Subgroups — C₂×C₅×#3136 #11983330

Order 1280.

2262 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#544	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#535	C₂	1	1	yes	maximal, characteristic
3	C₅×#3136	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₅×#490	C₂	1	2	yes	maximal, complemented
5	C₂×C₅×#489	C₂	1	2	yes	maximal, complemented
6	C₂×C₅×#488	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#486	C₂	1	2	yes	maximal, complemented
8	C₂×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×#418	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₅×#102	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂³×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₅×#544	—	2	4	no	—
18	C₅×#544	C₂²	1	8	yes	complemented
19	C₅×#535	—	2	4	no	—
20	C₅×#535	C₂²	1	8	yes	—
21	C₂×C₅×C₄⋊Q₈	—	2	1	no	—
22	C₂×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
23	C₂×C₅×#127	C₂²	1	2	yes	—
24	C₂×C₅×#125	—	2	1	no	—
25	C₂×C₅×#125	C₂²	1	2	yes	complemented
26	C₂×C₅×#124	C₂²	1	2	yes	—
27	C₂×C₅×C₂²⋊Q₈	—	2	2	no	—
28	C₂×C₅×#121	—	2	1	no	—
29	C₂×C₅×#121	—	2	1	no	—
30	C₂×C₅×#120	—	2	2	no	—
31	C₂×C₅×#117	C₂²	1	1	yes	characteristic
32	C₂×C₅×#117	C₂²	1	1	yes	characteristic
33	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₅×#490	C₂²	1	16	yes	complemented
35	C₅×#489	C₂²	1	16	yes	complemented
36	C₅×#488	C₂²	1	16	yes	complemented
37	C₅×#486	C₂²	1	16	yes	complemented
38	C₅×#418	C₂²	1	8	yes	complemented
39	C₅×#417	C₂²	1	8	yes	complemented
40	C₅×#416	C₂²	1	8	yes	complemented
41	C₂×C₅×#103	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₅×#103	C₂²	1	2	yes	complemented
43	C₂×C₅×#103	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₅×#102	C₂²	1	2	yes	—
45	C₂×C₅×#102	C₂²	1	2	yes	—
46	C₂×C₅×#102	C₂²	1	2	yes	—
47	C₂×C₅×#102	C₂²	1	2	yes	—
48	C₂×C₅×#102	C₂²	1	8	yes	complemented
49	C₂×C₅×#102	C₂²	1	1	yes	characteristic, complemented
50	C₂×C₅×#102	C₂²	1	2	yes	complemented
51	C₂×C₅×#102	C₂²	1	1	yes	characteristic, complemented
52	C₅×#405	C₂²	1	8	yes	complemented
53	C₂×C₅×#97	C₂²	1	2	yes	complemented
54	C₂×C₄×C₅×C₈	C₂²	1	2	yes	complemented
55	C₂×#3136	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
56	C₂⁵×C₅	—	2	1	no	—
57	C₂×C₅×#41	—	2	2	no	—
58	C₂×C₅×#41	—	2	4	no	—
59	C₂×C₅×#41	—	2	4	no	—
60	C₂×C₅×#41	C₂³	1	4	yes	—
61	C₂²×C₅×Q₈	—	2	2	no	—
62	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	—	2	1	no	—
65	C₂²×C₅×D₄	—	2	2	no	—
66	C₂²×C₅×D₄	—	2	2	no	—
67	C₂²×C₅×D₄	—	2	2	no	—
68	C₂²×C₅×D₄	—	2	4	no	—
69	C₂²×C₅×D₄	—	2	4	no	—
70	C₂²×C₅×D₄	C₂³	1	2	yes	—
71	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
72	C₂²×C₅×D₄	C₂³	1	4	yes	—
73	C₂³×C₄×C₅	—	2	1	no	—
74	C₂³×C₄×C₅	—	2	1	no	—
75	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₂×C₅×M₁₆	—	2	4	no	—
77	C₂×C₅×M₁₆	C₂³	1	4	yes	—
78	C₂²×C₅×C₈	—	2	4	no	—
79	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂²×C₅×C₈	C₂³	1	2	yes	—
81	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₂²×C₅×C₈	C₂³	1	4	yes	—
83	C₅×C₄⋊Q₈	—	2	8	no	—
84	C₅×C₄⋊Q₈	—	2	4	no	—
85	C₅×C₄⋊Q₈	C₂³	1	8	yes	complemented
86	C₅×#127	—	2	4	no	—
87	C₅×#127	C₂³	1	8	yes	—
88	C₅×#125	—	2	8	no	—
89	C₅×#125	—	2	4	no	—
90	C₅×#125	C₂³	1	8	yes	complemented
91	C₅×#124	—	2	4	no	—
92	C₅×#124	C₂³	1	8	yes	—
93	C₅×C₂²⋊Q₈	—	2	16	no	—
94	C₅×#121	—	2	8	no	—
95	C₅×#121	—	2	8	no	—
96	C₅×#120	—	2	16	no	—
97	C₅×#117	—	2	2	no	—
98	C₅×#117	D₄	1	4	yes	—
99	C₅×#117	C₂³	1	4	yes	—
100	C₅×#117	C₂³	1	4	yes	—
101	C₂×C₅×C₄⋊C₄	—	2	1	no	—
102	C₂×C₅×C₄⋊C₄	—	2	2	no	—
103	C₂×C₅×C₄⋊C₄	—	2	2	no	—
104	C₂×C₅×C₄⋊C₄	—	2	2	no	—
105	C₂×C₅×C₄⋊C₄	—	2	2	no	—
106	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
108	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
110	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₂×C₅×C₄⋊C₄	C₂³	1	4	yes	—
112	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
114	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
115	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
116	C₂×C₄²×C₅	—	2	1	no	—
117	C₂×C₄²×C₅	C₂³	1	2	yes	—
118	C₅×#103	C₂³	1	4	yes	complemented
119	C₅×#103	C₂³	1	4	yes	complemented
120	C₅×#103	C₂³	1	8	yes	complemented
121	C₅×#102	C₂³	1	8	yes	—
122	C₅×#102	C₂³	1	8	yes	—
123	C₅×#102	C₂³	1	8	yes	—
124	C₅×#102	C₂³	1	8	yes	—
125	C₅×#102	C₂³	1	4	yes	complemented
126	C₅×#102	C₂³	1	4	yes	complemented
127	C₅×#102	C₂³	1	8	yes	complemented
128	C₅×#97	C₂³	1	8	yes	complemented
129	C₄×C₅×C₈	C₂³	1	8	yes	complemented
130	C₂×#544	C₂×C₅	1	1	yes	characteristic, complemented
131	C₂×#535	C₂×C₅	1	1	yes	characteristic
132	#3136	C₂×C₅	1	16	yes	direct product factor
133	C₂×#490	C₂×C₅	1	2	yes	complemented
134	C₂×#489	C₂×C₅	1	2	yes	complemented
135	C₂×#488	C₂×C₅	1	2	yes	complemented
136	C₂×#486	C₂×C₅	1	2	yes	complemented
137	C₂×#417	C₂×C₅	1	1	yes	characteristic, complemented
138	C₂×#418	C₂×C₅	1	1	yes	characteristic, complemented
139	C₂×#416	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×#102	C₂×C₅	1	1	yes	characteristic, complemented
141	C₂×#405	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂⁴×C₅	—	2	2	no	—
143	C₂⁴×C₅	—	2	1	no	—
144	C₂⁴×C₅	—	2	4	no	—
145	C₂⁴×C₅	—	4	4	no	—
146	C₂⁴×C₅	—	8	2	no	—
147	C₂⁴×C₅	—	8	2	no	—
148	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
149	C₅×#41	—	2	8	no	—
150	C₅×#41	—	2	8	no	—
151	C₅×#41	—	4	8	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	8	no	—
154	C₂×C₅×Q₈	—	2	2	no	—
155	C₂×C₅×Q₈	—	2	2	no	—
156	C₂×C₅×Q₈	—	8	4	no	—
157	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
158	C₂×C₅×D₄	—	2	4	no	—
159	C₂×C₅×D₄	—	2	4	no	—
160	C₂×C₅×D₄	—	2	2	no	—
161	C₂×C₅×D₄	—	2	1	no	—
162	C₂×C₅×D₄	—	2	8	no	—
163	C₂×C₅×D₄	—	2	8	no	—
164	C₂×C₅×D₄	—	2	4	no	—
165	C₂×C₅×D₄	—	2	4	no	—
166	C₂×C₅×D₄	—	2	8	no	—
167	C₂×C₅×D₄	—	2	8	no	—
168	C₂×C₅×D₄	—	2	2	no	—
169	C₂×C₅×D₄	—	2	2	no	—
170	C₂×C₅×D₄	—	4	4	no	—
171	C₂×C₅×D₄	—	4	4	no	—
172	C₂×C₅×D₄	—	4	8	no	—
173	C₂×C₅×D₄	—	8	4	no	—
174	C₂×C₅×D₄	—	8	4	no	—
175	C₂×C₅×D₄	C₂⁴	1	4	yes	—
176	C₂×C₅×D₄	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₅	—	2	1	no	—
178	C₂²×C₄×C₅	—	2	1	no	—
179	C₂²×C₄×C₅	—	2	1	no	—
180	C₂²×C₄×C₅	—	2	2	no	—
181	C₂²×C₄×C₅	—	2	4	no	—
182	C₂²×C₄×C₅	—	2	4	no	—
183	C₂²×C₄×C₅	—	4	4	no	—
184	C₂²×C₄×C₅	—	8	2	no	—
185	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
186	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
187	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
188	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂²×C₄×C₅	#41	1	4	yes	—
190	C₂²×C₄×C₅	#41	1	4	yes	—
191	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
193	C₅×M₁₆	—	2	8	no	—
194	C₂×C₅×C₈	—	2	2	no	—
195	C₂×C₅×C₈	—	2	2	no	—
196	C₂×C₅×C₈	—	2	8	no	—
197	C₂×C₅×C₈	—	2	4	no	—
198	C₂×C₅×C₈	C₂⁴	1	2	yes	—
199	C₂×C₅×C₈	C₂⁴	1	2	yes	—
200	C₂×C₅×C₈	C₂⁴	1	4	yes	—
201	C₅×C₄⋊C₄	—	2	4	no	—
202	C₅×C₄⋊C₄	—	2	2	no	—
203	C₅×C₄⋊C₄	—	2	8	no	—
204	C₅×C₄⋊C₄	—	2	8	no	—
205	C₅×C₄⋊C₄	—	2	8	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
209	C₅×C₄⋊C₄	C₂×D₄	1	4	yes	—
210	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
211	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
212	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
213	C₅×C₂²⋊C₄	—	2	4	no	—
214	C₅×C₂²⋊C₄	—	2	8	no	—
215	C₅×C₂²⋊C₄	—	2	8	no	—
216	C₅×C₂²⋊C₄	C₂×D₄	1	8	yes	—
217	C₄²×C₅	—	2	4	no	—
218	C₄²×C₅	C₂×D₄	1	4	yes	—
219	C₄²×C₅	C₂⁴	1	4	yes	—
220	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
221	C₂³×D₄	C₂²×C₅	1	1	yes	characteristic
222	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
223	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
224	#544	—	2	4	no	—
225	#544	C₂²×C₅	1	8	yes	complemented
226	#535	—	2	4	no	—
227	#535	C₂²×C₅	1	8	yes	—
228	C₂×C₄⋊Q₈	—	2	1	no	—
229	C₂×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
230	C₂×#127	C₂²×C₅	1	2	yes	—
231	C₂×#125	—	2	1	no	—
232	C₂×#125	C₂²×C₅	1	2	yes	complemented
233	C₂×#124	C₂²×C₅	1	2	yes	—
234	C₂×C₂²⋊Q₈	—	2	2	no	—
235	C₂×#121	—	2	1	no	—
236	C₂×#121	—	2	1	no	—
237	C₂×#120	—	2	2	no	—
238	C₂×#117	C₂²×C₅	1	1	yes	characteristic
239	C₂×#117	C₂²×C₅	1	1	yes	characteristic
240	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
241	#490	C₂²×C₅	1	16	yes	complemented
242	#489	C₂²×C₅	1	16	yes	complemented
243	#488	C₂²×C₅	1	16	yes	complemented
244	#486	C₂²×C₅	1	16	yes	complemented
245	#418	C₂²×C₅	1	8	yes	complemented
246	#417	C₂²×C₅	1	8	yes	complemented
247	#416	C₂²×C₅	1	8	yes	complemented
248	C₂×#103	C₂²×C₅	1	1	yes	characteristic, complemented
249	C₂×#103	C₂²×C₅	1	2	yes	complemented
250	C₂×#103	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₂×#102	C₂²×C₅	1	2	yes	—
252	C₂×#102	C₂²×C₅	1	2	yes	—
253	C₂×#102	C₂²×C₅	1	2	yes	—
254	C₂×#102	C₂²×C₅	1	2	yes	—
255	C₂×#102	C₂²×C₅	1	8	yes	complemented
256	C₂×#102	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₂×#102	C₂²×C₅	1	2	yes	complemented
258	C₂×#102	C₂²×C₅	1	1	yes	characteristic, complemented
259	#405	C₂²×C₅	1	8	yes	complemented
260	C₂×#97	C₂²×C₅	1	2	yes	complemented
261	C₂×C₄×C₈	C₂²×C₅	1	2	yes	complemented
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	2	2	no	—
264	C₂³×C₅	—	2	4	no	—
265	C₂³×C₅	—	2	2	no	—
266	C₂³×C₅	—	4	2	no	—
267	C₂³×C₅	—	4	8	no	—
268	C₂³×C₅	—	4	4	no	—
269	C₂³×C₅	—	4	2	no	—
270	C₂³×C₅	—	4	4	no	—
271	C₂³×C₅	—	4	2	no	—
272	C₂³×C₅	—	4	4	no	—
273	C₂³×C₅	—	8	4	no	—
274	C₂³×C₅	—	8	4	no	—
275	C₂³×C₅	—	8	16	no	—
276	C₂³×C₅	#124	1	4	yes	—
277	C₂³×C₅	C₂²×D₄	1	2	yes	—
278	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₅×Q₈	—	2	2	no	—
280	C₅×Q₈	—	2	2	no	—
281	C₅×Q₈	—	4	2	no	—
282	C₅×Q₈	—	8	8	no	—
283	C₅×D₄	—	2	4	no	—
284	C₅×D₄	—	2	4	no	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	—	2	2	no	—
287	C₅×D₄	—	4	8	no	—
288	C₅×D₄	—	4	8	no	—
289	C₅×D₄	—	4	4	no	—
290	C₅×D₄	—	4	2	no	—
291	C₅×D₄	—	8	8	no	—
292	C₅×D₄	—	8	8	no	—
293	C₂×C₄×C₅	—	2	4	no	—
294	C₂×C₄×C₅	—	2	4	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	4	no	—
299	C₂×C₄×C₅	—	4	2	no	—
300	C₂×C₄×C₅	—	4	4	no	—
301	C₂×C₄×C₅	—	4	2	no	—
302	C₂×C₄×C₅	—	4	2	no	—
303	C₂×C₄×C₅	—	4	8	no	—
304	C₂×C₄×C₅	—	8	4	no	—
305	C₂×C₄×C₅	#124	1	4	yes	—
306	C₂×C₄×C₅	#124	1	8	yes	—
307	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
308	C₂×C₄×C₅	C₂²×D₄	1	4	yes	—
309	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂×#41	1	2	yes	—
312	C₂×C₄×C₅	C₂×#41	1	2	yes	—
313	C₂×C₄×C₅	C₂×#41	1	4	yes	—
314	C₂×C₄×C₅	C₂×#41	1	4	yes	—
315	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
316	C₅×C₈	—	2	2	no	—
317	C₅×C₈	—	2	2	no	—
318	C₅×C₈	—	2	4	no	—
319	C₂⁵	—	2	1	no	—
320	C₂×#41	—	2	2	no	—
321	C₂×#41	—	2	4	no	—
322	C₂×#41	—	2	4	no	—
323	C₂×#41	C₂³×C₅	1	4	yes	—
324	C₂²×Q₈	—	2	2	no	—
325	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	—	2	1	no	—
328	C₂²×D₄	—	2	2	no	—
329	C₂²×D₄	—	2	2	no	—
330	C₂²×D₄	—	2	2	no	—
331	C₂²×D₄	—	2	4	no	—
332	C₂²×D₄	—	2	4	no	—
333	C₂²×D₄	C₂³×C₅	1	2	yes	—
334	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
335	C₂²×D₄	C₂³×C₅	1	4	yes	—
336	C₂³×C₄	—	2	1	no	—
337	C₂³×C₄	—	2	1	no	—
338	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
339	C₂×M₁₆	—	2	4	no	—
340	C₂×M₁₆	C₂³×C₅	1	4	yes	—
341	C₂²×C₈	—	2	4	no	—
342	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
343	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
344	C₂²×C₈	C₂³×C₅	1	4	yes	—
345	C₂²×C₈	C₂³×C₅	1	2	yes	—
346	C₄⋊Q₈	—	2	8	no	—
347	C₄⋊Q₈	—	2	4	no	—
348	C₄⋊Q₈	C₂³×C₅	1	8	yes	complemented
349	#127	—	2	4	no	—
350	#127	C₂³×C₅	1	8	yes	—
351	#125	—	2	8	no	—
352	#125	—	2	4	no	—
353	#125	C₂³×C₅	1	8	yes	complemented
354	#124	—	2	4	no	—
355	#124	C₂³×C₅	1	8	yes	—
356	C₂²⋊Q₈	—	2	16	no	—
357	#121	—	2	8	no	—
358	#121	—	2	8	no	—
359	#120	—	2	16	no	—
360	#117	—	2	2	no	—
361	#117	C₅×D₄	1	4	yes	—
362	#117	C₂³×C₅	1	4	yes	—
363	#117	C₂³×C₅	1	4	yes	—
364	C₂×C₄⋊C₄	—	2	1	no	—
365	C₂×C₄⋊C₄	—	2	2	no	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
370	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
371	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
372	C₂×C₄⋊C₄	C₂³×C₅	1	4	yes	—
373	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
375	C₂×C₂²⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
379	C₂×C₄²	—	2	1	no	—
380	C₂×C₄²	C₂³×C₅	1	2	yes	—
381	#103	C₂³×C₅	1	4	yes	complemented
382	#103	C₂³×C₅	1	4	yes	complemented
383	#103	C₂³×C₅	1	8	yes	complemented
384	#102	C₂³×C₅	1	8	yes	—
385	#102	C₂³×C₅	1	8	yes	—
386	#102	C₂³×C₅	1	8	yes	—
387	#102	C₂³×C₅	1	8	yes	—
388	#102	C₂³×C₅	1	4	yes	complemented
389	#102	C₂³×C₅	1	4	yes	complemented
390	#102	C₂³×C₅	1	8	yes	complemented
391	#97	C₂³×C₅	1	8	yes	complemented
392	C₄×C₈	C₂³×C₅	1	8	yes	complemented
393	C₂²×C₅	—	2	8	no	—
394	C₂²×C₅	—	2	2	no	—
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	—	4	4	no	—
398	C₂²×C₅	—	4	2	no	—
399	C₂²×C₅	—	4	4	no	—
400	C₂²×C₅	—	4	2	no	—
401	C₂²×C₅	—	4	4	no	—
402	C₂²×C₅	—	8	16	no	—
403	C₂²×C₅	—	8	4	no	—
404	C₂²×C₅	—	8	8	no	—
405	C₂²×C₅	C₂×#124	1	4	yes	—
406	C₂²×C₅	C₂×#124	1	2	yes	—
407	C₂²×C₅	#576	1	2	yes	—
408	C₂²×C₅	#577	1	2	yes	—
409	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
410	C₄×C₅	—	2	4	no	—
411	C₄×C₅	—	2	4	no	—
412	C₄×C₅	—	4	2	no	—
413	C₄×C₅	—	4	4	no	—
414	C₄×C₅	—	4	2	no	—
415	C₄×C₅	—	4	2	no	—
416	C₄×C₅	C₂×#124	1	4	yes	—
417	C₄×C₅	C₂×#124	1	2	yes	—
418	C₄×C₅	C₂²×#41	1	1	yes	characteristic
419	C₄×C₅	C₂²×#41	1	1	yes	characteristic
420	C₂⁴	—	2	2	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	—	2	4	no	—
423	C₂⁴	—	4	4	no	—
424	C₂⁴	—	8	2	no	—
425	C₂⁴	—	8	2	no	—
426	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
427	#41	—	2	8	no	—
428	#41	—	2	8	no	—
429	#41	—	4	8	no	—
430	C₂×Q₈	—	2	1	no	—
431	C₂×Q₈	—	2	8	no	—
432	C₂×Q₈	—	2	2	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	8	4	no	—
435	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	2	no	—
447	C₂×D₄	—	2	2	no	—
448	C₂×D₄	—	4	4	no	—
449	C₂×D₄	—	4	4	no	—
450	C₂×D₄	—	4	8	no	—
451	C₂×D₄	—	8	4	no	—
452	C₂×D₄	—	8	4	no	—
453	C₂×D₄	C₂⁴×C₅	1	4	yes	—
454	C₂×D₄	C₂⁴×C₅	1	2	yes	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	4	no	—
461	C₂²×C₄	—	4	4	no	—
462	C₂²×C₄	—	8	2	no	—
463	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
464	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
465	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
467	C₂²×C₄	C₅×#41	1	4	yes	—
468	C₂²×C₄	C₅×#41	1	4	yes	—
469	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
471	M₁₆	—	2	8	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	8	no	—
475	C₂×C₈	—	2	4	no	—
476	C₂×C₈	C₂⁴×C₅	1	2	yes	—
477	C₂×C₈	C₂⁴×C₅	1	4	yes	—
478	C₂×C₈	C₂⁴×C₅	1	2	yes	—
479	C₄⋊C₄	—	2	4	no	—
480	C₄⋊C₄	—	2	2	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	2	8	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
487	C₄⋊C₄	C₂×C₅×D₄	1	4	yes	—
488	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
489	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
490	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
491	C₂²⋊C₄	—	2	4	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	8	no	—
494	C₂²⋊C₄	C₂×C₅×D₄	1	8	yes	—
495	C₄²	—	2	4	no	—
496	C₄²	C₂×C₅×D₄	1	4	yes	—
497	C₄²	C₂⁴×C₅	1	4	yes	—
498	C₂×C₅	—	2	4	no	—
499	C₂×C₅	—	8	2	no	—
500	C₂×C₅	—	8	4	no	—
501	C₂×C₅	#3136	1	4	yes	direct product factor
502	C₂×C₅	C₂²×#124	1	1	yes	characteristic
503	C₂×C₅	C₂×#576	1	1	yes	characteristic
504	C₂×C₅	C₂×#577	1	1	yes	characteristic
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	2	no	—
509	C₂³	—	4	2	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	2	no	—
513	C₂³	—	4	4	no	—
514	C₂³	—	4	2	no	—
515	C₂³	—	4	4	no	—
516	C₂³	—	8	4	no	—
517	C₂³	—	8	4	no	—
518	C₂³	—	8	16	no	—
519	C₂³	C₅×#124	1	4	yes	—
520	C₂³	C₂²×C₅×D₄	1	2	yes	—
521	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
522	Q₈	—	2	2	no	—
523	Q₈	—	2	2	no	—
524	Q₈	—	4	2	no	—
525	Q₈	—	8	8	no	—
526	D₄	—	2	4	no	—
527	D₄	—	2	4	no	—
528	D₄	—	2	2	no	—
529	D₄	—	2	2	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	8	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	2	no	—
534	D₄	—	8	8	no	—
535	D₄	—	8	8	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	4	4	no	—
544	C₂×C₄	—	4	2	no	—
545	C₂×C₄	—	4	2	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	8	4	no	—
548	C₂×C₄	C₅×#124	1	4	yes	—
549	C₂×C₄	C₅×#124	1	8	yes	—
550	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
551	C₂×C₄	C₂²×C₅×D₄	1	4	yes	—
552	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
553	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
554	C₂×C₄	C₂×C₅×#41	1	2	yes	—
555	C₂×C₄	C₂×C₅×#41	1	2	yes	—
556	C₂×C₄	C₂×C₅×#41	1	4	yes	—
557	C₂×C₄	C₂×C₅×#41	1	4	yes	—
558	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
559	C₈	—	2	2	no	—
560	C₈	—	2	2	no	—
561	C₈	—	2	4	no	—
562	C₅	C₂×#3136	1	1	yes	characteristic, direct product factor, Sylow
563	C₂²	—	2	8	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	4	2	no	—
567	C₂²	—	4	4	no	—
568	C₂²	—	4	2	no	—
569	C₂²	—	4	4	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	4	4	no	—
572	C₂²	—	8	16	no	—
573	C₂²	—	8	8	no	—
574	C₂²	—	8	4	no	—
575	C₂²	C₂×C₅×#124	1	4	yes	—
576	C₂²	C₂×C₅×#124	1	2	yes	—
577	C₂²	C₅×#576	1	2	yes	—
578	C₂²	C₅×#577	1	2	yes	—
579	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
580	C₄	—	2	4	no	—
581	C₄	—	2	4	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	4	no	—
584	C₄	—	4	2	no	—
585	C₄	—	4	2	no	—
586	C₄	C₂×C₅×#124	1	4	yes	—
587	C₄	C₂×C₅×#124	1	2	yes	—
588	C₄	C₂²×C₅×#41	1	1	yes	characteristic
589	C₄	C₂²×C₅×#41	1	1	yes	characteristic
590	C₂	—	2	4	no	—
591	C₂	—	8	4	no	—
592	C₂	—	8	2	no	—
593	C₂	C₅×#3136	1	4	yes	direct product factor
594	C₂	C₂²×C₅×#124	1	1	yes	characteristic
595	C₂	C₂×C₅×#576	1	1	yes	characteristic
596	C₂	C₂×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₂×C₅×#535	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. C₂×C₅×#544	C₂	semidirect
3. C₅×#3136	C₂	direct (N × H)
4. C₂×C₅×#490	C₂	semidirect
5. C₂×C₅×#489	C₂	semidirect
6. C₂×C₅×#488	C₂	semidirect
7. C₂×C₅×#486	C₂	semidirect
8. C₂×C₅×#417	C₂	semidirect
9. C₂×C₅×#418	C₂	semidirect
10. C₂×C₅×#416	C₂	semidirect
11. C₂²×C₅×#102	C₂	semidirect
12. C₂×C₅×#405	C₂	semidirect
18. C₅×#544	C₂²	semidirect
22. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₂×C₅×#125	C₂²	semidirect
34. C₅×#490	C₂²	semidirect
35. C₅×#489	C₂²	semidirect
36. C₅×#488	C₂²	semidirect
37. C₅×#486	C₂²	semidirect
38. C₅×#418	C₂²	semidirect
39. C₅×#417	C₂²	semidirect
40. C₅×#416	C₂²	semidirect
41. C₂×C₅×#103	C₂²	semidirect
42. C₂×C₅×#103	C₂²	semidirect
43. C₂×C₅×#103	C₂²	semidirect
48. C₂×C₅×#102	C₂²	semidirect
49. C₂×C₅×#102	C₂²	semidirect
50. C₂×C₅×#102	C₂²	semidirect
51. C₂×C₅×#102	C₂²	semidirect
52. C₅×#405	C₂²	semidirect
53. C₂×C₅×#97	C₂²	semidirect
54. C₂×C₄×C₅×C₈	C₂²	semidirect
55. C₂×#3136	C₅	direct (N × H)
85. C₅×C₄⋊Q₈	C₂³	semidirect
90. C₅×#125	C₂³	semidirect
118. C₅×#103	C₂³	semidirect
119. C₅×#103	C₂³	semidirect
120. C₅×#103	C₂³	semidirect
125. C₅×#102	C₂³	semidirect
126. C₅×#102	C₂³	semidirect
127. C₅×#102	C₂³	semidirect
128. C₅×#97	C₂³	semidirect
129. C₄×C₅×C₈	C₂³	semidirect
130. C₂×#544	C₂×C₅	semidirect
132. #3136	C₂×C₅	direct (N × H)
133. C₂×#490	C₂×C₅	semidirect
134. C₂×#489	C₂×C₅	semidirect
135. C₂×#488	C₂×C₅	semidirect
136. C₂×#486	C₂×C₅	semidirect
137. C₂×#417	C₂×C₅	semidirect
138. C₂×#418	C₂×C₅	semidirect
139. C₂×#416	C₂×C₅	semidirect
140. C₂²×#102	C₂×C₅	semidirect
141. C₂×#405	C₂×C₅	semidirect
225. #544	C₂²×C₅	semidirect
229. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
232. C₂×#125	C₂²×C₅	semidirect
241. #490	C₂²×C₅	semidirect
242. #489	C₂²×C₅	semidirect
243. #488	C₂²×C₅	semidirect
244. #486	C₂²×C₅	semidirect
245. #418	C₂²×C₅	semidirect
246. #417	C₂²×C₅	semidirect
247. #416	C₂²×C₅	semidirect
248. C₂×#103	C₂²×C₅	semidirect
249. C₂×#103	C₂²×C₅	semidirect
250. C₂×#103	C₂²×C₅	semidirect
255. C₂×#102	C₂²×C₅	semidirect
256. C₂×#102	C₂²×C₅	semidirect
257. C₂×#102	C₂²×C₅	semidirect
258. C₂×#102	C₂²×C₅	semidirect
259. #405	C₂²×C₅	semidirect
260. C₂×#97	C₂²×C₅	semidirect
261. C₂×C₄×C₈	C₂²×C₅	semidirect
348. C₄⋊Q₈	C₂³×C₅	semidirect
353. #125	C₂³×C₅	semidirect
381. #103	C₂³×C₅	semidirect
382. #103	C₂³×C₅	semidirect
383. #103	C₂³×C₅	semidirect
388. #102	C₂³×C₅	semidirect
389. #102	C₂³×C₅	semidirect
390. #102	C₂³×C₅	semidirect
391. #97	C₂³×C₅	semidirect
392. C₄×C₈	C₂³×C₅	semidirect
501. C₂×C₅	#3136	direct (N × H)
562. C₅	C₂×#3136	direct (N × H)
593. C₂	C₅×#3136	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×#544	2
C₂×C₅×#535	2
C₅×#3136	2
C₂×C₅×#490	2
C₂×C₅×#489	2
C₂×C₅×#488	2
C₂×C₅×#486	2
C₂×C₅×#417	2
C₂×C₅×#418	2
C₂×C₅×#416	2
C₂²×C₅×#102	2
C₂×C₅×#405	2
C₂×#3136	5

Subgroups — C2×C5×#3136 #11983330

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#3136 #11983330