Subgroups — C₂×C₅×#1861 #11943586

Order 1280.

1358 conjugacy classes of subgroups.

The subgroup lattice has 654 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#568	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#430	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#423	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
6	C₅×#1861	C₂	1	8	yes	maximal, direct product factor
7	C₂×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
10	C₅×#568	—	2	2	no	—
11	C₅×#568	—	2	2	no	—
12	C₅×#568	—	2	2	no	—
13	C₅×#568	C₂²	1	4	yes	—
14	C₂×C₅×#131	—	2	2	no	—
15	C₂×C₅×#131	—	2	2	no	—
16	C₂²×C₅×M₁₆	—	2	2	no	—
17	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₅×#430	—	2	2	no	—
24	C₅×#430	C₂²	1	4	yes	complemented
25	C₂×C₅×#108	—	2	2	no	—
26	C₅×#423	—	2	2	no	—
27	C₅×#423	C₂²	1	4	yes	complemented
28	C₂×C₅×C₄⋊C₈	—	2	2	no	—
29	C₅×#421	—	2	2	no	—
30	C₅×#421	C₂²	1	4	yes	—
31	C₂×C₅×#104	—	2	2	no	—
32	C₂×C₅×#104	C₄	1	2	yes	complemented
33	C₂×C₅×#104	C₄	1	4	yes	complemented
34	C₂×C₅×#104	C₄	1	2	yes	complemented
35	C₂×C₅×#104	C₂²	1	4	yes	—
36	C₅×#344	C₂²	1	4	yes	complemented
37	C₅×#339	C₂²	1	4	yes	complemented
38	C₂×#1861	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂×C₅×#41	—	2	1	no	—
40	C₂×C₅×#41	—	2	1	no	—
41	C₂×C₅×#41	—	2	1	no	—
42	C₂×C₅×#41	—	2	1	no	—
43	C₂×C₅×#41	—	2	1	no	—
44	C₂×C₅×#41	—	2	1	no	—
45	C₂×C₅×#41	C₂×C₄	1	2	yes	—
46	C₂×C₅×#41	C₂×C₄	1	2	yes	—
47	C₂×C₅×#41	D₄	1	2	yes	—
48	C₂×C₅×#41	D₄	1	2	yes	—
49	C₂×C₅×#41	Q₈	1	2	yes	—
50	C₂×C₅×#41	C₂³	1	2	yes	—
51	C₂²×C₅×Q₈	Q₈	1	1	yes	characteristic
52	C₂²×C₅×D₄	—	2	1	no	—
53	C₂²×C₅×D₄	Q₈	1	1	yes	characteristic
54	C₂³×C₄×C₅	—	2	1	no	—
55	C₂³×C₄×C₅	—	2	1	no	—
56	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₅×#131	—	2	8	no	—
58	C₅×#131	—	2	8	no	—
59	C₅×#131	—	2	8	no	—
60	C₅×#131	—	2	8	no	—
61	C₂×C₅×M₁₆	—	2	4	no	—
62	C₂×C₅×M₁₆	—	2	8	no	—
63	C₂×C₅×M₁₆	—	2	1	no	—
64	C₂×C₅×M₁₆	—	2	1	no	—
65	C₂×C₅×M₁₆	—	2	1	no	—
66	C₂×C₅×M₁₆	—	2	1	no	—
67	C₂×C₅×M₁₆	—	2	1	no	—
68	C₂×C₅×M₁₆	—	2	1	no	—
69	C₂×C₅×M₁₆	—	2	1	no	—
70	C₂×C₅×M₁₆	—	2	1	no	—
71	C₂×C₅×M₁₆	—	2	1	no	—
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂×C₅×M₁₆	—	2	8	no	—
74	C₂×C₅×M₁₆	—	2	1	no	—
75	C₂×C₅×M₁₆	—	2	1	no	—
76	C₂×C₅×M₁₆	—	2	1	no	—
77	C₂×C₅×M₁₆	—	2	1	no	—
78	C₂×C₅×M₁₆	—	2	1	no	—
79	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
80	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
81	C₂×C₅×M₁₆	D₄	1	2	yes	—
82	C₂×C₅×M₁₆	D₄	1	2	yes	—
83	C₂×C₅×M₁₆	D₄	1	2	yes	—
84	C₂×C₅×M₁₆	C₂³	1	2	yes	—
85	C₂×C₅×M₁₆	C₂³	1	2	yes	—
86	C₂×C₅×M₁₆	C₂³	1	2	yes	—
87	C₂×C₅×M₁₆	C₂³	1	2	yes	—
88	C₂²×C₅×C₈	—	2	4	no	—
89	C₂²×C₅×C₈	—	2	1	no	—
90	C₂²×C₅×C₈	—	2	1	no	—
91	C₂²×C₅×C₈	—	2	1	no	—
92	C₂²×C₅×C₈	D₄	1	2	yes	—
93	C₅×#117	—	2	1	no	—
94	C₅×#117	—	2	1	no	—
95	C₅×#117	—	2	1	no	—
96	C₅×#117	C₂³	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	—	2	1	no	—
98	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
99	C₂×C₄²×C₅	—	2	1	no	—
100	C₂×C₄²×C₅	—	2	1	no	—
101	C₂×C₄²×C₅	—	2	1	no	—
102	C₂×C₄²×C₅	—	2	1	no	—
103	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂×C₄	1	2	yes	—
105	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂³	1	2	yes	—
107	C₅×#108	—	2	8	no	—
108	C₅×C₄⋊C₈	—	2	8	no	—
109	C₅×#104	—	2	8	no	—
110	C₅×#104	C₂×C₄	1	8	yes	complemented
111	C₅×#104	C₂×C₄	1	8	yes	complemented
112	C₂×#568	C₂×C₅	1	1	yes	characteristic
113	C₂×#430	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×#423	C₂×C₅	1	1	yes	characteristic, complemented
115	C₂×#421	C₂×C₅	1	1	yes	characteristic
116	C₂²×#104	C₂×C₅	1	1	yes	characteristic
117	#1861	C₂×C₅	1	8	yes	direct product factor
118	C₂×#344	C₂×C₅	1	1	yes	characteristic, complemented
119	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂⁴×C₅	—	2	1	no	—
121	C₂⁴×C₅	#41	1	1	yes	characteristic
122	C₅×#41	—	2	2	no	—
123	C₅×#41	—	2	2	no	—
124	C₅×#41	—	2	2	no	—
125	C₅×#41	—	2	2	no	—
126	C₅×#41	—	2	2	no	—
127	C₅×#41	—	2	2	no	—
128	C₅×#41	—	2	2	no	—
129	C₅×#41	—	2	2	no	—
130	C₅×#41	—	2	2	no	—
131	C₅×#41	—	2	2	no	—
132	C₅×#41	—	2	2	no	—
133	C₅×#41	—	2	2	no	—
134	C₅×#41	C₄⋊C₄	1	4	yes	—
135	C₅×#41	C₄⋊C₄	1	4	yes	—
136	C₅×#41	C₂²×C₄	1	4	yes	—
137	C₅×#41	C₂×D₄	1	4	yes	—
138	C₂×C₅×Q₈	—	2	1	no	—
139	C₂×C₅×Q₈	—	2	1	no	—
140	C₂×C₅×Q₈	—	2	1	no	—
141	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
142	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
143	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
144	C₂×C₅×D₄	—	2	2	no	—
145	C₂×C₅×D₄	—	2	2	no	—
146	C₂×C₅×D₄	—	2	2	no	—
147	C₂×C₅×D₄	—	2	2	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
154	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
155	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
156	C₂²×C₄×C₅	—	2	1	no	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	—	2	2	no	—
160	C₂²×C₄×C₅	—	2	2	no	—
161	C₂²×C₄×C₅	—	2	2	no	—
162	C₂²×C₄×C₅	—	2	2	no	—
163	C₂²×C₄×C₅	—	2	2	no	—
164	C₂²×C₄×C₅	—	2	2	no	—
165	C₂²×C₄×C₅	—	2	1	no	—
166	C₂²×C₄×C₅	—	2	2	no	—
167	C₂²×C₄×C₅	—	4	4	no	—
168	C₂²×C₄×C₅	—	4	1	no	—
169	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
174	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
178	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
179	C₂²×C₄×C₅	#41	1	1	yes	characteristic
180	C₂²×C₄×C₅	#41	1	1	yes	characteristic
181	C₂²×C₄×C₅	#41	1	1	yes	characteristic
182	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
183	C₅×M₁₆	—	2	16	no	—
184	C₅×M₁₆	—	2	2	no	—
185	C₅×M₁₆	—	2	2	no	—
186	C₅×M₁₆	—	2	2	no	—
187	C₅×M₁₆	—	2	2	no	—
188	C₅×M₁₆	—	2	2	no	—
189	C₅×M₁₆	—	2	2	no	—
190	C₅×M₁₆	—	2	2	no	—
191	C₅×M₁₆	—	2	2	no	—
192	C₅×M₁₆	—	2	2	no	—
193	C₅×M₁₆	—	2	2	no	—
194	C₅×M₁₆	—	2	2	no	—
195	C₅×M₁₆	—	2	2	no	—
196	C₅×M₁₆	—	4	1	no	—
197	C₅×M₁₆	—	4	1	no	—
198	C₅×M₁₆	C₂²×C₄	1	4	yes	—
199	C₅×M₁₆	C₂×D₄	1	4	yes	—
200	C₂×C₅×C₈	—	2	16	no	—
201	C₂×C₅×C₈	—	2	2	no	—
202	C₂×C₅×C₈	—	2	2	no	—
203	C₂×C₅×C₈	—	2	2	no	—
204	C₂×C₅×C₈	—	2	2	no	—
205	C₂×C₅×C₈	—	2	2	no	—
206	C₂×C₅×C₈	—	2	2	no	—
207	C₂×C₅×C₈	—	2	2	no	—
208	C₂×C₅×C₈	—	2	2	no	—
209	C₂×C₅×C₈	—	2	2	no	—
210	C₂×C₅×C₈	—	4	1	no	—
211	C₂×C₅×C₈	—	4	1	no	—
212	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
213	C₅×C₄⋊C₄	—	2	2	no	—
214	C₅×C₄⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	4	1	no	—
217	C₄²×C₅	—	2	1	no	—
218	C₄²×C₅	—	2	2	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	—	2	2	no	—
221	C₄²×C₅	—	2	2	no	—
222	C₄²×C₅	—	4	1	no	—
223	C₄²×C₅	C₂²×C₄	1	2	yes	—
224	C₄²×C₅	C₂²×C₄	1	2	yes	—
225	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
226	#568	—	2	2	no	—
227	#568	—	2	2	no	—
228	#568	—	2	2	no	—
229	#568	C₂²×C₅	1	4	yes	—
230	C₂×#131	—	2	2	no	—
231	C₂×#131	—	2	2	no	—
232	C₂²×M₁₆	—	2	2	no	—
233	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
234	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
235	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
236	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
237	C₂×#117	C₂²×C₅	1	1	yes	characteristic
238	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
239	#430	—	2	2	no	—
240	#430	C₂²×C₅	1	4	yes	complemented
241	C₂×#108	—	2	2	no	—
242	#423	—	2	2	no	—
243	#423	C₂²×C₅	1	4	yes	complemented
244	C₂×C₄⋊C₈	—	2	2	no	—
245	#421	—	2	2	no	—
246	#421	C₂²×C₅	1	4	yes	—
247	C₂×#104	—	2	2	no	—
248	C₂×#104	C₄×C₅	1	2	yes	complemented
249	C₂×#104	C₄×C₅	1	4	yes	complemented
250	C₂×#104	C₄×C₅	1	2	yes	complemented
251	C₂×#104	C₂²×C₅	1	4	yes	—
252	#344	C₂²×C₅	1	4	yes	complemented
253	#339	C₂²×C₅	1	4	yes	complemented
254	C₂³×C₅	—	2	2	no	—
255	C₂³×C₅	—	2	2	no	—
256	C₂³×C₅	—	2	2	no	—
257	C₂³×C₅	—	4	2	no	—
258	C₂³×C₅	—	8	2	no	—
259	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
260	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
262	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
263	C₂³×C₅	#123	1	1	yes	characteristic
264	C₂³×C₅	#123	1	1	yes	characteristic
265	C₂³×C₅	C₂×#41	1	1	yes	characteristic
266	C₅×Q₈	—	2	2	no	—
267	C₅×Q₈	—	2	2	no	—
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	C₂×C₄⋊C₄	1	4	yes	—
270	C₅×D₄	—	2	4	no	—
271	C₅×D₄	—	2	4	no	—
272	C₅×D₄	—	2	4	no	—
273	C₅×D₄	—	2	4	no	—
274	C₅×D₄	—	2	2	no	—
275	C₅×D₄	—	2	2	no	—
276	C₅×D₄	—	2	2	no	—
277	C₅×D₄	C₂×C₄⋊C₄	1	4	yes	—
278	C₂×C₄×C₅	—	2	4	no	—
279	C₂×C₄×C₅	—	2	2	no	—
280	C₂×C₄×C₅	—	2	2	no	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	4	no	—
284	C₂×C₄×C₅	—	2	4	no	—
285	C₂×C₄×C₅	—	2	4	no	—
286	C₂×C₄×C₅	—	2	4	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	4	4	no	—
289	C₂×C₄×C₅	—	4	4	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	—	4	2	no	—
292	C₂×C₄×C₅	—	8	2	no	—
293	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
297	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	#120	1	1	yes	characteristic
304	C₂×C₄×C₅	#120	1	1	yes	characteristic
305	C₂×C₄×C₅	#120	1	1	yes	characteristic
306	C₂×C₄×C₅	#120	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
313	C₂×C₄×C₅	#123	1	1	yes	characteristic
314	C₂×C₄×C₅	#123	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
320	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
321	C₅×C₈	—	2	4	no	—
322	C₅×C₈	—	2	4	no	—
323	C₅×C₈	—	2	4	no	—
324	C₅×C₈	—	4	2	no	—
325	C₂×#41	—	2	1	no	—
326	C₂×#41	—	2	1	no	—
327	C₂×#41	—	2	1	no	—
328	C₂×#41	—	2	1	no	—
329	C₂×#41	—	2	1	no	—
330	C₂×#41	—	2	1	no	—
331	C₂×#41	C₂×C₄×C₅	1	2	yes	—
332	C₂×#41	C₂×C₄×C₅	1	2	yes	—
333	C₂×#41	C₅×D₄	1	2	yes	—
334	C₂×#41	C₅×D₄	1	2	yes	—
335	C₂×#41	C₅×Q₈	1	2	yes	—
336	C₂×#41	C₂³×C₅	1	2	yes	—
337	C₂²×Q₈	C₅×Q₈	1	1	yes	characteristic
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	C₅×Q₈	1	1	yes	characteristic
340	C₂³×C₄	—	2	1	no	—
341	C₂³×C₄	—	2	1	no	—
342	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
343	#131	—	2	8	no	—
344	#131	—	2	8	no	—
345	#131	—	2	8	no	—
346	#131	—	2	8	no	—
347	C₂×M₁₆	—	2	4	no	—
348	C₂×M₁₆	—	2	8	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	2	1	no	—
358	C₂×M₁₆	—	2	1	no	—
359	C₂×M₁₆	—	2	8	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₂×M₁₆	—	2	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	2	1	no	—
364	C₂×M₁₆	—	2	1	no	—
365	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
366	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
367	C₂×M₁₆	C₅×D₄	1	2	yes	—
368	C₂×M₁₆	C₅×D₄	1	2	yes	—
369	C₂×M₁₆	C₅×D₄	1	2	yes	—
370	C₂×M₁₆	C₂³×C₅	1	2	yes	—
371	C₂×M₁₆	C₂³×C₅	1	2	yes	—
372	C₂×M₁₆	C₂³×C₅	1	2	yes	—
373	C₂×M₁₆	C₂³×C₅	1	2	yes	—
374	C₂²×C₈	—	2	4	no	—
375	C₂²×C₈	—	2	1	no	—
376	C₂²×C₈	—	2	1	no	—
377	C₂²×C₈	—	2	1	no	—
378	C₂²×C₈	C₅×D₄	1	2	yes	—
379	#117	—	2	1	no	—
380	#117	—	2	1	no	—
381	#117	—	2	1	no	—
382	#117	C₂³×C₅	1	2	yes	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₄²	—	2	1	no	—
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	—	2	1	no	—
389	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
390	C₂×C₄²	C₂×C₄×C₅	1	2	yes	—
391	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₅	1	2	yes	—
393	#108	—	2	8	no	—
394	C₄⋊C₈	—	2	8	no	—
395	#104	—	2	8	no	—
396	#104	C₂×C₄×C₅	1	8	yes	complemented
397	#104	C₂×C₄×C₅	1	8	yes	complemented
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	4	no	—
402	C₂²×C₅	—	4	1	no	—
403	C₂²×C₅	—	4	1	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	—	4	4	no	—
407	C₂²×C₅	—	8	2	no	—
408	C₂²×C₅	—	8	2	no	—
409	C₂²×C₅	#385	1	1	yes	characteristic
410	C₂²×C₅	#385	1	1	yes	characteristic
411	C₂²×C₅	#385	1	1	yes	characteristic
412	C₂²×C₅	#385	1	1	yes	characteristic
413	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
415	C₂²×C₅	C₂×#123	1	1	yes	characteristic
416	C₄×C₅	—	2	4	no	—
417	C₄×C₅	—	2	4	no	—
418	C₄×C₅	—	4	2	no	—
419	C₄×C₅	—	8	2	no	—
420	C₄×C₅	#385	1	1	yes	characteristic
421	C₄×C₅	#385	1	1	yes	characteristic
422	C₄×C₅	#385	1	1	yes	characteristic
423	C₄×C₅	#385	1	1	yes	characteristic
424	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
425	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
426	C₄×C₅	C₂×#120	1	1	yes	characteristic
427	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
428	C₂⁴	—	2	1	no	—
429	C₂⁴	C₅×#41	1	1	yes	characteristic
430	#41	—	2	2	no	—
431	#41	—	2	2	no	—
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	2	2	no	—
435	#41	—	2	2	no	—
436	#41	—	2	2	no	—
437	#41	—	2	2	no	—
438	#41	—	2	2	no	—
439	#41	—	2	2	no	—
440	#41	—	2	2	no	—
441	#41	—	2	2	no	—
442	#41	C₅×C₄⋊C₄	1	4	yes	—
443	#41	C₅×C₄⋊C₄	1	4	yes	—
444	#41	C₂²×C₄×C₅	1	4	yes	—
445	#41	C₂×C₅×D₄	1	4	yes	—
446	C₂×Q₈	—	2	1	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
450	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
451	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
452	C₂×D₄	—	2	2	no	—
453	C₂×D₄	—	2	2	no	—
454	C₂×D₄	—	2	2	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	2	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
462	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
463	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	2	no	—
467	C₂²×C₄	—	2	2	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	no	—
471	C₂²×C₄	—	2	2	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	2	no	—
475	C₂²×C₄	—	4	4	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
480	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
481	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
482	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
483	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
484	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
485	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
486	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
487	C₂²×C₄	C₅×#41	1	1	yes	characteristic
488	C₂²×C₄	C₅×#41	1	1	yes	characteristic
489	C₂²×C₄	C₅×#41	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
491	M₁₆	—	2	16	no	—
492	M₁₆	—	2	2	no	—
493	M₁₆	—	2	2	no	—
494	M₁₆	—	2	2	no	—
495	M₁₆	—	2	2	no	—
496	M₁₆	—	2	2	no	—
497	M₁₆	—	2	2	no	—
498	M₁₆	—	2	2	no	—
499	M₁₆	—	2	2	no	—
500	M₁₆	—	2	2	no	—
501	M₁₆	—	2	2	no	—
502	M₁₆	—	2	2	no	—
503	M₁₆	—	2	2	no	—
504	M₁₆	—	4	1	no	—
505	M₁₆	—	4	1	no	—
506	M₁₆	C₂²×C₄×C₅	1	4	yes	—
507	M₁₆	C₂×C₅×D₄	1	4	yes	—
508	C₂×C₈	—	2	16	no	—
509	C₂×C₈	—	2	2	no	—
510	C₂×C₈	—	2	2	no	—
511	C₂×C₈	—	2	2	no	—
512	C₂×C₈	—	2	2	no	—
513	C₂×C₈	—	2	2	no	—
514	C₂×C₈	—	2	2	no	—
515	C₂×C₈	—	2	2	no	—
516	C₂×C₈	—	2	2	no	—
517	C₂×C₈	—	2	2	no	—
518	C₂×C₈	—	4	1	no	—
519	C₂×C₈	—	4	1	no	—
520	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
521	C₄⋊C₄	—	2	2	no	—
522	C₄⋊C₄	—	4	1	no	—
523	C₂²⋊C₄	—	2	2	no	—
524	C₂²⋊C₄	—	4	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	2	2	no	—
527	C₄²	—	2	1	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	4	1	no	—
531	C₄²	C₂²×C₄×C₅	1	2	yes	—
532	C₄²	C₂²×C₄×C₅	1	2	yes	—
533	C₂×C₅	—	2	1	no	—
534	C₂×C₅	—	2	1	no	—
535	C₂×C₅	—	2	1	no	—
536	C₂×C₅	—	2	1	no	—
537	C₂×C₅	—	2	1	no	—
538	C₂×C₅	—	2	1	no	—
539	C₂×C₅	—	4	4	no	—
540	C₂×C₅	#1861	1	2	yes	direct product factor
541	C₂×C₅	C₂×#385	1	1	yes	characteristic
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	4	2	no	—
546	C₂³	—	8	2	no	—
547	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
548	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
549	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
550	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
551	C₂³	C₅×#123	1	1	yes	characteristic
552	C₂³	C₅×#123	1	1	yes	characteristic
553	C₂³	C₂×C₅×#41	1	1	yes	characteristic
554	Q₈	—	2	2	no	—
555	Q₈	—	2	2	no	—
556	Q₈	—	2	2	no	—
557	Q₈	C₂×C₅×C₄⋊C₄	1	4	yes	—
558	D₄	—	2	4	no	—
559	D₄	—	2	4	no	—
560	D₄	—	2	4	no	—
561	D₄	—	2	4	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	2	no	—
564	D₄	—	2	2	no	—
565	D₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	4	no	—
575	C₂×C₄	—	2	2	no	—
576	C₂×C₄	—	4	4	no	—
577	C₂×C₄	—	4	4	no	—
578	C₂×C₄	—	4	2	no	—
579	C₂×C₄	—	4	2	no	—
580	C₂×C₄	—	8	2	no	—
581	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
582	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
583	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
584	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
585	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
586	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
587	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
588	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
589	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
590	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
591	C₂×C₄	C₅×#120	1	1	yes	characteristic
592	C₂×C₄	C₅×#120	1	1	yes	characteristic
593	C₂×C₄	C₅×#120	1	1	yes	characteristic
594	C₂×C₄	C₅×#120	1	1	yes	characteristic
595	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
596	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
597	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
598	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
599	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
600	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
601	C₂×C₄	C₅×#123	1	1	yes	characteristic
602	C₂×C₄	C₅×#123	1	1	yes	characteristic
603	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
604	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
605	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
606	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
607	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
608	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
609	C₈	—	2	4	no	—
610	C₈	—	2	4	no	—
611	C₈	—	2	4	no	—
612	C₈	—	4	2	no	—
613	C₅	C₂×#1861	1	1	yes	characteristic, direct product factor, Sylow
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	4	1	no	—
619	C₂²	—	4	1	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	8	2	no	—
624	C₂²	—	8	2	no	—
625	C₂²	C₅×#385	1	1	yes	characteristic
626	C₂²	C₅×#385	1	1	yes	characteristic
627	C₂²	C₅×#385	1	1	yes	characteristic
628	C₂²	C₅×#385	1	1	yes	characteristic
629	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
630	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
631	C₂²	C₂×C₅×#123	1	1	yes	characteristic
632	C₄	—	2	4	no	—
633	C₄	—	2	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	2	no	—
636	C₄	C₅×#385	1	1	yes	characteristic
637	C₄	C₅×#385	1	1	yes	characteristic
638	C₄	C₅×#385	1	1	yes	characteristic
639	C₄	C₅×#385	1	1	yes	characteristic
640	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
641	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
642	C₄	C₂×C₅×#120	1	1	yes	characteristic
643	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
644	C₂	—	2	1	no	—
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	2	1	no	—
650	C₂	—	4	4	no	—
651	C₂	C₅×#1861	1	2	yes	direct product factor
652	C₂	C₂×C₅×#385	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#120
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	#385
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. C₂×C₅×#430	C₂	semidirect
3. C₂×C₅×#423	C₂	semidirect
6. C₅×#1861	C₂	direct (N × H)
7. C₂×C₅×#344	C₂	semidirect
8. C₂×C₅×#339	C₂	semidirect
24. C₅×#430	C₂²	semidirect
27. C₅×#423	C₂²	semidirect
32. C₂×C₅×#104	C₄	semidirect
33. C₂×C₅×#104	C₄	semidirect
34. C₂×C₅×#104	C₄	semidirect
36. C₅×#344	C₂²	semidirect
37. C₅×#339	C₂²	semidirect
38. C₂×#1861	C₅	direct (N × H)
110. C₅×#104	C₂×C₄	semidirect
111. C₅×#104	C₂×C₄	semidirect
113. C₂×#430	C₂×C₅	semidirect
114. C₂×#423	C₂×C₅	semidirect
117. #1861	C₂×C₅	direct (N × H)
118. C₂×#344	C₂×C₅	semidirect
119. C₂×#339	C₂×C₅	semidirect
240. #430	C₂²×C₅	semidirect
243. #423	C₂²×C₅	semidirect
248. C₂×#104	C₄×C₅	semidirect
249. C₂×#104	C₄×C₅	semidirect
250. C₂×#104	C₄×C₅	semidirect
252. #344	C₂²×C₅	semidirect
253. #339	C₂²×C₅	semidirect
396. #104	C₂×C₄×C₅	semidirect
397. #104	C₂×C₄×C₅	semidirect
540. C₂×C₅	#1861	direct (N × H)
613. C₅	C₂×#1861	direct (N × H)
651. C₂	C₅×#1861	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×#568	2
C₂×C₅×#430	2
C₂×C₅×#423	2
C₂×C₅×#421	2
C₂²×C₅×#104	2
C₅×#1861	2
C₂×C₅×#344	2
C₂×C₅×#339	2
C₂×#1861	5

Subgroups — C2×C5×#1861 #11943586

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1861 #11943586