Subgroups — C₂×C₅×#1976 #11943963

Order 1280.

1474 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#135	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#427	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#421	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#410	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1976	C₂	1	8	yes	maximal, direct product factor
7	C₂²×C₅×#41	C₂²	1	2	yes	—
8	C₂×C₅×#135	—	2	1	no	—
9	C₂×C₅×#135	—	2	1	no	—
10	C₂×C₅×#135	—	2	2	no	—
11	C₂×C₅×#135	—	2	1	no	—
12	C₂×C₅×#135	—	2	1	no	—
13	C₂×C₅×#135	—	2	2	no	—
14	C₂×C₅×#135	C₄	1	4	yes	complemented
15	C₂×C₅×#135	C₂²	1	4	yes	—
16	C₂²×C₅×Q₁₆	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₅×SD₁₆	C₄	1	2	yes	complemented
18	C₂²×C₅×D₈	C₄	1	1	yes	characteristic, complemented
19	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
20	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₅×#117	C₂²	1	2	yes	—
22	C₂×C₅×#117	C₂²	1	1	yes	characteristic
23	C₅×#427	—	2	2	no	—
24	C₅×#427	C₂²	1	4	yes	complemented
25	C₂×C₅×#107	—	2	1	no	—
26	C₂×C₅×#106	—	2	1	no	—
27	C₅×#421	—	2	4	no	—
28	C₅×#421	C₂²	1	8	yes	complemented
29	C₂×C₅×#104	—	2	4	no	—
30	C₅×#410	—	2	4	no	—
31	C₅×#410	C₂²	1	8	yes	complemented
32	C₂×C₅×#99	—	2	4	no	—
33	C₅×#405	—	2	2	no	—
34	C₅×#405	C₂²	1	4	yes	complemented
35	C₂×C₅×#97	—	2	1	no	—
36	C₂×C₄×C₅×C₈	—	2	1	no	—
37	C₂×#1976	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
38	C₂×C₅×#41	—	2	2	no	—
39	C₂×C₅×#41	—	2	2	no	—
40	C₂×C₅×#41	—	2	2	no	—
41	C₂×C₅×#41	—	2	2	no	—
42	C₂×C₅×#41	—	2	2	no	—
43	C₂×C₅×#41	—	2	2	no	—
44	C₂×C₅×#41	—	2	2	no	—
45	C₂×C₅×#41	—	2	2	no	—
46	C₂×C₅×#41	—	2	2	no	—
47	C₂×C₅×#41	—	2	2	no	—
48	C₂×C₅×#41	C₂×C₄	1	4	yes	—
49	C₂×C₅×#41	C₂³	1	4	yes	—
50	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
51	C₂²×C₅×D₄	—	2	2	no	—
52	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
53	C₂³×C₄×C₅	—	2	2	no	—
54	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₅×#135	—	2	4	no	—
56	C₅×#135	—	2	4	no	—
57	C₅×#135	—	2	4	no	—
58	C₅×#135	—	2	4	no	—
59	C₅×#135	—	2	4	no	—
60	C₅×#135	—	2	4	no	—
61	C₅×#135	—	2	4	no	—
62	C₅×#135	—	2	4	no	—
63	C₂×C₅×Q₁₆	—	2	1	no	—
64	C₂×C₅×Q₁₆	—	2	1	no	—
65	C₂×C₅×Q₁₆	—	2	2	no	—
66	C₂×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
67	C₂×C₅×SD₁₆	—	2	2	no	—
68	C₂×C₅×SD₁₆	—	2	2	no	—
69	C₂×C₅×SD₁₆	—	2	4	no	—
70	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	complemented
71	C₂×C₅×D₈	—	2	1	no	—
72	C₂×C₅×D₈	—	2	1	no	—
73	C₂×C₅×D₈	—	2	2	no	—
74	C₂×C₅×D₈	C₂×C₄	1	4	yes	complemented
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	D₄	1	2	yes	—
79	C₂×C₅×M₁₆	D₄	1	2	yes	—
80	C₂×C₅×M₁₆	C₂³	1	2	yes	—
81	C₂²×C₅×C₈	—	2	1	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	1	no	—
93	C₅×#117	—	2	1	no	—
94	C₅×#117	—	2	2	no	—
95	C₅×#117	—	2	2	no	—
96	C₅×#117	—	2	2	no	—
97	C₅×#117	D₄	1	2	yes	—
98	C₅×#117	C₂³	1	4	yes	—
99	C₅×#117	C₂³	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	—	2	1	no	—
101	C₂×C₅×C₄⋊C₄	—	2	2	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
103	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
104	C₂×C₄²×C₅	—	2	1	no	—
105	C₂×C₄²×C₅	—	2	2	no	—
106	C₅×#107	—	2	4	no	—
107	C₅×#106	—	2	4	no	—
108	C₅×#104	—	2	16	no	—
109	C₅×#99	—	2	16	no	—
110	C₅×#97	—	2	4	no	—
111	C₄×C₅×C₈	—	2	4	no	—
112	C₂²×#135	C₂×C₅	1	1	yes	characteristic
113	C₂×#427	C₂×C₅	1	1	yes	characteristic, complemented
114	C₂×#421	C₂×C₅	1	2	yes	complemented
115	C₂×#410	C₂×C₅	1	2	yes	complemented
116	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
117	#1976	C₂×C₅	1	8	yes	direct product factor
118	C₂⁴×C₅	—	2	2	no	—
119	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×#41	—	2	4	no	—
121	C₅×#41	—	2	4	no	—
122	C₅×#41	—	2	4	no	—
123	C₅×#41	—	2	4	no	—
124	C₅×#41	—	2	4	no	—
125	C₅×#41	—	2	4	no	—
126	C₅×#41	—	2	4	no	—
127	C₅×#41	—	2	4	no	—
128	C₅×#41	—	4	2	no	—
129	C₅×#41	—	4	2	no	—
130	C₅×#41	—	4	2	no	—
131	C₅×#41	—	4	2	no	—
132	C₅×#41	—	4	2	no	—
133	C₅×#41	—	4	2	no	—
134	C₅×#41	—	4	2	no	—
135	C₅×#41	—	4	2	no	—
136	C₂×C₅×Q₈	—	2	2	no	—
137	C₂×C₅×Q₈	—	2	2	no	—
138	C₂×C₅×Q₈	—	2	2	no	—
139	C₂×C₅×Q₈	—	2	2	no	—
140	C₂×C₅×Q₈	—	2	2	no	—
141	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
142	C₂×C₅×D₄	—	2	4	no	—
143	C₂×C₅×D₄	—	2	4	no	—
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	—	4	2	no	—
150	C₂×C₅×D₄	—	4	2	no	—
151	C₂×C₅×D₄	—	4	2	no	—
152	C₂×C₅×D₄	—	4	2	no	—
153	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	4	no	—
157	C₂²×C₄×C₅	—	2	4	no	—
158	C₂²×C₄×C₅	—	4	2	no	—
159	C₂²×C₄×C₅	—	4	2	no	—
160	C₂²×C₄×C₅	—	4	2	no	—
161	C₂²×C₄×C₅	—	4	2	no	—
162	C₂²×C₄×C₅	—	4	2	no	—
163	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
166	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
167	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	#41	1	1	yes	characteristic
173	C₂²×C₄×C₅	#41	1	1	yes	characteristic
174	C₂²×C₄×C₅	#41	1	1	yes	characteristic
175	C₂²×C₄×C₅	#41	1	1	yes	characteristic
176	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
177	C₅×Q₁₆	—	2	4	no	—
178	C₅×Q₁₆	—	2	4	no	—
179	C₅×SD₁₆	—	2	8	no	—
180	C₅×SD₁₆	—	2	8	no	—
181	C₅×D₈	—	2	4	no	—
182	C₅×D₈	—	2	4	no	—
183	C₅×M₁₆	—	2	2	no	—
184	C₅×M₁₆	—	2	2	no	—
185	C₅×M₁₆	—	2	2	no	—
186	C₅×M₁₆	C₂×D₄	1	4	yes	—
187	C₂×C₅×C₈	—	2	2	no	—
188	C₂×C₅×C₈	—	2	2	no	—
189	C₂×C₅×C₈	—	2	2	no	—
190	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
191	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
192	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
193	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
194	C₂×C₅×C₈	C₂²⋊C₄	1	1	yes	characteristic
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	C₂²⋊C₄	1	2	yes	—
199	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
200	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
201	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
202	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
203	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
204	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
205	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	—	2	4	no	—
209	C₅×C₄⋊C₄	—	4	2	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	2	4	no	—
212	C₅×C₂²⋊C₄	—	4	2	no	—
213	C₅×C₂²⋊C₄	C₂×D₄	1	4	yes	—
214	C₄²×C₅	—	2	2	no	—
215	C₄²×C₅	—	2	2	no	—
216	C₄²×C₅	—	2	4	no	—
217	C₄²×C₅	—	4	2	no	—
218	C₂²×#41	C₂²×C₅	1	2	yes	—
219	C₂×#135	—	2	1	no	—
220	C₂×#135	—	2	1	no	—
221	C₂×#135	—	2	2	no	—
222	C₂×#135	—	2	1	no	—
223	C₂×#135	—	2	1	no	—
224	C₂×#135	—	2	2	no	—
225	C₂×#135	C₄×C₅	1	4	yes	complemented
226	C₂×#135	C₂²×C₅	1	4	yes	—
227	C₂²×Q₁₆	C₄×C₅	1	1	yes	characteristic, complemented
228	C₂²×SD₁₆	C₄×C₅	1	2	yes	complemented
229	C₂²×D₈	C₄×C₅	1	1	yes	characteristic, complemented
230	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
231	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
232	C₂×#117	C₂²×C₅	1	2	yes	—
233	C₂×#117	C₂²×C₅	1	1	yes	characteristic
234	#427	—	2	2	no	—
235	#427	C₂²×C₅	1	4	yes	complemented
236	C₂×#107	—	2	1	no	—
237	C₂×#106	—	2	1	no	—
238	#421	—	2	4	no	—
239	#421	C₂²×C₅	1	8	yes	complemented
240	C₂×#104	—	2	4	no	—
241	#410	—	2	4	no	—
242	#410	C₂²×C₅	1	8	yes	complemented
243	C₂×#99	—	2	4	no	—
244	#405	—	2	2	no	—
245	#405	C₂²×C₅	1	4	yes	complemented
246	C₂×#97	—	2	1	no	—
247	C₂×C₄×C₈	—	2	1	no	—
248	C₂³×C₅	—	2	4	no	—
249	C₂³×C₅	—	4	2	no	—
250	C₂³×C₅	—	4	2	no	—
251	C₂³×C₅	—	4	2	no	—
252	C₂³×C₅	—	8	4	no	—
253	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
254	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
255	C₂³×C₅	#121	1	1	yes	characteristic
256	C₂³×C₅	#121	1	1	yes	characteristic
257	C₂³×C₅	#127	1	1	yes	characteristic
258	C₂³×C₅	#127	1	1	yes	characteristic
259	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
260	C₅×Q₈	—	2	4	no	—
261	C₅×Q₈	—	2	4	no	—
262	C₅×Q₈	—	4	2	no	—
263	C₅×Q₈	—	4	2	no	—
264	C₅×D₄	—	2	4	no	—
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	—	4	4	no	—
267	C₅×D₄	—	4	4	no	—
268	C₅×D₄	—	4	4	no	—
269	C₅×D₄	—	4	4	no	—
270	C₅×D₄	—	4	2	no	—
271	C₅×D₄	—	4	2	no	—
272	C₂×C₄×C₅	—	2	4	no	—
273	C₂×C₄×C₅	—	2	4	no	—
274	C₂×C₄×C₅	—	4	4	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	4	2	no	—
277	C₂×C₄×C₅	—	4	4	no	—
278	C₂×C₄×C₅	—	4	4	no	—
279	C₂×C₄×C₅	—	4	4	no	—
280	C₂×C₄×C₅	—	4	4	no	—
281	C₂×C₄×C₅	—	4	4	no	—
282	C₂×C₄×C₅	—	8	4	no	—
283	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
287	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
288	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
289	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
290	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
291	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
293	C₂×C₄×C₅	#121	1	1	yes	characteristic
294	C₂×C₄×C₅	#121	1	1	yes	characteristic
295	C₂×C₄×C₅	#121	1	1	yes	characteristic
296	C₂×C₄×C₅	#121	1	1	yes	characteristic
297	C₂×C₄×C₅	#121	1	1	yes	characteristic
298	C₂×C₄×C₅	#121	1	1	yes	characteristic
299	C₂×C₄×C₅	#124	1	1	yes	characteristic
300	C₂×C₄×C₅	#124	1	1	yes	characteristic
301	C₂×C₄×C₅	#124	1	1	yes	characteristic
302	C₂×C₄×C₅	#124	1	1	yes	characteristic
303	C₂×C₄×C₅	#127	1	1	yes	characteristic
304	C₂×C₄×C₅	#127	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
311	C₅×C₈	—	2	4	no	—
312	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
313	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
314	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
315	C₅×C₈	C₂×C₂²⋊C₄	1	2	yes	—
316	C₂×#41	—	2	2	no	—
317	C₂×#41	—	2	2	no	—
318	C₂×#41	—	2	2	no	—
319	C₂×#41	—	2	2	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	2	no	—
322	C₂×#41	—	2	2	no	—
323	C₂×#41	—	2	2	no	—
324	C₂×#41	—	2	2	no	—
325	C₂×#41	—	2	2	no	—
326	C₂×#41	C₂×C₄×C₅	1	4	yes	—
327	C₂×#41	C₂³×C₅	1	4	yes	—
328	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
331	C₂³×C₄	—	2	2	no	—
332	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
333	#135	—	2	4	no	—
334	#135	—	2	4	no	—
335	#135	—	2	4	no	—
336	#135	—	2	4	no	—
337	#135	—	2	4	no	—
338	#135	—	2	4	no	—
339	#135	—	2	4	no	—
340	#135	—	2	4	no	—
341	C₂×Q₁₆	—	2	1	no	—
342	C₂×Q₁₆	—	2	1	no	—
343	C₂×Q₁₆	—	2	2	no	—
344	C₂×Q₁₆	C₂×C₄×C₅	1	4	yes	complemented
345	C₂×SD₁₆	—	2	2	no	—
346	C₂×SD₁₆	—	2	2	no	—
347	C₂×SD₁₆	—	2	4	no	—
348	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	complemented
349	C₂×D₈	—	2	1	no	—
350	C₂×D₈	—	2	1	no	—
351	C₂×D₈	—	2	2	no	—
352	C₂×D₈	C₂×C₄×C₅	1	4	yes	complemented
353	C₂×M₁₆	—	2	1	no	—
354	C₂×M₁₆	—	2	1	no	—
355	C₂×M₁₆	—	2	1	no	—
356	C₂×M₁₆	C₅×D₄	1	2	yes	—
357	C₂×M₁₆	C₅×D₄	1	2	yes	—
358	C₂×M₁₆	C₂³×C₅	1	2	yes	—
359	C₂²×C₈	—	2	1	no	—
360	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
361	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
362	C₂²×C₈	C₂×C₄×C₅	1	2	yes	—
363	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
364	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
365	C₂²×C₈	C₅×D₄	1	2	yes	—
366	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
367	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
368	C₂²×C₈	C₅×D₄	1	2	yes	—
369	C₂²×C₈	C₂³×C₅	1	2	yes	—
370	#117	—	2	1	no	—
371	#117	—	2	1	no	—
372	#117	—	2	2	no	—
373	#117	—	2	2	no	—
374	#117	—	2	2	no	—
375	#117	C₅×D₄	1	2	yes	—
376	#117	C₂³×C₅	1	4	yes	—
377	#117	C₂³×C₅	1	2	yes	—
378	C₂×C₄⋊C₄	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
382	C₂×C₄²	—	2	1	no	—
383	C₂×C₄²	—	2	2	no	—
384	#107	—	2	4	no	—
385	#106	—	2	4	no	—
386	#104	—	2	16	no	—
387	#99	—	2	16	no	—
388	#97	—	2	4	no	—
389	C₄×C₈	—	2	4	no	—
390	C₂²×C₅	—	2	2	no	—
391	C₂²×C₅	—	2	2	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	—	4	1	no	—
395	C₂²×C₅	—	4	1	no	—
396	C₂²×C₅	—	4	1	no	—
397	C₂²×C₅	—	4	4	no	—
398	C₂²×C₅	—	8	4	no	—
399	C₂²×C₅	—	8	4	no	—
400	C₂²×C₅	—	8	4	no	—
401	C₂²×C₅	#390	1	1	yes	characteristic
402	C₂²×C₅	#390	1	1	yes	characteristic
403	C₂²×C₅	#390	1	1	yes	characteristic
404	C₂²×C₅	#390	1	1	yes	characteristic
405	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
406	C₂²×C₅	C₂×#121	1	1	yes	characteristic
407	C₂²×C₅	C₂×#127	1	1	yes	characteristic
408	C₄×C₅	—	4	4	no	—
409	C₄×C₅	—	4	4	no	—
410	C₄×C₅	—	8	4	no	—
411	C₄×C₅	#390	1	1	yes	characteristic
412	C₄×C₅	#390	1	1	yes	characteristic
413	C₄×C₅	#390	1	1	yes	characteristic
414	C₄×C₅	#390	1	1	yes	characteristic
415	C₄×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
416	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
417	C₄×C₅	C₂×#121	1	1	yes	characteristic
418	C₄×C₅	C₂×#124	1	1	yes	characteristic
419	C₂⁴	—	2	2	no	—
420	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
421	#41	—	2	4	no	—
422	#41	—	2	4	no	—
423	#41	—	2	4	no	—
424	#41	—	2	4	no	—
425	#41	—	2	4	no	—
426	#41	—	2	4	no	—
427	#41	—	2	4	no	—
428	#41	—	2	4	no	—
429	#41	—	4	2	no	—
430	#41	—	4	2	no	—
431	#41	—	4	2	no	—
432	#41	—	4	2	no	—
433	#41	—	4	2	no	—
434	#41	—	4	2	no	—
435	#41	—	4	2	no	—
436	#41	—	4	2	no	—
437	C₂×Q₈	—	2	2	no	—
438	C₂×Q₈	—	2	2	no	—
439	C₂×Q₈	—	2	2	no	—
440	C₂×Q₈	—	2	2	no	—
441	C₂×Q₈	—	2	2	no	—
442	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	—	2	2	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	2	2	no	—
449	C₂×D₄	—	2	2	no	—
450	C₂×D₄	—	4	2	no	—
451	C₂×D₄	—	4	2	no	—
452	C₂×D₄	—	4	2	no	—
453	C₂×D₄	—	4	2	no	—
454	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	4	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	4	2	no	—
460	C₂²×C₄	—	4	2	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	2	no	—
463	C₂²×C₄	—	4	2	no	—
464	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
465	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
468	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₅×#41	1	1	yes	characteristic
474	C₂²×C₄	C₅×#41	1	1	yes	characteristic
475	C₂²×C₄	C₅×#41	1	1	yes	characteristic
476	C₂²×C₄	C₅×#41	1	1	yes	characteristic
477	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
478	Q₁₆	—	2	4	no	—
479	Q₁₆	—	2	4	no	—
480	SD₁₆	—	2	8	no	—
481	SD₁₆	—	2	8	no	—
482	D₈	—	2	4	no	—
483	D₈	—	2	4	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	2	2	no	—
487	M₁₆	C₂×C₅×D₄	1	4	yes	—
488	C₂×C₈	—	2	2	no	—
489	C₂×C₈	—	2	2	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
492	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
493	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
494	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
495	C₂×C₈	C₅×C₂²⋊C₄	1	1	yes	characteristic
496	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
497	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
498	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
499	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
500	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
501	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
502	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
503	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
504	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
505	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
506	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	4	no	—
510	C₄⋊C₄	—	4	2	no	—
511	C₂²⋊C₄	—	2	2	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	4	2	no	—
514	C₂²⋊C₄	C₂×C₅×D₄	1	4	yes	—
515	C₄²	—	2	2	no	—
516	C₄²	—	2	2	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	4	2	no	—
519	C₂×C₅	—	2	1	no	—
520	C₂×C₅	—	2	1	no	—
521	C₂×C₅	—	2	1	no	—
522	C₂×C₅	—	2	1	no	—
523	C₂×C₅	—	2	1	no	—
524	C₂×C₅	—	2	1	no	—
525	C₂×C₅	—	8	4	no	—
526	C₂×C₅	#1976	1	2	yes	direct product factor
527	C₂×C₅	C₂×#390	1	1	yes	characteristic
528	C₂³	—	2	4	no	—
529	C₂³	—	4	2	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	4	2	no	—
532	C₂³	—	8	4	no	—
533	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
534	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
535	C₂³	C₅×#121	1	1	yes	characteristic
536	C₂³	C₅×#121	1	1	yes	characteristic
537	C₂³	C₅×#127	1	1	yes	characteristic
538	C₂³	C₅×#127	1	1	yes	characteristic
539	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
540	Q₈	—	2	4	no	—
541	Q₈	—	2	4	no	—
542	Q₈	—	4	2	no	—
543	Q₈	—	4	2	no	—
544	D₄	—	2	4	no	—
545	D₄	—	2	4	no	—
546	D₄	—	4	4	no	—
547	D₄	—	4	4	no	—
548	D₄	—	4	4	no	—
549	D₄	—	4	4	no	—
550	D₄	—	4	2	no	—
551	D₄	—	4	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	4	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	4	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	4	no	—
562	C₂×C₄	—	8	4	no	—
563	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
564	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
565	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
567	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
568	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
569	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
570	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
571	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
572	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
573	C₂×C₄	C₅×#121	1	1	yes	characteristic
574	C₂×C₄	C₅×#121	1	1	yes	characteristic
575	C₂×C₄	C₅×#121	1	1	yes	characteristic
576	C₂×C₄	C₅×#121	1	1	yes	characteristic
577	C₂×C₄	C₅×#121	1	1	yes	characteristic
578	C₂×C₄	C₅×#121	1	1	yes	characteristic
579	C₂×C₄	C₅×#124	1	1	yes	characteristic
580	C₂×C₄	C₅×#124	1	1	yes	characteristic
581	C₂×C₄	C₅×#124	1	1	yes	characteristic
582	C₂×C₄	C₅×#124	1	1	yes	characteristic
583	C₂×C₄	C₅×#127	1	1	yes	characteristic
584	C₂×C₄	C₅×#127	1	1	yes	characteristic
585	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
586	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
587	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
588	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
589	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
590	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
591	C₈	—	2	4	no	—
592	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
593	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
594	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
595	C₈	C₂×C₅×C₂²⋊C₄	1	2	yes	—
596	C₅	C₂×#1976	1	1	yes	characteristic, direct product factor, Sylow
597	C₂²	—	2	2	no	—
598	C₂²	—	2	2	no	—
599	C₂²	—	2	2	no	—
600	C₂²	—	4	1	no	—
601	C₂²	—	4	1	no	—
602	C₂²	—	4	1	no	—
603	C₂²	—	4	1	no	—
604	C₂²	—	4	4	no	—
605	C₂²	—	8	4	no	—
606	C₂²	—	8	4	no	—
607	C₂²	—	8	4	no	—
608	C₂²	C₅×#390	1	1	yes	characteristic
609	C₂²	C₅×#390	1	1	yes	characteristic
610	C₂²	C₅×#390	1	1	yes	characteristic
611	C₂²	C₅×#390	1	1	yes	characteristic
612	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
613	C₂²	C₂×C₅×#121	1	1	yes	characteristic
614	C₂²	C₂×C₅×#127	1	1	yes	characteristic
615	C₄	—	4	4	no	—
616	C₄	—	4	4	no	—
617	C₄	—	8	4	no	—
618	C₄	C₅×#390	1	1	yes	characteristic
619	C₄	C₅×#390	1	1	yes	characteristic
620	C₄	C₅×#390	1	1	yes	characteristic
621	C₄	C₅×#390	1	1	yes	characteristic
622	C₄	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
623	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
624	C₄	C₂×C₅×#121	1	1	yes	characteristic
625	C₄	C₂×C₅×#124	1	1	yes	characteristic
626	C₂	—	2	1	no	—
627	C₂	—	2	1	no	—
628	C₂	—	2	1	no	—
629	C₂	—	2	1	no	—
630	C₂	—	2	1	no	—
631	C₂	—	2	1	no	—
632	C₂	—	8	4	no	—
633	C₂	C₅×#1976	1	2	yes	direct product factor
634	C₂	C₂×C₅×#390	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	#390
prime radical	C₂²×C₅×#135	C₂
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×#427	C₂	semidirect
3. C₂×C₅×#421	C₂	semidirect
4. C₂×C₅×#410	C₂	semidirect
5. C₂×C₅×#405	C₂	semidirect
6. C₅×#1976	C₂	direct (N × H)
14. C₂×C₅×#135	C₄	semidirect
16. C₂²×C₅×Q₁₆	C₄	semidirect
17. C₂²×C₅×SD₁₆	C₄	semidirect
18. C₂²×C₅×D₈	C₄	semidirect
24. C₅×#427	C₂²	semidirect
28. C₅×#421	C₂²	semidirect
31. C₅×#410	C₂²	semidirect
34. C₅×#405	C₂²	semidirect
37. C₂×#1976	C₅	direct (N × H)
66. C₂×C₅×Q₁₆	C₂×C₄	semidirect
70. C₂×C₅×SD₁₆	C₂×C₄	semidirect
74. C₂×C₅×D₈	C₂×C₄	semidirect
113. C₂×#427	C₂×C₅	semidirect
114. C₂×#421	C₂×C₅	semidirect
115. C₂×#410	C₂×C₅	semidirect
116. C₂×#405	C₂×C₅	semidirect
117. #1976	C₂×C₅	direct (N × H)
225. C₂×#135	C₄×C₅	semidirect
227. C₂²×Q₁₆	C₄×C₅	semidirect
228. C₂²×SD₁₆	C₄×C₅	semidirect
229. C₂²×D₈	C₄×C₅	semidirect
235. #427	C₂²×C₅	semidirect
239. #421	C₂²×C₅	semidirect
242. #410	C₂²×C₅	semidirect
245. #405	C₂²×C₅	semidirect
344. C₂×Q₁₆	C₂×C₄×C₅	semidirect
348. C₂×SD₁₆	C₂×C₄×C₅	semidirect
352. C₂×D₈	C₂×C₄×C₅	semidirect
526. C₂×C₅	#1976	direct (N × H)
596. C₅	C₂×#1976	direct (N × H)
633. C₂	C₅×#1976	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×#135	2
C₂×C₅×#427	2
C₂×C₅×#421	2
C₂×C₅×#410	2
C₂×C₅×#405	2
C₅×#1976	2
C₂×#1976	5

Subgroups — C2×C5×#1976 #11943963

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#1976 #11943963