Subgroups — C₂×C₅×#1814 #11943394

Order 1280.

1330 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#131	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#421	C₂	1	2	yes	maximal
5	C₅×#1814	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₅×#344	C₂	1	2	yes	maximal, complemented
7	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
8	C₂×C₅×#131	—	2	1	no	—
9	C₂×C₅×#131	—	2	1	no	—
10	C₂×C₅×#131	—	2	2	no	—
11	C₂×C₅×#131	—	2	2	no	—
12	C₂×C₅×#131	C₄	1	2	yes	complemented
13	C₂×C₅×#131	C₄	1	2	yes	complemented
14	C₂×C₅×#131	C₄	1	4	yes	complemented
15	C₂×C₅×#131	C₂²	1	4	yes	—
16	C₂²×C₅×M₁₆	—	2	1	no	—
17	C₂²×C₅×M₁₆	C₂²	1	2	yes	—
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂³×C₅×C₈	—	2	1	no	—
20	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	2	yes	—
22	C₂×C₅×#108	—	2	1	no	—
23	C₂×C₅×#108	—	2	1	no	—
24	C₂×C₅×#108	—	2	2	no	—
25	C₂×C₅×#108	C₂²	1	4	yes	complemented
26	C₅×#427	—	2	2	no	—
27	C₅×#427	C₂²	1	4	yes	complemented
28	C₂×C₅×#107	—	2	1	no	—
29	C₂×C₅×#106	—	2	1	no	—
30	C₅×#421	—	2	4	no	—
31	C₅×#421	C₂²	1	8	yes	—
32	C₂×C₅×#104	—	2	4	no	—
33	C₅×#344	C₂²	1	8	yes	complemented
34	C₂×#1814	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂×C₅×#41	—	2	1	no	—
36	C₂×C₅×#41	—	2	1	no	—
37	C₂×C₅×#41	—	2	1	no	—
38	C₂×C₅×#41	—	2	1	no	—
39	C₂×C₅×#41	—	2	1	no	—
40	C₂×C₅×#41	—	2	1	no	—
41	C₂×C₅×#41	C₂×C₄	1	2	yes	—
42	C₂×C₅×#41	C₂×C₄	1	2	yes	—
43	C₂×C₅×#41	D₄	1	2	yes	—
44	C₂×C₅×#41	D₄	1	2	yes	—
45	C₂×C₅×#41	Q₈	1	2	yes	—
46	C₂×C₅×#41	C₂³	1	2	yes	—
47	C₂²×C₅×Q₈	Q₈	1	1	yes	characteristic
48	C₂²×C₅×D₄	—	2	1	no	—
49	C₂²×C₅×D₄	Q₈	1	1	yes	characteristic
50	C₂³×C₄×C₅	—	2	1	no	—
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₅×#131	—	2	4	no	—
53	C₅×#131	—	2	4	no	—
54	C₅×#131	—	2	4	no	—
55	C₅×#131	—	2	4	no	—
56	C₅×#131	—	2	4	no	—
57	C₅×#131	—	2	4	no	—
58	C₅×#131	C₂×C₄	1	8	yes	complemented
59	C₅×#131	C₂×C₄	1	8	yes	complemented
60	C₂×C₅×M₁₆	—	2	1	no	—
61	C₂×C₅×M₁₆	—	2	1	no	—
62	C₂×C₅×M₁₆	—	2	1	no	—
63	C₂×C₅×M₁₆	—	2	2	no	—
64	C₂×C₅×M₁₆	—	2	2	no	—
65	C₂×C₅×M₁₆	—	2	2	no	—
66	C₂×C₅×M₁₆	—	2	4	no	—
67	C₂×C₅×M₁₆	—	2	4	no	—
68	C₂×C₅×M₁₆	—	2	2	no	—
69	C₂×C₅×M₁₆	—	2	2	no	—
70	C₂×C₅×M₁₆	—	2	2	no	—
71	C₂×C₅×M₁₆	—	2	2	no	—
72	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
73	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
74	C₂×C₅×M₁₆	C₂³	1	4	yes	—
75	C₂×C₅×M₁₆	C₂³	1	2	yes	—
76	C₂²×C₅×C₈	—	2	1	no	—
77	C₂²×C₅×C₈	—	2	2	no	—
78	C₂²×C₅×C₈	—	2	2	no	—
79	C₂²×C₅×C₈	—	2	4	no	—
80	C₂²×C₅×C₈	—	2	4	no	—
81	C₂²×C₅×C₈	—	2	2	no	—
82	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
83	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₅×C₈	C₂×C₄	1	2	yes	—
85	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
86	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
87	C₂²×C₅×C₈	D₄	1	2	yes	—
88	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
89	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
90	C₂²×C₅×C₈	D₄	1	2	yes	—
91	C₂²×C₅×C₈	C₂³	1	2	yes	—
92	C₅×#117	—	2	2	no	—
93	C₅×#117	—	2	2	no	—
94	C₅×#117	—	2	2	no	—
95	C₅×#117	C₂³	1	4	yes	—
96	C₂×C₅×C₄⋊C₄	—	2	2	no	—
97	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
98	C₂×C₄²×C₅	—	2	2	no	—
99	C₅×#108	—	2	4	no	—
100	C₅×#108	—	2	4	no	—
101	C₅×#107	—	2	4	no	—
102	C₅×#106	—	2	4	no	—
103	C₅×#104	—	2	16	no	—
104	C₂²×#131	C₂×C₅	1	1	yes	characteristic
105	C₂²×#108	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×#427	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×#421	C₂×C₅	1	2	yes	—
108	#1814	C₂×C₅	1	8	yes	direct product factor
109	C₂×#344	C₂×C₅	1	2	yes	complemented
110	C₂⁴×C₅	—	2	1	no	—
111	C₂⁴×C₅	#41	1	1	yes	characteristic
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	2	2	no	—
115	C₅×#41	—	2	2	no	—
116	C₅×#41	—	2	2	no	—
117	C₅×#41	—	2	2	no	—
118	C₅×#41	—	2	2	no	—
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₅×#41	—	2	2	no	—
122	C₅×#41	—	2	2	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	C₄⋊C₄	1	4	yes	—
125	C₅×#41	C₄⋊C₄	1	4	yes	—
126	C₅×#41	C₂²×C₄	1	4	yes	—
127	C₅×#41	C₂×D₄	1	4	yes	—
128	C₂×C₅×Q₈	—	2	1	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
132	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
133	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	—	2	2	no	—
139	C₂×C₅×D₄	—	2	2	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	2	1	no	—
143	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
144	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
145	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	2	no	—
151	C₂²×C₄×C₅	—	2	2	no	—
152	C₂²×C₄×C₅	—	2	2	no	—
153	C₂²×C₄×C₅	—	4	2	no	—
154	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
164	C₂²×C₄×C₅	#41	1	1	yes	characteristic
165	C₂²×C₄×C₅	#41	1	1	yes	characteristic
166	C₂²×C₄×C₅	#41	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
168	C₅×M₁₆	—	2	2	no	—
169	C₅×M₁₆	—	2	2	no	—
170	C₅×M₁₆	—	2	2	no	—
171	C₅×M₁₆	—	2	8	no	—
172	C₅×M₁₆	—	2	8	no	—
173	C₅×M₁₆	—	2	4	no	—
174	C₅×M₁₆	—	2	4	no	—
175	C₅×M₁₆	—	4	2	no	—
176	C₅×M₁₆	—	4	2	no	—
177	C₅×M₁₆	C₂²×C₄	1	4	yes	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	2	2	no	—
181	C₂×C₅×C₈	—	2	8	no	—
182	C₂×C₅×C₈	—	2	8	no	—
183	C₂×C₅×C₈	—	2	4	no	—
184	C₂×C₅×C₈	—	4	2	no	—
185	C₂×C₅×C₈	—	4	2	no	—
186	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
188	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
189	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
190	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
192	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
193	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
194	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
195	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
196	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
197	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
198	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
199	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
200	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
201	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
202	C₅×C₄⋊C₄	—	2	4	no	—
203	C₅×C₄⋊C₄	—	4	2	no	—
204	C₅×C₂²⋊C₄	—	2	4	no	—
205	C₅×C₂²⋊C₄	—	4	2	no	—
206	C₄²×C₅	—	2	4	no	—
207	C₄²×C₅	—	4	2	no	—
208	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
209	C₂×#131	—	2	1	no	—
210	C₂×#131	—	2	1	no	—
211	C₂×#131	—	2	2	no	—
212	C₂×#131	—	2	2	no	—
213	C₂×#131	C₄×C₅	1	2	yes	complemented
214	C₂×#131	C₄×C₅	1	2	yes	complemented
215	C₂×#131	C₄×C₅	1	4	yes	complemented
216	C₂×#131	C₂²×C₅	1	4	yes	—
217	C₂²×M₁₆	—	2	1	no	—
218	C₂²×M₁₆	C₂²×C₅	1	2	yes	—
219	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
220	C₂³×C₈	—	2	1	no	—
221	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
222	C₂×#117	C₂²×C₅	1	2	yes	—
223	C₂×#108	—	2	1	no	—
224	C₂×#108	—	2	1	no	—
225	C₂×#108	—	2	2	no	—
226	C₂×#108	C₂²×C₅	1	4	yes	complemented
227	#427	—	2	2	no	—
228	#427	C₂²×C₅	1	4	yes	complemented
229	C₂×#107	—	2	1	no	—
230	C₂×#106	—	2	1	no	—
231	#421	—	2	4	no	—
232	#421	C₂²×C₅	1	8	yes	—
233	C₂×#104	—	2	4	no	—
234	#344	C₂²×C₅	1	8	yes	complemented
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	2	2	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	—	4	2	no	—
239	C₂³×C₅	—	4	4	no	—
240	C₂³×C₅	#117	1	1	yes	characteristic
241	C₂³×C₅	#117	1	1	yes	characteristic
242	C₂³×C₅	#121	1	1	yes	characteristic
243	C₂³×C₅	#121	1	1	yes	characteristic
244	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
245	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
246	C₂³×C₅	C₂×#41	1	1	yes	characteristic
247	C₅×Q₈	—	2	2	no	—
248	C₅×Q₈	—	2	2	no	—
249	C₅×Q₈	—	2	2	no	—
250	C₅×Q₈	C₂×C₄⋊C₄	1	4	yes	—
251	C₅×D₄	—	2	4	no	—
252	C₅×D₄	—	2	4	no	—
253	C₅×D₄	—	2	4	no	—
254	C₅×D₄	—	2	4	no	—
255	C₅×D₄	—	2	2	no	—
256	C₅×D₄	—	2	2	no	—
257	C₅×D₄	—	2	2	no	—
258	C₅×D₄	C₂×C₄⋊C₄	1	4	yes	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	4	no	—
263	C₂×C₄×C₅	—	2	4	no	—
264	C₂×C₄×C₅	—	2	4	no	—
265	C₂×C₄×C₅	—	2	4	no	—
266	C₂×C₄×C₅	—	4	4	no	—
267	C₂×C₄×C₅	—	8	4	no	—
268	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
272	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	#117	1	1	yes	characteristic
277	C₂×C₄×C₅	#117	1	1	yes	characteristic
278	C₂×C₄×C₅	#121	1	1	yes	characteristic
279	C₂×C₄×C₅	#121	1	1	yes	characteristic
280	C₂×C₄×C₅	#121	1	1	yes	characteristic
281	C₂×C₄×C₅	#121	1	1	yes	characteristic
282	C₂×C₄×C₅	#121	1	1	yes	characteristic
283	C₂×C₄×C₅	#121	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
287	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
288	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
289	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
290	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
296	C₅×C₈	—	2	4	no	—
297	C₅×C₈	—	4	4	no	—
298	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
299	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
300	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
301	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
302	C₂×#41	—	2	1	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	1	no	—
305	C₂×#41	—	2	1	no	—
306	C₂×#41	—	2	1	no	—
307	C₂×#41	—	2	1	no	—
308	C₂×#41	C₂×C₄×C₅	1	2	yes	—
309	C₂×#41	C₂×C₄×C₅	1	2	yes	—
310	C₂×#41	C₅×D₄	1	2	yes	—
311	C₂×#41	C₅×D₄	1	2	yes	—
312	C₂×#41	C₅×Q₈	1	2	yes	—
313	C₂×#41	C₂³×C₅	1	2	yes	—
314	C₂²×Q₈	C₅×Q₈	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	C₅×Q₈	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
319	#131	—	2	4	no	—
320	#131	—	2	4	no	—
321	#131	—	2	4	no	—
322	#131	—	2	4	no	—
323	#131	—	2	4	no	—
324	#131	—	2	4	no	—
325	#131	C₂×C₄×C₅	1	8	yes	complemented
326	#131	C₂×C₄×C₅	1	8	yes	complemented
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	2	no	—
331	C₂×M₁₆	—	2	2	no	—
332	C₂×M₁₆	—	2	2	no	—
333	C₂×M₁₆	—	2	4	no	—
334	C₂×M₁₆	—	2	4	no	—
335	C₂×M₁₆	—	2	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	—	2	2	no	—
338	C₂×M₁₆	—	2	2	no	—
339	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
340	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
341	C₂×M₁₆	C₂³×C₅	1	4	yes	—
342	C₂×M₁₆	C₂³×C₅	1	2	yes	—
343	C₂²×C₈	—	2	1	no	—
344	C₂²×C₈	—	2	2	no	—
345	C₂²×C₈	—	2	2	no	—
346	C₂²×C₈	—	2	4	no	—
347	C₂²×C₈	—	2	4	no	—
348	C₂²×C₈	—	2	2	no	—
349	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
350	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
351	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
352	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
353	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
354	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
355	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
356	C₂²×C₈	C₅×D₄	1	2	yes	—
357	C₂²×C₈	C₅×D₄	1	2	yes	—
358	C₂²×C₈	C₂³×C₅	1	2	yes	—
359	#117	—	2	2	no	—
360	#117	—	2	2	no	—
361	#117	—	2	2	no	—
362	#117	C₂³×C₅	1	4	yes	—
363	C₂×C₄⋊C₄	—	2	2	no	—
364	C₂×C₂²⋊C₄	—	2	2	no	—
365	C₂×C₄²	—	2	2	no	—
366	#108	—	2	4	no	—
367	#108	—	2	4	no	—
368	#107	—	2	4	no	—
369	#106	—	2	4	no	—
370	#104	—	2	16	no	—
371	C₂²×C₅	—	2	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	4	1	no	—
376	C₂²×C₅	—	4	1	no	—
377	C₂²×C₅	—	4	1	no	—
378	C₂²×C₅	—	4	1	no	—
379	C₂²×C₅	—	4	4	no	—
380	C₂²×C₅	—	4	4	no	—
381	C₂²×C₅	—	4	4	no	—
382	C₂²×C₅	#380	1	1	yes	characteristic
383	C₂²×C₅	#380	1	1	yes	characteristic
384	C₂²×C₅	#380	1	1	yes	characteristic
385	C₂²×C₅	#380	1	1	yes	characteristic
386	C₂²×C₅	C₂×#117	1	1	yes	characteristic
387	C₂²×C₅	C₂×#121	1	1	yes	characteristic
388	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
389	C₄×C₅	—	2	4	no	—
390	C₄×C₅	—	8	4	no	—
391	C₄×C₅	#380	1	1	yes	characteristic
392	C₄×C₅	#380	1	1	yes	characteristic
393	C₄×C₅	#380	1	1	yes	characteristic
394	C₄×C₅	#380	1	1	yes	characteristic
395	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
396	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
397	C₄×C₅	C₂×#121	1	1	yes	characteristic
398	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
399	C₂⁴	—	2	1	no	—
400	C₂⁴	C₅×#41	1	1	yes	characteristic
401	#41	—	2	2	no	—
402	#41	—	2	2	no	—
403	#41	—	2	2	no	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	2	2	no	—
409	#41	—	2	2	no	—
410	#41	—	2	2	no	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	C₅×C₄⋊C₄	1	4	yes	—
414	#41	C₅×C₄⋊C₄	1	4	yes	—
415	#41	C₂²×C₄×C₅	1	4	yes	—
416	#41	C₂×C₅×D₄	1	4	yes	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
421	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
422	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	2	no	—
428	C₂×D₄	—	2	2	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
433	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
434	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
451	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
452	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
453	C₂²×C₄	C₅×#41	1	1	yes	characteristic
454	C₂²×C₄	C₅×#41	1	1	yes	characteristic
455	C₂²×C₄	C₅×#41	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	8	no	—
461	M₁₆	—	2	8	no	—
462	M₁₆	—	2	4	no	—
463	M₁₆	—	2	4	no	—
464	M₁₆	—	4	2	no	—
465	M₁₆	—	4	2	no	—
466	M₁₆	C₂²×C₄×C₅	1	4	yes	—
467	C₂×C₈	—	2	2	no	—
468	C₂×C₈	—	2	2	no	—
469	C₂×C₈	—	2	2	no	—
470	C₂×C₈	—	2	8	no	—
471	C₂×C₈	—	2	8	no	—
472	C₂×C₈	—	2	4	no	—
473	C₂×C₈	—	4	2	no	—
474	C₂×C₈	—	4	2	no	—
475	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
476	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
477	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
478	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
479	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
480	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
481	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
482	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
483	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
484	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
485	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
486	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
487	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
488	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
489	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
490	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₂²⋊C₄	—	2	4	no	—
494	C₂²⋊C₄	—	4	2	no	—
495	C₄²	—	2	4	no	—
496	C₄²	—	4	2	no	—
497	C₂×C₅	—	2	1	no	—
498	C₂×C₅	—	2	1	no	—
499	C₂×C₅	—	2	1	no	—
500	C₂×C₅	—	2	1	no	—
501	C₂×C₅	—	2	1	no	—
502	C₂×C₅	—	2	1	no	—
503	C₂×C₅	—	4	4	no	—
504	C₂×C₅	#1814	1	2	yes	direct product factor
505	C₂×C₅	C₂×#380	1	1	yes	characteristic
506	C₂³	—	2	2	no	—
507	C₂³	—	2	2	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	4	no	—
511	C₂³	C₅×#117	1	1	yes	characteristic
512	C₂³	C₅×#117	1	1	yes	characteristic
513	C₂³	C₅×#121	1	1	yes	characteristic
514	C₂³	C₅×#121	1	1	yes	characteristic
515	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
516	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
517	C₂³	C₂×C₅×#41	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	2	no	—
520	Q₈	—	2	2	no	—
521	Q₈	C₂×C₅×C₄⋊C₄	1	4	yes	—
522	D₄	—	2	4	no	—
523	D₄	—	2	4	no	—
524	D₄	—	2	4	no	—
525	D₄	—	2	4	no	—
526	D₄	—	2	2	no	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	4	4	no	—
538	C₂×C₄	—	8	4	no	—
539	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
540	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
541	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
542	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
543	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
544	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
545	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
546	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
547	C₂×C₄	C₅×#117	1	1	yes	characteristic
548	C₂×C₄	C₅×#117	1	1	yes	characteristic
549	C₂×C₄	C₅×#121	1	1	yes	characteristic
550	C₂×C₄	C₅×#121	1	1	yes	characteristic
551	C₂×C₄	C₅×#121	1	1	yes	characteristic
552	C₂×C₄	C₅×#121	1	1	yes	characteristic
553	C₂×C₄	C₅×#121	1	1	yes	characteristic
554	C₂×C₄	C₅×#121	1	1	yes	characteristic
555	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
556	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
557	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
558	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
559	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
560	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
561	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
562	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
563	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
564	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
565	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
567	C₈	—	2	4	no	—
568	C₈	—	4	4	no	—
569	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
570	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
571	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
572	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
573	C₅	C₂×#1814	1	1	yes	characteristic, direct product factor, Sylow
574	C₂²	—	2	2	no	—
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	—	4	1	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	4	no	—
584	C₂²	—	4	4	no	—
585	C₂²	C₅×#380	1	1	yes	characteristic
586	C₂²	C₅×#380	1	1	yes	characteristic
587	C₂²	C₅×#380	1	1	yes	characteristic
588	C₂²	C₅×#380	1	1	yes	characteristic
589	C₂²	C₂×C₅×#117	1	1	yes	characteristic
590	C₂²	C₂×C₅×#121	1	1	yes	characteristic
591	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
592	C₄	—	2	4	no	—
593	C₄	—	8	4	no	—
594	C₄	C₅×#380	1	1	yes	characteristic
595	C₄	C₅×#380	1	1	yes	characteristic
596	C₄	C₅×#380	1	1	yes	characteristic
597	C₄	C₅×#380	1	1	yes	characteristic
598	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
599	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
600	C₄	C₂×C₅×#121	1	1	yes	characteristic
601	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
602	C₂	—	2	1	no	—
603	C₂	—	2	1	no	—
604	C₂	—	2	1	no	—
605	C₂	—	2	1	no	—
606	C₂	—	2	1	no	—
607	C₂	—	2	1	no	—
608	C₂	—	4	4	no	—
609	C₂	C₅×#1814	1	2	yes	direct product factor
610	C₂	C₂×C₅×#380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	#380
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#108	C₂	semidirect
3. C₂×C₅×#427	C₂	semidirect
5. C₅×#1814	C₂	direct (N × H)
6. C₂×C₅×#344	C₂	semidirect
12. C₂×C₅×#131	C₄	semidirect
13. C₂×C₅×#131	C₄	semidirect
14. C₂×C₅×#131	C₄	semidirect
25. C₂×C₅×#108	C₂²	semidirect
27. C₅×#427	C₂²	semidirect
33. C₅×#344	C₂²	semidirect
34. C₂×#1814	C₅	direct (N × H)
58. C₅×#131	C₂×C₄	semidirect
59. C₅×#131	C₂×C₄	semidirect
105. C₂²×#108	C₂×C₅	semidirect
106. C₂×#427	C₂×C₅	semidirect
108. #1814	C₂×C₅	direct (N × H)
109. C₂×#344	C₂×C₅	semidirect
213. C₂×#131	C₄×C₅	semidirect
214. C₂×#131	C₄×C₅	semidirect
215. C₂×#131	C₄×C₅	semidirect
226. C₂×#108	C₂²×C₅	semidirect
228. #427	C₂²×C₅	semidirect
234. #344	C₂²×C₅	semidirect
325. #131	C₂×C₄×C₅	semidirect
326. #131	C₂×C₄×C₅	semidirect
504. C₂×C₅	#1814	direct (N × H)
573. C₅	C₂×#1814	direct (N × H)
609. C₂	C₅×#1814	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×#131	2
C₂²×C₅×#108	2
C₂×C₅×#427	2
C₂×C₅×#421	2
C₅×#1814	2
C₂×C₅×#344	2
C₂×#1814	5

Subgroups — C2×C5×#1814 #11943394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1814 #11943394