Subgroups — C₂×C₅×#3140 #11983335

Order 1280.

2246 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#124	C₂	1	1	yes	maximal, characteristic
3	C₅×#3140	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#489	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#488	C₂	1	4	yes	maximal, complemented
6	C₂×C₅×#419	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#418	C₂	1	2	yes	maximal
8	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
10	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
12	C₅×#533	—	2	4	no	—
13	C₅×#533	C₂²	1	8	yes	complemented
14	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
15	C₂×C₅×#125	C₂²	1	2	yes	complemented
16	C₂×C₅×#124	—	2	2	no	—
17	C₂×C₅×#124	—	2	4	no	—
18	C₂×C₅×#124	C₂²	1	2	yes	—
19	C₂×C₅×#124	C₂²	1	2	yes	—
20	C₂×C₅×#124	C₂²	1	8	yes	—
21	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₂×C₄×C₅×Q₈	—	2	2	no	—
23	C₂×C₅×#117	C₂²	1	2	yes	—
24	C₂²×C₅×C₂²⋊C₄	—	2	2	no	—
25	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₅×#489	C₂²	1	32	yes	complemented
27	C₅×#488	C₂²	1	32	yes	complemented
28	C₅×#419	C₂²	1	16	yes	complemented
29	C₅×#418	C₂²	1	16	yes	—
30	C₂×C₅×#103	C₂²	1	8	yes	complemented
31	C₂×C₅×#102	C₂²	1	8	yes	—
32	C₄×C₅×M₁₆	C₂²	1	8	yes	complemented
33	C₂×C₅×#97	C₂²	1	2	yes	complemented
34	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
35	C₂×#3140	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
36	C₂⁵×C₅	—	2	1	no	—
37	C₂²×C₅×Q₈	—	2	2	no	—
38	C₂²×C₅×Q₈	—	2	2	no	—
39	C₂²×C₅×Q₈	—	2	1	no	—
40	C₂²×C₅×Q₈	—	2	8	no	—
41	C₂²×C₅×Q₈	C₂³	1	2	yes	—
42	C₂²×C₅×Q₈	C₂³	1	4	yes	—
43	C₂²×C₅×D₄	—	2	2	no	—
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	8	no	—
46	C₂²×C₅×D₄	C₂³	1	2	yes	—
47	C₂²×C₅×D₄	C₂³	1	4	yes	—
48	C₂³×C₄×C₅	—	2	1	no	—
49	C₂³×C₄×C₅	D₄	1	2	yes	—
50	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₅×M₁₆	—	2	8	no	—
52	C₂×C₅×M₁₆	C₂³	1	8	yes	—
53	C₂²×C₅×C₈	C₂³	1	4	yes	—
54	C₅×C₄⋊Q₈	—	2	4	no	—
55	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
56	C₅×#125	—	2	4	no	—
57	C₅×#125	C₂³	1	8	yes	complemented
58	C₅×#124	—	2	16	no	—
59	C₅×#124	—	2	4	no	—
60	C₅×#124	—	2	4	no	—
61	C₅×#124	C₂³	1	8	yes	—
62	C₅×#124	C₂³	1	8	yes	—
63	C₅×C₂²⋊Q₈	—	2	16	no	—
64	C₄×C₅×Q₈	—	2	16	no	—
65	C₅×#117	—	2	4	no	—
66	C₅×#117	C₂³	1	8	yes	—
67	C₂×C₅×C₄⋊C₄	—	2	4	no	—
68	C₂×C₅×C₄⋊C₄	—	2	2	no	—
69	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	16	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
73	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	D₄	1	2	yes	—
76	C₂×C₄²×C₅	D₄	1	4	yes	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	4	yes	—
80	C₅×#103	C₂³	1	32	yes	complemented
81	C₅×#102	C₂³	1	32	yes	—
82	C₅×#97	C₂³	1	8	yes	complemented
83	C₄×C₅×C₈	C₂³	1	8	yes	complemented
84	C₂×#533	C₂×C₅	1	1	yes	characteristic, complemented
85	C₂²×#124	C₂×C₅	1	1	yes	characteristic
86	#3140	C₂×C₅	1	16	yes	direct product factor
87	C₂×#489	C₂×C₅	1	4	yes	complemented
88	C₂×#488	C₂×C₅	1	4	yes	complemented
89	C₂×#419	C₂×C₅	1	2	yes	complemented
90	C₂×#418	C₂×C₅	1	2	yes	—
91	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
92	C₂⁴×C₅	—	2	4	no	—
93	C₂⁴×C₅	—	2	2	no	—
94	C₂⁴×C₅	—	4	8	no	—
95	C₂⁴×C₅	—	4	4	no	—
96	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
97	C₂×C₅×Q₈	—	2	8	no	—
98	C₂×C₅×Q₈	—	2	4	no	—
99	C₂×C₅×Q₈	—	2	2	no	—
100	C₂×C₅×Q₈	—	2	8	no	—
101	C₂×C₅×Q₈	—	2	16	no	—
102	C₂×C₅×Q₈	—	4	8	no	—
103	C₂×C₅×Q₈	—	4	8	no	—
104	C₂×C₅×Q₈	—	4	4	no	—
105	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
106	C₂×C₅×D₄	—	2	4	no	—
107	C₂×C₅×D₄	—	2	2	no	—
108	C₂×C₅×D₄	—	2	8	no	—
109	C₂×C₅×D₄	—	2	16	no	—
110	C₂×C₅×D₄	—	4	8	no	—
111	C₂×C₅×D₄	—	4	4	no	—
112	C₂×C₅×D₄	C₂⁴	1	4	yes	—
113	C₂²×C₄×C₅	—	2	4	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	2	no	—
116	C₂²×C₄×C₅	—	4	4	no	—
117	C₂²×C₄×C₅	—	4	4	no	—
118	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₅	C₂×D₄	1	8	yes	—
121	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₅	#41	1	8	yes	—
124	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
125	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
126	C₅×M₁₆	—	2	16	no	—
127	C₂×C₅×C₈	—	2	8	no	—
128	C₂×C₅×C₈	C₂⁴	1	8	yes	—
129	C₅×C₄⋊C₄	—	2	16	no	—
130	C₅×C₄⋊C₄	—	2	8	no	—
131	C₅×C₄⋊C₄	—	2	4	no	—
132	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
133	C₅×C₂²⋊C₄	—	2	8	no	—
134	C₅×C₂²⋊C₄	—	2	16	no	—
135	C₅×C₂²⋊C₄	—	2	16	no	—
136	C₄²×C₅	—	2	8	no	—
137	C₄²×C₅	C₂×D₄	1	8	yes	—
138	C₄²×C₅	C₂×D₄	1	2	yes	—
139	C₄²×C₅	C₂×D₄	1	2	yes	—
140	C₄²×C₅	C₂⁴	1	2	yes	—
141	C₄²×C₅	C₂⁴	1	2	yes	—
142	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
143	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
144	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
145	#533	—	2	4	no	—
146	#533	C₂²×C₅	1	8	yes	complemented
147	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
148	C₂×#125	C₂²×C₅	1	2	yes	complemented
149	C₂×#124	—	2	2	no	—
150	C₂×#124	—	2	4	no	—
151	C₂×#124	C₂²×C₅	1	2	yes	—
152	C₂×#124	C₂²×C₅	1	2	yes	—
153	C₂×#124	C₂²×C₅	1	8	yes	—
154	C₂×C₂²⋊Q₈	—	2	2	no	—
155	C₂×C₄×Q₈	—	2	2	no	—
156	C₂×#117	C₂²×C₅	1	2	yes	—
157	C₂²×C₂²⋊C₄	—	2	2	no	—
158	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
159	#489	C₂²×C₅	1	32	yes	complemented
160	#488	C₂²×C₅	1	32	yes	complemented
161	#419	C₂²×C₅	1	16	yes	complemented
162	#418	C₂²×C₅	1	16	yes	—
163	C₂×#103	C₂²×C₅	1	8	yes	complemented
164	C₂×#102	C₂²×C₅	1	8	yes	—
165	C₄×M₁₆	C₂²×C₅	1	8	yes	complemented
166	C₂×#97	C₂²×C₅	1	2	yes	complemented
167	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
168	C₂³×C₅	—	2	4	no	—
169	C₂³×C₅	—	2	4	no	—
170	C₂³×C₅	—	4	16	no	—
171	C₂³×C₅	—	4	8	no	—
172	C₂³×C₅	—	4	4	no	—
173	C₂³×C₅	—	4	8	no	—
174	C₂³×C₅	—	8	16	no	—
175	C₂³×C₅	#124	1	4	yes	—
176	C₂³×C₅	C₂²×D₄	1	2	yes	—
177	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
178	C₅×Q₈	—	2	8	no	—
179	C₅×Q₈	—	4	16	no	—
180	C₅×Q₈	—	4	8	no	—
181	C₅×Q₈	—	4	4	no	—
182	C₅×D₄	—	2	8	no	—
183	C₅×D₄	—	4	8	no	—
184	C₅×D₄	—	4	4	no	—
185	C₂×C₄×C₅	—	2	4	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	8	no	—
188	C₂×C₄×C₅	—	2	4	no	—
189	C₂×C₄×C₅	—	4	8	no	—
190	C₂×C₄×C₅	—	4	8	no	—
191	C₂×C₄×C₅	—	4	4	no	—
192	C₂×C₄×C₅	—	4	8	no	—
193	C₂×C₄×C₅	#124	1	8	yes	—
194	C₂×C₄×C₅	#124	1	4	yes	—
195	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
197	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₅	C₂×#41	1	4	yes	—
200	C₂×C₄×C₅	C₂×#41	1	8	yes	—
201	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
202	C₅×C₈	—	2	8	no	—
203	C₂⁵	—	2	1	no	—
204	C₂²×Q₈	—	2	2	no	—
205	C₂²×Q₈	—	2	1	no	—
206	C₂²×Q₈	—	2	2	no	—
207	C₂²×Q₈	—	2	8	no	—
208	C₂²×Q₈	C₂³×C₅	1	2	yes	—
209	C₂²×Q₈	C₂³×C₅	1	4	yes	—
210	C₂²×D₄	—	2	1	no	—
211	C₂²×D₄	—	2	2	no	—
212	C₂²×D₄	—	2	8	no	—
213	C₂²×D₄	C₂³×C₅	1	2	yes	—
214	C₂²×D₄	C₂³×C₅	1	4	yes	—
215	C₂³×C₄	—	2	1	no	—
216	C₂³×C₄	C₅×D₄	1	2	yes	—
217	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
218	C₂×M₁₆	—	2	8	no	—
219	C₂×M₁₆	C₂³×C₅	1	8	yes	—
220	C₂²×C₈	C₂³×C₅	1	4	yes	—
221	C₄⋊Q₈	—	2	4	no	—
222	C₄⋊Q₈	C₂³×C₅	1	8	yes	complemented
223	#125	—	2	4	no	—
224	#125	C₂³×C₅	1	8	yes	complemented
225	#124	—	2	16	no	—
226	#124	—	2	4	no	—
227	#124	—	2	4	no	—
228	#124	C₂³×C₅	1	8	yes	—
229	#124	C₂³×C₅	1	8	yes	—
230	C₂²⋊Q₈	—	2	16	no	—
231	C₄×Q₈	—	2	16	no	—
232	#117	—	2	4	no	—
233	#117	C₂³×C₅	1	8	yes	—
234	C₂×C₄⋊C₄	—	2	4	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
237	C₂×C₂²⋊C₄	—	2	2	no	—
238	C₂×C₂²⋊C₄	—	2	4	no	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	—	2	16	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	C₅×D₄	1	2	yes	—
243	C₂×C₄²	C₅×D₄	1	4	yes	—
244	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
245	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
246	C₂×C₄²	C₂³×C₅	1	4	yes	—
247	#103	C₂³×C₅	1	32	yes	complemented
248	#102	C₂³×C₅	1	32	yes	—
249	#97	C₂³×C₅	1	8	yes	complemented
250	C₄×C₈	C₂³×C₅	1	8	yes	complemented
251	C₂²×C₅	—	2	8	no	—
252	C₂²×C₅	—	2	4	no	—
253	C₂²×C₅	—	4	4	no	—
254	C₂²×C₅	—	4	8	no	—
255	C₂²×C₅	—	8	16	no	—
256	C₂²×C₅	—	8	8	no	—
257	C₂²×C₅	C₂×#124	1	4	yes	—
258	C₂²×C₅	C₂×#124	1	2	yes	—
259	C₂²×C₅	#575	1	4	yes	—
260	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
261	C₄×C₅	—	2	4	no	—
262	C₄×C₅	—	2	4	no	—
263	C₄×C₅	—	4	4	no	—
264	C₄×C₅	—	4	8	no	—
265	C₄×C₅	C₂×#124	1	4	yes	—
266	C₄×C₅	C₂×#124	1	2	yes	—
267	C₄×C₅	C₂²×#41	1	2	yes	—
268	C₂⁴	—	2	4	no	—
269	C₂⁴	—	2	2	no	—
270	C₂⁴	—	4	8	no	—
271	C₂⁴	—	4	4	no	—
272	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
273	C₂×Q₈	—	2	8	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	—	2	16	no	—
278	C₂×Q₈	—	4	8	no	—
279	C₂×Q₈	—	4	8	no	—
280	C₂×Q₈	—	4	4	no	—
281	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	16	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂×D₄	—	4	4	no	—
288	C₂×D₄	C₂⁴×C₅	1	4	yes	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	4	4	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
296	C₂²×C₄	C₂×C₅×D₄	1	8	yes	—
297	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
299	C₂²×C₄	C₅×#41	1	8	yes	—
300	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
302	M₁₆	—	2	16	no	—
303	C₂×C₈	—	2	8	no	—
304	C₂×C₈	C₂⁴×C₅	1	8	yes	—
305	C₄⋊C₄	—	2	16	no	—
306	C₄⋊C₄	—	2	8	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
309	C₂²⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	2	16	no	—
311	C₂²⋊C₄	—	2	16	no	—
312	C₄²	—	2	8	no	—
313	C₄²	C₂×C₅×D₄	1	8	yes	—
314	C₄²	C₂×C₅×D₄	1	2	yes	—
315	C₄²	C₂×C₅×D₄	1	2	yes	—
316	C₄²	C₂⁴×C₅	1	2	yes	—
317	C₄²	C₂⁴×C₅	1	2	yes	—
318	C₂×C₅	—	2	4	no	—
319	C₂×C₅	—	8	4	no	—
320	C₂×C₅	#3140	1	4	yes	direct product factor
321	C₂×C₅	C₂²×#124	1	1	yes	characteristic
322	C₂×C₅	C₂×#575	1	2	yes	—
323	C₂³	—	2	4	no	—
324	C₂³	—	2	4	no	—
325	C₂³	—	4	16	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	4	no	—
328	C₂³	—	4	8	no	—
329	C₂³	—	8	16	no	—
330	C₂³	C₅×#124	1	4	yes	—
331	C₂³	C₂²×C₅×D₄	1	2	yes	—
332	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
333	Q₈	—	2	8	no	—
334	Q₈	—	4	16	no	—
335	Q₈	—	4	8	no	—
336	Q₈	—	4	4	no	—
337	D₄	—	2	8	no	—
338	D₄	—	4	8	no	—
339	D₄	—	4	4	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	8	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	8	no	—
345	C₂×C₄	—	4	8	no	—
346	C₂×C₄	—	4	4	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	C₅×#124	1	8	yes	—
349	C₂×C₄	C₅×#124	1	4	yes	—
350	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
351	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
352	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
353	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
354	C₂×C₄	C₂×C₅×#41	1	4	yes	—
355	C₂×C₄	C₂×C₅×#41	1	8	yes	—
356	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
357	C₈	—	2	8	no	—
358	C₅	C₂×#3140	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²	—	2	8	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	4	4	no	—
362	C₂²	—	4	8	no	—
363	C₂²	—	8	16	no	—
364	C₂²	—	8	8	no	—
365	C₂²	C₂×C₅×#124	1	4	yes	—
366	C₂²	C₂×C₅×#124	1	2	yes	—
367	C₂²	C₅×#575	1	4	yes	—
368	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
369	C₄	—	2	4	no	—
370	C₄	—	2	4	no	—
371	C₄	—	4	4	no	—
372	C₄	—	4	8	no	—
373	C₄	C₂×C₅×#124	1	4	yes	—
374	C₄	C₂×C₅×#124	1	2	yes	—
375	C₄	C₂²×C₅×#41	1	2	yes	—
376	C₂	—	2	4	no	—
377	C₂	—	8	4	no	—
378	C₂	C₅×#3140	1	4	yes	direct product factor
379	C₂	C₂²×C₅×#124	1	1	yes	characteristic
380	C₂	C₂×C₅×#575	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂³×C₅×D₄	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#533	C₂	semidirect
3. C₅×#3140	C₂	direct (N × H)
4. C₂×C₅×#489	C₂	semidirect
5. C₂×C₅×#488	C₂	semidirect
6. C₂×C₅×#419	C₂	semidirect
8. C₂×C₄×C₅×M₁₆	C₂	semidirect
13. C₅×#533	C₂²	semidirect
14. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
15. C₂×C₅×#125	C₂²	semidirect
26. C₅×#489	C₂²	semidirect
27. C₅×#488	C₂²	semidirect
28. C₅×#419	C₂²	semidirect
30. C₂×C₅×#103	C₂²	semidirect
32. C₄×C₅×M₁₆	C₂²	semidirect
33. C₂×C₅×#97	C₂²	semidirect
34. C₂×C₄×C₅×C₈	C₂²	semidirect
35. C₂×#3140	C₅	direct (N × H)
55. C₅×C₄⋊Q₈	C₂³	semidirect
57. C₅×#125	C₂³	semidirect
80. C₅×#103	C₂³	semidirect
82. C₅×#97	C₂³	semidirect
83. C₄×C₅×C₈	C₂³	semidirect
84. C₂×#533	C₂×C₅	semidirect
86. #3140	C₂×C₅	direct (N × H)
87. C₂×#489	C₂×C₅	semidirect
88. C₂×#488	C₂×C₅	semidirect
89. C₂×#419	C₂×C₅	semidirect
91. C₂×C₄×M₁₆	C₂×C₅	semidirect
146. #533	C₂²×C₅	semidirect
147. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
148. C₂×#125	C₂²×C₅	semidirect
159. #489	C₂²×C₅	semidirect
160. #488	C₂²×C₅	semidirect
161. #419	C₂²×C₅	semidirect
163. C₂×#103	C₂²×C₅	semidirect
165. C₄×M₁₆	C₂²×C₅	semidirect
166. C₂×#97	C₂²×C₅	semidirect
167. C₂×C₄×C₈	C₂²×C₅	semidirect
222. C₄⋊Q₈	C₂³×C₅	semidirect
224. #125	C₂³×C₅	semidirect
247. #103	C₂³×C₅	semidirect
249. #97	C₂³×C₅	semidirect
250. C₄×C₈	C₂³×C₅	semidirect
320. C₂×C₅	#3140	direct (N × H)
358. C₅	C₂×#3140	direct (N × H)
378. C₂	C₅×#3140	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#533	2
C₂²×C₅×#124	2
C₅×#3140	2
C₂×C₅×#489	2
C₂×C₅×#488	2
C₂×C₅×#419	2
C₂×C₅×#418	2
C₂×C₄×C₅×M₁₆	2
C₂×#3140	5

Subgroups — C2×C5×#3140 #11983335

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3140 #11983335