Subgroups — C₂×C₅×#3498 #11985515

Order 1280.

12982 conjugacy classes of subgroups.

The subgroup lattice has 356 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	2	yes	maximal, complemented
2	C₅×#3498	C₂	1	32	yes	maximal, direct product factor
3	C₂×C₅×#550	C₂	1	4	yes	maximal, complemented
4	C₂×C₅×D₄²	C₂	1	12	yes	maximal, complemented
5	C₂×C₅×#535	C₂	1	6	yes	maximal, complemented
6	C₂×C₅×#532	C₂	1	3	yes	maximal, complemented
7	C₂²×C₅×#127	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×H(5,𝔽₂)	—	2	32	no	—
10	C₂×C₅×H(5,𝔽₂)	C₂²	1	32	yes	complemented
11	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
12	C₂²×C₅×#41	C₂²	1	6	yes	complemented
13	C₂²×C₅×#41	C₂²	1	4	yes	complemented
14	C₂³×C₅×D₄	C₂²	1	6	yes	complemented
15	C₂³×C₅×D₄	C₂²	1	12	yes	complemented
16	C₂³×C₅×D₄	C₂²	1	12	yes	complemented
17	C₅×#550	C₂²	1	64	yes	complemented
18	C₅×D₄²	C₂²	1	192	yes	complemented
19	C₅×#535	C₂²	1	96	yes	complemented
20	C₅×#532	C₂²	1	48	yes	complemented
21	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₅×#127	C₂²	1	3	yes	complemented
23	C₂×C₅×#127	C₂²	1	6	yes	complemented
24	C₂×C₅×#127	C₂²	1	12	yes	complemented
25	C₂×C₅×#127	C₂²	1	48	yes	complemented
26	C₂×C₅×#124	C₂²	1	6	yes	complemented
27	C₂×C₅×#121	C₂²	1	12	yes	complemented
28	C₂×C₅×#121	C₂²	1	24	yes	complemented
29	C₂×C₅×#120	C₂²	1	24	yes	complemented
30	C₄×C₅×#41	C₂²	1	16	yes	complemented
31	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
32	C₂×C₄×C₅×D₄	C₂²	1	6	yes	complemented
33	C₂×C₄×C₅×D₄	C₂²	1	12	yes	complemented
34	C₂×C₅×#117	C₂²	1	3	yes	complemented
35	C₂²×C₄²×C₅	C₂²	1	3	yes	complemented
36	C₂×#3498	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂⁵×C₅	C₂³	1	12	yes	—
38	C₅×H(5,𝔽₂)	—	2	256	no	—
39	C₂×C₅×#41	—	2	32	no	—
40	C₂×C₅×#41	—	2	48	no	—
41	C₂×C₅×#41	D₄	1	16	yes	complemented
42	C₂×C₅×#41	C₂³	1	8	yes	—
43	C₂×C₅×#41	C₂³	1	48	yes	complemented
44	C₂×C₅×#41	C₂³	1	32	yes	complemented
45	C₂²×C₅×Q₈	C₂³	1	2	yes	—
46	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
47	C₂²×C₅×D₄	—	2	96	no	—
48	C₂²×C₅×D₄	—	2	48	no	—
49	C₂²×C₅×D₄	—	4	48	no	—
50	C₂²×C₅×D₄	C₂³	1	12	yes	—
51	C₂²×C₅×D₄	C₂³	1	12	yes	—
52	C₂²×C₅×D₄	C₂³	1	12	yes	—
53	C₂²×C₅×D₄	C₂³	1	6	yes	—
54	C₂²×C₅×D₄	C₂³	1	24	yes	—
55	C₂²×C₅×D₄	C₂³	1	3	yes	—
56	C₂²×C₅×D₄	C₂³	1	48	yes	complemented
57	C₂²×C₅×D₄	C₂³	1	96	yes	complemented
58	C₂²×C₅×D₄	C₂³	1	96	yes	complemented
59	C₂³×C₄×C₅	C₂³	1	6	yes	—
60	C₂³×C₄×C₅	C₂³	1	12	yes	—
61	C₂³×C₄×C₅	C₂³	1	3	yes	—
62	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
63	C₅×#127	C₂³	1	24	yes	complemented
64	C₅×#127	C₂³	1	48	yes	complemented
65	C₅×#127	C₂³	1	96	yes	complemented
66	C₅×#124	C₂³	1	48	yes	complemented
67	C₅×#121	C₂³	1	96	yes	complemented
68	C₅×#121	C₂³	1	192	yes	complemented
69	C₅×#120	C₂³	1	192	yes	complemented
70	C₄×C₅×Q₈	C₂³	1	16	yes	complemented
71	C₄×C₅×D₄	C₂³	1	48	yes	complemented
72	C₄×C₅×D₄	C₂³	1	96	yes	complemented
73	C₅×#117	C₂³	1	24	yes	complemented
74	C₂×C₅×C₄⋊C₄	C₂³	1	6	yes	—
75	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
76	C₂×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
77	C₂×C₅×C₂²⋊C₄	C₂³	1	24	yes	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	3	yes	—
80	C₂×C₄²×C₅	C₂³	1	6	yes	—
81	C₂×C₄²×C₅	C₂³	1	24	yes	complemented
82	C₂²×H(5,𝔽₂)	C₂×C₅	1	2	yes	complemented
83	#3498	C₂×C₅	1	32	yes	direct product factor
84	C₂×#550	C₂×C₅	1	4	yes	complemented
85	C₂×D₄²	C₂×C₅	1	12	yes	complemented
86	C₂×#535	C₂×C₅	1	6	yes	complemented
87	C₂×#532	C₂×C₅	1	3	yes	complemented
88	C₂²×#127	C₂×C₅	1	3	yes	complemented
89	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	—	2	48	no	—
91	C₂⁴×C₅	—	4	48	no	—
92	C₂⁴×C₅	C₂⁴	1	12	yes	—
93	C₂⁴×C₅	C₂⁴	1	3	yes	—
94	C₂⁴×C₅	C₂⁴	1	48	yes	—
95	C₅×#41	—	2	128	no	—
96	C₅×#41	—	2	192	no	—
97	C₅×#41	C₂×D₄	1	64	yes	complemented
98	C₂×C₅×Q₈	—	2	8	no	—
99	C₂×C₅×Q₈	C₂×D₄	1	8	yes	complemented
100	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
101	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
102	C₂×C₅×D₄	—	2	48	no	—
103	C₂×C₅×D₄	—	2	384	no	—
104	C₂×C₅×D₄	—	2	48	no	—
105	C₂×C₅×D₄	—	2	24	no	—
106	C₂×C₅×D₄	—	2	192	no	—
107	C₂×C₅×D₄	—	2	48	no	—
108	C₂×C₅×D₄	—	4	192	no	—
109	C₂×C₅×D₄	—	4	48	no	—
110	C₂×C₅×D₄	C₂×D₄	1	24	yes	complemented
111	C₂×C₅×D₄	C₂⁴	1	48	yes	—
112	C₂×C₅×D₄	C₂⁴	1	48	yes	—
113	C₂×C₅×D₄	C₂⁴	1	48	yes	—
114	C₂×C₅×D₄	C₂⁴	1	24	yes	—
115	C₂×C₅×D₄	C₂⁴	1	96	yes	—
116	C₂×C₅×D₄	C₂⁴	1	12	yes	—
117	C₂²×C₄×C₅	—	2	48	no	—
118	C₂²×C₄×C₅	—	2	24	no	—
119	C₂²×C₄×C₅	C₂×D₄	1	24	yes	complemented
120	C₂²×C₄×C₅	C₂⁴	1	24	yes	—
121	C₂²×C₄×C₅	C₂⁴	1	48	yes	—
122	C₂²×C₄×C₅	C₂⁴	1	6	yes	—
123	C₂²×C₄×C₅	C₂⁴	1	4	yes	—
124	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂⁴	1	3	yes	—
126	C₂²×C₄×C₅	C₂⁴	1	12	yes	—
127	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
128	C₅×C₄⋊C₄	C₂⁴	1	24	yes	—
129	C₅×C₄⋊C₄	C₂⁴	1	16	yes	—
130	C₅×C₂²⋊C₄	C₂⁴	1	24	yes	—
131	C₅×C₂²⋊C₄	C₂⁴	1	96	yes	—
132	C₄²×C₅	C₂⁴	1	4	yes	—
133	C₄²×C₅	C₂⁴	1	12	yes	—
134	C₄²×C₅	C₂⁴	1	24	yes	—
135	C₂×H(5,𝔽₂)	—	2	32	no	—
136	C₂×H(5,𝔽₂)	C₂²×C₅	1	32	yes	complemented
137	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
138	C₂²×#41	C₂²×C₅	1	6	yes	complemented
139	C₂²×#41	C₂²×C₅	1	4	yes	complemented
140	C₂³×D₄	C₂²×C₅	1	6	yes	complemented
141	C₂³×D₄	C₂²×C₅	1	12	yes	complemented
142	C₂³×D₄	C₂²×C₅	1	12	yes	complemented
143	#550	C₂²×C₅	1	64	yes	complemented
144	D₄²	C₂²×C₅	1	192	yes	complemented
145	#535	C₂²×C₅	1	96	yes	complemented
146	#532	C₂²×C₅	1	48	yes	complemented
147	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
148	C₂×#127	C₂²×C₅	1	3	yes	complemented
149	C₂×#127	C₂²×C₅	1	6	yes	complemented
150	C₂×#127	C₂²×C₅	1	12	yes	complemented
151	C₂×#127	C₂²×C₅	1	48	yes	complemented
152	C₂×#124	C₂²×C₅	1	6	yes	complemented
153	C₂×#121	C₂²×C₅	1	12	yes	complemented
154	C₂×#121	C₂²×C₅	1	24	yes	complemented
155	C₂×#120	C₂²×C₅	1	24	yes	complemented
156	C₄×#41	C₂²×C₅	1	16	yes	complemented
157	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
158	C₂×C₄×D₄	C₂²×C₅	1	6	yes	complemented
159	C₂×C₄×D₄	C₂²×C₅	1	12	yes	complemented
160	C₂×#117	C₂²×C₅	1	3	yes	complemented
161	C₂²×C₄²	C₂²×C₅	1	3	yes	complemented
162	C₂³×C₅	—	2	12	no	—
163	C₂³×C₅	—	2	24	no	—
164	C₂³×C₅	—	2	48	no	—
165	C₂³×C₅	—	2	96	no	—
166	C₂³×C₅	—	4	96	no	—
167	C₂³×C₅	—	8	96	no	—
168	C₂³×C₅	C₂²×D₄	1	12	yes	—
169	C₂³×C₅	C₂⁵	1	24	yes	—
170	C₂³×C₅	C₂⁵	1	6	yes	—
171	C₂³×C₅	C₂⁵	1	1	yes	characteristic
172	C₅×Q₈	—	2	16	no	—
173	C₅×Q₈	C₂²×D₄	1	16	yes	complemented
174	C₅×D₄	—	2	96	no	—
175	C₅×D₄	—	2	96	no	—
176	C₅×D₄	—	2	48	no	—
177	C₅×D₄	—	2	96	no	—
178	C₅×D₄	—	4	96	no	—
179	C₅×D₄	C₂²×D₄	1	48	yes	complemented
180	C₂×C₄×C₅	—	2	8	no	—
181	C₂×C₄×C₅	—	2	12	no	—
182	C₂×C₄×C₅	—	2	96	no	—
183	C₂×C₄×C₅	—	2	48	no	—
184	C₂×C₄×C₅	C₂²×D₄	1	12	yes	—
185	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
186	C₂×C₄×C₅	C₂²×D₄	1	48	yes	complemented
187	C₂×C₄×C₅	H(5,𝔽₂)	1	8	yes	complemented
188	C₂×C₄×C₅	C₂⁵	1	12	yes	—
189	C₂×C₄×C₅	C₂⁵	1	8	yes	—
190	C₂×C₄×C₅	C₂⁵	1	2	yes	—
191	C₂×C₄×C₅	C₂⁵	1	6	yes	—
192	C₂×C₄×C₅	C₂⁵	1	4	yes	—
193	C₂⁵	C₂³×C₅	1	12	yes	—
194	H(5,𝔽₂)	—	2	256	no	—
195	C₂×#41	—	2	32	no	—
196	C₂×#41	—	2	48	no	—
197	C₂×#41	C₅×D₄	1	16	yes	complemented
198	C₂×#41	C₂³×C₅	1	8	yes	—
199	C₂×#41	C₂³×C₅	1	48	yes	complemented
200	C₂×#41	C₂³×C₅	1	32	yes	complemented
201	C₂²×Q₈	C₂³×C₅	1	2	yes	—
202	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
203	C₂²×D₄	—	2	96	no	—
204	C₂²×D₄	—	2	48	no	—
205	C₂²×D₄	—	4	48	no	—
206	C₂²×D₄	C₂³×C₅	1	12	yes	—
207	C₂²×D₄	C₂³×C₅	1	12	yes	—
208	C₂²×D₄	C₂³×C₅	1	12	yes	—
209	C₂²×D₄	C₂³×C₅	1	6	yes	—
210	C₂²×D₄	C₂³×C₅	1	24	yes	—
211	C₂²×D₄	C₂³×C₅	1	3	yes	—
212	C₂²×D₄	C₂³×C₅	1	48	yes	complemented
213	C₂²×D₄	C₂³×C₅	1	96	yes	complemented
214	C₂²×D₄	C₂³×C₅	1	96	yes	complemented
215	C₂³×C₄	C₂³×C₅	1	6	yes	—
216	C₂³×C₄	C₂³×C₅	1	12	yes	—
217	C₂³×C₄	C₂³×C₅	1	3	yes	—
218	C₄⋊Q₈	C₂³×C₅	1	8	yes	complemented
219	#127	C₂³×C₅	1	24	yes	complemented
220	#127	C₂³×C₅	1	48	yes	complemented
221	#127	C₂³×C₅	1	96	yes	complemented
222	#124	C₂³×C₅	1	48	yes	complemented
223	#121	C₂³×C₅	1	96	yes	complemented
224	#121	C₂³×C₅	1	192	yes	complemented
225	#120	C₂³×C₅	1	192	yes	complemented
226	C₄×Q₈	C₂³×C₅	1	16	yes	complemented
227	C₄×D₄	C₂³×C₅	1	48	yes	complemented
228	C₄×D₄	C₂³×C₅	1	96	yes	complemented
229	#117	C₂³×C₅	1	24	yes	complemented
230	C₂×C₄⋊C₄	C₂³×C₅	1	6	yes	—
231	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
232	C₂×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
233	C₂×C₂²⋊C₄	C₂³×C₅	1	24	yes	—
234	C₂×C₄²	C₂³×C₅	1	3	yes	—
235	C₂×C₄²	C₂³×C₅	1	6	yes	—
236	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
237	C₂×C₄²	C₂³×C₅	1	24	yes	complemented
238	C₂²×C₅	—	2	12	no	—
239	C₂²×C₅	—	2	24	no	—
240	C₂²×C₅	—	2	24	no	—
241	C₂²×C₅	—	2	48	no	—
242	C₂²×C₅	—	4	48	no	—
243	C₂²×C₅	—	8	96	no	—
244	C₂²×C₅	C₂³×D₄	1	12	yes	—
245	C₂²×C₅	C₂³×D₄	1	2	yes	—
246	C₂²×C₅	C₂×H(5,𝔽₂)	1	4	yes	—
247	C₂²×C₅	C₂⁶	1	1	yes	characteristic
248	C₄×C₅	—	2	8	no	—
249	C₄×C₅	—	2	12	no	—
250	C₄×C₅	C₂³×D₄	1	12	yes	—
251	C₄×C₅	C₂³×D₄	1	4	yes	—
252	C₄×C₅	C₂×H(5,𝔽₂)	1	8	yes	complemented
253	C₂⁴	—	2	48	no	—
254	C₂⁴	—	4	48	no	—
255	C₂⁴	C₂⁴×C₅	1	12	yes	—
256	C₂⁴	C₂⁴×C₅	1	3	yes	—
257	C₂⁴	C₂⁴×C₅	1	48	yes	—
258	#41	—	2	128	no	—
259	#41	—	2	192	no	—
260	#41	C₂×C₅×D₄	1	64	yes	complemented
261	C₂×Q₈	—	2	8	no	—
262	C₂×Q₈	C₂×C₅×D₄	1	8	yes	complemented
263	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
264	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
265	C₂×D₄	—	2	48	no	—
266	C₂×D₄	—	2	384	no	—
267	C₂×D₄	—	2	48	no	—
268	C₂×D₄	—	2	24	no	—
269	C₂×D₄	—	2	192	no	—
270	C₂×D₄	—	2	48	no	—
271	C₂×D₄	—	4	192	no	—
272	C₂×D₄	—	4	48	no	—
273	C₂×D₄	C₂×C₅×D₄	1	24	yes	complemented
274	C₂×D₄	C₂⁴×C₅	1	48	yes	—
275	C₂×D₄	C₂⁴×C₅	1	48	yes	—
276	C₂×D₄	C₂⁴×C₅	1	48	yes	—
277	C₂×D₄	C₂⁴×C₅	1	24	yes	—
278	C₂×D₄	C₂⁴×C₅	1	96	yes	—
279	C₂×D₄	C₂⁴×C₅	1	12	yes	—
280	C₂²×C₄	—	2	48	no	—
281	C₂²×C₄	—	2	24	no	—
282	C₂²×C₄	C₂×C₅×D₄	1	24	yes	complemented
283	C₂²×C₄	C₂⁴×C₅	1	6	yes	—
284	C₂²×C₄	C₂⁴×C₅	1	24	yes	—
285	C₂²×C₄	C₂⁴×C₅	1	4	yes	—
286	C₂²×C₄	C₂⁴×C₅	1	48	yes	—
287	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴×C₅	1	3	yes	—
289	C₂²×C₄	C₂⁴×C₅	1	12	yes	—
290	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
291	C₄⋊C₄	C₂⁴×C₅	1	24	yes	—
292	C₄⋊C₄	C₂⁴×C₅	1	16	yes	—
293	C₂²⋊C₄	C₂⁴×C₅	1	24	yes	—
294	C₂²⋊C₄	C₂⁴×C₅	1	96	yes	—
295	C₄²	C₂⁴×C₅	1	4	yes	—
296	C₄²	C₂⁴×C₅	1	12	yes	—
297	C₄²	C₂⁴×C₅	1	24	yes	—
298	C₂×C₅	—	2	12	no	—
299	C₂×C₅	—	4	24	no	—
300	C₂×C₅	#3498	1	4	yes	direct product factor
301	C₂×C₅	C₂⁴×D₄	1	1	yes	characteristic
302	C₂×C₅	C₂²×H(5,𝔽₂)	1	2	yes	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	24	no	—
305	C₂³	—	2	48	no	—
306	C₂³	—	2	96	no	—
307	C₂³	—	4	96	no	—
308	C₂³	—	8	96	no	—
309	C₂³	C₂²×C₅×D₄	1	12	yes	—
310	C₂³	C₂⁵×C₅	1	24	yes	—
311	C₂³	C₂⁵×C₅	1	6	yes	—
312	C₂³	C₂⁵×C₅	1	1	yes	characteristic
313	Q₈	—	2	16	no	—
314	Q₈	C₂²×C₅×D₄	1	16	yes	complemented
315	D₄	—	2	96	no	—
316	D₄	—	2	96	no	—
317	D₄	—	2	48	no	—
318	D₄	—	2	96	no	—
319	D₄	—	4	96	no	—
320	D₄	C₂²×C₅×D₄	1	48	yes	complemented
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	12	no	—
323	C₂×C₄	—	2	96	no	—
324	C₂×C₄	—	2	48	no	—
325	C₂×C₄	C₂²×C₅×D₄	1	12	yes	—
326	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
327	C₂×C₄	C₂²×C₅×D₄	1	48	yes	complemented
328	C₂×C₄	C₅×H(5,𝔽₂)	1	8	yes	complemented
329	C₂×C₄	C₂⁵×C₅	1	12	yes	—
330	C₂×C₄	C₂⁵×C₅	1	8	yes	—
331	C₂×C₄	C₂⁵×C₅	1	2	yes	—
332	C₂×C₄	C₂⁵×C₅	1	6	yes	—
333	C₂×C₄	C₂⁵×C₅	1	4	yes	—
334	C₅	C₂×#3498	1	1	yes	characteristic, direct product factor, Sylow
335	C₂²	—	2	12	no	—
336	C₂²	—	2	24	no	—
337	C₂²	—	2	24	no	—
338	C₂²	—	2	48	no	—
339	C₂²	—	4	48	no	—
340	C₂²	—	8	96	no	—
341	C₂²	C₂³×C₅×D₄	1	12	yes	—
342	C₂²	C₂³×C₅×D₄	1	2	yes	—
343	C₂²	C₂×C₅×H(5,𝔽₂)	1	4	yes	—
344	C₂²	C₂⁶×C₅	1	1	yes	characteristic
345	C₄	—	2	8	no	—
346	C₄	—	2	12	no	—
347	C₄	C₂³×C₅×D₄	1	12	yes	—
348	C₄	C₂³×C₅×D₄	1	4	yes	—
349	C₄	C₂×C₅×H(5,𝔽₂)	1	8	yes	complemented
350	C₂	—	2	12	no	—
351	C₂	—	4	24	no	—
352	C₂	C₅×#3498	1	4	yes	direct product factor
353	C₂	C₂⁴×C₅×D₄	1	1	yes	characteristic
354	C₂	C₂²×C₅×H(5,𝔽₂)	1	2	yes	—

	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. C₅×#3498	C₂	direct (N × H)
3. C₂×C₅×#550	C₂	semidirect
4. C₂×C₅×D₄²	C₂	semidirect
5. C₂×C₅×#535	C₂	semidirect
6. C₂×C₅×#532	C₂	semidirect
7. C₂²×C₅×#127	C₂	semidirect
8. C₂×C₄×C₅×#41	C₂	semidirect
10. C₂×C₅×H(5,𝔽₂)	C₂²	semidirect
12. C₂²×C₅×#41	C₂²	semidirect
13. C₂²×C₅×#41	C₂²	semidirect
14. C₂³×C₅×D₄	C₂²	semidirect
15. C₂³×C₅×D₄	C₂²	semidirect
16. C₂³×C₅×D₄	C₂²	semidirect
17. C₅×#550	C₂²	semidirect
18. C₅×D₄²	C₂²	semidirect
19. C₅×#535	C₂²	semidirect
20. C₅×#532	C₂²	semidirect
21. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
22. C₂×C₅×#127	C₂²	semidirect
23. C₂×C₅×#127	C₂²	semidirect
24. C₂×C₅×#127	C₂²	semidirect
25. C₂×C₅×#127	C₂²	semidirect
26. C₂×C₅×#124	C₂²	semidirect
27. C₂×C₅×#121	C₂²	semidirect
28. C₂×C₅×#121	C₂²	semidirect
29. C₂×C₅×#120	C₂²	semidirect
30. C₄×C₅×#41	C₂²	semidirect
31. C₂×C₄×C₅×Q₈	C₂²	semidirect
32. C₂×C₄×C₅×D₄	C₂²	semidirect
33. C₂×C₄×C₅×D₄	C₂²	semidirect
34. C₂×C₅×#117	C₂²	semidirect
35. C₂²×C₄²×C₅	C₂²	semidirect
36. C₂×#3498	C₅	direct (N × H)
41. C₂×C₅×#41	D₄	semidirect
43. C₂×C₅×#41	C₂³	semidirect
44. C₂×C₅×#41	C₂³	semidirect
56. C₂²×C₅×D₄	C₂³	semidirect
57. C₂²×C₅×D₄	C₂³	semidirect
58. C₂²×C₅×D₄	C₂³	semidirect
62. C₅×C₄⋊Q₈	C₂³	semidirect
63. C₅×#127	C₂³	semidirect
64. C₅×#127	C₂³	semidirect
65. C₅×#127	C₂³	semidirect
66. C₅×#124	C₂³	semidirect
67. C₅×#121	C₂³	semidirect
68. C₅×#121	C₂³	semidirect
69. C₅×#120	C₂³	semidirect
70. C₄×C₅×Q₈	C₂³	semidirect
71. C₄×C₅×D₄	C₂³	semidirect
72. C₄×C₅×D₄	C₂³	semidirect
73. C₅×#117	C₂³	semidirect
81. C₂×C₄²×C₅	C₂³	semidirect
82. C₂²×H(5,𝔽₂)	C₂×C₅	semidirect
83. #3498	C₂×C₅	direct (N × H)
84. C₂×#550	C₂×C₅	semidirect
85. C₂×D₄²	C₂×C₅	semidirect
86. C₂×#535	C₂×C₅	semidirect
87. C₂×#532	C₂×C₅	semidirect
88. C₂²×#127	C₂×C₅	semidirect
89. C₂×C₄×#41	C₂×C₅	semidirect
97. C₅×#41	C₂×D₄	semidirect
99. C₂×C₅×Q₈	C₂×D₄	semidirect
110. C₂×C₅×D₄	C₂×D₄	semidirect
119. C₂²×C₄×C₅	C₂×D₄	semidirect
136. C₂×H(5,𝔽₂)	C₂²×C₅	semidirect
138. C₂²×#41	C₂²×C₅	semidirect
139. C₂²×#41	C₂²×C₅	semidirect
140. C₂³×D₄	C₂²×C₅	semidirect
141. C₂³×D₄	C₂²×C₅	semidirect
142. C₂³×D₄	C₂²×C₅	semidirect
143. #550	C₂²×C₅	semidirect
144. D₄²	C₂²×C₅	semidirect
145. #535	C₂²×C₅	semidirect
146. #532	C₂²×C₅	semidirect
147. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
148. C₂×#127	C₂²×C₅	semidirect
149. C₂×#127	C₂²×C₅	semidirect
150. C₂×#127	C₂²×C₅	semidirect
151. C₂×#127	C₂²×C₅	semidirect
152. C₂×#124	C₂²×C₅	semidirect
153. C₂×#121	C₂²×C₅	semidirect
154. C₂×#121	C₂²×C₅	semidirect
155. C₂×#120	C₂²×C₅	semidirect
156. C₄×#41	C₂²×C₅	semidirect
157. C₂×C₄×Q₈	C₂²×C₅	semidirect
158. C₂×C₄×D₄	C₂²×C₅	semidirect
159. C₂×C₄×D₄	C₂²×C₅	semidirect
160. C₂×#117	C₂²×C₅	semidirect
161. C₂²×C₄²	C₂²×C₅	semidirect
173. C₅×Q₈	C₂²×D₄	semidirect
179. C₅×D₄	C₂²×D₄	semidirect
186. C₂×C₄×C₅	C₂²×D₄	semidirect
187. C₂×C₄×C₅	H(5,𝔽₂)	semidirect
197. C₂×#41	C₅×D₄	semidirect
199. C₂×#41	C₂³×C₅	semidirect
200. C₂×#41	C₂³×C₅	semidirect
212. C₂²×D₄	C₂³×C₅	semidirect
213. C₂²×D₄	C₂³×C₅	semidirect
214. C₂²×D₄	C₂³×C₅	semidirect
218. C₄⋊Q₈	C₂³×C₅	semidirect
219. #127	C₂³×C₅	semidirect
220. #127	C₂³×C₅	semidirect
221. #127	C₂³×C₅	semidirect
222. #124	C₂³×C₅	semidirect
223. #121	C₂³×C₅	semidirect
224. #121	C₂³×C₅	semidirect
225. #120	C₂³×C₅	semidirect
226. C₄×Q₈	C₂³×C₅	semidirect
227. C₄×D₄	C₂³×C₅	semidirect
228. C₄×D₄	C₂³×C₅	semidirect
229. #117	C₂³×C₅	semidirect
237. C₂×C₄²	C₂³×C₅	semidirect
252. C₄×C₅	C₂×H(5,𝔽₂)	semidirect
260. #41	C₂×C₅×D₄	semidirect
262. C₂×Q₈	C₂×C₅×D₄	semidirect
273. C₂×D₄	C₂×C₅×D₄	semidirect
282. C₂²×C₄	C₂×C₅×D₄	semidirect
300. C₂×C₅	#3498	direct (N × H)
314. Q₈	C₂²×C₅×D₄	semidirect
320. D₄	C₂²×C₅×D₄	semidirect
327. C₂×C₄	C₂²×C₅×D₄	semidirect
328. C₂×C₄	C₅×H(5,𝔽₂)	semidirect
334. C₅	C₂×#3498	direct (N × H)
349. C₄	C₂×C₅×H(5,𝔽₂)	semidirect
352. C₂	C₅×#3498	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
C₅×#3498	2
C₂×C₅×#550	2
C₂×C₅×D₄²	2
C₂×C₅×#535	2
C₂×C₅×#532	2
C₂²×C₅×#127	2
C₂×C₄×C₅×#41	2
C₂×#3498	5

Subgroups — C2×C5×#3498 #11985515

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3498 #11985515