Subgroups — C₂×C₅×#3511 #11985519

Order 1280.

7758 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3511	C₂	1	32	yes	maximal, direct product factor
2	C₂×C₅×#556	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#555	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#554	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#553	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#548	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#547	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#542	C₂	1	4	yes	maximal, complemented
9	C₂×C₅×#537	C₂	1	2	yes	maximal, complemented
10	C₂×C₅×#533	C₂	1	2	yes	maximal, complemented
11	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#532	C₂	1	2	yes	maximal, complemented
13	C₂²×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#520	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂²×C₅×#41	C₂²	1	2	yes	—
18	C₂²×C₅×#41	C₂²	1	4	yes	—
19	C₂³×C₅×Q₈	C₂²	1	2	yes	—
20	C₅×#556	C₂²	1	32	yes	complemented
21	C₅×#555	C₂²	1	32	yes	complemented
22	C₅×#554	C₂²	1	32	yes	complemented
23	C₅×#553	C₂²	1	64	yes	complemented
24	C₅×#548	C₂²	1	64	yes	complemented
25	C₅×#547	C₂²	1	32	yes	complemented
26	C₅×#542	C₂²	1	64	yes	complemented
27	C₅×#537	C₂²	1	32	yes	complemented
28	C₅×#533	C₂²	1	32	yes	complemented
29	C₅×#532	C₂²	1	16	yes	complemented
30	C₅×#532	C₂²	1	32	yes	complemented
31	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
32	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
33	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
34	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
35	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
36	C₂×C₅×C₄⋊Q₈	C₂²	1	16	yes	complemented
37	C₂×C₅×#127	C₂²	1	1	yes	characteristic
38	C₂×C₅×#126	C₂²	1	8	yes	—
39	C₂×C₅×#125	C₂²	1	4	yes	—
40	C₂×C₅×#124	C₂²	1	2	yes	—
41	C₂×C₅×#124	C₂²	1	4	yes	—
42	C₂×C₅×#124	C₂²	1	8	yes	—
43	C₂×C₅×#123	C₂²	1	8	yes	—
44	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
45	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
46	C₂×C₅×C₂²⋊Q₈	C₂²	1	4	yes	—
47	C₂×C₅×C₂²⋊Q₈	C₂²	1	8	yes	—
48	C₂×C₅×#121	C₂²	1	4	yes	—
49	C₂×C₅×#121	C₂²	1	2	yes	—
50	C₂×C₅×#121	C₂²	1	2	yes	—
51	C₂×C₅×#121	C₂²	1	4	yes	—
52	C₂×C₅×#121	C₂²	1	4	yes	—
53	C₂×C₅×#121	C₂²	1	8	yes	—
54	C₅×#520	C₂²	1	32	yes	complemented
55	C₄×C₅×#41	C₂²	1	16	yes	complemented
56	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
57	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
59	C₂×C₄×C₅×Q₈	C₂²	1	4	yes	—
60	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
61	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
62	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
63	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
64	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
65	C₂×C₄×C₅×D₄	C₂²	1	8	yes	—
66	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
67	C₂×C₄×C₅×D₄	C₂²	1	4	yes	—
68	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
69	C₂×C₅×#117	C₂²	1	1	yes	characteristic
70	C₂×C₅×#117	C₂²	1	2	yes	—
71	C₂×C₅×#117	C₂²	1	4	yes	—
72	C₂×C₅×#117	C₂²	1	4	yes	—
73	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
74	C₂²×C₅×C₄⋊C₄	C₂²	1	4	yes	—
75	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
76	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
77	C₂²×C₄²×C₅	C₂²	1	2	yes	—
78	C₂×#3511	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
79	C₂×C₅×#41	—	2	8	no	—
80	C₂×C₅×#41	—	2	16	no	—
81	C₂×C₅×#41	—	4	16	no	—
82	C₂×C₅×#41	C₂³	1	8	yes	—
83	C₂×C₅×#41	C₂³	1	16	yes	—
84	C₂×C₅×#41	C₂³	1	32	yes	—
85	C₂²×C₅×Q₈	—	4	8	no	—
86	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×Q₈	C₂³	1	2	yes	—
88	C₂²×C₅×Q₈	C₂³	1	4	yes	—
89	C₂²×C₅×Q₈	C₂³	1	4	yes	—
90	C₂²×C₅×Q₈	C₂³	1	16	yes	—
91	C₂²×C₅×D₄	C₂³	1	2	yes	—
92	C₂²×C₅×D₄	C₂³	1	2	yes	—
93	C₂²×C₅×D₄	C₂³	1	4	yes	—
94	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₅×D₄	C₂³	1	2	yes	—
96	C₂²×C₅×D₄	C₂³	1	2	yes	—
97	C₂²×C₅×D₄	C₂³	1	8	yes	—
98	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₅	C₂³	1	2	yes	—
100	C₂³×C₄×C₅	C₂³	1	2	yes	—
101	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₅	C₂³	1	2	yes	—
103	C₂³×C₄×C₅	C₂³	1	4	yes	—
104	C₂³×C₄×C₅	C₂³	1	4	yes	—
105	C₂³×C₄×C₅	C₂³	1	8	yes	—
106	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₅×C₄⋊Q₈	C₂³	1	16	yes	—
108	C₅×C₄⋊Q₈	C₂³	1	16	yes	—
109	C₅×C₄⋊Q₈	C₂³	1	16	yes	—
110	C₅×C₄⋊Q₈	C₂³	1	16	yes	—
111	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
112	C₅×#127	C₂³	1	8	yes	—
113	C₅×#126	C₂³	1	64	yes	—
114	C₅×#125	C₂³	1	32	yes	—
115	C₅×#124	C₂³	1	16	yes	—
116	C₅×#124	C₂³	1	32	yes	—
117	C₅×#124	C₂³	1	64	yes	—
118	C₅×#123	C₂³	1	64	yes	—
119	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
120	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
121	C₅×C₂²⋊Q₈	C₂³	1	32	yes	—
122	C₅×C₂²⋊Q₈	C₂³	1	64	yes	—
123	C₅×#121	C₂³	1	32	yes	—
124	C₅×#121	C₂³	1	16	yes	—
125	C₅×#121	C₂³	1	16	yes	—
126	C₅×#121	C₂³	1	32	yes	—
127	C₅×#121	C₂³	1	32	yes	—
128	C₅×#121	C₂³	1	64	yes	—
129	C₄×C₅×Q₈	C₂³	1	8	yes	—
130	C₄×C₅×Q₈	C₂³	1	8	yes	—
131	C₄×C₅×Q₈	C₂³	1	32	yes	—
132	C₄×C₅×Q₈	C₂³	1	32	yes	—
133	C₄×C₅×D₄	C₂³	1	8	yes	—
134	C₄×C₅×D₄	C₂³	1	16	yes	—
135	C₄×C₅×D₄	C₂³	1	16	yes	—
136	C₄×C₅×D₄	C₂³	1	8	yes	—
137	C₄×C₅×D₄	C₂³	1	32	yes	—
138	C₄×C₅×D₄	C₂³	1	64	yes	—
139	C₄×C₅×D₄	C₂³	1	16	yes	—
140	C₄×C₅×D₄	C₂³	1	32	yes	—
141	C₄×C₅×D₄	C₂³	1	16	yes	—
142	C₅×#117	C₂³	1	8	yes	—
143	C₅×#117	C₂³	1	16	yes	—
144	C₅×#117	C₂³	1	32	yes	—
145	C₅×#117	C₂³	1	32	yes	—
146	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
148	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
149	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
150	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
151	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
152	C₂×C₅×C₄⋊C₄	C₂³	1	32	yes	—
153	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
154	C₂×C₅×C₄⋊C₄	C₂³	1	16	yes	—
155	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
157	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
158	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
159	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
160	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
161	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
163	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₂×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
166	C₂×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
167	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₅	C₂³	1	2	yes	—
171	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
172	C₂×C₄²×C₅	C₂³	1	2	yes	—
173	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
174	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
175	C₂×C₄²×C₅	C₂³	1	2	yes	—
176	C₂×C₄²×C₅	C₂³	1	8	yes	—
177	C₂×C₄²×C₅	C₂³	1	16	yes	—
178	C₂×C₄²×C₅	C₂³	1	8	yes	—
179	#3511	C₂×C₅	1	32	yes	direct product factor
180	C₂×#556	C₂×C₅	1	2	yes	complemented
181	C₂×#555	C₂×C₅	1	2	yes	complemented
182	C₂×#554	C₂×C₅	1	2	yes	complemented
183	C₂×#553	C₂×C₅	1	4	yes	complemented
184	C₂×#548	C₂×C₅	1	4	yes	complemented
185	C₂×#547	C₂×C₅	1	2	yes	complemented
186	C₂×#542	C₂×C₅	1	4	yes	complemented
187	C₂×#537	C₂×C₅	1	2	yes	complemented
188	C₂×#533	C₂×C₅	1	2	yes	complemented
189	C₂×#532	C₂×C₅	1	2	yes	complemented
190	C₂×#532	C₂×C₅	1	1	yes	characteristic, complemented
191	C₂²×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
192	C₂×#520	C₂×C₅	1	2	yes	complemented
193	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
194	C₂⁴×C₅	C₂⁴	1	2	yes	—
195	C₂⁴×C₅	C₂⁴	1	4	yes	—
196	C₂⁴×C₅	C₂⁴	1	1	yes	characteristic
197	C₅×#41	—	2	32	no	—
198	C₅×#41	—	2	64	no	—
199	C₅×#41	—	4	64	no	—
200	C₂×C₅×Q₈	—	2	4	no	—
201	C₂×C₅×Q₈	—	2	8	no	—
202	C₂×C₅×Q₈	—	2	16	no	—
203	C₂×C₅×Q₈	—	4	8	no	—
204	C₂×C₅×Q₈	—	4	32	no	—
205	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
206	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
207	C₂×C₅×Q₈	C₂⁴	1	16	yes	—
208	C₂×C₅×Q₈	C₂⁴	1	16	yes	—
209	C₂×C₅×D₄	—	2	8	no	—
210	C₂×C₅×D₄	—	2	16	no	—
211	C₂×C₅×D₄	—	2	4	no	—
212	C₂×C₅×D₄	—	2	8	no	—
213	C₂×C₅×D₄	—	2	8	no	—
214	C₂×C₅×D₄	—	2	8	no	—
215	C₂×C₅×D₄	—	4	16	no	—
216	C₂×C₅×D₄	C₂⁴	1	8	yes	—
217	C₂×C₅×D₄	C₂⁴	1	8	yes	—
218	C₂×C₅×D₄	C₂⁴	1	16	yes	—
219	C₂×C₅×D₄	C₂⁴	1	4	yes	—
220	C₂×C₅×D₄	C₂⁴	1	8	yes	—
221	C₂×C₅×D₄	C₂⁴	1	8	yes	—
222	C₂×C₅×D₄	C₂⁴	1	32	yes	—
223	C₂²×C₄×C₅	—	2	16	no	—
224	C₂²×C₄×C₅	—	2	8	no	—
225	C₂²×C₄×C₅	—	2	4	no	—
226	C₂²×C₄×C₅	—	2	8	no	—
227	C₂²×C₄×C₅	—	2	4	no	—
228	C₂²×C₄×C₅	—	2	8	no	—
229	C₂²×C₄×C₅	—	4	8	no	—
230	C₂²×C₄×C₅	—	4	16	no	—
231	C₂²×C₄×C₅	#41	1	8	yes	complemented
232	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
233	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
234	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
235	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
236	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
237	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
238	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
239	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
240	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
241	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
243	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₅	C₂⁴	1	8	yes	—
245	C₂²×C₄×C₅	C₂⁴	1	16	yes	—
246	C₂²×C₄×C₅	C₂⁴	1	32	yes	—
247	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
249	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
251	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
252	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
253	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
254	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
255	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
256	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
257	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
258	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
259	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
260	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
261	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
262	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
263	C₅×C₄⋊C₄	C₂⁴	1	32	yes	—
264	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
265	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
266	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
267	C₅×C₂²⋊C₄	C₂⁴	1	8	yes	—
268	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
269	C₅×C₂²⋊C₄	C₂⁴	1	32	yes	—
270	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
271	C₅×C₂²⋊C₄	C₂⁴	1	16	yes	—
272	C₄²×C₅	C₂⁴	1	4	yes	—
273	C₄²×C₅	C₂⁴	1	8	yes	—
274	C₄²×C₅	C₂⁴	1	4	yes	—
275	C₄²×C₅	C₂⁴	1	8	yes	—
276	C₄²×C₅	C₂⁴	1	4	yes	—
277	C₄²×C₅	C₂⁴	1	4	yes	—
278	C₄²×C₅	C₂⁴	1	8	yes	—
279	C₄²×C₅	C₂⁴	1	32	yes	—
280	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
281	C₂²×#41	C₂²×C₅	1	2	yes	—
282	C₂²×#41	C₂²×C₅	1	4	yes	—
283	C₂³×Q₈	C₂²×C₅	1	2	yes	—
284	#556	C₂²×C₅	1	32	yes	complemented
285	#555	C₂²×C₅	1	32	yes	complemented
286	#554	C₂²×C₅	1	32	yes	complemented
287	#553	C₂²×C₅	1	64	yes	complemented
288	#548	C₂²×C₅	1	64	yes	complemented
289	#547	C₂²×C₅	1	32	yes	complemented
290	#542	C₂²×C₅	1	64	yes	complemented
291	#537	C₂²×C₅	1	32	yes	complemented
292	#533	C₂²×C₅	1	32	yes	complemented
293	#532	C₂²×C₅	1	16	yes	complemented
294	#532	C₂²×C₅	1	32	yes	complemented
295	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
296	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
297	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
298	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
299	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
300	C₂×C₄⋊Q₈	C₂²×C₅	1	16	yes	complemented
301	C₂×#127	C₂²×C₅	1	1	yes	characteristic
302	C₂×#126	C₂²×C₅	1	8	yes	—
303	C₂×#125	C₂²×C₅	1	4	yes	—
304	C₂×#124	C₂²×C₅	1	2	yes	—
305	C₂×#124	C₂²×C₅	1	4	yes	—
306	C₂×#124	C₂²×C₅	1	8	yes	—
307	C₂×#123	C₂²×C₅	1	8	yes	—
308	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
309	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
310	C₂×C₂²⋊Q₈	C₂²×C₅	1	4	yes	—
311	C₂×C₂²⋊Q₈	C₂²×C₅	1	8	yes	—
312	C₂×#121	C₂²×C₅	1	4	yes	—
313	C₂×#121	C₂²×C₅	1	2	yes	—
314	C₂×#121	C₂²×C₅	1	2	yes	—
315	C₂×#121	C₂²×C₅	1	4	yes	—
316	C₂×#121	C₂²×C₅	1	4	yes	—
317	C₂×#121	C₂²×C₅	1	8	yes	—
318	#520	C₂²×C₅	1	32	yes	complemented
319	C₄×#41	C₂²×C₅	1	16	yes	complemented
320	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
321	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
322	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
323	C₂×C₄×Q₈	C₂²×C₅	1	4	yes	—
324	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
325	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
326	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
327	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
328	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
329	C₂×C₄×D₄	C₂²×C₅	1	8	yes	—
330	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
331	C₂×C₄×D₄	C₂²×C₅	1	4	yes	—
332	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
333	C₂×#117	C₂²×C₅	1	1	yes	characteristic
334	C₂×#117	C₂²×C₅	1	2	yes	—
335	C₂×#117	C₂²×C₅	1	4	yes	—
336	C₂×#117	C₂²×C₅	1	4	yes	—
337	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
338	C₂²×C₄⋊C₄	C₂²×C₅	1	4	yes	—
339	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
340	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
341	C₂²×C₄²	C₂²×C₅	1	2	yes	—
342	C₂³×C₅	—	2	2	no	—
343	C₂³×C₅	—	2	2	no	—
344	C₂³×C₅	—	2	4	no	—
345	C₂³×C₅	—	2	8	no	—
346	C₂³×C₅	—	2	4	no	—
347	C₂³×C₅	—	2	8	no	—
348	C₂³×C₅	—	2	4	no	—
349	C₂³×C₅	—	2	8	no	—
350	C₂³×C₅	C₂×#41	1	4	yes	—
351	C₂³×C₅	C₂⁵	1	4	yes	—
352	C₂³×C₅	C₂⁵	1	8	yes	—
353	C₂³×C₅	C₂⁵	1	2	yes	—
354	C₂³×C₅	C₂⁵	1	1	yes	characteristic
355	C₅×Q₈	—	2	8	no	—
356	C₅×Q₈	—	2	16	no	—
357	C₅×Q₈	—	2	32	no	—
358	C₅×Q₈	—	4	16	no	—
359	C₅×D₄	—	2	16	no	—
360	C₅×D₄	—	2	32	no	—
361	C₅×D₄	—	2	8	no	—
362	C₅×D₄	—	2	16	no	—
363	C₅×D₄	—	2	16	no	—
364	C₅×D₄	—	2	16	no	—
365	C₅×D₄	—	4	32	no	—
366	C₂×C₄×C₅	—	2	8	no	—
367	C₂×C₄×C₅	—	2	4	no	—
368	C₂×C₄×C₅	—	2	4	no	—
369	C₂×C₄×C₅	—	2	2	no	—
370	C₂×C₄×C₅	—	2	16	no	—
371	C₂×C₄×C₅	—	2	4	no	—
372	C₂×C₄×C₅	—	2	2	no	—
373	C₂×C₄×C₅	—	2	32	no	—
374	C₂×C₄×C₅	—	2	16	no	—
375	C₂×C₄×C₅	—	2	8	no	—
376	C₂×C₄×C₅	—	2	16	no	—
377	C₂×C₄×C₅	—	2	8	no	—
378	C₂×C₄×C₅	—	2	16	no	—
379	C₂×C₄×C₅	—	4	16	no	—
380	C₂×C₄×C₅	—	4	32	no	—
381	C₂×C₄×C₅	C₂×#41	1	4	yes	—
382	C₂×C₄×C₅	C₂×#41	1	4	yes	—
383	C₂×C₄×C₅	C₂×#41	1	16	yes	complemented
384	C₂×C₄×C₅	H(5,𝔽₂)	1	4	yes	—
385	C₂×C₄×C₅	2₋¹⁺⁴	1	4	yes	—
386	C₂×C₄×C₅	C₂⁵	1	4	yes	—
387	C₂×C₄×C₅	C₂⁵	1	2	yes	—
388	C₂×C₄×C₅	C₂⁵	1	2	yes	—
389	C₂×C₄×C₅	C₂⁵	1	4	yes	—
390	C₂×C₄×C₅	C₂⁵	1	8	yes	—
391	C₂×C₄×C₅	C₂⁵	1	4	yes	—
392	C₂×C₄×C₅	C₂⁵	1	16	yes	—
393	C₂×C₄×C₅	C₂⁵	1	2	yes	—
394	C₂×C₄×C₅	C₂⁵	1	2	yes	—
395	C₂×C₄×C₅	C₂⁵	1	2	yes	—
396	C₂×C₄×C₅	C₂⁵	1	2	yes	—
397	C₂×#41	—	2	8	no	—
398	C₂×#41	—	2	16	no	—
399	C₂×#41	—	4	16	no	—
400	C₂×#41	C₂³×C₅	1	8	yes	—
401	C₂×#41	C₂³×C₅	1	16	yes	—
402	C₂×#41	C₂³×C₅	1	32	yes	—
403	C₂²×Q₈	—	4	8	no	—
404	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
405	C₂²×Q₈	C₂³×C₅	1	2	yes	—
406	C₂²×Q₈	C₂³×C₅	1	4	yes	—
407	C₂²×Q₈	C₂³×C₅	1	4	yes	—
408	C₂²×Q₈	C₂³×C₅	1	16	yes	—
409	C₂²×D₄	C₂³×C₅	1	2	yes	—
410	C₂²×D₄	C₂³×C₅	1	2	yes	—
411	C₂²×D₄	C₂³×C₅	1	4	yes	—
412	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
413	C₂²×D₄	C₂³×C₅	1	2	yes	—
414	C₂²×D₄	C₂³×C₅	1	2	yes	—
415	C₂²×D₄	C₂³×C₅	1	8	yes	—
416	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
417	C₂³×C₄	C₂³×C₅	1	4	yes	—
418	C₂³×C₄	C₂³×C₅	1	2	yes	—
419	C₂³×C₄	C₂³×C₅	1	2	yes	—
420	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₅	1	2	yes	—
422	C₂³×C₄	C₂³×C₅	1	4	yes	—
423	C₂³×C₄	C₂³×C₅	1	8	yes	—
424	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
425	C₄⋊Q₈	C₂³×C₅	1	16	yes	—
426	C₄⋊Q₈	C₂³×C₅	1	16	yes	—
427	C₄⋊Q₈	C₂³×C₅	1	16	yes	—
428	C₄⋊Q₈	C₂³×C₅	1	16	yes	—
429	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
430	#127	C₂³×C₅	1	8	yes	—
431	#126	C₂³×C₅	1	64	yes	—
432	#125	C₂³×C₅	1	32	yes	—
433	#124	C₂³×C₅	1	16	yes	—
434	#124	C₂³×C₅	1	32	yes	—
435	#124	C₂³×C₅	1	64	yes	—
436	#123	C₂³×C₅	1	64	yes	—
437	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
438	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
439	C₂²⋊Q₈	C₂³×C₅	1	32	yes	—
440	C₂²⋊Q₈	C₂³×C₅	1	64	yes	—
441	#121	C₂³×C₅	1	32	yes	—
442	#121	C₂³×C₅	1	16	yes	—
443	#121	C₂³×C₅	1	16	yes	—
444	#121	C₂³×C₅	1	32	yes	—
445	#121	C₂³×C₅	1	32	yes	—
446	#121	C₂³×C₅	1	64	yes	—
447	C₄×Q₈	C₂³×C₅	1	8	yes	—
448	C₄×Q₈	C₂³×C₅	1	8	yes	—
449	C₄×Q₈	C₂³×C₅	1	32	yes	—
450	C₄×Q₈	C₂³×C₅	1	32	yes	—
451	C₄×D₄	C₂³×C₅	1	8	yes	—
452	C₄×D₄	C₂³×C₅	1	16	yes	—
453	C₄×D₄	C₂³×C₅	1	16	yes	—
454	C₄×D₄	C₂³×C₅	1	8	yes	—
455	C₄×D₄	C₂³×C₅	1	32	yes	—
456	C₄×D₄	C₂³×C₅	1	64	yes	—
457	C₄×D₄	C₂³×C₅	1	16	yes	—
458	C₄×D₄	C₂³×C₅	1	32	yes	—
459	C₄×D₄	C₂³×C₅	1	16	yes	—
460	#117	C₂³×C₅	1	8	yes	—
461	#117	C₂³×C₅	1	16	yes	—
462	#117	C₂³×C₅	1	32	yes	—
463	#117	C₂³×C₅	1	32	yes	—
464	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
466	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
467	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
468	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
469	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
470	C₂×C₄⋊C₄	C₂³×C₅	1	32	yes	—
471	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
472	C₂×C₄⋊C₄	C₂³×C₅	1	16	yes	—
473	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
474	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
475	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
476	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
477	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
478	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
479	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
481	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
482	C₂×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
483	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
484	C₂×C₂²⋊C₄	C₂³×C₅	1	8	yes	—
485	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
486	C₂×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
487	C₂×C₄²	C₂³×C₅	1	2	yes	—
488	C₂×C₄²	C₂³×C₅	1	8	yes	—
489	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
490	C₂×C₄²	C₂³×C₅	1	2	yes	—
491	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
492	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
493	C₂×C₄²	C₂³×C₅	1	2	yes	—
494	C₂×C₄²	C₂³×C₅	1	8	yes	—
495	C₂×C₄²	C₂³×C₅	1	16	yes	—
496	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
497	C₂²×C₅	—	2	2	no	—
498	C₂²×C₅	—	2	2	no	—
499	C₂²×C₅	—	2	8	no	—
500	C₂²×C₅	—	2	4	no	—
501	C₂²×C₅	—	2	8	no	—
502	C₂²×C₅	—	2	4	no	—
503	C₂²×C₅	—	2	8	no	—
504	C₂²×C₅	—	2	4	no	—
505	C₂²×C₅	—	2	8	no	—
506	C₂²×C₅	—	4	8	no	—
507	C₂²×C₅	—	4	16	no	—
508	C₂²×C₅	C₂²×#41	1	4	yes	—
509	C₂²×C₅	C₂²×#41	1	2	yes	—
510	C₂²×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
511	C₂²×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
512	C₂²×C₅	C₂⁶	1	1	yes	characteristic
513	C₄×C₅	—	2	8	no	—
514	C₄×C₅	—	2	4	no	—
515	C₄×C₅	—	2	4	no	—
516	C₄×C₅	—	2	2	no	—
517	C₄×C₅	—	2	16	no	—
518	C₄×C₅	—	2	4	no	—
519	C₄×C₅	—	2	2	no	—
520	C₄×C₅	C₂²×#41	1	4	yes	—
521	C₄×C₅	C₂²×#41	1	4	yes	—
522	C₄×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
523	C₄×C₅	C₂×2₋¹⁺⁴	1	4	yes	—
524	C₂⁴	C₂⁴×C₅	1	2	yes	—
525	C₂⁴	C₂⁴×C₅	1	4	yes	—
526	C₂⁴	C₂⁴×C₅	1	1	yes	characteristic
527	#41	—	2	32	no	—
528	#41	—	2	64	no	—
529	#41	—	4	64	no	—
530	C₂×Q₈	—	2	4	no	—
531	C₂×Q₈	—	2	8	no	—
532	C₂×Q₈	—	2	16	no	—
533	C₂×Q₈	—	4	8	no	—
534	C₂×Q₈	—	4	32	no	—
535	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
536	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
537	C₂×Q₈	C₂⁴×C₅	1	16	yes	—
538	C₂×Q₈	C₂⁴×C₅	1	16	yes	—
539	C₂×D₄	—	2	8	no	—
540	C₂×D₄	—	2	16	no	—
541	C₂×D₄	—	2	4	no	—
542	C₂×D₄	—	2	8	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	8	no	—
545	C₂×D₄	—	4	16	no	—
546	C₂×D₄	C₂⁴×C₅	1	8	yes	—
547	C₂×D₄	C₂⁴×C₅	1	8	yes	—
548	C₂×D₄	C₂⁴×C₅	1	16	yes	—
549	C₂×D₄	C₂⁴×C₅	1	4	yes	—
550	C₂×D₄	C₂⁴×C₅	1	8	yes	—
551	C₂×D₄	C₂⁴×C₅	1	8	yes	—
552	C₂×D₄	C₂⁴×C₅	1	32	yes	—
553	C₂²×C₄	—	2	16	no	—
554	C₂²×C₄	—	2	8	no	—
555	C₂²×C₄	—	2	4	no	—
556	C₂²×C₄	—	2	8	no	—
557	C₂²×C₄	—	2	4	no	—
558	C₂²×C₄	—	2	8	no	—
559	C₂²×C₄	—	4	8	no	—
560	C₂²×C₄	—	4	16	no	—
561	C₂²×C₄	C₅×#41	1	8	yes	complemented
562	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
563	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
564	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
565	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
566	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
567	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
568	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
569	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
570	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
571	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
572	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
573	C₂²×C₄	C₂⁴×C₅	1	8	yes	—
574	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
575	C₂²×C₄	C₂⁴×C₅	1	16	yes	—
576	C₂²×C₄	C₂⁴×C₅	1	32	yes	—
577	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
578	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
579	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
580	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
582	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
583	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
584	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
585	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
586	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
587	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
588	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
589	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
590	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
591	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
592	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
593	C₄⋊C₄	C₂⁴×C₅	1	32	yes	—
594	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
595	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
596	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
597	C₂²⋊C₄	C₂⁴×C₅	1	8	yes	—
598	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
599	C₂²⋊C₄	C₂⁴×C₅	1	32	yes	—
600	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
601	C₂²⋊C₄	C₂⁴×C₅	1	16	yes	—
602	C₄²	C₂⁴×C₅	1	4	yes	—
603	C₄²	C₂⁴×C₅	1	8	yes	—
604	C₄²	C₂⁴×C₅	1	4	yes	—
605	C₄²	C₂⁴×C₅	1	8	yes	—
606	C₄²	C₂⁴×C₅	1	4	yes	—
607	C₄²	C₂⁴×C₅	1	4	yes	—
608	C₄²	C₂⁴×C₅	1	8	yes	—
609	C₄²	C₂⁴×C₅	1	32	yes	—
610	C₂×C₅	—	2	4	no	—
611	C₂×C₅	—	4	4	no	—
612	C₂×C₅	—	4	8	no	—
613	C₂×C₅	#3511	1	4	yes	direct product factor
614	C₂×C₅	C₂³×#41	1	1	yes	characteristic
615	C₂×C₅	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
616	C₂×C₅	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
617	C₂³	—	2	2	no	—
618	C₂³	—	2	2	no	—
619	C₂³	—	2	4	no	—
620	C₂³	—	2	8	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	8	no	—
623	C₂³	—	2	4	no	—
624	C₂³	—	2	8	no	—
625	C₂³	C₂×C₅×#41	1	4	yes	—
626	C₂³	C₂⁵×C₅	1	4	yes	—
627	C₂³	C₂⁵×C₅	1	8	yes	—
628	C₂³	C₂⁵×C₅	1	2	yes	—
629	C₂³	C₂⁵×C₅	1	1	yes	characteristic
630	Q₈	—	2	8	no	—
631	Q₈	—	2	16	no	—
632	Q₈	—	2	32	no	—
633	Q₈	—	4	16	no	—
634	D₄	—	2	16	no	—
635	D₄	—	2	32	no	—
636	D₄	—	2	8	no	—
637	D₄	—	2	16	no	—
638	D₄	—	2	16	no	—
639	D₄	—	2	16	no	—
640	D₄	—	4	32	no	—
641	C₂×C₄	—	2	8	no	—
642	C₂×C₄	—	2	4	no	—
643	C₂×C₄	—	2	4	no	—
644	C₂×C₄	—	2	2	no	—
645	C₂×C₄	—	2	16	no	—
646	C₂×C₄	—	2	4	no	—
647	C₂×C₄	—	2	2	no	—
648	C₂×C₄	—	2	32	no	—
649	C₂×C₄	—	2	16	no	—
650	C₂×C₄	—	2	8	no	—
651	C₂×C₄	—	2	16	no	—
652	C₂×C₄	—	2	8	no	—
653	C₂×C₄	—	2	16	no	—
654	C₂×C₄	—	4	16	no	—
655	C₂×C₄	—	4	32	no	—
656	C₂×C₄	C₂×C₅×#41	1	4	yes	—
657	C₂×C₄	C₂×C₅×#41	1	4	yes	—
658	C₂×C₄	C₂×C₅×#41	1	16	yes	complemented
659	C₂×C₄	C₅×H(5,𝔽₂)	1	4	yes	—
660	C₂×C₄	C₅×2₋¹⁺⁴	1	4	yes	—
661	C₂×C₄	C₂⁵×C₅	1	4	yes	—
662	C₂×C₄	C₂⁵×C₅	1	2	yes	—
663	C₂×C₄	C₂⁵×C₅	1	2	yes	—
664	C₂×C₄	C₂⁵×C₅	1	4	yes	—
665	C₂×C₄	C₂⁵×C₅	1	8	yes	—
666	C₂×C₄	C₂⁵×C₅	1	4	yes	—
667	C₂×C₄	C₂⁵×C₅	1	16	yes	—
668	C₂×C₄	C₂⁵×C₅	1	2	yes	—
669	C₂×C₄	C₂⁵×C₅	1	2	yes	—
670	C₂×C₄	C₂⁵×C₅	1	2	yes	—
671	C₂×C₄	C₂⁵×C₅	1	2	yes	—
672	C₅	C₂×#3511	1	1	yes	characteristic, direct product factor, Sylow
673	C₂²	—	2	2	no	—
674	C₂²	—	2	2	no	—
675	C₂²	—	2	8	no	—
676	C₂²	—	2	4	no	—
677	C₂²	—	2	8	no	—
678	C₂²	—	2	4	no	—
679	C₂²	—	2	8	no	—
680	C₂²	—	2	4	no	—
681	C₂²	—	2	8	no	—
682	C₂²	—	4	8	no	—
683	C₂²	—	4	16	no	—
684	C₂²	C₂²×C₅×#41	1	4	yes	—
685	C₂²	C₂²×C₅×#41	1	2	yes	—
686	C₂²	C₂×C₅×H(5,𝔽₂)	1	2	yes	—
687	C₂²	C₂×C₅×2₋¹⁺⁴	1	2	yes	—
688	C₂²	C₂⁶×C₅	1	1	yes	characteristic
689	C₄	—	2	8	no	—
690	C₄	—	2	4	no	—
691	C₄	—	2	4	no	—
692	C₄	—	2	2	no	—
693	C₄	—	2	16	no	—
694	C₄	—	2	4	no	—
695	C₄	—	2	2	no	—
696	C₄	C₂²×C₅×#41	1	4	yes	—
697	C₄	C₂²×C₅×#41	1	4	yes	—
698	C₄	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
699	C₄	C₂×C₅×2₋¹⁺⁴	1	4	yes	—
700	C₂	—	2	4	no	—
701	C₂	—	4	4	no	—
702	C₂	—	4	8	no	—
703	C₂	C₅×#3511	1	4	yes	direct product factor
704	C₂	C₂³×C₅×#41	1	1	yes	characteristic
705	C₂	C₂²×C₅×H(5,𝔽₂)	1	1	yes	characteristic
706	C₂	C₂²×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶×C₅
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3511	C₂	direct (N × H)
2. C₂×C₅×#556	C₂	semidirect
3. C₂×C₅×#555	C₂	semidirect
4. C₂×C₅×#554	C₂	semidirect
5. C₂×C₅×#553	C₂	semidirect
6. C₂×C₅×#548	C₂	semidirect
7. C₂×C₅×#547	C₂	semidirect
8. C₂×C₅×#542	C₂	semidirect
9. C₂×C₅×#537	C₂	semidirect
10. C₂×C₅×#533	C₂	semidirect
11. C₂×C₅×#532	C₂	semidirect
12. C₂×C₅×#532	C₂	semidirect
13. C₂²×C₅×C₄⋊Q₈	C₂	semidirect
14. C₂×C₅×#520	C₂	semidirect
15. C₂×C₄×C₅×#41	C₂	semidirect
20. C₅×#556	C₂²	semidirect
21. C₅×#555	C₂²	semidirect
22. C₅×#554	C₂²	semidirect
23. C₅×#553	C₂²	semidirect
24. C₅×#548	C₂²	semidirect
25. C₅×#547	C₂²	semidirect
26. C₅×#542	C₂²	semidirect
27. C₅×#537	C₂²	semidirect
28. C₅×#533	C₂²	semidirect
29. C₅×#532	C₂²	semidirect
30. C₅×#532	C₂²	semidirect
36. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
54. C₅×#520	C₂²	semidirect
55. C₄×C₅×#41	C₂²	semidirect
78. C₂×#3511	C₅	direct (N × H)
179. #3511	C₂×C₅	direct (N × H)
180. C₂×#556	C₂×C₅	semidirect
181. C₂×#555	C₂×C₅	semidirect
182. C₂×#554	C₂×C₅	semidirect
183. C₂×#553	C₂×C₅	semidirect
184. C₂×#548	C₂×C₅	semidirect
185. C₂×#547	C₂×C₅	semidirect
186. C₂×#542	C₂×C₅	semidirect
187. C₂×#537	C₂×C₅	semidirect
188. C₂×#533	C₂×C₅	semidirect
189. C₂×#532	C₂×C₅	semidirect
190. C₂×#532	C₂×C₅	semidirect
191. C₂²×C₄⋊Q₈	C₂×C₅	semidirect
192. C₂×#520	C₂×C₅	semidirect
193. C₂×C₄×#41	C₂×C₅	semidirect
231. C₂²×C₄×C₅	#41	semidirect
284. #556	C₂²×C₅	semidirect
285. #555	C₂²×C₅	semidirect
286. #554	C₂²×C₅	semidirect
287. #553	C₂²×C₅	semidirect
288. #548	C₂²×C₅	semidirect
289. #547	C₂²×C₅	semidirect
290. #542	C₂²×C₅	semidirect
291. #537	C₂²×C₅	semidirect
292. #533	C₂²×C₅	semidirect
293. #532	C₂²×C₅	semidirect
294. #532	C₂²×C₅	semidirect
300. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
318. #520	C₂²×C₅	semidirect
319. C₄×#41	C₂²×C₅	semidirect
383. C₂×C₄×C₅	C₂×#41	semidirect
561. C₂²×C₄	C₅×#41	semidirect
613. C₂×C₅	#3511	direct (N × H)
658. C₂×C₄	C₂×C₅×#41	semidirect
672. C₅	C₂×#3511	direct (N × H)
703. C₂	C₅×#3511	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3511	2
C₂×C₅×#556	2
C₂×C₅×#555	2
C₂×C₅×#554	2
C₂×C₅×#553	2
C₂×C₅×#548	2
C₂×C₅×#547	2
C₂×C₅×#542	2
C₂×C₅×#537	2
C₂×C₅×#533	2
C₂×C₅×#532	2
C₂²×C₅×C₄⋊Q₈	2
C₂×C₅×#520	2
C₂×C₄×C₅×#41	2
C₂×#3511	5

Subgroups — C2×C5×#3511 #11985519

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3511 #11985519