Subgroups — C₂×C₅×#3165 #11983381

Order 1280.

2118 conjugacy classes of subgroups.

The subgroup lattice has 410 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
2	C₂²×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₅×#3165	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#501	C₂	1	4	yes	maximal, complemented
5	C₂×C₅×#500	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#498	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#428	C₂	1	4	yes	maximal
8	C₂×C₄×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₅×Q₈	—	2	1	no	—
10	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
11	C₅×#533	—	2	4	no	—
12	C₅×#533	C₂²	1	8	yes	—
13	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
14	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
15	C₂×C₅×C₄⋊Q₈	—	2	4	no	—
16	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₂×C₅×C₄⋊Q₈	C₂²	1	8	yes	—
19	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#125	C₂²	1	2	yes	—
22	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
23	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
24	C₂×C₄×C₅×Q₈	—	2	1	no	—
25	C₂×C₄×C₅×Q₈	—	2	1	no	—
26	C₂×C₅×#117	C₂²	1	2	yes	—
27	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
28	C₂²×C₅×C₄⋊C₄	C₂²	1	2	yes	—
29	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₅×#501	C₂²	1	32	yes	complemented
31	C₅×#500	C₂²	1	16	yes	complemented
32	C₅×#498	C₂²	1	16	yes	complemented
33	C₅×#428	C₂²	1	32	yes	—
34	C₂×C₅×#107	C₂²	1	8	yes	—
35	C₂×C₅×#106	C₂²	1	8	yes	—
36	C₄×C₅×M₁₆	C₂²	1	8	yes	—
37	C₂×C₅×#97	C₂²	1	2	yes	—
38	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
39	C₂×#3165	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
40	C₂²×C₅×Q₈	—	2	1	no	—
41	C₂²×C₅×Q₈	—	2	1	no	—
42	C₂²×C₅×Q₈	—	2	8	no	—
43	C₂²×C₅×Q₈	—	2	2	no	—
44	C₂²×C₅×Q₈	—	2	2	no	—
45	C₂²×C₅×Q₈	—	4	8	no	—
46	C₂³×C₄×C₅	—	2	2	no	—
47	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂×C₅×M₁₆	Q₈	1	16	yes	complemented
51	C₂×C₅×M₁₆	C₂³	1	8	yes	—
52	C₂²×C₅×C₈	C₂³	1	4	yes	—
53	C₅×C₄⋊Q₈	—	2	8	no	—
54	C₅×C₄⋊Q₈	—	2	8	no	—
55	C₅×C₄⋊Q₈	—	2	4	no	—
56	C₅×C₄⋊Q₈	—	2	4	no	—
57	C₅×C₄⋊Q₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	—	2	2	no	—
59	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
60	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
61	C₅×C₄⋊Q₈	C₂³	1	4	yes	—
62	C₅×C₄⋊Q₈	C₂³	1	8	yes	—
63	C₅×#125	—	2	4	no	—
64	C₅×#125	C₂³	1	8	yes	—
65	C₅×C₂²⋊Q₈	—	2	8	no	—
66	C₅×C₂²⋊Q₈	—	2	8	no	—
67	C₄×C₅×Q₈	—	2	8	no	—
68	C₄×C₅×Q₈	—	2	8	no	—
69	C₅×#117	—	2	4	no	—
70	C₅×#117	C₂³	1	8	yes	—
71	C₂×C₅×C₄⋊C₄	—	2	8	no	—
72	C₂×C₅×C₄⋊C₄	—	2	2	no	—
73	C₂×C₅×C₄⋊C₄	—	2	2	no	—
74	C₂×C₅×C₄⋊C₄	—	2	4	no	—
75	C₂×C₅×C₄⋊C₄	—	2	2	no	—
76	C₂×C₅×C₄⋊C₄	—	2	2	no	—
77	C₂×C₅×C₄⋊C₄	—	2	2	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
82	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂³	1	8	yes	—
84	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₂×C₄²×C₅	—	2	2	no	—
86	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
87	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
88	C₂×C₄²×C₅	D₄	1	4	yes	—
89	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂³	1	4	yes	—
92	C₅×#107	C₂³	1	32	yes	—
93	C₅×#106	C₂³	1	32	yes	—
94	C₅×#97	C₂³	1	8	yes	—
95	C₄×C₅×C₈	C₂³	1	8	yes	—
96	C₂×#533	C₂×C₅	1	1	yes	characteristic
97	C₂²×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
98	#3165	C₂×C₅	1	16	yes	direct product factor
99	C₂×#501	C₂×C₅	1	4	yes	complemented
100	C₂×#500	C₂×C₅	1	2	yes	complemented
101	C₂×#498	C₂×C₅	1	2	yes	complemented
102	C₂×#428	C₂×C₅	1	4	yes	—
103	C₂×C₄×M₁₆	C₂×C₅	1	1	yes	characteristic
104	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₅×Q₈	—	2	4	no	—
106	C₂×C₅×Q₈	—	2	4	no	—
107	C₂×C₅×Q₈	—	2	8	no	—
108	C₂×C₅×Q₈	—	2	8	no	—
109	C₂×C₅×Q₈	—	4	8	no	—
110	C₂×C₅×Q₈	—	4	32	no	—
111	C₂×C₅×Q₈	—	4	4	no	—
112	C₂×C₅×Q₈	—	4	8	no	—
113	C₂×C₅×Q₈	—	4	4	no	—
114	C₂²×C₄×C₅	—	2	4	no	—
115	C₂²×C₄×C₅	—	2	4	no	—
116	C₂²×C₄×C₅	—	2	8	no	—
117	C₂²×C₄×C₅	—	2	2	no	—
118	C₂²×C₄×C₅	—	2	2	no	—
119	C₂²×C₄×C₅	—	2	4	no	—
120	C₂²×C₄×C₅	—	4	8	no	—
121	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
122	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×Q₈	1	8	yes	—
130	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
132	C₅×M₁₆	C₂×Q₈	1	32	yes	complemented
133	C₂×C₅×C₈	C₂×Q₈	1	16	yes	complemented
134	C₂×C₅×C₈	C₂⁴	1	8	yes	—
135	C₅×C₄⋊C₄	—	2	8	no	—
136	C₅×C₄⋊C₄	—	2	8	no	—
137	C₅×C₄⋊C₄	—	2	8	no	—
138	C₅×C₄⋊C₄	—	2	4	no	—
139	C₅×C₄⋊C₄	—	2	8	no	—
140	C₅×C₄⋊C₄	—	2	8	no	—
141	C₅×C₄⋊C₄	—	2	4	no	—
142	C₅×C₄⋊C₄	—	2	4	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	2	2	no	—
145	C₅×C₄⋊C₄	C₂⁴	1	8	yes	—
146	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
147	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
148	C₅×C₂²⋊C₄	—	2	8	no	—
149	C₄²×C₅	—	2	8	no	—
150	C₄²×C₅	C₂×D₄	1	4	yes	—
151	C₄²×C₅	C₂×D₄	1	4	yes	—
152	C₄²×C₅	C₂×D₄	1	2	yes	—
153	C₄²×C₅	C₂×D₄	1	2	yes	—
154	C₄²×C₅	C₂⁴	1	2	yes	—
155	C₄²×C₅	C₂⁴	1	2	yes	—
156	C₂³×Q₈	—	2	1	no	—
157	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
158	#533	—	2	4	no	—
159	#533	C₂²×C₅	1	8	yes	—
160	C₂×C₄⋊Q₈	—	2	1	no	—
161	C₂×C₄⋊Q₈	—	2	1	no	—
162	C₂×C₄⋊Q₈	—	2	4	no	—
163	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
165	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
167	C₂×C₄⋊Q₈	C₂²×C₅	1	8	yes	—
168	C₂×#125	C₂²×C₅	1	2	yes	—
169	C₂×C₂²⋊Q₈	—	2	1	no	—
170	C₂×C₂²⋊Q₈	—	2	1	no	—
171	C₂×C₄×Q₈	—	2	1	no	—
172	C₂×C₄×Q₈	—	2	1	no	—
173	C₂×#117	C₂²×C₅	1	2	yes	—
174	C₂²×C₄⋊C₄	—	2	1	no	—
175	C₂²×C₄⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
177	#501	C₂²×C₅	1	32	yes	complemented
178	#500	C₂²×C₅	1	16	yes	complemented
179	#498	C₂²×C₅	1	16	yes	complemented
180	#428	C₂²×C₅	1	32	yes	—
181	C₂×#107	C₂²×C₅	1	8	yes	—
182	C₂×#106	C₂²×C₅	1	8	yes	—
183	C₄×M₁₆	C₂²×C₅	1	8	yes	—
184	C₂×#97	C₂²×C₅	1	2	yes	—
185	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
186	C₂³×C₅	—	2	2	no	—
187	C₂³×C₅	—	2	2	no	—
188	C₂³×C₅	C₄⋊Q₈	1	4	yes	—
189	C₂³×C₅	C₂²×D₄	1	2	yes	—
190	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
191	C₅×Q₈	—	4	16	no	—
192	C₅×Q₈	—	4	8	no	—
193	C₅×Q₈	—	4	16	no	—
194	C₅×Q₈	—	4	8	no	—
195	C₂×C₄×C₅	—	2	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	8	no	—
198	C₂×C₄×C₅	—	2	8	no	—
199	C₂×C₄×C₅	—	2	4	no	—
200	C₂×C₄×C₅	—	2	4	no	—
201	C₂×C₄×C₅	—	2	8	no	—
202	C₂×C₄×C₅	—	4	16	no	—
203	C₂×C₄×C₅	—	4	8	no	—
204	C₂×C₄×C₅	—	4	4	no	—
205	C₂×C₄×C₅	—	4	4	no	—
206	C₂×C₄×C₅	C₄⋊Q₈	1	8	yes	—
207	C₂×C₄×C₅	C₄⋊Q₈	1	4	yes	—
208	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	—
209	C₂×C₄×C₅	#137	1	4	yes	—
210	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
211	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
212	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
213	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₅	C₂²×Q₈	1	4	yes	—
217	C₂×C₄×C₅	C₂²×Q₈	1	8	yes	—
218	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
219	C₅×C₈	C₂²×Q₈	1	16	yes	complemented
220	C₂²×Q₈	—	2	1	no	—
221	C₂²×Q₈	—	2	1	no	—
222	C₂²×Q₈	—	2	2	no	—
223	C₂²×Q₈	—	2	8	no	—
224	C₂²×Q₈	—	2	2	no	—
225	C₂²×Q₈	—	4	8	no	—
226	C₂³×C₄	—	2	2	no	—
227	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
228	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
229	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
230	C₂×M₁₆	C₅×Q₈	1	16	yes	complemented
231	C₂×M₁₆	C₂³×C₅	1	8	yes	—
232	C₂²×C₈	C₂³×C₅	1	4	yes	—
233	C₄⋊Q₈	—	2	8	no	—
234	C₄⋊Q₈	—	2	8	no	—
235	C₄⋊Q₈	—	2	4	no	—
236	C₄⋊Q₈	—	2	4	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	2	2	no	—
239	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
240	C₄⋊Q₈	C₂³×C₅	1	8	yes	—
241	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
242	C₄⋊Q₈	C₂³×C₅	1	4	yes	—
243	#125	—	2	4	no	—
244	#125	C₂³×C₅	1	8	yes	—
245	C₂²⋊Q₈	—	2	8	no	—
246	C₂²⋊Q₈	—	2	8	no	—
247	C₄×Q₈	—	2	8	no	—
248	C₄×Q₈	—	2	8	no	—
249	#117	—	2	4	no	—
250	#117	C₂³×C₅	1	8	yes	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	8	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
261	C₂×C₄⋊C₄	C₂³×C₅	1	8	yes	—
262	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
264	C₂×C₂²⋊C₄	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
267	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
268	C₂×C₄²	C₅×D₄	1	4	yes	—
269	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
270	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₅	1	4	yes	—
272	#107	C₂³×C₅	1	32	yes	—
273	#106	C₂³×C₅	1	32	yes	—
274	#97	C₂³×C₅	1	8	yes	—
275	C₄×C₈	C₂³×C₅	1	8	yes	—
276	C₂²×C₅	—	2	8	no	—
277	C₂²×C₅	—	2	2	no	—
278	C₂²×C₅	—	2	2	no	—
279	C₂²×C₅	C₂×C₄⋊Q₈	1	4	yes	—
280	C₂²×C₅	C₂×C₄⋊Q₈	1	2	yes	—
281	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
282	C₂²×C₅	C₂×#137	1	2	yes	—
283	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
284	C₄×C₅	—	2	2	no	—
285	C₄×C₅	—	2	2	no	—
286	C₄×C₅	—	4	8	no	—
287	C₄×C₅	—	4	4	no	—
288	C₄×C₅	—	4	4	no	—
289	C₄×C₅	C₂×C₄⋊Q₈	1	4	yes	—
290	C₄×C₅	C₂×C₄⋊Q₈	1	2	yes	—
291	C₄×C₅	C₂×AGL(1,ℤ/8)	1	4	yes	—
292	C₄×C₅	C₂×#137	1	4	yes	—
293	C₄×C₅	C₂³×Q₈	1	2	yes	—
294	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×Q₈	—	2	4	no	—
296	C₂×Q₈	—	2	4	no	—
297	C₂×Q₈	—	2	8	no	—
298	C₂×Q₈	—	2	8	no	—
299	C₂×Q₈	—	4	8	no	—
300	C₂×Q₈	—	4	32	no	—
301	C₂×Q₈	—	4	8	no	—
302	C₂×Q₈	—	4	4	no	—
303	C₂×Q₈	—	4	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	8	no	—
309	C₂²×C₄	—	2	4	no	—
310	C₂²×C₄	—	4	8	no	—
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
317	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₅×Q₈	1	8	yes	—
320	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
321	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
322	M₁₆	C₂×C₅×Q₈	1	32	yes	complemented
323	C₂×C₈	C₂×C₅×Q₈	1	16	yes	complemented
324	C₂×C₈	C₂⁴×C₅	1	8	yes	—
325	C₄⋊C₄	—	2	8	no	—
326	C₄⋊C₄	—	2	8	no	—
327	C₄⋊C₄	—	2	8	no	—
328	C₄⋊C₄	—	2	4	no	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄⋊C₄	—	2	4	no	—
332	C₄⋊C₄	—	2	4	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
336	C₄⋊C₄	C₂⁴×C₅	1	8	yes	—
337	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
338	C₂²⋊C₄	—	2	8	no	—
339	C₄²	—	2	8	no	—
340	C₄²	C₂×C₅×D₄	1	4	yes	—
341	C₄²	C₂×C₅×D₄	1	4	yes	—
342	C₄²	C₂×C₅×D₄	1	2	yes	—
343	C₄²	C₂×C₅×D₄	1	2	yes	—
344	C₄²	C₂⁴×C₅	1	2	yes	—
345	C₄²	C₂⁴×C₅	1	2	yes	—
346	C₂×C₅	—	2	4	no	—
347	C₂×C₅	#3165	1	4	yes	direct product factor
348	C₂×C₅	C₂²×C₄⋊Q₈	1	1	yes	characteristic
349	C₂×C₅	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
350	C₂×C₅	C₂²×#137	1	1	yes	characteristic
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	C₅×C₄⋊Q₈	1	4	yes	—
354	C₂³	C₂²×C₅×D₄	1	2	yes	—
355	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
356	Q₈	—	4	16	no	—
357	Q₈	—	4	16	no	—
358	Q₈	—	4	8	no	—
359	Q₈	—	4	8	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	8	no	—
363	C₂×C₄	—	2	8	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	8	no	—
367	C₂×C₄	—	4	16	no	—
368	C₂×C₄	—	4	8	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	C₅×C₄⋊Q₈	1	8	yes	—
372	C₂×C₄	C₅×C₄⋊Q₈	1	4	yes	—
373	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	—
374	C₂×C₄	C₅×#137	1	4	yes	—
375	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
376	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
377	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
378	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
379	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
380	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
381	C₂×C₄	C₂²×C₅×Q₈	1	4	yes	—
382	C₂×C₄	C₂²×C₅×Q₈	1	8	yes	—
383	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
384	C₈	C₂²×C₅×Q₈	1	16	yes	complemented
385	C₅	C₂×#3165	1	1	yes	characteristic, direct product factor, Sylow
386	C₂²	—	2	8	no	—
387	C₂²	—	2	2	no	—
388	C₂²	—	2	2	no	—
389	C₂²	C₂×C₅×C₄⋊Q₈	1	4	yes	—
390	C₂²	C₂×C₅×C₄⋊Q₈	1	2	yes	—
391	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
392	C₂²	C₂×C₅×#137	1	2	yes	—
393	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	8	no	—
397	C₄	—	4	4	no	—
398	C₄	—	4	4	no	—
399	C₄	C₂×C₅×C₄⋊Q₈	1	4	yes	—
400	C₄	C₂×C₅×C₄⋊Q₈	1	2	yes	—
401	C₄	C₂×C₅×AGL(1,ℤ/8)	1	4	yes	—
402	C₄	C₂×C₅×#137	1	4	yes	—
403	C₄	C₂³×C₅×Q₈	1	2	yes	—
404	C₂	—	2	4	no	—
405	C₂	C₅×#3165	1	4	yes	direct product factor
406	C₂	C₂²×C₅×C₄⋊Q₈	1	1	yes	characteristic
407	C₂	C₂²×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₂	C₂²×C₅×#137	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂⁴×C₅	C₂×D₄
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
3. C₅×#3165	C₂	direct (N × H)
4. C₂×C₅×#501	C₂	semidirect
5. C₂×C₅×#500	C₂	semidirect
6. C₂×C₅×#498	C₂	semidirect
30. C₅×#501	C₂²	semidirect
31. C₅×#500	C₂²	semidirect
32. C₅×#498	C₂²	semidirect
39. C₂×#3165	C₅	direct (N × H)
50. C₂×C₅×M₁₆	Q₈	semidirect
98. #3165	C₂×C₅	direct (N × H)
99. C₂×#501	C₂×C₅	semidirect
100. C₂×#500	C₂×C₅	semidirect
101. C₂×#498	C₂×C₅	semidirect
132. C₅×M₁₆	C₂×Q₈	semidirect
133. C₂×C₅×C₈	C₂×Q₈	semidirect
177. #501	C₂²×C₅	semidirect
178. #500	C₂²×C₅	semidirect
179. #498	C₂²×C₅	semidirect
219. C₅×C₈	C₂²×Q₈	semidirect
230. C₂×M₁₆	C₅×Q₈	semidirect
322. M₁₆	C₂×C₅×Q₈	semidirect
323. C₂×C₈	C₂×C₅×Q₈	semidirect
347. C₂×C₅	#3165	direct (N × H)
384. C₈	C₂²×C₅×Q₈	semidirect
385. C₅	C₂×#3165	direct (N × H)
405. C₂	C₅×#3165	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×C₄⋊Q₈	2
C₅×#3165	2
C₂×C₅×#501	2
C₂×C₅×#500	2
C₂×C₅×#498	2
C₂×C₅×#428	2
C₂×C₄×C₅×M₁₆	2
C₂×#3165	5

Subgroups — C2×C5×#3165 #11983381

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3165 #11983381