Subgroups — C₂×C₅×#1917 #11943739

Order 1280.

1070 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#97	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₅×#1917	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
6	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
7	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
8	C₂×C₅×#336	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
10	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂²×C₅×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₅×C₄⋊C₈	—	2	4	no	—
19	C₂×C₅×C₄⋊C₈	C₂²	1	4	yes	—
20	C₂×C₅×#97	—	2	4	no	—
21	C₂×C₅×#97	C₂²	1	4	yes	—
22	C₄×C₅×C₄⋊C₄	C₄	1	4	yes	—
23	C₄×C₅×C₄⋊C₄	C₂²	1	4	yes	—
24	C₂×C₅×#95	C₄	1	1	yes	characteristic
25	C₂×C₅×#95	C₄	1	1	yes	characteristic
26	C₅×#336	C₂²	1	4	yes	—
27	C₅×#336	C₂²	1	4	yes	—
28	C₅×#336	C₂²	1	4	yes	—
29	C₅×#336	C₂²	1	4	yes	—
30	C₂×#1917	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
32	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
33	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
36	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
38	C₂²×C₅×C₈	—	2	2	no	—
39	C₂²×C₅×C₈	—	2	2	no	—
40	C₂²×C₅×C₈	—	2	2	no	—
41	C₂²×C₅×C₈	—	2	2	no	—
42	C₂²×C₅×C₈	—	2	2	no	—
43	C₂²×C₅×C₈	—	2	2	no	—
44	C₂²×C₅×C₈	—	2	2	no	—
45	C₂²×C₅×C₈	—	2	2	no	—
46	C₂²×C₅×C₈	—	2	2	no	—
47	C₂²×C₅×C₈	—	2	2	no	—
48	C₂²×C₅×C₈	D₄	1	4	yes	—
49	C₂²×C₅×C₈	Q₈	1	4	yes	—
50	C₂²×C₅×C₈	C₂³	1	2	yes	—
51	C₂²×C₅×C₈	C₂³	1	2	yes	—
52	C₂²×C₅×C₈	C₂³	1	2	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂×C₅×C₄⋊C₄	—	2	4	no	—
55	C₂×C₅×C₄⋊C₄	—	2	4	no	—
56	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×C₄²×C₅	—	2	2	no	—
59	C₂×C₄²×C₅	—	2	2	no	—
60	C₂×C₄²×C₅	—	2	2	no	—
61	C₂×C₄²×C₅	—	2	2	no	—
62	C₂×C₄²×C₅	—	2	2	no	—
63	C₂×C₄²×C₅	—	2	2	no	—
64	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
66	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
67	C₂×C₄²×C₅	C₂³	1	2	yes	—
68	C₂×C₄²×C₅	C₂³	1	2	yes	—
69	C₂×C₄²×C₅	C₂³	1	2	yes	—
70	C₅×C₄⋊C₈	—	2	8	no	—
71	C₅×#97	—	2	8	no	—
72	C₅×#95	C₂×C₄	1	4	yes	—
73	C₅×#95	C₂×C₄	1	4	yes	—
74	C₂²×C₄⋊C₈	C₂×C₅	1	1	yes	characteristic
75	C₂²×#97	C₂×C₅	1	1	yes	characteristic
76	C₂×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
77	#1917	C₂×C₅	1	8	yes	direct product factor
78	C₂×#336	C₂×C₅	1	1	yes	characteristic
79	C₂×#336	C₂×C₅	1	1	yes	characteristic
80	C₂×#336	C₂×C₅	1	1	yes	characteristic
81	C₂×#336	C₂×C₅	1	1	yes	characteristic
82	C₂⁴×C₅	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₅	—	2	2	no	—
84	C₂²×C₄×C₅	—	2	2	no	—
85	C₂²×C₄×C₅	—	2	2	no	—
86	C₂²×C₄×C₅	—	2	2	no	—
87	C₂²×C₄×C₅	—	2	2	no	—
88	C₂²×C₄×C₅	—	2	2	no	—
89	C₂²×C₄×C₅	—	2	2	no	—
90	C₂²×C₄×C₅	—	2	2	no	—
91	C₂²×C₄×C₅	—	2	2	no	—
92	C₂²×C₄×C₅	—	2	2	no	—
93	C₂²×C₄×C₅	—	2	2	no	—
94	C₂²×C₄×C₅	—	2	2	no	—
95	C₂²×C₄×C₅	—	2	2	no	—
96	C₂²×C₄×C₅	—	2	2	no	—
97	C₂²×C₄×C₅	—	2	2	no	—
98	C₂²×C₄×C₅	—	2	2	no	—
99	C₂²×C₄×C₅	M₁₆	1	4	yes	—
100	C₂²×C₄×C₅	M₁₆	1	4	yes	—
101	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
102	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₅	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₅	C₂×Q₈	1	2	yes	—
110	C₂²×C₄×C₅	#41	1	2	yes	—
111	C₂²×C₄×C₅	#41	1	2	yes	—
112	C₂²×C₄×C₅	#41	1	2	yes	—
113	C₂²×C₄×C₅	#41	1	2	yes	—
114	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×C₅×C₈	—	2	8	no	—
116	C₂×C₅×C₈	—	2	8	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	—	2	2	no	—
125	C₂×C₅×C₈	—	2	2	no	—
126	C₂×C₅×C₈	—	2	2	no	—
127	C₂×C₅×C₈	—	4	4	no	—
128	C₂×C₅×C₈	—	4	4	no	—
129	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
130	C₂×C₅×C₈	C₂×Q₈	1	4	yes	—
131	C₅×C₄⋊C₄	—	2	8	no	—
132	C₅×C₄⋊C₄	—	2	8	no	—
133	C₄²×C₅	—	2	4	no	—
134	C₄²×C₅	—	2	4	no	—
135	C₄²×C₅	—	2	4	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
143	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
144	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
145	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
146	C₂²×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
147	C₂²×C₄⋊C₄	C₄×C₅	1	1	yes	characteristic
148	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
150	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
151	C₂×C₄⋊C₈	—	2	4	no	—
152	C₂×C₄⋊C₈	C₂²×C₅	1	4	yes	—
153	C₂×#97	—	2	4	no	—
154	C₂×#97	C₂²×C₅	1	4	yes	—
155	C₄×C₄⋊C₄	C₄×C₅	1	4	yes	—
156	C₄×C₄⋊C₄	C₂²×C₅	1	4	yes	—
157	C₂×#95	C₄×C₅	1	1	yes	characteristic
158	C₂×#95	C₄×C₅	1	1	yes	characteristic
159	#336	C₂²×C₅	1	4	yes	—
160	#336	C₂²×C₅	1	4	yes	—
161	#336	C₂²×C₅	1	4	yes	—
162	#336	C₂²×C₅	1	4	yes	—
163	C₂³×C₅	#117	1	2	yes	—
164	C₂³×C₅	C₄×D₄	1	2	yes	—
165	C₂³×C₅	C₄×Q₈	1	2	yes	—
166	C₂³×C₅	C₂×M₁₆	1	2	yes	—
167	C₂³×C₅	C₂×M₁₆	1	2	yes	—
168	C₂³×C₅	#131	1	2	yes	—
169	C₂³×C₅	#131	1	2	yes	—
170	C₂³×C₅	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	2	no	—
175	C₂×C₄×C₅	—	2	8	no	—
176	C₂×C₄×C₅	—	2	8	no	—
177	C₂×C₄×C₅	—	2	2	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	2	no	—
180	C₂×C₄×C₅	—	2	2	no	—
181	C₂×C₄×C₅	—	2	2	no	—
182	C₂×C₄×C₅	—	2	2	no	—
183	C₂×C₄×C₅	—	2	2	no	—
184	C₂×C₄×C₅	—	2	2	no	—
185	C₂×C₄×C₅	—	2	2	no	—
186	C₂×C₄×C₅	—	2	2	no	—
187	C₂×C₄×C₅	—	2	2	no	—
188	C₂×C₄×C₅	—	2	2	no	—
189	C₂×C₄×C₅	—	4	4	no	—
190	C₂×C₄×C₅	—	4	4	no	—
191	C₂×C₄×C₅	—	4	4	no	—
192	C₂×C₄×C₅	—	4	4	no	—
193	C₂×C₄×C₅	#117	1	2	yes	—
194	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
195	C₂×C₄×C₅	C₄×Q₈	1	2	yes	—
196	C₂×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
197	C₂×C₄×C₅	#123	1	4	yes	—
198	C₂×C₄×C₅	#125	1	4	yes	—
199	C₂×C₄×C₅	#126	1	4	yes	—
200	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
201	C₂×C₄×C₅	C₂×M₁₆	1	4	yes	—
202	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
206	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
207	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
208	C₅×C₈	—	2	4	no	—
209	C₅×C₈	—	2	4	no	—
210	C₅×C₈	—	4	2	no	—
211	C₅×C₈	—	4	2	no	—
212	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
213	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
214	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
215	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
216	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
217	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
218	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₈	—	2	2	no	—
220	C₂²×C₈	—	2	2	no	—
221	C₂²×C₈	—	2	2	no	—
222	C₂²×C₈	—	2	2	no	—
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	2	2	no	—
226	C₂²×C₈	—	2	2	no	—
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	2	2	no	—
229	C₂²×C₈	C₅×D₄	1	4	yes	—
230	C₂²×C₈	C₅×Q₈	1	4	yes	—
231	C₂²×C₈	C₂³×C₅	1	2	yes	—
232	C₂²×C₈	C₂³×C₅	1	2	yes	—
233	C₂²×C₈	C₂³×C₅	1	2	yes	—
234	C₂²×C₈	C₂³×C₅	1	2	yes	—
235	C₂×C₄⋊C₄	—	2	4	no	—
236	C₂×C₄⋊C₄	—	2	4	no	—
237	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
238	C₂×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	2	2	no	—
242	C₂×C₄²	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
246	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
247	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
248	C₂×C₄²	C₂³×C₅	1	2	yes	—
249	C₂×C₄²	C₂³×C₅	1	2	yes	—
250	C₂×C₄²	C₂³×C₅	1	2	yes	—
251	C₄⋊C₈	—	2	8	no	—
252	#97	—	2	8	no	—
253	#95	C₂×C₄×C₅	1	4	yes	—
254	#95	C₂×C₄×C₅	1	4	yes	—
255	C₂²×C₅	#387	1	4	yes	—
256	C₂²×C₅	#432	1	4	yes	—
257	C₂²×C₅	#433	1	4	yes	—
258	C₂²×C₅	#435	1	4	yes	—
259	C₂²×C₅	#436	1	4	yes	—
260	C₂²×C₅	#446	1	4	yes	—
261	C₂²×C₅	#446	1	4	yes	—
262	C₂²×C₅	C₂×#117	1	1	yes	characteristic
263	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
264	C₂²×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
265	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
266	C₂²×C₅	C₂²×M₁₆	1	1	yes	characteristic
267	C₂²×C₅	C₂×#131	1	1	yes	characteristic
268	C₂²×C₅	C₂×#131	1	1	yes	characteristic
269	C₄×C₅	—	2	4	no	—
270	C₄×C₅	—	2	4	no	—
271	C₄×C₅	—	4	2	no	—
272	C₄×C₅	—	4	2	no	—
273	C₄×C₅	—	4	2	no	—
274	C₄×C₅	—	4	2	no	—
275	C₄×C₅	#387	1	4	yes	—
276	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
277	C₄×C₅	C₂×#123	1	1	yes	characteristic
278	C₄×C₅	C₂×#125	1	1	yes	characteristic
279	C₄×C₅	C₂×#126	1	1	yes	characteristic
280	C₂⁴	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₅×M₁₆	1	4	yes	—
298	C₂²×C₄	C₅×M₁₆	1	4	yes	—
299	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
301	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
304	C₂²×C₄	C₂²×C₄×C₅	1	2	yes	—
305	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂²×C₄	C₂×C₅×Q₈	1	2	yes	—
308	C₂²×C₄	C₅×#41	1	2	yes	—
309	C₂²×C₄	C₅×#41	1	2	yes	—
310	C₂²×C₄	C₅×#41	1	2	yes	—
311	C₂²×C₄	C₅×#41	1	2	yes	—
312	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
313	C₂×C₈	—	2	8	no	—
314	C₂×C₈	—	2	8	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	—	4	4	no	—
327	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
328	C₂×C₈	C₂×C₅×Q₈	1	4	yes	—
329	C₄⋊C₄	—	2	8	no	—
330	C₄⋊C₄	—	2	8	no	—
331	C₄²	—	2	4	no	—
332	C₄²	—	2	4	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₂×C₅	#1917	1	8	yes	direct product factor
341	C₂×C₅	C₂×#387	1	1	yes	characteristic
342	C₂×C₅	C₂×#432	1	1	yes	characteristic
343	C₂×C₅	C₂×#433	1	1	yes	characteristic
344	C₂×C₅	C₂×#435	1	1	yes	characteristic
345	C₂×C₅	C₂×#436	1	1	yes	characteristic
346	C₂×C₅	C₂×#446	1	1	yes	characteristic
347	C₂×C₅	C₂×#446	1	1	yes	characteristic
348	C₂³	C₅×#117	1	2	yes	—
349	C₂³	C₄×C₅×D₄	1	2	yes	—
350	C₂³	C₄×C₅×Q₈	1	2	yes	—
351	C₂³	C₂×C₅×M₁₆	1	2	yes	—
352	C₂³	C₂×C₅×M₁₆	1	2	yes	—
353	C₂³	C₅×#131	1	2	yes	—
354	C₂³	C₅×#131	1	2	yes	—
355	C₂³	C₂³×C₄×C₅	1	1	yes	characteristic
356	C₂×C₄	—	2	8	no	—
357	C₂×C₄	—	2	8	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	C₅×#117	1	2	yes	—
379	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
380	C₂×C₄	C₄×C₅×Q₈	1	2	yes	—
381	C₂×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
382	C₂×C₄	C₅×#123	1	4	yes	—
383	C₂×C₄	C₅×#125	1	4	yes	—
384	C₂×C₄	C₅×#126	1	4	yes	—
385	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
386	C₂×C₄	C₂×C₅×M₁₆	1	4	yes	—
387	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
390	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
391	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
393	C₈	—	2	4	no	—
394	C₈	—	2	4	no	—
395	C₈	—	4	2	no	—
396	C₈	—	4	2	no	—
397	C₅	C₂×#1917	1	1	yes	characteristic, direct product factor, Sylow
398	C₂²	C₅×#387	1	4	yes	—
399	C₂²	C₅×#432	1	4	yes	—
400	C₂²	C₅×#433	1	4	yes	—
401	C₂²	C₅×#435	1	4	yes	—
402	C₂²	C₅×#436	1	4	yes	—
403	C₂²	C₅×#446	1	4	yes	—
404	C₂²	C₅×#446	1	4	yes	—
405	C₂²	C₂×C₅×#117	1	1	yes	characteristic
406	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
407	C₂²	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
408	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
409	C₂²	C₂²×C₅×M₁₆	1	1	yes	characteristic
410	C₂²	C₂×C₅×#131	1	1	yes	characteristic
411	C₂²	C₂×C₅×#131	1	1	yes	characteristic
412	C₄	—	2	4	no	—
413	C₄	—	2	4	no	—
414	C₄	—	4	2	no	—
415	C₄	—	4	2	no	—
416	C₄	—	4	2	no	—
417	C₄	—	4	2	no	—
418	C₄	C₅×#387	1	4	yes	—
419	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
420	C₄	C₂×C₅×#123	1	1	yes	characteristic
421	C₄	C₂×C₅×#125	1	1	yes	characteristic
422	C₄	C₂×C₅×#126	1	1	yes	characteristic
423	C₂	C₅×#1917	1	8	yes	direct product factor
424	C₂	C₂×C₅×#387	1	1	yes	characteristic
425	C₂	C₂×C₅×#432	1	1	yes	characteristic
426	C₂	C₂×C₅×#433	1	1	yes	characteristic
427	C₂	C₂×C₅×#435	1	1	yes	characteristic
428	C₂	C₂×C₅×#436	1	1	yes	characteristic
429	C₂	C₂×C₅×#446	1	1	yes	characteristic
430	C₂	C₂×C₅×#446	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄×C₅	C₂³
commutator	C₂³	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle, prime radical	C₂⁴×C₅	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₅×#1917	C₂	direct (N × H)
30. C₂×#1917	C₅	direct (N × H)
77. #1917	C₂×C₅	direct (N × H)
340. C₂×C₅	#1917	direct (N × H)
397. C₅	C₂×#1917	direct (N × H)
423. C₂	C₅×#1917	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×C₄⋊C₈	2
C₂²×C₅×#97	2
C₂×C₄×C₅×C₄⋊C₄	2
C₅×#1917	2
C₂×C₅×#336	2
C₂×#1917	5

Subgroups — C2×C5×#1917 #11943739

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1917 #11943739