Subgroups — C₂×C₅×#3488 #11985514

Order 1280.

12366 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

Subgroups — C2×C5×#3488 #11985514

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3488 #11985514