Subgroups — C₅×#17714 #11940434

Order 1280.

1252 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic
2	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1551	C₂	1	4	yes	maximal, complemented
5	C₅×#1548	C₂	1	2	yes	maximal, complemented
6	C₅×#1545	C₂	1	2	yes	maximal, complemented
7	C₅×#1543	C₂	1	4	yes	maximal, complemented
8	C₂²×C₅×#41	C₄	1	2	yes	—
9	C₅×#532	—	2	1	no	—
10	C₅×#532	—	2	1	no	—
11	C₅×#532	—	2	1	no	—
12	C₅×#532	—	2	1	no	—
13	C₅×#532	C₄	1	2	yes	—
14	C₅×#532	C₄	1	2	yes	—
15	C₅×#532	C₂²	1	2	yes	—
16	C₅×#532	C₂²	1	2	yes	—
17	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₂×C₅×#127	C₂²	1	1	yes	characteristic
19	C₂×C₅×#124	C₄	1	2	yes	—
20	C₂×C₅×#121	—	2	1	no	—
21	C₂×C₅×#121	—	2	1	no	—
22	C₂×C₄×C₅×D₄	—	2	1	no	—
23	C₂×C₄×C₅×D₄	—	2	1	no	—
24	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₅×#432	—	2	1	no	—
26	C₅×#432	C₂²	1	2	yes	complemented
27	C₅×#431	—	2	1	no	—
28	C₅×#431	—	2	1	no	—
29	C₅×#431	—	2	1	no	—
30	C₅×#431	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	2	yes	complemented
32	C₅×#431	C₂²	1	2	yes	complemented
33	C₅×#423	C₂²	1	2	yes	—
34	C₂×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
35	C₅×#407	—	2	1	no	—
36	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
37	C₄×C₅×M₁₆	—	2	1	no	—
38	C₂×C₄×C₅×C₈	—	2	1	no	—
39	C₅×#333	C₂²	1	8	yes	complemented
40	C₅×#331	C₂²	1	8	yes	complemented
41	#17714	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
42	C₂×C₅×#41	—	2	2	no	—
43	C₂×C₅×#41	—	2	2	no	—
44	C₂×C₅×#41	—	4	8	no	—
45	C₂×C₅×#41	C₂×C₄	1	4	yes	—
46	C₂×C₅×#41	C₂×C₄	1	4	yes	—
47	C₂²×C₅×Q₈	C₂×C₄	1	2	yes	—
48	C₂²×C₅×D₄	—	2	2	no	—
49	C₂²×C₅×D₄	—	2	1	no	—
50	C₂²×C₅×D₄	—	2	1	no	—
51	C₂²×C₅×D₄	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₅	—	2	2	no	—
53	C₂³×C₄×C₅	C₂×C₄	1	1	yes	characteristic
54	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
56	C₂×C₅×M₁₆	—	2	2	no	—
57	C₂²×C₅×C₈	—	2	2	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	C₂×C₄	1	2	yes	—
61	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
62	C₅×#127	—	2	1	no	—
63	C₅×#127	—	2	1	no	—
64	C₅×#127	C₂×C₄	1	2	yes	—
65	C₅×#127	C₂³	1	2	yes	—
66	C₅×#124	—	2	2	no	—
67	C₅×#124	—	2	2	no	—
68	C₅×#124	C₂×C₄	1	4	yes	—
69	C₅×#124	C₂×C₄	1	4	yes	—
70	C₅×#121	—	2	2	no	—
71	C₅×#121	—	2	2	no	—
72	C₅×#121	—	2	2	no	—
73	C₅×#121	—	2	2	no	—
74	C₅×#121	—	2	2	no	—
75	C₅×#121	—	2	2	no	—
76	C₅×#121	—	2	2	no	—
77	C₅×#121	—	2	2	no	—
78	C₄×C₅×D₄	—	2	2	no	—
79	C₄×C₅×D₄	—	2	2	no	—
80	C₄×C₅×D₄	—	2	2	no	—
81	C₄×C₅×D₄	—	2	2	no	—
82	C₄×C₅×D₄	—	2	2	no	—
83	C₄×C₅×D₄	—	2	2	no	—
84	C₄×C₅×D₄	—	2	2	no	—
85	C₄×C₅×D₄	—	2	2	no	—
86	C₂×C₅×C₄⋊C₄	—	2	1	no	—
87	C₂×C₅×C₄⋊C₄	—	2	1	no	—
88	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
94	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
95	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
96	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
97	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
98	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
102	C₅×C₄⋊C₈	—	2	2	no	—
103	C₅×C₄⋊C₈	—	2	2	no	—
104	C₅×C₄⋊C₈	C₂³	1	4	yes	—
105	C₅×C₄⋊C₈	C₂³	1	4	yes	—
106	C₅×C₂²⋊C₈	—	2	2	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×C₂²⋊C₈	—	2	2	no	—
109	C₅×C₂²⋊C₈	—	2	2	no	—
110	C₅×#97	—	2	2	no	—
111	C₄×C₅×C₈	—	2	2	no	—
112	C₄×C₅×C₈	—	2	2	no	—
113	C₄×C₅×C₈	—	2	2	no	—
114	C₂×#532	C₂×C₅	1	1	yes	characteristic
115	#2920	C₂×C₅	1	1	yes	characteristic, complemented
116	C₂×#431	C₂×C₅	1	1	yes	characteristic, complemented
117	#1551	C₂×C₅	1	4	yes	complemented
118	#1548	C₂×C₅	1	2	yes	complemented
119	#1545	C₂×C₅	1	2	yes	complemented
120	#1543	C₂×C₅	1	4	yes	complemented
121	C₂⁴×C₅	—	2	2	no	—
122	C₂⁴×C₅	C₂²⋊C₄	1	1	yes	characteristic
123	C₅×#41	—	4	8	no	—
124	C₅×#41	—	4	8	no	—
125	C₅×#41	—	4	8	no	—
126	C₅×#41	—	4	8	no	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	4	4	no	—
129	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
130	C₂×C₅×D₄	—	2	4	no	—
131	C₂×C₅×D₄	—	2	4	no	—
132	C₂×C₅×D₄	—	2	2	no	—
133	C₂×C₅×D₄	—	2	2	no	—
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	—	4	4	no	—
138	C₂×C₅×D₄	—	4	4	no	—
139	C₂×C₅×D₄	—	4	8	no	—
140	C₂×C₅×D₄	—	4	4	no	—
141	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
142	C₂²×C₄×C₅	—	2	4	no	—
143	C₂²×C₄×C₅	—	2	4	no	—
144	C₂²×C₄×C₅	—	2	2	no	—
145	C₂²×C₄×C₅	—	2	4	no	—
146	C₂²×C₄×C₅	—	2	4	no	—
147	C₂²×C₄×C₅	—	4	2	no	—
148	C₂²×C₄×C₅	—	4	8	no	—
149	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
155	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
156	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂×D₄	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	C₅×M₁₆	—	4	4	no	—
168	C₂×C₅×C₈	—	2	4	no	—
169	C₂×C₅×C₈	—	2	4	no	—
170	C₂×C₅×C₈	—	4	4	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	2	no	—
173	C₅×C₄⋊C₄	—	2	2	no	—
174	C₅×C₄⋊C₄	—	2	2	no	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₅×C₂²⋊C₄	—	2	4	no	—
177	C₅×C₂²⋊C₄	—	2	4	no	—
178	C₅×C₂²⋊C₄	—	2	4	no	—
179	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
180	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
181	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
182	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
183	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
184	C₄²×C₅	C₂²⋊C₄	1	1	yes	characteristic
185	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
186	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
187	C₄²×C₅	C₂²×C₄	1	1	yes	characteristic
188	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₅	C₂⁴	1	1	yes	characteristic
195	C₂²×#41	C₄×C₅	1	2	yes	—
196	#532	—	2	1	no	—
197	#532	—	2	1	no	—
198	#532	—	2	1	no	—
199	#532	—	2	1	no	—
200	#532	C₄×C₅	1	2	yes	—
201	#532	C₄×C₅	1	2	yes	—
202	#532	C₂²×C₅	1	2	yes	—
203	#532	C₂²×C₅	1	2	yes	—
204	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
205	C₂×#127	C₂²×C₅	1	1	yes	characteristic
206	C₂×#124	C₄×C₅	1	2	yes	—
207	C₂×#121	—	2	1	no	—
208	C₂×#121	—	2	1	no	—
209	C₂×C₄×D₄	—	2	1	no	—
210	C₂×C₄×D₄	—	2	1	no	—
211	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
212	#432	—	2	1	no	—
213	#432	C₂²×C₅	1	2	yes	complemented
214	#431	—	2	1	no	—
215	#431	—	2	1	no	—
216	#431	—	2	1	no	—
217	#431	C₂²×C₅	1	2	yes	—
218	#431	C₂²×C₅	1	2	yes	complemented
219	#431	C₂²×C₅	1	2	yes	complemented
220	#423	C₂²×C₅	1	2	yes	—
221	C₂×C₄⋊C₈	C₂²×C₅	1	2	yes	complemented
222	#407	—	2	1	no	—
223	C₂×C₂²⋊C₈	—	2	1	no	—
224	C₄×M₁₆	—	2	1	no	—
225	C₂×C₄×C₈	—	2	1	no	—
226	#333	C₂²×C₅	1	8	yes	complemented
227	#331	C₂²×C₅	1	8	yes	complemented
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	—	2	2	no	—
230	C₂³×C₅	—	2	4	no	—
231	C₂³×C₅	—	4	1	no	—
232	C₂³×C₅	—	4	4	no	—
233	C₂³×C₅	—	4	4	no	—
234	C₂³×C₅	—	4	4	no	—
235	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂³×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₅×Q₈	—	4	4	no	—
239	C₅×Q₈	—	4	4	no	—
240	C₅×D₄	—	4	4	no	—
241	C₅×D₄	—	4	4	no	—
242	C₅×D₄	—	4	8	no	—
243	C₅×D₄	—	4	8	no	—
244	C₅×D₄	—	4	4	no	—
245	C₅×D₄	—	4	4	no	—
246	C₅×D₄	—	4	4	no	—
247	C₅×D₄	—	4	4	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	2	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	4	no	—
262	C₂×C₄×C₅	—	4	1	no	—
263	C₂×C₄×C₅	—	4	1	no	—
264	C₂×C₄×C₅	—	4	1	no	—
265	C₂×C₄×C₅	—	4	8	no	—
266	C₂×C₄×C₅	—	4	4	no	—
267	C₂×C₄×C₅	—	4	8	no	—
268	C₂×C₄×C₅	#100	1	4	yes	—
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×C₂²⋊C₄	1	1	yes	characteristic
273	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
278	C₂×C₄×C₅	#135	1	4	yes	—
279	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
280	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
282	C₅×C₈	—	4	4	no	—
283	C₅×C₈	—	4	4	no	—
284	C₂×#41	—	2	2	no	—
285	C₂×#41	—	2	2	no	—
286	C₂×#41	—	4	8	no	—
287	C₂×#41	C₂×C₄×C₅	1	4	yes	—
288	C₂×#41	C₂×C₄×C₅	1	4	yes	—
289	C₂²×Q₈	C₂×C₄×C₅	1	2	yes	—
290	C₂²×D₄	—	2	2	no	—
291	C₂²×D₄	—	2	1	no	—
292	C₂²×D₄	—	2	1	no	—
293	C₂²×D₄	C₂×C₄×C₅	1	2	yes	—
294	C₂³×C₄	—	2	2	no	—
295	C₂³×C₄	C₂×C₄×C₅	1	1	yes	characteristic
296	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
297	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
298	C₂×M₁₆	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	1	no	—
301	C₄⋊Q₈	—	2	1	no	—
302	C₄⋊Q₈	C₂×C₄×C₅	1	2	yes	—
303	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
304	#127	—	2	1	no	—
305	#127	—	2	1	no	—
306	#127	C₂×C₄×C₅	1	2	yes	—
307	#127	C₂³×C₅	1	2	yes	—
308	#124	—	2	2	no	—
309	#124	—	2	2	no	—
310	#124	C₂×C₄×C₅	1	4	yes	—
311	#124	C₂×C₄×C₅	1	4	yes	—
312	#121	—	2	2	no	—
313	#121	—	2	2	no	—
314	#121	—	2	2	no	—
315	#121	—	2	2	no	—
316	#121	—	2	2	no	—
317	#121	—	2	2	no	—
318	#121	—	2	2	no	—
319	#121	—	2	2	no	—
320	C₄×D₄	—	2	2	no	—
321	C₄×D₄	—	2	2	no	—
322	C₄×D₄	—	2	2	no	—
323	C₄×D₄	—	2	2	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	C₄×D₄	—	2	2	no	—
327	C₄×D₄	—	2	2	no	—
328	C₂×C₄⋊C₄	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
333	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
334	C₂×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
335	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
336	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
337	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
338	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
339	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
340	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
341	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
344	C₄⋊C₈	—	2	2	no	—
345	C₄⋊C₈	—	2	2	no	—
346	C₄⋊C₈	C₂³×C₅	1	4	yes	—
347	C₄⋊C₈	C₂³×C₅	1	4	yes	—
348	C₂²⋊C₈	—	2	2	no	—
349	C₂²⋊C₈	—	2	2	no	—
350	C₂²⋊C₈	—	2	2	no	—
351	C₂²⋊C₈	—	2	2	no	—
352	#97	—	2	2	no	—
353	C₄×C₈	—	2	2	no	—
354	C₄×C₈	—	2	2	no	—
355	C₄×C₈	—	2	2	no	—
356	C₂²×C₅	—	2	1	no	—
357	C₂²×C₅	—	2	1	no	—
358	C₂²×C₅	—	2	1	no	—
359	C₂²×C₅	—	2	1	no	—
360	C₂²×C₅	—	2	1	no	—
361	C₂²×C₅	—	2	1	no	—
362	C₂²×C₅	—	2	1	no	—
363	C₂²×C₅	—	4	4	no	—
364	C₂²×C₅	—	4	4	no	—
365	C₂²×C₅	—	4	4	no	—
366	C₂²×C₅	—	4	4	no	—
367	C₂²×C₅	—	8	8	no	—
368	C₂²×C₅	C₂×#100	1	2	yes	—
369	C₂²×C₅	#416	1	2	yes	—
370	C₂²×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	—	2	1	no	—
375	C₄×C₅	—	2	1	no	—
376	C₄×C₅	—	2	1	no	—
377	C₄×C₅	—	2	1	no	—
378	C₄×C₅	—	4	4	no	—
379	C₄×C₅	C₂×#100	1	2	yes	—
380	C₄×C₅	C₂×#100	1	2	yes	—
381	C₄×C₅	#416	1	2	yes	—
382	C₄×C₅	C₂×#135	1	2	yes	—
383	C₄×C₅	#575	1	2	yes	—
384	C₂⁴	—	2	2	no	—
385	C₂⁴	C₅×C₂²⋊C₄	1	1	yes	characteristic
386	#41	—	4	8	no	—
387	#41	—	4	8	no	—
388	#41	—	4	8	no	—
389	#41	—	4	8	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	4	4	no	—
392	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
393	C₂×D₄	—	2	4	no	—
394	C₂×D₄	—	2	4	no	—
395	C₂×D₄	—	2	2	no	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	—	4	4	no	—
401	C₂×D₄	—	4	4	no	—
402	C₂×D₄	—	4	8	no	—
403	C₂×D₄	—	4	4	no	—
404	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	4	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	8	no	—
412	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
413	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
414	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
415	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
416	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
417	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
418	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
419	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
420	C₂²×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
421	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
424	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
426	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
427	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
428	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
429	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
430	M₁₆	—	4	4	no	—
431	C₂×C₈	—	2	4	no	—
432	C₂×C₈	—	2	4	no	—
433	C₂×C₈	—	4	4	no	—
434	C₄⋊C₄	—	2	2	no	—
435	C₄⋊C₄	—	2	2	no	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	—	2	4	no	—
440	C₂²⋊C₄	—	2	4	no	—
441	C₂²⋊C₄	—	2	4	no	—
442	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
443	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
444	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
445	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
446	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
447	C₄²	C₅×C₂²⋊C₄	1	1	yes	characteristic
448	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
449	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
450	C₄²	C₂²×C₄×C₅	1	1	yes	characteristic
451	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
452	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
453	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
454	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
455	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
456	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
457	C₄²	C₂⁴×C₅	1	1	yes	characteristic
458	C₂×C₅	—	2	2	no	—
459	C₂×C₅	—	2	2	no	—
460	C₂×C₅	—	4	1	no	—
461	C₂×C₅	—	8	4	no	—
462	C₂×C₅	C₂²×#100	1	1	yes	characteristic
463	C₂×C₅	C₂×#416	1	1	yes	characteristic
464	C₂×C₅	#2896	1	1	yes	characteristic
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	4	no	—
470	C₂³	—	4	4	no	—
471	C₂³	—	4	4	no	—
472	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
473	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
474	C₂³	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
475	Q₈	—	4	4	no	—
476	Q₈	—	4	4	no	—
477	D₄	—	4	4	no	—
478	D₄	—	4	4	no	—
479	D₄	—	4	8	no	—
480	D₄	—	4	8	no	—
481	D₄	—	4	4	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	2	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	4	no	—
499	C₂×C₄	—	4	1	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	1	no	—
502	C₂×C₄	—	4	8	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	C₅×#100	1	4	yes	—
506	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
507	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
508	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
509	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
510	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
511	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
512	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
513	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
514	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
515	C₂×C₄	C₅×#135	1	4	yes	—
516	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
517	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
518	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
519	C₈	—	4	4	no	—
520	C₈	—	4	4	no	—
521	C₅	#17714	1	1	yes	characteristic, direct product factor, Sylow
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	4	4	no	—
530	C₂²	—	4	4	no	—
531	C₂²	—	4	4	no	—
532	C₂²	—	4	4	no	—
533	C₂²	—	8	8	no	—
534	C₂²	C₂×C₅×#100	1	2	yes	—
535	C₂²	C₅×#416	1	2	yes	—
536	C₂²	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	2	1	no	—
542	C₄	—	2	1	no	—
543	C₄	—	2	1	no	—
544	C₄	—	4	4	no	—
545	C₄	C₂×C₅×#100	1	2	yes	—
546	C₄	C₂×C₅×#100	1	2	yes	—
547	C₄	C₅×#416	1	2	yes	—
548	C₄	C₂×C₅×#135	1	2	yes	—
549	C₄	C₅×#575	1	2	yes	—
550	C₂	—	2	2	no	—
551	C₂	—	2	2	no	—
552	C₂	—	4	1	no	—
553	C₂	—	8	4	no	—
554	C₂	C₂²×C₅×#100	1	1	yes	characteristic
555	C₂	C₂×C₅×#416	1	1	yes	characteristic
556	C₂	C₅×#2896	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂²×C₂²⋊C₄
prime radical	C₂×C₅×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2920	C₂	semidirect
3. C₂×C₅×#431	C₂	semidirect
4. C₅×#1551	C₂	semidirect
5. C₅×#1548	C₂	semidirect
6. C₅×#1545	C₂	semidirect
7. C₅×#1543	C₂	semidirect
26. C₅×#432	C₂²	semidirect
31. C₅×#431	C₂²	semidirect
32. C₅×#431	C₂²	semidirect
34. C₂×C₅×C₄⋊C₈	C₂²	semidirect
39. C₅×#333	C₂²	semidirect
40. C₅×#331	C₂²	semidirect
41. #17714	C₅	direct (N × H)
115. #2920	C₂×C₅	semidirect
116. C₂×#431	C₂×C₅	semidirect
117. #1551	C₂×C₅	semidirect
118. #1548	C₂×C₅	semidirect
119. #1545	C₂×C₅	semidirect
120. #1543	C₂×C₅	semidirect
213. #432	C₂²×C₅	semidirect
218. #431	C₂²×C₅	semidirect
219. #431	C₂²×C₅	semidirect
221. C₂×C₄⋊C₈	C₂²×C₅	semidirect
226. #333	C₂²×C₅	semidirect
227. #331	C₂²×C₅	semidirect
521. C₅	#17714	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×#532	2
C₅×#2920	2
C₂×C₅×#431	2
C₅×#1551	2
C₅×#1548	2
C₅×#1545	2
C₅×#1543	2
#17714	5

Subgroups — C5×#17714 #11940434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#17714 #11940434