Subgroups — C₅×#20867 #11943587

Order 1280.

1312 conjugacy classes of subgroups.

The subgroup lattice has 630 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	C₅×#2905	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
6	C₅×#1861	C₂	1	8	yes	maximal, complemented
7	C₂×C₅×#344	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1733	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	C₂×C₅×#117	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×#424	—	2	2	no	—
27	C₅×#424	—	2	2	no	—
28	C₅×#423	C₂²	1	4	yes	complemented
29	C₅×#421	—	2	2	no	—
30	C₅×#421	C₄	1	4	yes	complemented
31	C₅×#421	C₄	1	4	yes	complemented
32	C₅×#421	C₂²	1	4	yes	—
33	C₂×C₅×#104	—	2	2	no	—
34	C₂×C₅×#104	C₂²	1	4	yes	—
35	C₅×#344	C₂²	1	4	yes	complemented
36	C₅×#339	C₂²	1	4	yes	complemented
37	#20867	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	C₂×C₄	1	2	yes	—
45	C₂×C₅×#41	C₂×C₄	1	2	yes	—
46	C₂×C₅×#41	D₄	1	2	yes	—
47	C₂×C₅×#41	D₄	1	2	yes	—
48	C₂×C₅×#41	Q₈	1	2	yes	—
49	C₂×C₅×#41	C₂³	1	2	yes	—
50	C₂²×C₅×Q₈	Q₈	1	1	yes	characteristic
51	C₂²×C₅×D₄	—	2	1	no	—
52	C₂²×C₅×D₄	Q₈	1	1	yes	characteristic
53	C₂³×C₄×C₅	—	2	1	no	—
54	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₅×#131	—	2	8	no	—
56	C₅×#131	—	2	8	no	—
57	C₅×#131	—	2	8	no	—
58	C₅×#131	—	2	8	no	—
59	C₂×C₅×M₁₆	—	2	4	no	—
60	C₂×C₅×M₁₆	—	2	8	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	8	no	—
72	C₂×C₅×M₁₆	—	2	1	no	—
73	C₂×C₅×M₁₆	—	2	1	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	C₂×C₄	1	2	yes	—
78	C₂×C₅×M₁₆	C₂×C₄	1	2	yes	—
79	C₂×C₅×M₁₆	D₄	1	2	yes	—
80	C₂×C₅×M₁₆	D₄	1	2	yes	—
81	C₂×C₅×M₁₆	D₄	1	2	yes	—
82	C₂×C₅×M₁₆	C₂³	1	2	yes	—
83	C₂×C₅×M₁₆	C₂³	1	2	yes	—
84	C₂×C₅×M₁₆	C₂³	1	2	yes	—
85	C₂×C₅×M₁₆	C₂³	1	2	yes	—
86	C₂²×C₅×C₈	—	2	4	no	—
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₂²×C₅×C₈	—	2	1	no	—
89	C₂²×C₅×C₈	—	2	1	no	—
90	C₂²×C₅×C₈	D₄	1	2	yes	—
91	C₅×#117	—	2	1	no	—
92	C₅×#117	—	2	1	no	—
93	C₅×#117	—	2	1	no	—
94	C₅×#117	—	2	1	no	—
95	C₅×#117	—	2	1	no	—
96	C₅×#117	C₂×C₄	1	2	yes	—
97	C₅×#117	C₂×C₄	1	2	yes	—
98	C₅×#117	C₂³	1	2	yes	—
99	C₂×C₅×C₄⋊C₄	—	2	1	no	—
100	C₂×C₅×C₄⋊C₄	—	2	1	no	—
101	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
102	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
103	C₂×C₄²×C₅	—	2	1	no	—
104	C₂×C₄²×C₅	C₂³	1	2	yes	—
105	C₅×#108	—	2	8	no	—
106	C₅×C₄⋊C₈	—	2	8	no	—
107	C₅×#104	—	2	8	no	—
108	C₅×#104	C₂×C₄	1	16	yes	complemented
109	C₂×#568	C₂×C₅	1	1	yes	characteristic
110	C₂×#430	C₂×C₅	1	1	yes	characteristic, complemented
111	#2905	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×#421	C₂×C₅	1	1	yes	characteristic
113	C₂×#421	C₂×C₅	1	1	yes	characteristic
114	#1861	C₂×C₅	1	8	yes	complemented
115	C₂×#344	C₂×C₅	1	1	yes	characteristic, complemented
116	#1733	C₂×C₅	1	1	yes	characteristic, complemented
117	C₂⁴×C₅	—	2	1	no	—
118	C₂⁴×C₅	#41	1	1	yes	characteristic
119	C₅×#41	—	2	2	no	—
120	C₅×#41	—	2	2	no	—
121	C₅×#41	—	2	2	no	—
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	C₄⋊C₄	1	4	yes	—
132	C₅×#41	C₄⋊C₄	1	4	yes	—
133	C₅×#41	C₂²×C₄	1	4	yes	—
134	C₅×#41	C₂×D₄	1	4	yes	—
135	C₂×C₅×Q₈	—	2	1	no	—
136	C₂×C₅×Q₈	—	2	1	no	—
137	C₂×C₅×Q₈	—	2	1	no	—
138	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
139	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
140	C₂×C₅×Q₈	C₂×Q₈	1	2	yes	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	—	2	2	no	—
143	C₂×C₅×D₄	—	2	2	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	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
151	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
152	C₂×C₅×D₄	C₂×Q₈	1	2	yes	—
153	C₂²×C₄×C₅	—	2	1	no	—
154	C₂²×C₄×C₅	—	2	2	no	—
155	C₂²×C₄×C₅	—	2	2	no	—
156	C₂²×C₄×C₅	—	2	2	no	—
157	C₂²×C₄×C₅	—	2	2	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	—	4	1	no	—
162	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂²×C₄	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	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×Q₈	1	1	yes	characteristic
171	C₂²×C₄×C₅	C₂×Q₈	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	C₂⁴	1	1	yes	characteristic
176	C₅×M₁₆	—	2	16	no	—
177	C₅×M₁₆	—	2	2	no	—
178	C₅×M₁₆	—	2	2	no	—
179	C₅×M₁₆	—	2	2	no	—
180	C₅×M₁₆	—	2	2	no	—
181	C₅×M₁₆	—	2	2	no	—
182	C₅×M₁₆	—	2	2	no	—
183	C₅×M₁₆	—	2	2	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	—	4	1	no	—
190	C₅×M₁₆	—	4	1	no	—
191	C₅×M₁₆	C₂²×C₄	1	4	yes	—
192	C₅×M₁₆	C₂×D₄	1	4	yes	—
193	C₂×C₅×C₈	—	2	16	no	—
194	C₂×C₅×C₈	—	2	2	no	—
195	C₂×C₅×C₈	—	2	2	no	—
196	C₂×C₅×C₈	—	2	2	no	—
197	C₂×C₅×C₈	—	2	2	no	—
198	C₂×C₅×C₈	—	2	2	no	—
199	C₂×C₅×C₈	—	2	2	no	—
200	C₂×C₅×C₈	—	2	2	no	—
201	C₂×C₅×C₈	—	2	2	no	—
202	C₂×C₅×C₈	—	2	2	no	—
203	C₂×C₅×C₈	—	4	1	no	—
204	C₂×C₅×C₈	—	4	1	no	—
205	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	—	2	2	no	—
209	C₅×C₄⋊C₄	—	4	1	no	—
210	C₅×C₂²⋊C₄	—	2	2	no	—
211	C₅×C₂²⋊C₄	—	2	2	no	—
212	C₅×C₂²⋊C₄	—	2	2	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₄²×C₅	—	2	2	no	—
215	C₄²×C₅	—	2	2	no	—
216	C₄²×C₅	—	4	1	no	—
217	C₄²×C₅	C₂²×C₄	1	4	yes	—
218	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
219	#568	—	2	2	no	—
220	#568	—	2	2	no	—
221	#568	—	2	2	no	—
222	#568	C₂²×C₅	1	4	yes	—
223	C₂×#131	—	2	2	no	—
224	C₂×#131	—	2	2	no	—
225	C₂²×M₁₆	—	2	2	no	—
226	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
228	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
229	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
230	C₂×#117	C₂²×C₅	1	1	yes	characteristic
231	C₂×#117	C₂²×C₅	1	1	yes	characteristic
232	#430	—	2	2	no	—
233	#430	C₂²×C₅	1	4	yes	complemented
234	C₂×#108	—	2	2	no	—
235	#424	—	2	2	no	—
236	#424	—	2	2	no	—
237	#423	C₂²×C₅	1	4	yes	complemented
238	#421	—	2	2	no	—
239	#421	C₄×C₅	1	4	yes	complemented
240	#421	C₄×C₅	1	4	yes	complemented
241	#421	C₂²×C₅	1	4	yes	—
242	C₂×#104	—	2	2	no	—
243	C₂×#104	C₂²×C₅	1	4	yes	—
244	#344	C₂²×C₅	1	4	yes	complemented
245	#339	C₂²×C₅	1	4	yes	complemented
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	—	8	1	no	—
250	C₂³×C₅	—	8	2	no	—
251	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
252	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
253	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
254	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
255	C₂³×C₅	#123	1	1	yes	characteristic
256	C₂³×C₅	#123	1	1	yes	characteristic
257	C₂³×C₅	C₂×#41	1	1	yes	characteristic
258	C₅×Q₈	—	2	2	no	—
259	C₅×Q₈	—	2	2	no	—
260	C₅×Q₈	—	2	2	no	—
261	C₅×Q₈	C₂×C₄⋊C₄	1	4	yes	—
262	C₅×D₄	—	2	4	no	—
263	C₅×D₄	—	2	4	no	—
264	C₅×D₄	—	2	4	no	—
265	C₅×D₄	—	2	4	no	—
266	C₅×D₄	—	2	2	no	—
267	C₅×D₄	—	2	2	no	—
268	C₅×D₄	—	2	2	no	—
269	C₅×D₄	C₂×C₄⋊C₄	1	4	yes	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	4	no	—
274	C₂×C₄×C₅	—	2	4	no	—
275	C₂×C₄×C₅	—	2	4	no	—
276	C₂×C₄×C₅	—	2	4	no	—
277	C₂×C₄×C₅	—	2	4	no	—
278	C₂×C₄×C₅	—	4	2	no	—
279	C₂×C₄×C₅	—	8	2	no	—
280	C₂×C₄×C₅	—	8	2	no	—
281	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
282	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
283	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
286	C₂×C₄×C₅	C₄×D₄	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	#120	1	1	yes	characteristic
292	C₂×C₄×C₅	#120	1	1	yes	characteristic
293	C₂×C₄×C₅	#120	1	1	yes	characteristic
294	C₂×C₄×C₅	#120	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
297	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
301	C₂×C₄×C₅	#123	1	1	yes	characteristic
302	C₂×C₄×C₅	#123	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
309	C₅×C₈	—	2	4	no	—
310	C₅×C₈	—	2	4	no	—
311	C₅×C₈	—	2	4	no	—
312	C₅×C₈	—	4	2	no	—
313	C₂×#41	—	2	1	no	—
314	C₂×#41	—	2	1	no	—
315	C₂×#41	—	2	1	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	1	no	—
319	C₂×#41	C₂×C₄×C₅	1	2	yes	—
320	C₂×#41	C₂×C₄×C₅	1	2	yes	—
321	C₂×#41	C₅×D₄	1	2	yes	—
322	C₂×#41	C₅×D₄	1	2	yes	—
323	C₂×#41	C₅×Q₈	1	2	yes	—
324	C₂×#41	C₂³×C₅	1	2	yes	—
325	C₂²×Q₈	C₅×Q₈	1	1	yes	characteristic
326	C₂²×D₄	—	2	1	no	—
327	C₂²×D₄	C₅×Q₈	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
330	#131	—	2	8	no	—
331	#131	—	2	8	no	—
332	#131	—	2	8	no	—
333	#131	—	2	8	no	—
334	C₂×M₁₆	—	2	4	no	—
335	C₂×M₁₆	—	2	8	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₂×M₁₆	—	2	1	no	—
338	C₂×M₁₆	—	2	1	no	—
339	C₂×M₁₆	—	2	1	no	—
340	C₂×M₁₆	—	2	1	no	—
341	C₂×M₁₆	—	2	1	no	—
342	C₂×M₁₆	—	2	1	no	—
343	C₂×M₁₆	—	2	1	no	—
344	C₂×M₁₆	—	2	1	no	—
345	C₂×M₁₆	—	2	1	no	—
346	C₂×M₁₆	—	2	8	no	—
347	C₂×M₁₆	—	2	1	no	—
348	C₂×M₁₆	—	2	1	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	2	1	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
353	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
354	C₂×M₁₆	C₅×D₄	1	2	yes	—
355	C₂×M₁₆	C₅×D₄	1	2	yes	—
356	C₂×M₁₆	C₅×D₄	1	2	yes	—
357	C₂×M₁₆	C₂³×C₅	1	2	yes	—
358	C₂×M₁₆	C₂³×C₅	1	2	yes	—
359	C₂×M₁₆	C₂³×C₅	1	2	yes	—
360	C₂×M₁₆	C₂³×C₅	1	2	yes	—
361	C₂²×C₈	—	2	4	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₂²×C₈	—	2	1	no	—
365	C₂²×C₈	C₅×D₄	1	2	yes	—
366	#117	—	2	1	no	—
367	#117	—	2	1	no	—
368	#117	—	2	1	no	—
369	#117	—	2	1	no	—
370	#117	—	2	1	no	—
371	#117	C₂×C₄×C₅	1	2	yes	—
372	#117	C₂×C₄×C₅	1	2	yes	—
373	#117	C₂³×C₅	1	2	yes	—
374	C₂×C₄⋊C₄	—	2	1	no	—
375	C₂×C₄⋊C₄	—	2	1	no	—
376	C₂×C₂²⋊C₄	—	2	1	no	—
377	C₂×C₂²⋊C₄	—	2	1	no	—
378	C₂×C₄²	—	2	1	no	—
379	C₂×C₄²	C₂³×C₅	1	2	yes	—
380	#108	—	2	8	no	—
381	C₄⋊C₈	—	2	8	no	—
382	#104	—	2	8	no	—
383	#104	C₂×C₄×C₅	1	16	yes	complemented
384	C₂²×C₅	—	2	4	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	—	4	1	no	—
389	C₂²×C₅	—	4	1	no	—
390	C₂²×C₅	—	4	1	no	—
391	C₂²×C₅	—	4	1	no	—
392	C₂²×C₅	—	4	4	no	—
393	C₂²×C₅	—	8	2	no	—
394	C₂²×C₅	—	8	2	no	—
395	C₂²×C₅	#385	1	1	yes	characteristic
396	C₂²×C₅	#385	1	1	yes	characteristic
397	C₂²×C₅	#385	1	1	yes	characteristic
398	C₂²×C₅	#385	1	1	yes	characteristic
399	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
400	C₂²×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
401	C₂²×C₅	C₂×#123	1	1	yes	characteristic
402	C₄×C₅	—	2	4	no	—
403	C₄×C₅	—	4	4	no	—
404	C₄×C₅	—	8	2	no	—
405	C₄×C₅	#385	1	1	yes	characteristic
406	C₄×C₅	#385	1	1	yes	characteristic
407	C₄×C₅	#385	1	1	yes	characteristic
408	C₄×C₅	#385	1	1	yes	characteristic
409	C₄×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
410	C₄×C₅	C₂×C₄×D₄	1	1	yes	characteristic
411	C₄×C₅	C₂×#120	1	1	yes	characteristic
412	C₄×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
413	C₂⁴	—	2	1	no	—
414	C₂⁴	C₅×#41	1	1	yes	characteristic
415	#41	—	2	2	no	—
416	#41	—	2	2	no	—
417	#41	—	2	2	no	—
418	#41	—	2	2	no	—
419	#41	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	2	2	no	—
422	#41	—	2	2	no	—
423	#41	—	2	2	no	—
424	#41	—	2	2	no	—
425	#41	—	2	2	no	—
426	#41	—	2	2	no	—
427	#41	C₅×C₄⋊C₄	1	4	yes	—
428	#41	C₅×C₄⋊C₄	1	4	yes	—
429	#41	C₂²×C₄×C₅	1	4	yes	—
430	#41	C₂×C₅×D₄	1	4	yes	—
431	C₂×Q₈	—	2	1	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	1	no	—
434	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
435	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
436	C₂×Q₈	C₂×C₅×Q₈	1	2	yes	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	2	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
447	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
448	C₂×D₄	C₂×C₅×Q₈	1	2	yes	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	4	1	no	—
458	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
459	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
460	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
461	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
462	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
464	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
465	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
466	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
467	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
468	C₂²×C₄	C₅×#41	1	1	yes	characteristic
469	C₂²×C₄	C₅×#41	1	1	yes	characteristic
470	C₂²×C₄	C₅×#41	1	1	yes	characteristic
471	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
472	M₁₆	—	2	16	no	—
473	M₁₆	—	2	2	no	—
474	M₁₆	—	2	2	no	—
475	M₁₆	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	M₁₆	—	2	2	no	—
478	M₁₆	—	2	2	no	—
479	M₁₆	—	2	2	no	—
480	M₁₆	—	2	2	no	—
481	M₁₆	—	2	2	no	—
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	4	1	no	—
486	M₁₆	—	4	1	no	—
487	M₁₆	C₂²×C₄×C₅	1	4	yes	—
488	M₁₆	C₂×C₅×D₄	1	4	yes	—
489	C₂×C₈	—	2	16	no	—
490	C₂×C₈	—	2	2	no	—
491	C₂×C₈	—	2	2	no	—
492	C₂×C₈	—	2	2	no	—
493	C₂×C₈	—	2	2	no	—
494	C₂×C₈	—	2	2	no	—
495	C₂×C₈	—	2	2	no	—
496	C₂×C₈	—	2	2	no	—
497	C₂×C₈	—	2	2	no	—
498	C₂×C₈	—	2	2	no	—
499	C₂×C₈	—	4	1	no	—
500	C₂×C₈	—	4	1	no	—
501	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
502	C₄⋊C₄	—	2	2	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	2	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	2	2	no	—
507	C₂²⋊C₄	—	2	2	no	—
508	C₂²⋊C₄	—	2	2	no	—
509	C₂²⋊C₄	—	4	1	no	—
510	C₄²	—	2	2	no	—
511	C₄²	—	2	2	no	—
512	C₄²	—	4	1	no	—
513	C₄²	C₂²×C₄×C₅	1	4	yes	—
514	C₂×C₅	—	2	1	no	—
515	C₂×C₅	—	2	1	no	—
516	C₂×C₅	—	2	1	no	—
517	C₂×C₅	—	2	1	no	—
518	C₂×C₅	—	2	1	no	—
519	C₂×C₅	—	2	1	no	—
520	C₂×C₅	—	2	1	no	—
521	C₂×C₅	—	4	4	no	—
522	C₂×C₅	C₂×#385	1	1	yes	characteristic
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	2	no	—
526	C₂³	—	8	1	no	—
527	C₂³	—	8	2	no	—
528	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
529	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
530	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
531	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
532	C₂³	C₅×#123	1	1	yes	characteristic
533	C₂³	C₅×#123	1	1	yes	characteristic
534	C₂³	C₂×C₅×#41	1	1	yes	characteristic
535	Q₈	—	2	2	no	—
536	Q₈	—	2	2	no	—
537	Q₈	—	2	2	no	—
538	Q₈	C₂×C₅×C₄⋊C₄	1	4	yes	—
539	D₄	—	2	4	no	—
540	D₄	—	2	4	no	—
541	D₄	—	2	4	no	—
542	D₄	—	2	4	no	—
543	D₄	—	2	2	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	2	no	—
546	D₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	4	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	8	2	no	—
557	C₂×C₄	—	8	2	no	—
558	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
559	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
560	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
561	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
562	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
563	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
564	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
565	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
566	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
567	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
568	C₂×C₄	C₅×#120	1	1	yes	characteristic
569	C₂×C₄	C₅×#120	1	1	yes	characteristic
570	C₂×C₄	C₅×#120	1	1	yes	characteristic
571	C₂×C₄	C₅×#120	1	1	yes	characteristic
572	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
573	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
574	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
575	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
576	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
577	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
578	C₂×C₄	C₅×#123	1	1	yes	characteristic
579	C₂×C₄	C₅×#123	1	1	yes	characteristic
580	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
581	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
582	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
583	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
584	C₂×C₄	C₂²×C₅×Q₈	1	1	yes	characteristic
585	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
586	C₈	—	2	4	no	—
587	C₈	—	2	4	no	—
588	C₈	—	2	4	no	—
589	C₈	—	4	2	no	—
590	C₅	#20867	1	1	yes	characteristic, direct product factor, Sylow
591	C₂²	—	2	4	no	—
592	C₂²	—	4	1	no	—
593	C₂²	—	4	1	no	—
594	C₂²	—	4	1	no	—
595	C₂²	—	4	1	no	—
596	C₂²	—	4	1	no	—
597	C₂²	—	4	1	no	—
598	C₂²	—	4	1	no	—
599	C₂²	—	4	4	no	—
600	C₂²	—	8	2	no	—
601	C₂²	—	8	2	no	—
602	C₂²	C₅×#385	1	1	yes	characteristic
603	C₂²	C₅×#385	1	1	yes	characteristic
604	C₂²	C₅×#385	1	1	yes	characteristic
605	C₂²	C₅×#385	1	1	yes	characteristic
606	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
607	C₂²	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
608	C₂²	C₂×C₅×#123	1	1	yes	characteristic
609	C₄	—	2	4	no	—
610	C₄	—	4	4	no	—
611	C₄	—	8	2	no	—
612	C₄	C₅×#385	1	1	yes	characteristic
613	C₄	C₅×#385	1	1	yes	characteristic
614	C₄	C₅×#385	1	1	yes	characteristic
615	C₄	C₅×#385	1	1	yes	characteristic
616	C₄	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
617	C₄	C₂×C₄×C₅×D₄	1	1	yes	characteristic
618	C₄	C₂×C₅×#120	1	1	yes	characteristic
619	C₄	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
620	C₂	—	2	1	no	—
621	C₂	—	2	1	no	—
622	C₂	—	2	1	no	—
623	C₂	—	2	1	no	—
624	C₂	—	2	1	no	—
625	C₂	—	2	1	no	—
626	C₂	—	2	1	no	—
627	C₂	—	4	4	no	—
628	C₂	C₂×C₅×#385	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₅	C₂×#120
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂×C₅	C₂×#385
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂×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
2. C₂×C₅×#430	C₂	semidirect
3. C₅×#2905	C₂	semidirect
6. C₅×#1861	C₂	semidirect
7. C₂×C₅×#344	C₂	semidirect
8. C₅×#1733	C₂	semidirect
24. C₅×#430	C₂²	semidirect
28. C₅×#423	C₂²	semidirect
30. C₅×#421	C₄	semidirect
31. C₅×#421	C₄	semidirect
35. C₅×#344	C₂²	semidirect
36. C₅×#339	C₂²	semidirect
37. #20867	C₅	direct (N × H)
108. C₅×#104	C₂×C₄	semidirect
110. C₂×#430	C₂×C₅	semidirect
111. #2905	C₂×C₅	semidirect
114. #1861	C₂×C₅	semidirect
115. C₂×#344	C₂×C₅	semidirect
116. #1733	C₂×C₅	semidirect
233. #430	C₂²×C₅	semidirect
237. #423	C₂²×C₅	semidirect
239. #421	C₄×C₅	semidirect
240. #421	C₄×C₅	semidirect
244. #344	C₂²×C₅	semidirect
245. #339	C₂²×C₅	semidirect
383. #104	C₂×C₄×C₅	semidirect
590. C₅	#20867	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
C₅×#2905	2
C₂×C₅×#421	2
C₅×#1861	2
C₂×C₅×#344	2
C₅×#1733	2
#20867	5

Subgroups — C5×#20867 #11943587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#20867 #11943587