Subgroups — C₂×C₅×#3489 #11985521

Order 1280.

11438 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

Maximal subgroups

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

subgroup	index
C₂²×C₅×2₋¹⁺⁴	2
C₂³×C₅×#41	2
C₅×#3489	2
C₂×C₅×D₄×Q₈	2
C₂×C₅×#548	2
C₂×C₅×#547	2
C₂×C₅×#546	2
C₂×C₅×#537	2
C₂×C₅×#536	2
C₂×C₅×#525	2
C₂²×C₅×C₂²⋊Q₈	2
C₂×C₅×#520	2
C₂×#3489	5

Subgroups — C2×C5×#3489 #11985521

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3489 #11985521