6	yes	complemented
17	C₂×C₅×H(5,𝔽₂)	C₂²	1	4	yes	complemented
18	C₂²×C₅×#41	—	2	16	no	—
19	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂²×C₅×#41	C₂²	1	3	yes	complemented
21	C₂²×C₅×#41	C₂²	1	8	yes	complemented
22	C₂²×C₅×#41	C₂²	1	3	yes	complemented
23	C₂²×C₅×#41	C₂²	1	1	yes	characteristic, complemented
24	C₂²×C₅×#41	C₂²	1	8	yes	complemented
25	C₂²×C₅×#41	C₂²	1	6	yes	complemented
26	C₂²×C₅×#41	C₂²	1	8	yes	complemented
27	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₂³×C₅×D₄	C₂²	1	3	yes	complemented
29	C₂⁴×C₄×C₅	C₂²	1	3	yes	complemented
30	C₅×#550	C₂²	1	16	yes	complemented
31	C₅×D₄×Q₈	C₂²	1	16	yes	complemented
32	C₅×#548	C₂²	1	16	yes	complemented
33	C₅×#548	C₂²	1	16	yes	complemented
34	C₅×#547	C₂²	1	48	yes	complemented
35	C₅×#546	C₂²	1	48	yes	complemented
36	C₅×#546	C₂²	1	48	yes	complemented
37	C₅×D₄²	C₂²	1	48	yes	complemented
38	C₅×#537	C₂²	1	24	yes	complemented
39	C₅×#536	C₂²	1	12	yes	complemented
40	C₅×#536	C₂²	1	12	yes	complemented
41	C₅×#535	C₂²	1	12	yes	complemented
42	C₅×#535	C₂²	1	12	yes	complemented
43	C₅×#534	C₂²	1	24	yes	complemented
44	C₅×#532	C₂²	1	24	yes	complemented
45	C₅×#525	C₂²	1	4	yes	complemented
46	C₅×#525	C₂²	1	12	yes	complemented
47	C₅×#525	C₂²	1	12	yes	complemented
48	C₅×#525	C₂²	1	12	yes	complemented
49	C₅×#525	C₂²	1	24	yes	complemented
50	C₅×#525	C₂²	1	24	yes	complemented
51	C₅×#525	C₂²	1	24	yes	complemented
52	C₂×C₅×#123	C₂²	1	12	yes	complemented
53	C₂×C₅×C₂²⋊Q₈	C₂²	1	12	yes	complemented
54	C₂×C₅×#121	C₂²	1	12	yes	complemented
55	C₂×C₅×#120	C₂²	1	12	yes	complemented
56	C₅×#520	C₂²	1	8	yes	complemented
57	C₅×#519	C₂²	1	2	yes	complemented
58	C₅×#518	C₂²	1	6	yes	complemented
59	C₄×C₅×#41	C₂²	1	8	yes	complemented
60	C₂×C₄×C₅×D₄	C₂²	1	24	yes	complemented
61	C₂×C₅×#117	C₂²	1	6	yes	complemented
62	#62811	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
63	C₂⁵×C₅	C₂³	1	3	yes	—
64	C₅×2₋¹⁺⁴	—	2	32	no	—
65	C₅×2₋¹⁺⁴	—	2	16	no	—
66	C₅×H(5,𝔽₂)	—	2	32	no	—
67	C₅×H(5,𝔽₂)	—	2	48	no	—
68	C₂×C₅×#41	—	2	64	no	—
69	C₂×C₅×#41	—	2	64	no	—
70	C₂×C₅×#41	—	2	64	no	—
71	C₂×C₅×#41	—	2	8	no	—
72	C₂×C₅×#41	—	2	24	no	—
73	C₂×C₅×#41	—	2	24	no	—
74	C₂×C₅×#41	—	2	48	no	—
75	C₂×C₅×#41	D₄	1	16	yes	complemented
76	C₂×C₅×#41	C₂³	1	4	yes	—
77	C₂×C₅×#41	C₂³	1	12	yes	—
78	C₂×C₅×#41	C₂³	1	12	yes	—
79	C₂×C₅×#41	C₂³	1	12	yes	—
80	C₂×C₅×#41	C₂³	1	24	yes	—
81	C₂×C₅×#41	C₂³	1	8	yes	—
82	C₂×C₅×#41	C₂³	1	4	yes	—
83	C₂×C₅×#41	C₂³	1	4	yes	—
84	C₂×C₅×#41	C₂³	1	12	yes	complemented
85	C₂×C₅×#41	C₂³	1	12	yes	complemented
86	C₂×C₅×#41	C₂³	1	24	yes	complemented
87	C₂×C₅×#41	C₂³	1	8	yes	complemented
88	C₂²×C₅×Q₈	—	2	8	no	—
89	C₂²×C₅×Q₈	C₂³	1	3	yes	—
90	C₂²×C₅×Q₈	C₂³	1	8	yes	—
91	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
92	C₂²×C₅×Q₈	C₂³	1	6	yes	complemented
93	C₂²×C₅×Q₈	C₂³	1	8	yes	complemented
94	C₂²×C₅×D₄	—	2	24	no	—
95	C₂²×C₅×D₄	C₂³	1	12	yes	—
96	C₂²×C₅×D₄	C₂³	1	6	yes	—
97	C₂²×C₅×D₄	C₂³	1	3	yes	—
98	C₂²×C₅×D₄	C₂³	1	24	yes	—
99	C₂²×C₅×D₄	C₂³	1	24	yes	—
100	C₂²×C₅×D₄	C₂³	1	3	yes	—
101	C₂²×C₅×D₄	C₂³	1	6	yes	complemented
102	C₂²×C₅×D₄	C₂³	1	24	yes	complemented
103	C₂³×C₄×C₅	—	2	24	no	—
104	C₂³×C₄×C₅	C₂³	1	12	yes	—
105	C₂³×C₄×C₅	C₂³	1	12	yes	—
106	C₂³×C₄×C₅	C₂³	1	3	yes	—
107	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅	C₂³	1	3	yes	—
109	C₂³×C₄×C₅	C₂³	1	3	yes	—
110	C₂³×C₄×C₅	C₂³	1	3	yes	—
111	C₂³×C₄×C₅	C₂³	1	3	yes	—
112	C₂³×C₄×C₅	C₂³	1	12	yes	complemented
113	C₅×C₄⋊Q₈	C₂³	1	24	yes	complemented
114	C₅×#127	C₂³	1	24	yes	complemented
115	C₅×#124	C₂³	1	24	yes	complemented
116	C₅×#124	C₂³	1	24	yes	complemented
117	C₅×#123	C₂³	1	8	yes	—
118	C₅×#123	C₂³	1	24	yes	—
119	C₅×#123	C₂³	1	48	yes	complemented
120	C₅×#123	C₂³	1	48	yes	complemented
121	C₅×C₂²⋊Q₈	C₂³	1	8	yes	—
122	C₅×C₂²⋊Q₈	C₂³	1	24	yes	—
123	C₅×C₂²⋊Q₈	C₂³	1	24	yes	complemented
124	C₅×C₂²⋊Q₈	C₂³	1	24	yes	complemented
125	C₅×C₂²⋊Q₈	C₂³	1	48	yes	complemented
126	C₅×#121	C₂³	1	8	yes	—
127	C₅×#121	C₂³	1	24	yes	—
128	C₅×#121	C₂³	1	24	yes	complemented
129	C₅×#121	C₂³	1	24	yes	complemented
130	C₅×#121	C₂³	1	48	yes	complemented
131	C₅×#121	C₂³	1	96	yes	complemented
132	C₅×#120	C₂³	1	8	yes	—
133	C₅×#120	C₂³	1	24	yes	—
134	C₅×#120	C₂³	1	48	yes	—
135	C₅×#120	C₂³	1	48	yes	complemented
136	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
137	C₄×C₅×D₄	C₂³	1	16	yes	—
138	C₄×C₅×D₄	C₂³	1	48	yes	—
139	C₄×C₅×D₄	C₂³	1	48	yes	complemented
140	C₄×C₅×D₄	C₂³	1	48	yes	complemented
141	C₄×C₅×D₄	C₂³	1	48	yes	complemented
142	C₅×#117	C₂³	1	4	yes	—
143	C₅×#117	C₂³	1	12	yes	—
144	C₅×#117	C₂³	1	12	yes	complemented
145	C₅×#117	C₂³	1	12	yes	complemented
146	C₂×C₅×C₄⋊C₄	C₂³	1	12	yes	complemented
147	C₂×C₅×C₄⋊C₄	C₂³	1	24	yes	complemented
148	C₂×C₅×C₂²⋊C₄	C₂³	1	12	yes	—
149	C₂×C₅×C₂²⋊C₄	C₂³	1	24	yes	—
150	C₂×C₅×C₂²⋊C₄	C₂³	1	24	yes	complemented
151	C₂×C₄²×C₅	C₂³	1	12	yes	complemented
152	C₂×#585	C₂×C₅	1	1	yes	characteristic, complemented
153	C₂³×#41	C₂×C₅	1	1	yes	characteristic, complemented
154	#3489	C₂×C₅	1	8	yes	complemented
155	#3488	C₂×C₅	1	8	yes	complemented
156	#3487	C₂×C₅	1	2	yes	complemented
157	#3486	C₂×C₅	1	2	yes	complemented
158	#3485	C₂×C₅	1	6	yes	complemented
159	#3484	C₂×C₅	1	6	yes	complemented
160	D₄×#41	C₂×C₅	1	16	yes	complemented
161	#3449	C₂×C₅	1	6	yes	complemented
162	C₂×#525	C₂×C₅	1	6	yes	complemented
163	#3428	C₂×C₅	1	1	yes	characteristic, complemented
164	C₂⁴×C₅	—	2	12	no	—
165	C₂⁴×C₅	—	4	12	no	—
166	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
167	C₂⁴×C₅	C₂⁴	1	12	yes	—
168	C₂⁴×C₅	C₂⁴	1	12	yes	—
169	C₂⁴×C₅	C₂⁴	1	3	yes	—
170	C₂⁴×C₅	C₂⁴	1	3	yes	—
171	C₅×#41	—	2	32	no	—
172	C₅×#41	—	2	32	no	—
173	C₅×#41	—	2	96	no	—
174	C₅×#41	—	2	96	no	—
175	C₅×#41	—	2	16	no	—
176	C₅×#41	—	2	48	no	—
177	C₅×#41	—	2	48	no	—
178	C₅×#41	—	2	48	no	—
179	C₅×#41	—	2	48	no	—
180	C₅×#41	—	2	48	no	—
181	C₅×#41	C₂×D₄	1	32	yes	complemented
182	C₅×#41	C₂×D₄	1	32	yes	complemented
183	C₂×C₅×Q₈	—	2	32	no	—
184	C₂×C₅×Q₈	—	2	32	no	—
185	C₂×C₅×Q₈	—	2	12	no	—
186	C₂×C₅×Q₈	—	2	24	no	—
187	C₂×C₅×Q₈	C₂×D₄	1	8	yes	complemented
188	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
189	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
190	C₂×C₅×Q₈	C₂⁴	1	12	yes	—
191	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
192	C₂×C₅×D₄	—	2	24	no	—
193	C₂×C₅×D₄	—	2	48	no	—
194	C₂×C₅×D₄	—	2	96	no	—
195	C₂×C₅×D₄	—	2	96	no	—
196	C₂×C₅×D₄	—	2	12	no	—
197	C₂×C₅×D₄	—	2	24	no	—
198	C₂×C₅×D₄	—	4	48	no	—
199	C₂×C₅×D₄	C₂×D₄	1	24	yes	complemented
200	C₂×C₅×D₄	C₂⁴	1	16	yes	—
201	C₂×C₅×D₄	C₂⁴	1	8	yes	—
202	C₂×C₅×D₄	C₂⁴	1	24	yes	—
203	C₂×C₅×D₄	C₂⁴	1	24	yes	—
204	C₂×C₅×D₄	C₂⁴	1	4	yes	—
205	C₂×C₅×D₄	C₂⁴	1	12	yes	—
206	C₂×C₅×D₄	C₂⁴	1	12	yes	—
207	C₂×C₅×D₄	C₂⁴	1	48	yes	—
208	C₂×C₅×D₄	C₂⁴	1	12	yes	—
209	C₂²×C₄×C₅	—	2	12	no	—
210	C₂²×C₄×C₅	—	2	4	no	—
211	C₂²×C₄×C₅	—	2	12	no	—
212	C₂²×C₄×C₅	—	2	12	no	—
213	C₂²×C₄×C₅	—	2	12	no	—
214	C₂²×C₄×C₅	—	2	48	no	—
215	C₂²×C₄×C₅	—	2	48	no	—
216	C₂²×C₄×C₅	—	2	48	no	—
217	C₂²×C₄×C₅	C₂×D₄	1	24	yes	complemented
218	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
219	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
220	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
221	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
222	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
223	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
224	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
225	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
227	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
228	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
229	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
230	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
231	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
232	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
233	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
235	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
236	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
237	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
238	C₅×C₄⋊C₄	C₂⁴	1	48	yes	—
239	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
240	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
241	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
242	C₅×C₂²⋊C₄	C₂⁴	1	48	yes	—
243	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
244	C₅×C₂²⋊C₄	C₂⁴	1	48	yes	—
245	C₄²×C₅	C₂⁴	1	24	yes	—
246	C₄²×C₅	C₂⁴	1	8	yes	—
247	#585	—	2	16	no	—
248	C₂×2₋¹⁺⁴	C₂²×C₅	1	2	yes	complemented
249	C₂×2₋¹⁺⁴	C₂²×C₅	1	4	yes	complemented
250	C₂×H(5,𝔽₂)	C₂²×C₅	1	6	yes	complemented
251	C₂×H(5,𝔽₂)	C₂²×C₅	1	4	yes	complemented
252	C₂²×#41	—	2	16	no	—
253	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
254	C₂²×#41	C₂²×C₅	1	3	yes	complemented
255	C₂²×#41	C₂²×C₅	1	8	yes	complemented
256	C₂²×#41	C₂²×C₅	1	3	yes	complemented
257	C₂²×#41	C₂²×C₅	1	1	yes	characteristic, complemented
258	C₂²×#41	C₂²×C₅	1	8	yes	complemented
259	C₂²×#41	C₂²×C₅	1	6	yes	complemented
260	C₂²×#41	C₂²×C₅	1	8	yes	complemented
261	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₂³×D₄	C₂²×C₅	1	3	yes	complemented
263	C₂⁴×C₄	C₂²×C₅	1	3	yes	complemented
264	#550	C₂²×C₅	1	16	yes	complemented
265	D₄×Q₈	C₂²×C₅	1	16	yes	complemented
266	#548	C₂²×C₅	1	16	yes	complemented
267	#548	C₂²×C₅	1	16	yes	complemented
268	#547	C₂²×C₅	1	48	yes	complemented
269	#546	C₂²×C₅	1	48	yes	complemented
270	#546	C₂²×C₅	1	48	yes	complemented
271	D₄²	C₂²×C₅	1	48	yes	complemented
272	#537	C₂²×C₅	1	24	yes	complemented
273	#536	C₂²×C₅	1	12	yes	complemented
274	#536	C₂²×C₅	1	12	yes	complemented
275	#535	C₂²×C₅	1	12	yes	complemented
276	#535	C₂²×C₅	1	12	yes	complemented
277	#534	C₂²×C₅	1	24	yes	complemented
278	#532	C₂²×C₅	1	24	yes	complemented
279	#525	C₂²×C₅	1	4	yes	complemented
280	#525	C₂²×C₅	1	12	yes	complemented
281	#525	C₂²×C₅	1	12	yes	complemented
282	#525	C₂²×C₅	1	12	yes	complemented
283	#525	C₂²×C₅	1	24	yes	complemented
284	#525	C₂²×C₅	1	24	yes	complemented
285	#525	C₂²×C₅	1	24	yes	complemented
286	C₂×#123	C₂²×C₅	1	12	yes	complemented
287	C₂×C₂²⋊Q₈	C₂²×C₅	1	12	yes	complemented
288	C₂×#121	C₂²×C₅	1	12	yes	complemented
289	C₂×#120	C₂²×C₅	1	12	yes	complemented
290	#520	C₂²×C₅	1	8	yes	complemented
291	#519	C₂²×C₅	1	2	yes	complemented
292	#518	C₂²×C₅	1	6	yes	complemented
293	C₄×#41	C₂²×C₅	1	8	yes	complemented
294	C₂×C₄×D₄	C₂²×C₅	1	24	yes	complemented
295	C₂×#117	C₂²×C₅	1	6	yes	complemented
296	C₂³×C₅	—	2	2	no	—
297	C₂³×C₅	—	2	4	no	—
298	C₂³×C₅	—	2	24	no	—
299	C₂³×C₅	—	2	6	no	—
300	C₂³×C₅	—	2	24	no	—
301	C₂³×C₅	—	2	24	no	—
302	C₂³×C₅	—	4	6	no	—
303	C₂³×C₅	—	4	12	no	—
304	C₂³×C₅	—	4	6	no	—
305	C₂³×C₅	—	4	24	no	—
306	C₂³×C₅	—	4	48	no	—
307	C₂³×C₅	C₂²×D₄	1	12	yes	—
308	C₂³×C₅	C₂⁵	1	8	yes	—
309	C₂³×C₅	C₂⁵	1	6	yes	—
310	C₂³×C₅	C₂⁵	1	1	yes	characteristic
311	C₂³×C₅	C₂⁵	1	6	yes	—
312	C₂³×C₅	C₂⁵	1	2	yes	—
313	C₅×Q₈	—	2	8	no	—
314	C₅×Q₈	—	2	24	no	—
315	C₅×Q₈	—	2	24	no	—
316	C₅×Q₈	C₂²×D₄	1	16	yes	—
317	C₅×D₄	—	2	16	no	—
318	C₅×D₄	—	2	48	no	—
319	C₅×D₄	—	2	48	no	—
320	C₅×D₄	—	2	32	no	—
321	C₅×D₄	—	2	8	no	—
322	C₅×D₄	—	2	24	no	—
323	C₅×D₄	—	2	24	no	—
324	C₅×D₄	—	4	48	no	—
325	C₅×D₄	C₂²×D₄	1	48	yes	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	6	no	—
328	C₂×C₄×C₅	—	2	24	no	—
329	C₂×C₄×C₅	—	2	24	no	—
330	C₂×C₄×C₅	—	2	4	no	—
331	C₂×C₄×C₅	—	2	4	no	—
332	C₂×C₄×C₅	—	2	24	no	—
333	C₂×C₄×C₅	—	2	24	no	—
334	C₂×C₄×C₅	—	2	12	no	—
335	C₂×C₄×C₅	—	2	16	no	—
336	C₂×C₄×C₅	—	2	12	no	—
337	C₂×C₄×C₅	—	2	48	no	—
338	C₂×C₄×C₅	—	4	24	no	—
339	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
340	C₂×C₄×C₅	C₂²×D₄	1	24	yes	—
341	C₂×C₄×C₅	C₂²×D₄	1	12	yes	—
342	C₂×C₄×C₅	C₂²×D₄	1	24	yes	—
343	C₂×C₄×C₅	C₂⁵	1	16	yes	—
344	C₂×C₄×C₅	C₂⁵	1	2	yes	—
345	C₂×C₄×C₅	C₂⁵	1	8	yes	—
346	C₂×C₄×C₅	C₂⁵	1	6	yes	—
347	C₂×C₄×C₅	C₂⁵	1	6	yes	—
348	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
349	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
350	C₂⁵	C₂³×C₅	1	3	yes	—
351	2₋¹⁺⁴	—	2	32	no	—
352	2₋¹⁺⁴	—	2	16	no	—
353	H(5,𝔽₂)	—	2	32	no	—
354	H(5,𝔽₂)	—	2	48	no	—
355	C₂×#41	—	2	64	no	—
356	C₂×#41	—	2	64	no	—
357	C₂×#41	—	2	64	no	—
358	C₂×#41	—	2	8	no	—
359	C₂×#41	—	2	24	no	—
360	C₂×#41	—	2	24	no	—
361	C₂×#41	—	2	48	no	—
362	C₂×#41	C₅×D₄	1	16	yes	complemented
363	C₂×#41	C₂³×C₅	1	4	yes	—
364	C₂×#41	C₂³×C₅	1	12	yes	—
365	C₂×#41	C₂³×C₅	1	12	yes	—
366	C₂×#41	C₂³×C₅	1	12	yes	—
367	C₂×#41	C₂³×C₅	1	24	yes	—
368	C₂×#41	C₂³×C₅	1	8	yes	—
369	C₂×#41	C₂³×C₅	1	4	yes	—
370	C₂×#41	C₂³×C₅	1	4	yes	—
371	C₂×#41	C₂³×C₅	1	12	yes	complemented
372	C₂×#41	C₂³×C₅	1	12	yes	complemented
373	C₂×#41	C₂³×C₅	1	24	yes	complemented
374	C₂×#41	C₂³×C₅	1	8	yes	complemented
375	C₂²×Q₈	—	2	8	no	—
376	C₂²×Q₈	C₂³×C₅	1	3	yes	—
377	C₂²×Q₈	C₂³×C₅	1	8	yes	—
378	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
379	C₂²×Q₈	C₂³×C₅	1	6	yes	complemented
380	C₂²×Q₈	C₂³×C₅	1	8	yes	complemented
381	C₂²×D₄	—	2	24	no	—
382	C₂²×D₄	C₂³×C₅	1	12	yes	—
383	C₂²×D₄	C₂³×C₅	1	6	yes	—
384	C₂²×D₄	C₂³×C₅	1	3	yes	—
385	C₂²×D₄	C₂³×C₅	1	24	yes	—
386	C₂²×D₄	C₂³×C₅	1	24	yes	—
387	C₂²×D₄	C₂³×C₅	1	3	yes	—
388	C₂²×D₄	C₂³×C₅	1	6	yes	complemented
389	C₂²×D₄	C₂³×C₅	1	24	yes	complemented
390	C₂³×C₄	—	2	24	no	—
391	C₂³×C₄	C₂³×C₅	1	12	yes	—
392	C₂³×C₄	C₂³×C₅	1	12	yes	—
393	C₂³×C₄	C₂³×C₅	1	3	yes	—
394	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
395	C₂³×C₄	C₂³×C₅	1	3	yes	—
396	C₂³×C₄	C₂³×C₅	1	3	yes	—
397	C₂³×C₄	C₂³×C₅	1	3	yes	—
398	C₂³×C₄	C₂³×C₅	1	3	yes	—
399	C₂³×C₄	C₂³×C₅	1	12	yes	complemented
400	C₄⋊Q₈	C₂³×C₅	1	24	yes	complemented
401	#127	C₂³×C₅	1	24	yes	complemented
402	#124	C₂³×C₅	1	24	yes	complemented
403	#124	C₂³×C₅	1	24	yes	complemented
404	#123	C₂³×C₅	1	8	yes	—
405	#123	C₂³×C₅	1	24	yes	—
406	#123	C₂³×C₅	1	48	yes	complemented
407	#123	C₂³×C₅	1	48	yes	complemented
408	C₂²⋊Q₈	C₂³×C₅	1	8	yes	—
409	C₂²⋊Q₈	C₂³×C₅	1	24	yes	—
410	C₂²⋊Q₈	C₂³×C₅	1	24	yes	complemented
411	C₂²⋊Q₈	C₂³×C₅	1	24	yes	complemented
412	C₂²⋊Q₈	C₂³×C₅	1	48	yes	complemented
413	#121	C₂³×C₅	1	8	yes	—
414	#121	C₂³×C₅	1	24	yes	—
415	#121	C₂³×C₅	1	24	yes	complemented
416	#121	C₂³×C₅	1	24	yes	complemented
417	#121	C₂³×C₅	1	48	yes	complemented
418	#121	C₂³×C₅	1	96	yes	complemented
419	#120	C₂³×C₅	1	8	yes	—
420	#120	C₂³×C₅	1	24	yes	—
421	#120	C₂³×C₅	1	48	yes	—
422	#120	C₂³×C₅	1	48	yes	complemented
423	C₄×Q₈	C₂³×C₅	1	16	yes	complemented
424	C₄×D₄	C₂³×C₅	1	16	yes	—
425	C₄×D₄	C₂³×C₅	1	48	yes	—
426	C₄×D₄	C₂³×C₅	1	48	yes	complemented
427	C₄×D₄	C₂³×C₅	1	48	yes	complemented
428	C₄×D₄	C₂³×C₅	1	48	yes	complemented
429	#117	C₂³×C₅	1	4	yes	—
430	#117	C₂³×C₅	1	12	yes	—
431	#117	C₂³×C₅	1	12	yes	complemented
432	#117	C₂³×C₅	1	12	yes	complemented
433	C₂×C₄⋊C₄	C₂³×C₅	1	12	yes	complemented
434	C₂×C₄⋊C₄	C₂³×C₅	1	24	yes	complemented
435	C₂×C₂²⋊C₄	C₂³×C₅	1	12	yes	—
436	C₂×C₂²⋊C₄	C₂³×C₅	1	24	yes	—
437	C₂×C₂²⋊C₄	C₂³×C₅	1	24	yes	complemented
438	C₂×C₄²	C₂³×C₅	1	12	yes	complemented
439	C₂²×C₅	—	2	8	no	—
440	C₂²×C₅	—	2	2	no	—
441	C₂²×C₅	—	2	12	no	—
442	C₂²×C₅	—	2	2	no	—
443	C₂²×C₅	—	2	2	no	—
444	C₂²×C₅	—	2	6	no	—
445	C₂²×C₅	—	2	8	no	—
446	C₂²×C₅	—	2	16	no	—
447	C₂²×C₅	—	2	12	no	—
448	C₂²×C₅	—	4	12	no	—
449	C₂²×C₅	—	4	48	no	—
450	C₂²×C₅	—	4	12	no	—
451	C₂²×C₅	—	8	24	no	—
452	C₂²×C₅	C₂³×D₄	1	2	yes	—
453	C₂²×C₅	C₂³×D₄	1	12	yes	—
454	C₂²×C₅	#585	1	4	yes	complemented
455	C₂²×C₅	C₂⁶	1	1	yes	characteristic
456	C₄×C₅	—	2	2	no	—
457	C₄×C₅	—	2	6	no	—
458	C₄×C₅	—	2	8	no	—
459	C₄×C₅	—	2	16	no	—
460	C₄×C₅	C₂³×D₄	1	2	yes	—
461	C₄×C₅	C₂³×D₄	1	2	yes	—
462	C₄×C₅	C₂³×D₄	1	12	yes	—
463	C₂⁴	—	2	12	no	—
464	C₂⁴	—	4	12	no	—
465	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
466	C₂⁴	C₂⁴×C₅	1	12	yes	—
467	C₂⁴	C₂⁴×C₅	1	12	yes	—
468	C₂⁴	C₂⁴×C₅	1	3	yes	—
469	C₂⁴	C₂⁴×C₅	1	3	yes	—
470	#41	—	2	32	no	—
471	#41	—	2	32	no	—
472	#41	—	2	96	no	—
473	#41	—	2	96	no	—
474	#41	—	2	16	no	—
475	#41	—	2	48	no	—
476	#41	—	2	48	no	—
477	#41	—	2	48	no	—
478	#41	—	2	48	no	—
479	#41	—	2	48	no	—
480	#41	C₂×C₅×D₄	1	32	yes	complemented
481	#41	C₂×C₅×D₄	1	32	yes	complemented
482	C₂×Q₈	—	2	32	no	—
483	C₂×Q₈	—	2	32	no	—
484	C₂×Q₈	—	2	12	no	—
485	C₂×Q₈	—	2	24	no	—
486	C₂×Q₈	C₂×C₅×D₄	1	8	yes	complemented
487	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
488	C₂×Q₈	C₂⁴×C₅	1	12	yes	—
489	C₂×Q₈	C₂⁴×C₅	1	12	yes	—
490	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
491	C₂×D₄	—	2	24	no	—
492	C₂×D₄	—	2	48	no	—
493	C₂×D₄	—	2	96	no	—
494	C₂×D₄	—	2	96	no	—
495	C₂×D₄	—	2	12	no	—
496	C₂×D₄	—	2	24	no	—
497	C₂×D₄	—	4	48	no	—
498	C₂×D₄	C₂×C₅×D₄	1	24	yes	complemented
499	C₂×D₄	C₂⁴×C₅	1	16	yes	—
500	C₂×D₄	C₂⁴×C₅	1	8	yes	—
501	C₂×D₄	C₂⁴×C₅	1	24	yes	—
502	C₂×D₄	C₂⁴×C₅	1	24	yes	—
503	C₂×D₄	C₂⁴×C₅	1	4	yes	—
504	C₂×D₄	C₂⁴×C₅	1	12	yes	—
505	C₂×D₄	C₂⁴×C₅	1	12	yes	—
506	C₂×D₄	C₂⁴×C₅	1	48	yes	—
507	C₂×D₄	C₂⁴×C₅	1	12	yes	—
508	C₂²×C₄	—	2	12	no	—
509	C₂²×C₄	—	2	4	no	—
510	C₂²×C₄	—	2	12	no	—
511	C₂²×C₄	—	2	12	no	—
512	C₂²×C₄	—	2	12	no	—
513	C₂²×C₄	—	2	48	no	—
514	C₂²×C₄	—	2	48	no	—
515	C₂²×C₄	—	2	48	no	—
516	C₂²×C₄	C₂×C₅×D₄	1	24	yes	complemented
517	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
518	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
519	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
520	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
521	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
522	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
523	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
524	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
525	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
526	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
527	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
528	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
529	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
530	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
531	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
532	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
533	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
534	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
535	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
536	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
537	C₄⋊C₄	C₂⁴×C₅	1	48	yes	—
538	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
539	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
540	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
541	C₂²⋊C₄	C₂⁴×C₅	1	48	yes	—
542	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
543	C₂²⋊C₄	C₂⁴×C₅	1	48	yes	—
544	C₄²	C₂⁴×C₅	1	8	yes	—
545	C₄²	C₂⁴×C₅	1	24	yes	—
546	C₂×C₅	—	2	2	no	—
547	C₂×C₅	—	2	4	no	—
548	C₂×C₅	—	2	12	no	—
549	C₂×C₅	—	4	6	no	—
550	C₂×C₅	—	4	8	no	—
551	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
552	C₂×C₅	C₂×#585	1	2	yes	—
553	C₂³	—	2	2	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	24	no	—
556	C₂³	—	2	6	no	—
557	C₂³	—	2	24	no	—
558	C₂³	—	2	24	no	—
559	C₂³	—	4	6	no	—
560	C₂³	—	4	12	no	—
561	C₂³	—	4	6	no	—
562	C₂³	—	4	24	no	—
563	C₂³	—	4	48	no	—
564	C₂³	C₂²×C₅×D₄	1	12	yes	—
565	C₂³	C₂⁵×C₅	1	8	yes	—
566	C₂³	C₂⁵×C₅	1	6	yes	—
567	C₂³	C₂⁵×C₅	1	1	yes	characteristic
568	C₂³	C₂⁵×C₅	1	6	yes	—
569	C₂³	C₂⁵×C₅	1	2	yes	—
570	Q₈	—	2	8	no	—
571	Q₈	—	2	24	no	—
572	Q₈	—	2	24	no	—
573	Q₈	C₂²×C₅×D₄	1	16	yes	—
574	D₄	—	2	16	no	—
575	D₄	—	2	48	no	—
576	D₄	—	2	48	no	—
577	D₄	—	2	32	no	—
578	D₄	—	2	8	no	—
579	D₄	—	2	24	no	—
580	D₄	—	2	24	no	—
581	D₄	—	4	48	no	—
582	D₄	C₂²×C₅×D₄	1	48	yes	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	6	no	—
585	C₂×C₄	—	2	24	no	—
586	C₂×C₄	—	2	24	no	—
587	C₂×C₄	—	2	4	no	—
588	C₂×C₄	—	2	4	no	—
589	C₂×C₄	—	2	24	no	—
590	C₂×C₄	—	2	24	no	—
591	C₂×C₄	—	2	12	no	—
592	C₂×C₄	—	2	16	no	—
593	C₂×C₄	—	2	12	no	—
594	C₂×C₄	—	2	48	no	—
595	C₂×C₄	—	4	24	no	—
596	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
597	C₂×C₄	C₂²×C₅×D₄	1	24	yes	—
598	C₂×C₄	C₂²×C₅×D₄	1	12	yes	—
599	C₂×C₄	C₂²×C₅×D₄	1	24	yes	—
600	C₂×C₄	C₂⁵×C₅	1	16	yes	—
601	C₂×C₄	C₂⁵×C₅	1	2	yes	—
602	C₂×C₄	C₂⁵×C₅	1	8	yes	—
603	C₂×C₄	C₂⁵×C₅	1	6	yes	—
604	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
605	C₂×C₄	C₂⁵×C₅	1	6	yes	—
606	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
607	C₅	#62811	1	1	yes	characteristic, direct product factor, Sylow
608	C₂²	—	2	8	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	12	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	6	no	—
614	C₂²	—	2	8	no	—
615	C₂²	—	2	16	no	—
616	C₂²	—	2	12	no	—
617	C₂²	—	4	12	no	—
618	C₂²	—	4	48	no	—
619	C₂²	—	4	12	no	—
620	C₂²	—	8	24	no	—
621	C₂²	C₂³×C₅×D₄	1	2	yes	—
622	C₂²	C₂³×C₅×D₄	1	12	yes	—
623	C₂²	C₅×#585	1	4	yes	complemented
624	C₂²	C₂⁶×C₅	1	1	yes	characteristic
625	C₄	—	2	2	no	—
626	C₄	—	2	6	no	—
627	C₄	—	2	8	no	—
628	C₄	—	2	16	no	—
629	C₄	C₂³×C₅×D₄	1	2	yes	—
630	C₄	C₂³×C₅×D₄	1	2	yes	—
631	C₄	C₂³×C₅×D₄	1	12	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	2	4	no	—
634	C₂	—	2	12	no	—
635	C₂	—	4	6	no	—
636	C₂	—	4	8	no	—
637	C₂	C₂⁴×C₅×D₄	1	1	yes	characteristic
638	C₂	C₂×C₅×#585	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
socle	C₂²×C₅	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#585	C₂	semidirect
2. C₂³×C₅×#41	C₂	semidirect
3. C₅×#3489	C₂	semidirect
4. C₅×#3488	C₂	semidirect
5. C₅×#3487	C₂	semidirect
6. C₅×#3486	C₂	semidirect
7. C₅×#3485	C₂	semidirect
8. C₅×#3484	C₂	semidirect
9. C₅×D₄×#41	C₂	semidirect
10. C₅×#3449	C₂	semidirect
11. C₂×C₅×#525	C₂	semidirect
12. C₅×#3428	C₂	semidirect
14. C₂×C₅×2₋¹⁺⁴	C₂²	semidirect
15. C₂×C₅×2₋¹⁺⁴	C₂²	semidirect
16. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
17. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
20. C₂²×C₅×#41	C₂²	semidirect
21. C₂²×C₅×#41	C₂²	semidirect
22. C₂²×C₅×#41	C₂²	semidirect
23. C₂²×C₅×#41	C₂²	semidirect
24. C₂²×C₅×#41	C₂²	semidirect
25. C₂²×C₅×#41	C₂²	semidirect
26. C₂²×C₅×#41	C₂²	semidirect
27. C₂³×C₅×Q₈	C₂²	semidirect
28. C₂³×C₅×D₄	C₂²	semidirect
29. C₂⁴×C₄×C₅	C₂²	semidirect
30. C₅×#550	C₂²	semidirect
31. C₅×D₄×Q₈	C₂²	semidirect
32. C₅×#548	C₂²	semidirect
33. C₅×#548	C₂²	semidirect
34. C₅×#547	C₂²	semidirect
35. C₅×#546	C₂²	semidirect
36. C₅×#546	C₂²	semidirect
37. C₅×D₄²	C₂²	semidirect
38. C₅×#537	C₂²	semidirect
39. C₅×#536	C₂²	semidirect
40. C₅×#536	C₂²	semidirect
41. C₅×#535	C₂²	semidirect
42. C₅×#535	C₂²	semidirect
43. C₅×#534	C₂²	semidirect
44. C₅×#532	C₂²	semidirect
45. C₅×#525	C₂²	semidirect
46. C₅×#525	C₂²	semidirect
47. C₅×#525	C₂²	semidirect
48. C₅×#525	C₂²	semidirect
49. C₅×#525	C₂²	semidirect
50. C₅×#525	C₂²	semidirect
51. C₅×#525	C₂²	semidirect
52. C₂×C₅×#123	C₂²	semidirect
53. C₂×C₅×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₅×#121	C₂²	semidirect
55. C₂×C₅×#120	C₂²	semidirect
56. C₅×#520	C₂²	semidirect
57. C₅×#519	C₂²	semidirect
58. C₅×#518	C₂²	semidirect
59. C₄×C₅×#41	C₂²	semidirect
60. C₂×C₄×C₅×D₄	C₂²	semidirect
61. C₂×C₅×#117	C₂²	semidirect
62. #62811	C₅	direct (N × H)
75. C₂×C₅×#41	D₄	semidirect
84. C₂×C₅×#41	C₂³	semidirect
85. C₂×C₅×#41	C₂³	semidirect
86. C₂×C₅×#41	C₂³	semidirect
87. C₂×C₅×#41	C₂³	semidirect
92. C₂²×C₅×Q₈	C₂³	semidirect
93. C₂²×C₅×Q₈	C₂³	semidirect
101. C₂²×C₅×D₄	C₂³	semidirect
102. C₂²×C₅×D₄	C₂³	semidirect
112. C₂³×C₄×C₅	C₂³	semidirect
113. C₅×C₄⋊Q₈	C₂³	semidirect
114. C₅×#127	C₂³	semidirect
115. C₅×#124	C₂³	semidirect
116. C₅×#124	C₂³	semidirect
119. C₅×#123	C₂³	semidirect
120. C₅×#123	C₂³	semidirect
123. C₅×C₂²⋊Q₈	C₂³	semidirect
124. C₅×C₂²⋊Q₈	C₂³	semidirect
125. C₅×C₂²⋊Q₈	C₂³	semidirect
128. C₅×#121	C₂³	semidirect
129. C₅×#121	C₂³	semidirect
130. C₅×#121	C₂³	semidirect
131. C₅×#121	C₂³	semidirect
135. C₅×#120	C₂³	semidirect
136. C₄×C₅×Q₈	C₂³	semidirect
139. C₄×C₅×D₄	C₂³	semidirect
140. C₄×C₅×D₄	C₂³	semidirect
141. C₄×C₅×D₄	C₂³	semidirect
144. C₅×#117	C₂³	semidirect
145. C₅×#117	C₂³	semidirect
146. C₂×C₅×C₄⋊C₄	C₂³	semidirect
147. C₂×C₅×C₄⋊C₄	C₂³	semidirect
150. C₂×C₅×C₂²⋊C₄	C₂³	semidirect
151. C₂×C₄²×C₅	C₂³	semidirect
152. C₂×#585	C₂×C₅	semidirect
153. C₂³×#41	C₂×C₅	semidirect
154. #3489	C₂×C₅	semidirect
155. #3488	C₂×C₅	semidirect
156. #3487	C₂×C₅	semidirect
157. #3486	C₂×C₅	semidirect
158. #3485	C₂×C₅	semidirect
159. #3484	C₂×C₅	semidirect
160. D₄×#41	C₂×C₅	semidirect
161. #3449	C₂×C₅	semidirect
162. C₂×#525	C₂×C₅	semidirect
163. #3428	C₂×C₅	semidirect
181. C₅×#41	C₂×D₄	semidirect
182. C₅×#41	C₂×D₄	semidirect
187. C₂×C₅×Q₈	C₂×D₄	semidirect
199. C₂×C₅×D₄	C₂×D₄	semidirect
217. C₂²×C₄×C₅	C₂×D₄	semidirect
248. C₂×2₋¹⁺⁴	C₂²×C₅	semidirect
249. C₂×2₋¹⁺⁴	C₂²×C₅	semidirect
250. C₂×H(5,𝔽₂)	C₂²×C₅	semidirect
251. C₂×H(5,𝔽₂)	C₂²×C₅	semidirect
254. C₂²×#41	C₂²×C₅	semidirect
255. C₂²×#41	C₂²×C₅	semidirect
256. C₂²×#41	C₂²×C₅	semidirect
257. C₂²×#41	C₂²×C₅	semidirect
258. C₂²×#41	C₂²×C₅	semidirect
259. C₂²×#41	C₂²×C₅	semidirect
260. C₂²×#41	C₂²×C₅	semidirect
261. C₂³×Q₈	C₂²×C₅	semidirect
262. C₂³×D₄	C₂²×C₅	semidirect
263. C₂⁴×C₄	C₂²×C₅	semidirect
264. #550	C₂²×C₅	semidirect
265. D₄×Q₈	C₂²×C₅	semidirect
266. #548	C₂²×C₅	semidirect
267. #548	C₂²×C₅	semidirect
268. #547	C₂²×C₅	semidirect
269. #546	C₂²×C₅	semidirect
270. #546	C₂²×C₅	semidirect
271. D₄²	C₂²×C₅	semidirect
272. #537	C₂²×C₅	semidirect
273. #536	C₂²×C₅	semidirect
274. #536	C₂²×C₅	semidirect
275. #535	C₂²×C₅	semidirect
276. #535	C₂²×C₅	semidirect
277. #534	C₂²×C₅	semidirect
278. #532	C₂²×C₅	semidirect
279. #525	C₂²×C₅	semidirect
280. #525	C₂²×C₅	semidirect
281. #525	C₂²×C₅	semidirect
282. #525	C₂²×C₅	semidirect
283. #525	C₂²×C₅	semidirect
284. #525	C₂²×C₅	semidirect
285. #525	C₂²×C₅	semidirect
286. C₂×#123	C₂²×C₅	semidirect
287. C₂×C₂²⋊Q₈	C₂²×C₅	semidirect
288. C₂×#121	C₂²×C₅	semidirect
289. C₂×#120	C₂²×C₅	semidirect
290. #520	C₂²×C₅	semidirect
291. #519	C₂²×C₅	semidirect
292. #518	C₂²×C₅	semidirect
293. C₄×#41	C₂²×C₅	semidirect
294. C₂×C₄×D₄	C₂²×C₅	semidirect
295. C₂×#117	C₂²×C₅	semidirect
362. C₂×#41	C₅×D₄	semidirect
371. C₂×#41	C₂³×C₅	semidirect
372. C₂×#41	C₂³×C₅	semidirect
373. C₂×#41	C₂³×C₅	semidirect
374. C₂×#41	C₂³×C₅	semidirect
379. C₂²×Q₈	C₂³×C₅	semidirect
380. C₂²×Q₈	C₂³×C₅	semidirect
388. C₂²×D₄	C₂³×C₅	semidirect
389. C₂²×D₄	C₂³×C₅	semidirect
399. C₂³×C₄	C₂³×C₅	semidirect
400. C₄⋊Q₈	C₂³×C₅	semidirect
401. #127	C₂³×C₅	semidirect
402. #124	C₂³×C₅	semidirect
403. #124	C₂³×C₅	semidirect
406. #123	C₂³×C₅	semidirect
407. #123	C₂³×C₅	semidirect
410. C₂²⋊Q₈	C₂³×C₅	semidirect
411. C₂²⋊Q₈	C₂³×C₅	semidirect
412. C₂²⋊Q₈	C₂³×C₅	semidirect
415. #121	C₂³×C₅	semidirect
416. #121	C₂³×C₅	semidirect
417. #121	C₂³×C₅	semidirect
418. #121	C₂³×C₅	semidirect
422. #120	C₂³×C₅	semidirect
423. C₄×Q₈	C₂³×C₅	semidirect
426. C₄×D₄	C₂³×C₅	semidirect
427. C₄×D₄	C₂³×C₅	semidirect
428. C₄×D₄	C₂³×C₅	semidirect
431. #117	C₂³×C₅	semidirect
432. #117	C₂³×C₅	semidirect
433. C₂×C₄⋊C₄	C₂³×C₅	semidirect
434. C₂×C₄⋊C₄	C₂³×C₅	semidirect
437. C₂×C₂²⋊C₄	C₂³×C₅	semidirect
438. C₂×C₄²	C₂³×C₅	semidirect
454. C₂²×C₅	#585	semidirect
480. #41	C₂×C₅×D₄	semidirect
481. #41	C₂×C₅×D₄	semidirect
486. C₂×Q₈	C₂×C₅×D₄	semidirect
498. C₂×D₄	C₂×C₅×D₄	semidirect
516. C₂²×C₄	C₂×C₅×D₄	semidirect
607. C₅	#62811	direct (N × H)
623. C₂²	C₅×#585	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#585	2
C₂³×C₅×#41	2
C₅×#3489	2
C₅×#3488	2
C₅×#3487	2
C₅×#3486	2
C₅×#3485	2
C₅×#3484	2
C₅×D₄×#41	2
C₅×#3449	2
C₂×C₅×#525	2
C₅×#3428	2
#62811	5

Subgroups — C5×#62811 #11985531

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#62811 #11985531