Subgroups — C₅×#23652 #11946372

Order 1280.

888 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	C₂×C₅×#430	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#2896	C₂	1	1	yes	maximal, characteristic
3	C₅×#2896	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#413	C₂	1	1	yes	maximal, characteristic
5	C₅×#2082	C₂	1	4	yes	maximal, complemented
6	C₅×#2081	C₂	1	4	yes	maximal, complemented
7	C₂×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₅×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₅×#117	C₂²	1	1	yes	characteristic
16	C₂×C₅×#117	C₂²	1	1	yes	characteristic
17	C₅×#430	—	2	2	no	—
18	C₅×#430	C₂²	1	4	yes	—
19	C₂×C₅×#108	—	2	2	no	—
20	C₅×#419	C₂²	1	2	yes	—
21	C₅×#419	C₂²	1	2	yes	—
22	C₅×#418	C₂²	1	2	yes	—
23	C₅×#418	C₂²	1	2	yes	—
24	C₅×#417	—	2	2	no	—
25	C₅×#417	—	2	2	no	—
26	C₅×#416	—	2	2	no	—
27	C₅×#416	—	2	2	no	—
28	C₅×#413	—	2	2	no	—
29	C₅×#413	—	2	2	no	—
30	C₂×C₅×#101	C₂²	1	2	yes	—
31	C₂×C₅×#100	C₂²	1	2	yes	—
32	C₅×#344	C₂²	1	4	yes	—
33	C₅×#344	C₂²	1	4	yes	—
34	C₅×H(3,ℤ/4)	C₂²	1	4	yes	—
35	#23652	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	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	—	2	1	no	—
46	C₂×C₅×#41	D₄	1	2	yes	—
47	C₂×C₅×#41	D₄	1	2	yes	—
48	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
49	C₂²×C₅×D₄	—	2	1	no	—
50	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₅	—	2	1	no	—
52	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂×C₅×M₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	1	no	—
58	C₂×C₅×M₁₆	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
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	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	D₄	1	2	yes	—
73	C₂×C₅×M₁₆	C₂³	1	2	yes	—
74	C₂×C₅×M₁₆	C₂³	1	2	yes	—
75	C₂×C₅×M₁₆	C₂³	1	2	yes	—
76	C₂×C₅×M₁₆	C₂³	1	2	yes	—
77	C₂²×C₅×C₈	—	2	1	no	—
78	C₂²×C₅×C₈	—	2	1	no	—
79	C₂²×C₅×C₈	—	2	1	no	—
80	C₂²×C₅×C₈	D₄	1	2	yes	—
81	C₅×#117	—	2	1	no	—
82	C₅×#117	—	2	1	no	—
83	C₅×#117	—	2	1	no	—
84	C₅×#117	—	2	1	no	—
85	C₅×#117	—	2	1	no	—
86	C₅×#117	—	2	1	no	—
87	C₅×#117	C₂³	1	2	yes	—
88	C₅×#117	C₂³	1	2	yes	—
89	C₂×C₅×C₄⋊C₄	—	2	1	no	—
90	C₂×C₅×C₄⋊C₄	—	2	1	no	—
91	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
93	C₂×C₄²×C₅	—	2	1	no	—
94	C₂×C₄²×C₅	—	2	1	no	—
95	C₅×#108	—	2	8	no	—
96	C₅×#103	—	2	4	no	—
97	C₅×#103	—	2	4	no	—
98	C₅×#102	—	2	4	no	—
99	C₅×#102	—	2	4	no	—
100	C₅×#101	—	2	4	no	—
101	C₅×#100	—	2	4	no	—
102	C₂×#430	C₂×C₅	1	1	yes	characteristic, complemented
103	#2896	C₂×C₅	1	1	yes	characteristic
104	#2896	C₂×C₅	1	1	yes	characteristic
105	C₂×#413	C₂×C₅	1	1	yes	characteristic
106	#2082	C₂×C₅	1	4	yes	complemented
107	#2081	C₂×C₅	1	4	yes	complemented
108	C₂×#344	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂×#344	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂⁴×C₅	—	2	1	no	—
112	C₂⁴×C₅	#41	1	1	yes	characteristic
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	—	4	1	no	—
122	C₅×#41	—	4	1	no	—
123	C₅×#41	—	4	1	no	—
124	C₅×#41	—	4	1	no	—
125	C₅×#41	—	4	1	no	—
126	C₅×#41	—	4	1	no	—
127	C₅×#41	—	4	1	no	—
128	C₅×#41	—	4	1	no	—
129	C₂×C₅×Q₈	—	2	1	no	—
130	C₂×C₅×Q₈	—	2	1	no	—
131	C₂×C₅×Q₈	—	2	1	no	—
132	C₂×C₅×Q₈	—	2	1	no	—
133	C₂×C₅×Q₈	—	2	1	no	—
134	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	2	1	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	2	1	no	—
141	C₂×C₅×D₄	—	2	1	no	—
142	C₂×C₅×D₄	—	4	1	no	—
143	C₂×C₅×D₄	—	4	1	no	—
144	C₂×C₅×D₄	—	4	1	no	—
145	C₂×C₅×D₄	—	4	1	no	—
146	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₅	—	2	1	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	4	1	no	—
151	C₂²×C₄×C₅	—	4	1	no	—
152	C₂²×C₄×C₅	—	4	1	no	—
153	C₂²×C₄×C₅	—	4	1	no	—
154	C₂²×C₄×C₅	—	4	1	no	—
155	C₂²×C₄×C₅	—	4	1	no	—
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	#41	1	1	yes	characteristic
161	C₂²×C₄×C₅	#41	1	1	yes	characteristic
162	C₂²×C₄×C₅	#41	1	1	yes	characteristic
163	C₂²×C₄×C₅	#41	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	#41	1	1	yes	characteristic
168	C₂²×C₄×C₅	#41	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
170	C₅×M₁₆	—	2	2	no	—
171	C₅×M₁₆	—	2	2	no	—
172	C₅×M₁₆	—	2	2	no	—
173	C₅×M₁₆	—	2	2	no	—
174	C₅×M₁₆	—	2	2	no	—
175	C₅×M₁₆	—	2	2	no	—
176	C₅×M₁₆	—	2	2	no	—
177	C₅×M₁₆	—	2	2	no	—
178	C₅×M₁₆	—	2	2	no	—
179	C₅×M₁₆	—	2	2	no	—
180	C₅×M₁₆	—	4	1	no	—
181	C₅×M₁₆	—	4	1	no	—
182	C₅×M₁₆	—	4	1	no	—
183	C₅×M₁₆	—	4	1	no	—
184	C₅×M₁₆	—	4	1	no	—
185	C₅×M₁₆	—	4	1	no	—
186	C₂×C₅×C₈	—	2	2	no	—
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	—	2	2	no	—
191	C₂×C₅×C₈	—	4	1	no	—
192	C₂×C₅×C₈	—	4	1	no	—
193	C₂×C₅×C₈	—	4	1	no	—
194	C₂×C₅×C₈	—	4	1	no	—
195	C₂×C₅×C₈	—	4	1	no	—
196	C₂×C₅×C₈	—	4	1	no	—
197	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₄⋊C₄	—	4	1	no	—
201	C₅×C₄⋊C₄	—	4	1	no	—
202	C₅×C₂²⋊C₄	—	2	2	no	—
203	C₅×C₂²⋊C₄	—	2	2	no	—
204	C₅×C₂²⋊C₄	—	4	1	no	—
205	C₅×C₂²⋊C₄	—	4	1	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	—	2	2	no	—
208	C₄²×C₅	—	4	1	no	—
209	C₄²×C₅	—	4	1	no	—
210	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
211	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
212	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
215	C₂×#117	C₂²×C₅	1	1	yes	characteristic
216	C₂×#117	C₂²×C₅	1	1	yes	characteristic
217	#430	—	2	2	no	—
218	#430	C₂²×C₅	1	4	yes	—
219	C₂×#108	—	2	2	no	—
220	#419	C₂²×C₅	1	2	yes	—
221	#419	C₂²×C₅	1	2	yes	—
222	#418	C₂²×C₅	1	2	yes	—
223	#418	C₂²×C₅	1	2	yes	—
224	#417	—	2	2	no	—
225	#417	—	2	2	no	—
226	#416	—	2	2	no	—
227	#416	—	2	2	no	—
228	#413	—	2	2	no	—
229	#413	—	2	2	no	—
230	C₂×#101	C₂²×C₅	1	2	yes	—
231	C₂×#100	C₂²×C₅	1	2	yes	—
232	#344	C₂²×C₅	1	4	yes	—
233	#344	C₂²×C₅	1	4	yes	—
234	H(3,ℤ/4)	C₂²×C₅	1	4	yes	—
235	C₂³×C₅	—	2	2	no	—
236	C₂³×C₅	—	4	1	no	—
237	C₂³×C₅	—	4	1	no	—
238	C₂³×C₅	—	8	1	no	—
239	C₂³×C₅	—	8	2	no	—
240	C₂³×C₅	#123	1	1	yes	characteristic
241	C₂³×C₅	#123	1	1	yes	characteristic
242	C₂³×C₅	#124	1	1	yes	characteristic
243	C₂³×C₅	#124	1	1	yes	characteristic
244	C₂³×C₅	#126	1	1	yes	characteristic
245	C₂³×C₅	#126	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	—	4	1	no	—
250	C₅×Q₈	—	4	1	no	—
251	C₅×D₄	—	2	2	no	—
252	C₅×D₄	—	2	2	no	—
253	C₅×D₄	—	4	2	no	—
254	C₅×D₄	—	4	2	no	—
255	C₅×D₄	—	4	2	no	—
256	C₅×D₄	—	4	2	no	—
257	C₅×D₄	—	4	1	no	—
258	C₅×D₄	—	4	1	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	4	1	no	—
261	C₂×C₄×C₅	—	4	1	no	—
262	C₂×C₄×C₅	—	4	2	no	—
263	C₂×C₄×C₅	—	4	2	no	—
264	C₂×C₄×C₅	—	4	2	no	—
265	C₂×C₄×C₅	—	4	2	no	—
266	C₂×C₄×C₅	—	4	2	no	—
267	C₂×C₄×C₅	—	4	2	no	—
268	C₂×C₄×C₅	—	8	2	no	—
269	C₂×C₄×C₅	—	8	2	no	—
270	C₂×C₄×C₅	#121	1	1	yes	characteristic
271	C₂×C₄×C₅	#121	1	1	yes	characteristic
272	C₂×C₄×C₅	#121	1	1	yes	characteristic
273	C₂×C₄×C₅	#121	1	1	yes	characteristic
274	C₂×C₄×C₅	#123	1	1	yes	characteristic
275	C₂×C₄×C₅	#123	1	1	yes	characteristic
276	C₂×C₄×C₅	#123	1	1	yes	characteristic
277	C₂×C₄×C₅	#123	1	1	yes	characteristic
278	C₂×C₄×C₅	#123	1	1	yes	characteristic
279	C₂×C₄×C₅	#123	1	1	yes	characteristic
280	C₂×C₄×C₅	#123	1	1	yes	characteristic
281	C₂×C₄×C₅	#123	1	1	yes	characteristic
282	C₂×C₄×C₅	#123	1	1	yes	characteristic
283	C₂×C₄×C₅	#123	1	1	yes	characteristic
284	C₂×C₄×C₅	#124	1	1	yes	characteristic
285	C₂×C₄×C₅	#124	1	1	yes	characteristic
286	C₂×C₄×C₅	#126	1	1	yes	characteristic
287	C₂×C₄×C₅	#126	1	1	yes	characteristic
288	C₂×C₄×C₅	#126	1	1	yes	characteristic
289	C₂×C₄×C₅	#126	1	1	yes	characteristic
290	C₂×C₄×C₅	#126	1	1	yes	characteristic
291	C₂×C₄×C₅	#126	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	C₂×#41	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
298	C₅×C₈	—	2	4	no	—
299	C₅×C₈	—	4	2	no	—
300	C₅×C₈	—	4	2	no	—
301	C₅×C₈	—	4	2	no	—
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	—	2	1	no	—
309	C₂×#41	—	2	1	no	—
310	C₂×#41	—	2	1	no	—
311	C₂×#41	—	2	1	no	—
312	C₂×#41	C₅×D₄	1	2	yes	—
313	C₂×#41	C₅×D₄	1	2	yes	—
314	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	—	2	1	no	—
323	C₂×M₁₆	—	2	1	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₂×M₁₆	—	2	1	no	—
326	C₂×M₁₆	—	2	1	no	—
327	C₂×M₁₆	—	2	1	no	—
328	C₂×M₁₆	—	2	1	no	—
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	2	1	no	—
331	C₂×M₁₆	—	2	1	no	—
332	C₂×M₁₆	—	2	1	no	—
333	C₂×M₁₆	—	2	1	no	—
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	C₅×D₄	1	2	yes	—
339	C₂×M₁₆	C₂³×C₅	1	2	yes	—
340	C₂×M₁₆	C₂³×C₅	1	2	yes	—
341	C₂×M₁₆	C₂³×C₅	1	2	yes	—
342	C₂×M₁₆	C₂³×C₅	1	2	yes	—
343	C₂²×C₈	—	2	1	no	—
344	C₂²×C₈	—	2	1	no	—
345	C₂²×C₈	—	2	1	no	—
346	C₂²×C₈	C₅×D₄	1	2	yes	—
347	#117	—	2	1	no	—
348	#117	—	2	1	no	—
349	#117	—	2	1	no	—
350	#117	—	2	1	no	—
351	#117	—	2	1	no	—
352	#117	—	2	1	no	—
353	#117	C₂³×C₅	1	2	yes	—
354	#117	C₂³×C₅	1	2	yes	—
355	C₂×C₄⋊C₄	—	2	1	no	—
356	C₂×C₄⋊C₄	—	2	1	no	—
357	C₂×C₂²⋊C₄	—	2	1	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₄²	—	2	1	no	—
360	C₂×C₄²	—	2	1	no	—
361	#108	—	2	8	no	—
362	#103	—	2	4	no	—
363	#103	—	2	4	no	—
364	#102	—	2	4	no	—
365	#102	—	2	4	no	—
366	#101	—	2	4	no	—
367	#100	—	2	4	no	—
368	C₂²×C₅	—	4	1	no	—
369	C₂²×C₅	—	4	1	no	—
370	C₂²×C₅	—	4	1	no	—
371	C₂²×C₅	—	4	1	no	—
372	C₂²×C₅	—	4	1	no	—
373	C₂²×C₅	—	4	1	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	—	4	2	no	—
376	C₂²×C₅	—	8	2	no	—
377	C₂²×C₅	—	8	2	no	—
378	C₂²×C₅	—	8	2	no	—
379	C₂²×C₅	#397	1	1	yes	characteristic
380	C₂²×C₅	#397	1	1	yes	characteristic
381	C₂²×C₅	#397	1	1	yes	characteristic
382	C₂²×C₅	#397	1	1	yes	characteristic
383	C₂²×C₅	C₂×#123	1	1	yes	characteristic
384	C₂²×C₅	C₂×#124	1	1	yes	characteristic
385	C₂²×C₅	C₂×#126	1	1	yes	characteristic
386	C₄×C₅	—	4	2	no	—
387	C₄×C₅	—	8	2	no	—
388	C₄×C₅	—	8	2	no	—
389	C₄×C₅	#397	1	1	yes	characteristic
390	C₄×C₅	#397	1	1	yes	characteristic
391	C₄×C₅	#397	1	1	yes	characteristic
392	C₄×C₅	#397	1	1	yes	characteristic
393	C₄×C₅	C₂×#121	1	1	yes	characteristic
394	C₄×C₅	C₂×#123	1	1	yes	characteristic
395	C₄×C₅	C₂×#123	1	1	yes	characteristic
396	C₄×C₅	C₂×#126	1	1	yes	characteristic
397	C₂⁴	—	2	1	no	—
398	C₂⁴	C₅×#41	1	1	yes	characteristic
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
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	—	4	1	no	—
408	#41	—	4	1	no	—
409	#41	—	4	1	no	—
410	#41	—	4	1	no	—
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	#41	—	4	1	no	—
414	#41	—	4	1	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	2	1	no	—
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	4	1	no	—
430	C₂×D₄	—	4	1	no	—
431	C₂×D₄	—	4	1	no	—
432	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	4	1	no	—
437	C₂²×C₄	—	4	1	no	—
438	C₂²×C₄	—	4	1	no	—
439	C₂²×C₄	—	4	1	no	—
440	C₂²×C₄	—	4	1	no	—
441	C₂²×C₄	—	4	1	no	—
442	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
444	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
446	C₂²×C₄	C₅×#41	1	1	yes	characteristic
447	C₂²×C₄	C₅×#41	1	1	yes	characteristic
448	C₂²×C₄	C₅×#41	1	1	yes	characteristic
449	C₂²×C₄	C₅×#41	1	1	yes	characteristic
450	C₂²×C₄	C₅×#41	1	1	yes	characteristic
451	C₂²×C₄	C₅×#41	1	1	yes	characteristic
452	C₂²×C₄	C₅×#41	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	C₂⁴×C₅	1	1	yes	characteristic
456	M₁₆	—	2	2	no	—
457	M₁₆	—	2	2	no	—
458	M₁₆	—	2	2	no	—
459	M₁₆	—	2	2	no	—
460	M₁₆	—	2	2	no	—
461	M₁₆	—	2	2	no	—
462	M₁₆	—	2	2	no	—
463	M₁₆	—	2	2	no	—
464	M₁₆	—	2	2	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	4	1	no	—
467	M₁₆	—	4	1	no	—
468	M₁₆	—	4	1	no	—
469	M₁₆	—	4	1	no	—
470	M₁₆	—	4	1	no	—
471	M₁₆	—	4	1	no	—
472	C₂×C₈	—	2	2	no	—
473	C₂×C₈	—	2	2	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	2	no	—
477	C₂×C₈	—	4	1	no	—
478	C₂×C₈	—	4	1	no	—
479	C₂×C₈	—	4	1	no	—
480	C₂×C₈	—	4	1	no	—
481	C₂×C₈	—	4	1	no	—
482	C₂×C₈	—	4	1	no	—
483	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	—	2	2	no	—
486	C₄⋊C₄	—	4	1	no	—
487	C₄⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₄²	—	2	2	no	—
493	C₄²	—	2	2	no	—
494	C₄²	—	4	1	no	—
495	C₄²	—	4	1	no	—
496	C₂×C₅	—	2	1	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	—	8	2	no	—
504	C₂×C₅	C₂×#397	1	1	yes	characteristic
505	C₂³	—	2	2	no	—
506	C₂³	—	4	1	no	—
507	C₂³	—	4	1	no	—
508	C₂³	—	8	1	no	—
509	C₂³	—	8	2	no	—
510	C₂³	C₅×#123	1	1	yes	characteristic
511	C₂³	C₅×#123	1	1	yes	characteristic
512	C₂³	C₅×#124	1	1	yes	characteristic
513	C₂³	C₅×#124	1	1	yes	characteristic
514	C₂³	C₅×#126	1	1	yes	characteristic
515	C₂³	C₅×#126	1	1	yes	characteristic
516	C₂³	C₂×C₅×#41	1	1	yes	characteristic
517	Q₈	—	2	2	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	4	1	no	—
520	Q₈	—	4	1	no	—
521	D₄	—	2	2	no	—
522	D₄	—	2	2	no	—
523	D₄	—	4	2	no	—
524	D₄	—	4	2	no	—
525	D₄	—	4	2	no	—
526	D₄	—	4	2	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	4	2	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	8	2	no	—
539	C₂×C₄	—	8	2	no	—
540	C₂×C₄	C₅×#121	1	1	yes	characteristic
541	C₂×C₄	C₅×#121	1	1	yes	characteristic
542	C₂×C₄	C₅×#121	1	1	yes	characteristic
543	C₂×C₄	C₅×#121	1	1	yes	characteristic
544	C₂×C₄	C₅×#123	1	1	yes	characteristic
545	C₂×C₄	C₅×#123	1	1	yes	characteristic
546	C₂×C₄	C₅×#123	1	1	yes	characteristic
547	C₂×C₄	C₅×#123	1	1	yes	characteristic
548	C₂×C₄	C₅×#123	1	1	yes	characteristic
549	C₂×C₄	C₅×#123	1	1	yes	characteristic
550	C₂×C₄	C₅×#123	1	1	yes	characteristic
551	C₂×C₄	C₅×#123	1	1	yes	characteristic
552	C₂×C₄	C₅×#123	1	1	yes	characteristic
553	C₂×C₄	C₅×#123	1	1	yes	characteristic
554	C₂×C₄	C₅×#124	1	1	yes	characteristic
555	C₂×C₄	C₅×#124	1	1	yes	characteristic
556	C₂×C₄	C₅×#126	1	1	yes	characteristic
557	C₂×C₄	C₅×#126	1	1	yes	characteristic
558	C₂×C₄	C₅×#126	1	1	yes	characteristic
559	C₂×C₄	C₅×#126	1	1	yes	characteristic
560	C₂×C₄	C₅×#126	1	1	yes	characteristic
561	C₂×C₄	C₅×#126	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	C₂×C₅×#41	1	1	yes	characteristic
565	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
566	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
567	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
568	C₈	—	2	4	no	—
569	C₈	—	4	2	no	—
570	C₈	—	4	2	no	—
571	C₈	—	4	2	no	—
572	C₅	#23652	1	1	yes	characteristic, direct product factor, Sylow
573	C₂²	—	4	1	no	—
574	C₂²	—	4	1	no	—
575	C₂²	—	4	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	8	2	no	—
582	C₂²	—	8	2	no	—
583	C₂²	—	8	2	no	—
584	C₂²	C₅×#397	1	1	yes	characteristic
585	C₂²	C₅×#397	1	1	yes	characteristic
586	C₂²	C₅×#397	1	1	yes	characteristic
587	C₂²	C₅×#397	1	1	yes	characteristic
588	C₂²	C₂×C₅×#123	1	1	yes	characteristic
589	C₂²	C₂×C₅×#124	1	1	yes	characteristic
590	C₂²	C₂×C₅×#126	1	1	yes	characteristic
591	C₄	—	4	2	no	—
592	C₄	—	8	2	no	—
593	C₄	—	8	2	no	—
594	C₄	C₅×#397	1	1	yes	characteristic
595	C₄	C₅×#397	1	1	yes	characteristic
596	C₄	C₅×#397	1	1	yes	characteristic
597	C₄	C₅×#397	1	1	yes	characteristic
598	C₄	C₂×C₅×#121	1	1	yes	characteristic
599	C₄	C₂×C₅×#123	1	1	yes	characteristic
600	C₄	C₂×C₅×#123	1	1	yes	characteristic
601	C₄	C₂×C₅×#126	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	—	2	1	no	—
609	C₂	—	8	2	no	—
610	C₂	C₂×C₅×#397	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	#397
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂×C₅	C₂×#397
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₅ ◁ C₂³×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#430	C₂	semidirect
5. C₅×#2082	C₂	semidirect
6. C₅×#2081	C₂	semidirect
7. C₂×C₅×#344	C₂	semidirect
8. C₂×C₅×#344	C₂	semidirect
9. C₂×C₅×H(3,ℤ/4)	C₂	semidirect
35. #23652	C₅	direct (N × H)
102. C₂×#430	C₂×C₅	semidirect
106. #2082	C₂×C₅	semidirect
107. #2081	C₂×C₅	semidirect
108. C₂×#344	C₂×C₅	semidirect
109. C₂×#344	C₂×C₅	semidirect
110. C₂×H(3,ℤ/4)	C₂×C₅	semidirect
572. C₅	#23652	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×#430	2
C₅×#2896	2
C₂×C₅×#413	2
C₅×#2082	2
C₅×#2081	2
C₂×C₅×#344	2
C₂×C₅×H(3,ℤ/4)	2
#23652	5

Subgroups — C5×#23652 #11946372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#23652 #11946372