Subgroups — C₂×C₅×#3156 #11983362

Order 1280.

3150 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₂²×C₅×#135	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#536	C₂	1	2	yes	maximal, complemented
5	C₅×#3156	C₂	1	16	yes	maximal, direct product factor
6	C₂×C₅×#497	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#495	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#494	C₂	1	2	yes	maximal, complemented
9	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×#41	C₂²	1	2	yes	—
11	C₂³×C₅×Q₈	C₂²	1	2	yes	—
12	C₂×C₅×#137	—	2	16	no	—
13	C₂×C₅×#137	C₂²	1	16	yes	complemented
14	C₂×C₅×#135	—	2	8	no	—
15	C₂×C₅×#135	C₂²	1	8	yes	—
16	C₂²×C₅×Q₁₆	—	2	8	no	—
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
19	C₂²×C₅×Q₁₆	C₂²	1	4	yes	—
20	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
21	C₂²×C₅×Q₁₆	C₂²	1	8	yes	complemented
22	C₂²×C₅×SD₁₆	C₂²	1	4	yes	—
23	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
26	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
27	C₅×#536	—	2	8	no	—
28	C₅×#536	C₂²	1	16	yes	complemented
29	C₂×C₅×C₄⋊Q₈	C₂²	1	4	yes	—
30	C₂×C₅×#124	C₂²	1	4	yes	—
31	C₂×C₅×#123	—	2	4	no	—
32	C₂×C₅×C₂²⋊Q₈	—	2	4	no	—
33	C₂×C₅×#117	C₂²	1	1	yes	characteristic
34	C₅×#497	C₂²	1	32	yes	complemented
35	C₅×#495	C₂²	1	16	yes	complemented
36	C₅×#494	C₂²	1	16	yes	complemented
37	C₅×#405	C₂²	1	8	yes	complemented
38	C₂×C₅×#97	C₂²	1	2	yes	—
39	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
40	C₂×#3156	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	C₂×C₅×#41	—	2	4	no	—
42	C₂×C₅×#41	—	2	8	no	—
43	C₂×C₅×#41	—	2	8	no	—
44	C₂×C₅×#41	C₂³	1	8	yes	—
45	C₂²×C₅×Q₈	—	2	2	no	—
46	C₂²×C₅×Q₈	—	2	4	no	—
47	C₂²×C₅×Q₈	—	2	8	no	—
48	C₂²×C₅×Q₈	—	2	8	no	—
49	C₂²×C₅×Q₈	C₂³	1	4	yes	—
50	C₂²×C₅×Q₈	C₂³	1	2	yes	—
51	C₂²×C₅×Q₈	C₂³	1	8	yes	—
52	C₂²×C₅×D₄	—	2	2	no	—
53	C₂²×C₅×D₄	C₂³	1	2	yes	—
54	C₂³×C₄×C₅	—	2	2	no	—
55	C₂³×C₄×C₅	—	2	2	no	—
56	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₅×#137	—	2	64	no	—
58	C₅×#135	—	2	32	no	—
59	C₂×C₅×Q₁₆	—	2	8	no	—
60	C₂×C₅×Q₁₆	—	2	8	no	—
61	C₂×C₅×Q₁₆	—	2	32	no	—
62	C₂×C₅×Q₁₆	—	2	4	no	—
63	C₂×C₅×Q₁₆	—	2	16	no	—
64	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
65	C₂×C₅×Q₁₆	C₂³	1	8	yes	—
66	C₂×C₅×Q₁₆	C₂³	1	16	yes	—
67	C₂×C₅×Q₁₆	C₂³	1	8	yes	—
68	C₂×C₅×SD₁₆	—	2	8	no	—
69	C₂×C₅×SD₁₆	—	2	16	no	—
70	C₂×C₅×SD₁₆	C₂³	1	16	yes	—
71	C₂×C₅×SD₁₆	C₂³	1	8	yes	—
72	C₂×C₅×D₈	—	2	4	no	—
73	C₂×C₅×D₈	C₂³	1	4	yes	—
74	C₂×C₅×M₁₆	D₄	1	8	yes	—
75	C₂×C₅×M₁₆	C₂³	1	4	yes	—
76	C₂²×C₅×C₈	D₄	1	8	yes	—
77	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₅×C₈	C₂³	1	2	yes	—
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	4	yes	—
81	C₅×C₄⋊Q₈	—	2	8	no	—
82	C₅×C₄⋊Q₈	C₂³	1	16	yes	—
83	C₅×#124	—	2	8	no	—
84	C₅×#124	C₂³	1	16	yes	—
85	C₅×#123	—	2	32	no	—
86	C₅×C₂²⋊Q₈	—	2	32	no	—
87	C₅×#117	D₄	1	4	yes	—
88	C₅×#117	C₂³	1	4	yes	—
89	C₂×C₅×C₄⋊C₄	—	2	8	no	—
90	C₂×C₅×C₄⋊C₄	D₄	1	2	yes	—
91	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
92	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
93	C₂×C₄²×C₅	C₂³	1	2	yes	—
94	C₅×#97	C₂³	1	8	yes	—
95	C₄×C₅×C₈	C₂³	1	8	yes	—
96	C₂²×#137	C₂×C₅	1	2	yes	complemented
97	C₂²×#135	C₂×C₅	1	1	yes	characteristic
98	C₂³×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×#536	C₂×C₅	1	2	yes	complemented
100	#3156	C₂×C₅	1	16	yes	direct product factor
101	C₂×#497	C₂×C₅	1	4	yes	complemented
102	C₂×#495	C₂×C₅	1	2	yes	complemented
103	C₂×#494	C₂×C₅	1	2	yes	complemented
104	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	2	2	no	—
106	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
107	C₅×#41	—	2	16	no	—
108	C₅×#41	—	2	16	no	—
109	C₅×#41	—	4	16	no	—
110	C₂×C₅×Q₈	—	2	8	no	—
111	C₂×C₅×Q₈	—	2	4	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	—	2	8	no	—
114	C₂×C₅×Q₈	—	2	4	no	—
115	C₂×C₅×Q₈	—	2	8	no	—
116	C₂×C₅×Q₈	—	2	16	no	—
117	C₂×C₅×Q₈	—	2	4	no	—
118	C₂×C₅×Q₈	—	2	16	no	—
119	C₂×C₅×Q₈	—	4	8	no	—
120	C₂×C₅×Q₈	—	4	16	no	—
121	C₂×C₅×Q₈	C₂⁴	1	8	yes	—
122	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
123	C₂×C₅×D₄	—	2	8	no	—
124	C₂×C₅×D₄	—	2	4	no	—
125	C₂×C₅×D₄	—	2	4	no	—
126	C₂×C₅×D₄	—	2	2	no	—
127	C₂×C₅×D₄	—	4	8	no	—
128	C₂×C₅×D₄	C₂⁴	1	4	yes	—
129	C₂²×C₄×C₅	—	2	8	no	—
130	C₂²×C₄×C₅	—	2	4	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	2	8	no	—
133	C₂²×C₄×C₅	—	4	8	no	—
134	C₂²×C₄×C₅	—	4	8	no	—
135	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₅	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₅×Q₁₆	—	2	16	no	—
143	C₅×Q₁₆	—	2	16	no	—
144	C₅×Q₁₆	—	2	8	no	—
145	C₅×Q₁₆	—	2	32	no	—
146	C₅×SD₁₆	—	2	16	no	—
147	C₅×SD₁₆	—	2	32	no	—
148	C₅×D₈	—	2	8	no	—
149	C₅×M₁₆	C₂×D₄	1	16	yes	—
150	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
151	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
152	C₂×C₅×C₈	C₂×D₄	1	16	yes	—
153	C₂×C₅×C₈	C₂×D₄	1	8	yes	—
154	C₂×C₅×C₈	C₂⁴	1	2	yes	—
155	C₂×C₅×C₈	C₂⁴	1	2	yes	—
156	C₂×C₅×C₈	C₂⁴	1	4	yes	—
157	C₅×C₄⋊C₄	—	2	32	no	—
158	C₅×C₄⋊C₄	C₂×D₄	1	8	yes	—
159	C₅×C₂²⋊C₄	—	2	32	no	—
160	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
161	C₄²×C₅	C₂×D₄	1	4	yes	—
162	C₄²×C₅	C₂⁴	1	4	yes	—
163	C₂²×#41	C₂²×C₅	1	2	yes	—
164	C₂³×Q₈	C₂²×C₅	1	2	yes	—
165	C₂×#137	—	2	16	no	—
166	C₂×#137	C₂²×C₅	1	16	yes	complemented
167	C₂×#135	—	2	8	no	—
168	C₂×#135	C₂²×C₅	1	8	yes	—
169	C₂²×Q₁₆	—	2	8	no	—
170	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
172	C₂²×Q₁₆	C₂²×C₅	1	4	yes	—
173	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
174	C₂²×Q₁₆	C₂²×C₅	1	8	yes	complemented
175	C₂²×SD₁₆	C₂²×C₅	1	4	yes	—
176	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
177	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
178	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
179	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
180	#536	—	2	8	no	—
181	#536	C₂²×C₅	1	16	yes	complemented
182	C₂×C₄⋊Q₈	C₂²×C₅	1	4	yes	—
183	C₂×#124	C₂²×C₅	1	4	yes	—
184	C₂×#123	—	2	4	no	—
185	C₂×C₂²⋊Q₈	—	2	4	no	—
186	C₂×#117	C₂²×C₅	1	1	yes	characteristic
187	#497	C₂²×C₅	1	32	yes	complemented
188	#495	C₂²×C₅	1	16	yes	complemented
189	#494	C₂²×C₅	1	16	yes	complemented
190	#405	C₂²×C₅	1	8	yes	complemented
191	C₂×#97	C₂²×C₅	1	2	yes	—
192	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
193	C₂³×C₅	—	2	4	no	—
194	C₂³×C₅	—	2	4	no	—
195	C₂³×C₅	—	4	4	no	—
196	C₂³×C₅	—	4	8	no	—
197	C₂³×C₅	#127	1	4	yes	—
198	C₂³×C₅	C₂²×D₄	1	2	yes	—
199	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
200	C₅×Q₈	—	2	8	no	—
201	C₅×Q₈	—	2	4	no	—
202	C₅×Q₈	—	2	8	no	—
203	C₅×Q₈	—	2	4	no	—
204	C₅×Q₈	—	4	16	no	—
205	C₅×Q₈	—	4	8	no	—
206	C₅×Q₈	—	4	4	no	—
207	C₅×D₄	—	2	4	no	—
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	4	16	no	—
210	C₅×D₄	—	4	4	no	—
211	C₂×C₄×C₅	—	2	8	no	—
212	C₂×C₄×C₅	—	2	8	no	—
213	C₂×C₄×C₅	—	2	4	no	—
214	C₂×C₄×C₅	—	4	4	no	—
215	C₂×C₄×C₅	—	4	16	no	—
216	C₂×C₄×C₅	—	4	8	no	—
217	C₂×C₄×C₅	—	4	16	no	—
218	C₂×C₄×C₅	#127	1	4	yes	—
219	C₂×C₄×C₅	#127	1	8	yes	—
220	C₂×C₄×C₅	C₂²×D₄	1	8	yes	—
221	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
228	C₅×C₈	C₂²×D₄	1	4	yes	—
229	C₅×C₈	C₂²×D₄	1	4	yes	—
230	C₅×C₈	C₂²×D₄	1	8	yes	—
231	C₂×#41	—	2	4	no	—
232	C₂×#41	—	2	8	no	—
233	C₂×#41	—	2	8	no	—
234	C₂×#41	C₂³×C₅	1	8	yes	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	4	no	—
237	C₂²×Q₈	—	2	8	no	—
238	C₂²×Q₈	—	2	8	no	—
239	C₂²×Q₈	C₂³×C₅	1	4	yes	—
240	C₂²×Q₈	C₂³×C₅	1	2	yes	—
241	C₂²×Q₈	C₂³×C₅	1	8	yes	—
242	C₂²×D₄	—	2	2	no	—
243	C₂²×D₄	C₂³×C₅	1	2	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	—	2	2	no	—
246	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
247	#137	—	2	64	no	—
248	#135	—	2	32	no	—
249	C₂×Q₁₆	—	2	8	no	—
250	C₂×Q₁₆	—	2	8	no	—
251	C₂×Q₁₆	—	2	32	no	—
252	C₂×Q₁₆	—	2	4	no	—
253	C₂×Q₁₆	—	2	16	no	—
254	C₂×Q₁₆	C₂³×C₅	1	8	yes	—
255	C₂×Q₁₆	C₂³×C₅	1	8	yes	—
256	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
257	C₂×Q₁₆	C₂³×C₅	1	16	yes	—
258	C₂×SD₁₆	—	2	8	no	—
259	C₂×SD₁₆	—	2	16	no	—
260	C₂×SD₁₆	C₂³×C₅	1	8	yes	—
261	C₂×SD₁₆	C₂³×C₅	1	16	yes	—
262	C₂×D₈	—	2	4	no	—
263	C₂×D₈	C₂³×C₅	1	4	yes	—
264	C₂×M₁₆	C₅×D₄	1	8	yes	—
265	C₂×M₁₆	C₂³×C₅	1	4	yes	—
266	C₂²×C₈	C₅×D₄	1	8	yes	—
267	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₅	1	4	yes	—
270	C₂²×C₈	C₂³×C₅	1	2	yes	—
271	C₄⋊Q₈	—	2	8	no	—
272	C₄⋊Q₈	C₂³×C₅	1	16	yes	—
273	#124	—	2	8	no	—
274	#124	C₂³×C₅	1	16	yes	—
275	#123	—	2	32	no	—
276	C₂²⋊Q₈	—	2	32	no	—
277	#117	C₅×D₄	1	4	yes	—
278	#117	C₂³×C₅	1	4	yes	—
279	C₂×C₄⋊C₄	—	2	8	no	—
280	C₂×C₄⋊C₄	C₅×D₄	1	2	yes	—
281	C₂×C₂²⋊C₄	—	2	8	no	—
282	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
283	C₂×C₄²	C₂³×C₅	1	2	yes	—
284	#97	C₂³×C₅	1	8	yes	—
285	C₄×C₈	C₂³×C₅	1	8	yes	—
286	C₂²×C₅	—	2	8	no	—
287	C₂²×C₅	—	2	4	no	—
288	C₂²×C₅	—	4	4	no	—
289	C₂²×C₅	—	4	8	no	—
290	C₂²×C₅	—	8	8	no	—
291	C₂²×C₅	C₂×#127	1	4	yes	—
292	C₂²×C₅	C₂×#127	1	2	yes	—
293	C₂²×C₅	#578	1	4	yes	—
294	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
295	C₄×C₅	—	2	8	no	—
296	C₄×C₅	—	4	4	no	—
297	C₄×C₅	—	4	8	no	—
298	C₄×C₅	C₂×#127	1	4	yes	—
299	C₄×C₅	C₂×#127	1	2	yes	—
300	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
301	C₄×C₅	C₂³×D₄	1	1	yes	characteristic
302	C₂⁴	—	2	2	no	—
303	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
304	#41	—	2	16	no	—
305	#41	—	2	16	no	—
306	#41	—	4	16	no	—
307	C₂×Q₈	—	2	8	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	8	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	8	no	—
313	C₂×Q₈	—	2	16	no	—
314	C₂×Q₈	—	2	4	no	—
315	C₂×Q₈	—	2	16	no	—
316	C₂×Q₈	—	4	8	no	—
317	C₂×Q₈	—	4	16	no	—
318	C₂×Q₈	C₂⁴×C₅	1	8	yes	—
319	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	4	no	—
322	C₂×D₄	—	2	4	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	4	8	no	—
325	C₂×D₄	C₂⁴×C₅	1	4	yes	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	8	no	—
329	C₂²×C₄	—	2	8	no	—
330	C₂²×C₄	—	4	8	no	—
331	C₂²×C₄	—	4	8	no	—
332	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
333	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
335	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
336	C₂²×C₄	C₂×C₅×D₄	1	4	yes	—
337	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
338	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
339	Q₁₆	—	2	16	no	—
340	Q₁₆	—	2	16	no	—
341	Q₁₆	—	2	8	no	—
342	Q₁₆	—	2	32	no	—
343	SD₁₆	—	2	16	no	—
344	SD₁₆	—	2	32	no	—
345	D₈	—	2	8	no	—
346	M₁₆	C₂×C₅×D₄	1	16	yes	—
347	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
348	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
349	C₂×C₈	C₂×C₅×D₄	1	16	yes	—
350	C₂×C₈	C₂×C₅×D₄	1	8	yes	—
351	C₂×C₈	C₂⁴×C₅	1	2	yes	—
352	C₂×C₈	C₂⁴×C₅	1	4	yes	—
353	C₂×C₈	C₂⁴×C₅	1	2	yes	—
354	C₄⋊C₄	—	2	32	no	—
355	C₄⋊C₄	C₂×C₅×D₄	1	8	yes	—
356	C₂²⋊C₄	—	2	32	no	—
357	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
358	C₄²	C₂×C₅×D₄	1	4	yes	—
359	C₄²	C₂⁴×C₅	1	4	yes	—
360	C₂×C₅	—	2	4	no	—
361	C₂×C₅	—	8	4	no	—
362	C₂×C₅	#3156	1	4	yes	direct product factor
363	C₂×C₅	C₂²×#127	1	1	yes	characteristic
364	C₂×C₅	C₂×#578	1	2	yes	—
365	C₂³	—	2	4	no	—
366	C₂³	—	2	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	8	no	—
369	C₂³	C₅×#127	1	4	yes	—
370	C₂³	C₂²×C₅×D₄	1	2	yes	—
371	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
372	Q₈	—	2	8	no	—
373	Q₈	—	2	4	no	—
374	Q₈	—	2	8	no	—
375	Q₈	—	2	4	no	—
376	Q₈	—	4	16	no	—
377	Q₈	—	4	8	no	—
378	Q₈	—	4	4	no	—
379	D₄	—	2	4	no	—
380	D₄	—	2	4	no	—
381	D₄	—	4	16	no	—
382	D₄	—	4	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	16	no	—
388	C₂×C₄	—	4	8	no	—
389	C₂×C₄	—	4	16	no	—
390	C₂×C₄	C₅×#127	1	4	yes	—
391	C₂×C₄	C₅×#127	1	8	yes	—
392	C₂×C₄	C₂²×C₅×D₄	1	8	yes	—
393	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
395	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
396	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
397	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
398	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
399	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
400	C₈	C₂²×C₅×D₄	1	4	yes	—
401	C₈	C₂²×C₅×D₄	1	4	yes	—
402	C₈	C₂²×C₅×D₄	1	8	yes	—
403	C₅	C₂×#3156	1	1	yes	characteristic, direct product factor, Sylow
404	C₂²	—	2	8	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	4	4	no	—
407	C₂²	—	4	8	no	—
408	C₂²	—	8	8	no	—
409	C₂²	C₂×C₅×#127	1	4	yes	—
410	C₂²	C₂×C₅×#127	1	2	yes	—
411	C₂²	C₅×#578	1	4	yes	—
412	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
413	C₄	—	2	8	no	—
414	C₄	—	4	4	no	—
415	C₄	—	4	8	no	—
416	C₄	C₂×C₅×#127	1	4	yes	—
417	C₄	C₂×C₅×#127	1	2	yes	—
418	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
419	C₄	C₂³×C₅×D₄	1	1	yes	characteristic
420	C₂	—	2	4	no	—
421	C₂	—	8	4	no	—
422	C₂	C₅×#3156	1	4	yes	direct product factor
423	C₂	C₂²×C₅×#127	1	1	yes	characteristic
424	C₂	C₂×C₅×#578	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂²×C₅×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#137	C₂	semidirect
3. C₂³×C₅×Q₁₆	C₂	semidirect
4. C₂×C₅×#536	C₂	semidirect
5. C₅×#3156	C₂	direct (N × H)
6. C₂×C₅×#497	C₂	semidirect
7. C₂×C₅×#495	C₂	semidirect
8. C₂×C₅×#494	C₂	semidirect
9. C₂×C₅×#405	C₂	semidirect
13. C₂×C₅×#137	C₂²	semidirect
21. C₂²×C₅×Q₁₆	C₂²	semidirect
28. C₅×#536	C₂²	semidirect
34. C₅×#497	C₂²	semidirect
35. C₅×#495	C₂²	semidirect
36. C₅×#494	C₂²	semidirect
37. C₅×#405	C₂²	semidirect
40. C₂×#3156	C₅	direct (N × H)
96. C₂²×#137	C₂×C₅	semidirect
98. C₂³×Q₁₆	C₂×C₅	semidirect
99. C₂×#536	C₂×C₅	semidirect
100. #3156	C₂×C₅	direct (N × H)
101. C₂×#497	C₂×C₅	semidirect
102. C₂×#495	C₂×C₅	semidirect
103. C₂×#494	C₂×C₅	semidirect
104. C₂×#405	C₂×C₅	semidirect
166. C₂×#137	C₂²×C₅	semidirect
174. C₂²×Q₁₆	C₂²×C₅	semidirect
181. #536	C₂²×C₅	semidirect
187. #497	C₂²×C₅	semidirect
188. #495	C₂²×C₅	semidirect
189. #494	C₂²×C₅	semidirect
190. #405	C₂²×C₅	semidirect
362. C₂×C₅	#3156	direct (N × H)
403. C₅	C₂×#3156	direct (N × H)
422. C₂	C₅×#3156	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×#137	2
C₂²×C₅×#135	2
C₂³×C₅×Q₁₆	2
C₂×C₅×#536	2
C₅×#3156	2
C₂×C₅×#497	2
C₂×C₅×#495	2
C₂×C₅×#494	2
C₂×C₅×#405	2
C₂×#3156	5

Subgroups — C2×C5×#3156 #11983362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3156 #11983362