Subgroups — C₅×#11084 #11933804

Order 1280.

878 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#421	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#408	C₂	1	1	yes	maximal, characteristic
5	C₅×#1738	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₅×H(3,ℤ/4)	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1729	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
10	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂×C₅×#117	C₂²	1	1	yes	characteristic
15	C₅×#424	—	2	2	no	—
16	C₅×#424	—	2	2	no	—
17	C₂×C₅×C₄⋊C₈	—	2	2	no	—
18	C₅×#421	—	2	2	no	—
19	C₅×#421	—	2	2	no	—
20	C₅×#421	—	2	2	no	—
21	C₅×#421	C₄	1	4	yes	complemented
22	C₂×C₅×#104	—	2	2	no	—
23	C₂×C₅×#104	—	2	2	no	—
24	C₅×#408	—	2	2	no	—
25	C₅×#408	—	2	2	no	—
26	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
27	C₅×#341	—	2	2	no	—
28	C₅×H(3,ℤ/4)	—	2	2	no	—
29	C₅×#336	—	2	2	no	—
30	#11084	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
31	C₂×C₅×#41	—	2	1	no	—
32	C₂×C₅×#41	—	2	1	no	—
33	C₂×C₅×#41	—	2	1	no	—
34	C₂×C₅×#41	—	2	1	no	—
35	C₂×C₅×#41	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
42	C₂×C₅×#41	D₄	1	2	yes	—
43	C₂²×C₅×Q₈	Q₈	1	1	yes	characteristic
44	C₂²×C₅×D₄	—	2	1	no	—
45	C₂²×C₅×D₄	Q₈	1	1	yes	characteristic
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₅×M₁₆	—	2	1	no	—
49	C₂×C₅×M₁₆	—	2	1	no	—
50	C₂×C₅×M₁₆	—	2	1	no	—
51	C₂×C₅×M₁₆	—	2	1	no	—
52	C₂×C₅×M₁₆	—	2	1	no	—
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	C₂×C₄	1	2	yes	—
65	C₂×C₅×M₁₆	D₄	1	2	yes	—
66	C₂²×C₅×C₈	—	2	1	no	—
67	C₂²×C₅×C₈	—	2	1	no	—
68	C₂²×C₅×C₈	—	2	1	no	—
69	C₂²×C₅×C₈	—	2	1	no	—
70	C₂²×C₅×C₈	—	2	1	no	—
71	C₂²×C₅×C₈	—	2	1	no	—
72	C₂²×C₅×C₈	—	2	1	no	—
73	C₂²×C₅×C₈	—	2	1	no	—
74	C₂²×C₅×C₈	D₄	1	2	yes	—
75	C₂²×C₅×C₈	D₄	1	2	yes	—
76	C₅×#117	—	2	1	no	—
77	C₅×#117	—	2	1	no	—
78	C₅×#117	—	2	1	no	—
79	C₅×#117	—	2	1	no	—
80	C₅×#117	—	2	1	no	—
81	C₅×#117	—	2	1	no	—
82	C₅×#117	C₂×C₄	1	2	yes	—
83	C₅×#117	D₄	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	—	2	1	no	—
86	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₅	D₄	1	2	yes	—
89	C₂×C₄²×C₅	D₄	1	2	yes	—
90	C₅×C₄⋊C₈	—	2	8	no	—
91	C₅×#104	—	2	8	no	—
92	C₅×#104	—	2	8	no	—
93	C₅×C₂²⋊C₈	—	2	8	no	—
94	C₂×#424	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#421	C₂×C₅	1	1	yes	characteristic
96	C₂×#421	C₂×C₅	1	1	yes	characteristic
97	C₂×#408	C₂×C₅	1	1	yes	characteristic
98	#1738	C₂×C₅	1	1	yes	characteristic, complemented
99	C₂×H(3,ℤ/4)	C₂×C₅	1	1	yes	characteristic, complemented
100	#1729	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂⁴×C₅	—	2	1	no	—
102	C₂⁴×C₅	#41	1	1	yes	characteristic
103	C₅×#41	—	2	2	no	—
104	C₅×#41	—	2	2	no	—
105	C₅×#41	—	2	2	no	—
106	C₅×#41	—	2	2	no	—
107	C₅×#41	—	2	2	no	—
108	C₅×#41	—	2	2	no	—
109	C₅×#41	—	2	2	no	—
110	C₅×#41	—	2	2	no	—
111	C₅×#41	—	4	1	no	—
112	C₅×#41	—	4	1	no	—
113	C₅×#41	—	4	1	no	—
114	C₅×#41	—	4	1	no	—
115	C₅×#41	—	4	1	no	—
116	C₅×#41	—	4	1	no	—
117	C₅×#41	—	4	1	no	—
118	C₅×#41	—	4	1	no	—
119	C₂×C₅×Q₈	—	2	1	no	—
120	C₂×C₅×Q₈	—	2	1	no	—
121	C₂×C₅×Q₈	—	2	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	C₄⋊C₄	1	2	yes	—
125	C₂×C₅×D₄	—	2	2	no	—
126	C₂×C₅×D₄	—	2	2	no	—
127	C₂×C₅×D₄	—	2	1	no	—
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	—	2	1	no	—
130	C₂×C₅×D₄	—	2	1	no	—
131	C₂×C₅×D₄	—	2	1	no	—
132	C₂×C₅×D₄	—	4	1	no	—
133	C₂×C₅×D₄	—	4	1	no	—
134	C₂×C₅×D₄	—	4	1	no	—
135	C₂×C₅×D₄	—	4	1	no	—
136	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
137	C₂²×C₄×C₅	—	2	1	no	—
138	C₂²×C₄×C₅	—	2	2	no	—
139	C₂²×C₄×C₅	—	2	2	no	—
140	C₂²×C₄×C₅	—	2	2	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	4	1	no	—
143	C₂²×C₄×C₅	—	4	1	no	—
144	C₂²×C₄×C₅	—	4	1	no	—
145	C₂²×C₄×C₅	—	4	1	no	—
146	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
155	C₂²×C₄×C₅	#41	1	1	yes	characteristic
156	C₂²×C₄×C₅	#41	1	1	yes	characteristic
157	C₂²×C₄×C₅	#41	1	1	yes	characteristic
158	C₂²×C₄×C₅	#41	1	1	yes	characteristic
159	C₂²×C₄×C₅	#41	1	1	yes	characteristic
160	C₅×M₁₆	—	2	2	no	—
161	C₅×M₁₆	—	2	2	no	—
162	C₅×M₁₆	—	2	2	no	—
163	C₅×M₁₆	—	2	2	no	—
164	C₅×M₁₆	—	4	1	no	—
165	C₅×M₁₆	—	4	1	no	—
166	C₅×M₁₆	—	4	1	no	—
167	C₅×M₁₆	—	4	1	no	—
168	C₅×M₁₆	—	4	1	no	—
169	C₅×M₁₆	—	4	1	no	—
170	C₅×M₁₆	—	4	1	no	—
171	C₅×M₁₆	—	4	1	no	—
172	C₂×C₅×C₈	—	2	2	no	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₂×C₅×C₈	—	2	2	no	—
175	C₂×C₅×C₈	—	2	2	no	—
176	C₂×C₅×C₈	—	2	2	no	—
177	C₂×C₅×C₈	—	2	2	no	—
178	C₂×C₅×C₈	—	2	2	no	—
179	C₂×C₅×C₈	—	2	2	no	—
180	C₂×C₅×C₈	—	4	1	no	—
181	C₂×C₅×C₈	—	4	1	no	—
182	C₂×C₅×C₈	—	4	1	no	—
183	C₂×C₅×C₈	—	4	1	no	—
184	C₂×C₅×C₈	—	4	1	no	—
185	C₂×C₅×C₈	—	4	1	no	—
186	C₂×C₅×C₈	—	4	1	no	—
187	C₂×C₅×C₈	—	4	1	no	—
188	C₅×C₄⋊C₄	—	2	2	no	—
189	C₅×C₄⋊C₄	—	2	2	no	—
190	C₅×C₄⋊C₄	—	4	1	no	—
191	C₅×C₄⋊C₄	—	4	1	no	—
192	C₅×C₂²⋊C₄	—	2	2	no	—
193	C₅×C₂²⋊C₄	—	2	2	no	—
194	C₅×C₂²⋊C₄	—	4	1	no	—
195	C₅×C₂²⋊C₄	—	4	1	no	—
196	C₄²×C₅	—	2	2	no	—
197	C₄²×C₅	—	2	2	no	—
198	C₄²×C₅	—	2	2	no	—
199	C₄²×C₅	C₂²⋊C₄	1	4	yes	—
200	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
201	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
202	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
203	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
204	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
205	C₂×#117	C₂²×C₅	1	1	yes	characteristic
206	C₂×#117	C₂²×C₅	1	1	yes	characteristic
207	#424	—	2	2	no	—
208	#424	—	2	2	no	—
209	C₂×C₄⋊C₈	—	2	2	no	—
210	#421	—	2	2	no	—
211	#421	—	2	2	no	—
212	#421	—	2	2	no	—
213	#421	C₄×C₅	1	4	yes	complemented
214	C₂×#104	—	2	2	no	—
215	C₂×#104	—	2	2	no	—
216	#408	—	2	2	no	—
217	#408	—	2	2	no	—
218	C₂×C₂²⋊C₈	—	2	2	no	—
219	#341	—	2	2	no	—
220	H(3,ℤ/4)	—	2	2	no	—
221	#336	—	2	2	no	—
222	C₂³×C₅	—	2	2	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	—	4	4	no	—
225	C₂³×C₅	—	4	1	no	—
226	C₂³×C₅	—	4	1	no	—
227	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
228	C₂³×C₅	#121	1	1	yes	characteristic
229	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
230	C₂³×C₅	#123	1	1	yes	characteristic
231	C₂³×C₅	#123	1	1	yes	characteristic
232	C₂³×C₅	#123	1	1	yes	characteristic
233	C₂³×C₅	#126	1	1	yes	characteristic
234	C₅×Q₈	—	2	2	no	—
235	C₅×Q₈	—	2	2	no	—
236	C₅×Q₈	—	4	1	no	—
237	C₅×Q₈	—	4	1	no	—
238	C₅×D₄	—	2	2	no	—
239	C₅×D₄	—	2	2	no	—
240	C₅×D₄	—	4	2	no	—
241	C₅×D₄	—	4	2	no	—
242	C₅×D₄	—	4	2	no	—
243	C₅×D₄	—	4	2	no	—
244	C₅×D₄	—	4	1	no	—
245	C₅×D₄	—	4	1	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	4	no	—
248	C₂×C₄×C₅	—	4	4	no	—
249	C₂×C₄×C₅	—	4	1	no	—
250	C₂×C₄×C₅	—	4	1	no	—
251	C₂×C₄×C₅	—	4	2	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	2	no	—
254	C₂×C₄×C₅	—	4	2	no	—
255	C₂×C₄×C₅	—	4	4	no	—
256	C₂×C₄×C₅	—	4	2	no	—
257	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
258	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
259	C₂×C₄×C₅	#117	1	1	yes	characteristic
260	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
262	C₂×C₄×C₅	C₄×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	#120	1	1	yes	characteristic
264	C₂×C₄×C₅	#120	1	1	yes	characteristic
265	C₂×C₄×C₅	#120	1	1	yes	characteristic
266	C₂×C₄×C₅	#121	1	1	yes	characteristic
267	C₂×C₄×C₅	#121	1	1	yes	characteristic
268	C₂×C₄×C₅	#121	1	1	yes	characteristic
269	C₂×C₄×C₅	#121	1	1	yes	characteristic
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	C₂²⋊Q₈	1	1	yes	characteristic
274	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
275	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
276	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
277	C₂×C₄×C₅	C₂²⋊Q₈	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	#124	1	1	yes	characteristic
281	C₂×C₄×C₅	#124	1	1	yes	characteristic
282	C₂×C₄×C₅	#124	1	1	yes	characteristic
283	C₂×C₄×C₅	#126	1	1	yes	characteristic
284	C₂×C₄×C₅	#127	1	1	yes	characteristic
285	C₅×C₈	—	4	2	no	—
286	C₅×C₈	—	4	2	no	—
287	C₅×C₈	—	4	2	no	—
288	C₅×C₈	—	4	2	no	—
289	C₂×#41	—	2	1	no	—
290	C₂×#41	—	2	1	no	—
291	C₂×#41	—	2	1	no	—
292	C₂×#41	—	2	1	no	—
293	C₂×#41	—	2	1	no	—
294	C₂×#41	—	2	1	no	—
295	C₂×#41	—	2	1	no	—
296	C₂×#41	—	2	1	no	—
297	C₂×#41	—	2	1	no	—
298	C₂×#41	—	2	1	no	—
299	C₂×#41	C₂×C₄×C₅	1	2	yes	—
300	C₂×#41	C₅×D₄	1	2	yes	—
301	C₂²×Q₈	C₅×Q₈	1	1	yes	characteristic
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	C₅×Q₈	1	1	yes	characteristic
304	C₂³×C₄	—	2	1	no	—
305	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
306	C₂×M₁₆	—	2	1	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂×M₁₆	—	2	1	no	—
309	C₂×M₁₆	—	2	1	no	—
310	C₂×M₁₆	—	2	1	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	1	no	—
313	C₂×M₁₆	—	2	1	no	—
314	C₂×M₁₆	—	2	1	no	—
315	C₂×M₁₆	—	2	1	no	—
316	C₂×M₁₆	—	2	1	no	—
317	C₂×M₁₆	—	2	1	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₂×M₁₆	—	2	1	no	—
320	C₂×M₁₆	—	2	1	no	—
321	C₂×M₁₆	—	2	1	no	—
322	C₂×M₁₆	C₂×C₄×C₅	1	2	yes	—
323	C₂×M₁₆	C₅×D₄	1	2	yes	—
324	C₂²×C₈	—	2	1	no	—
325	C₂²×C₈	—	2	1	no	—
326	C₂²×C₈	—	2	1	no	—
327	C₂²×C₈	—	2	1	no	—
328	C₂²×C₈	—	2	1	no	—
329	C₂²×C₈	—	2	1	no	—
330	C₂²×C₈	—	2	1	no	—
331	C₂²×C₈	—	2	1	no	—
332	C₂²×C₈	C₅×D₄	1	2	yes	—
333	C₂²×C₈	C₅×D₄	1	2	yes	—
334	#117	—	2	1	no	—
335	#117	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	C₂×C₄×C₅	1	2	yes	—
341	#117	C₅×D₄	1	2	yes	—
342	C₂×C₄⋊C₄	—	2	1	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	1	no	—
346	C₂×C₄²	C₅×D₄	1	2	yes	—
347	C₂×C₄²	C₅×D₄	1	2	yes	—
348	C₄⋊C₈	—	2	8	no	—
349	#104	—	2	8	no	—
350	#104	—	2	8	no	—
351	C₂²⋊C₈	—	2	8	no	—
352	C₂²×C₅	—	2	2	no	—
353	C₂²×C₅	—	2	2	no	—
354	C₂²×C₅	—	2	2	no	—
355	C₂²×C₅	—	4	1	no	—
356	C₂²×C₅	—	4	1	no	—
357	C₂²×C₅	—	4	1	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	4	no	—
360	C₂²×C₅	—	4	2	no	—
361	C₂²×C₅	—	8	2	no	—
362	C₂²×C₅	—	8	2	no	—
363	C₂²×C₅	#385	1	1	yes	characteristic
364	C₂²×C₅	#386	1	1	yes	characteristic
365	C₂²×C₅	#388	1	1	yes	characteristic
366	C₂²×C₅	#394	1	1	yes	characteristic
367	C₂²×C₅	#396	1	1	yes	characteristic
368	C₂²×C₅	#397	1	1	yes	characteristic
369	C₂²×C₅	#399	1	1	yes	characteristic
370	C₄×C₅	—	4	4	no	—
371	C₄×C₅	—	4	2	no	—
372	C₄×C₅	—	8	2	no	—
373	C₄×C₅	#380	1	1	yes	characteristic
374	C₄×C₅	#385	1	1	yes	characteristic
375	C₄×C₅	#388	1	1	yes	characteristic
376	C₄×C₅	#390	1	1	yes	characteristic
377	C₄×C₅	#392	1	1	yes	characteristic
378	C₄×C₅	#393	1	1	yes	characteristic
379	C₄×C₅	#394	1	1	yes	characteristic
380	C₄×C₅	#396	1	1	yes	characteristic
381	C₂⁴	—	2	1	no	—
382	C₂⁴	C₅×#41	1	1	yes	characteristic
383	#41	—	2	2	no	—
384	#41	—	2	2	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	2	2	no	—
391	#41	—	4	1	no	—
392	#41	—	4	1	no	—
393	#41	—	4	1	no	—
394	#41	—	4	1	no	—
395	#41	—	4	1	no	—
396	#41	—	4	1	no	—
397	#41	—	4	1	no	—
398	#41	—	4	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	—	2	1	no	—
404	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
405	C₂×D₄	—	2	2	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	1	no	—
408	C₂×D₄	—	2	1	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	1	no	—
414	C₂×D₄	—	4	1	no	—
415	C₂×D₄	—	4	1	no	—
416	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	4	1	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	4	1	no	—
426	C₂²×C₄	C₂²×C₄×C₅	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	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
431	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
432	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
434	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
435	C₂²×C₄	C₅×#41	1	1	yes	characteristic
436	C₂²×C₄	C₅×#41	1	1	yes	characteristic
437	C₂²×C₄	C₅×#41	1	1	yes	characteristic
438	C₂²×C₄	C₅×#41	1	1	yes	characteristic
439	C₂²×C₄	C₅×#41	1	1	yes	characteristic
440	M₁₆	—	2	2	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	2	2	no	—
443	M₁₆	—	2	2	no	—
444	M₁₆	—	4	1	no	—
445	M₁₆	—	4	1	no	—
446	M₁₆	—	4	1	no	—
447	M₁₆	—	4	1	no	—
448	M₁₆	—	4	1	no	—
449	M₁₆	—	4	1	no	—
450	M₁₆	—	4	1	no	—
451	M₁₆	—	4	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	2	2	no	—
454	C₂×C₈	—	2	2	no	—
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	—	2	2	no	—
459	C₂×C₈	—	2	2	no	—
460	C₂×C₈	—	4	1	no	—
461	C₂×C₈	—	4	1	no	—
462	C₂×C₈	—	4	1	no	—
463	C₂×C₈	—	4	1	no	—
464	C₂×C₈	—	4	1	no	—
465	C₂×C₈	—	4	1	no	—
466	C₂×C₈	—	4	1	no	—
467	C₂×C₈	—	4	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	no	—
470	C₄⋊C₄	—	4	1	no	—
471	C₄⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	2	2	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₄²	—	2	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	C₅×C₂²⋊C₄	1	4	yes	—
480	C₂×C₅	—	2	1	no	—
481	C₂×C₅	—	2	1	no	—
482	C₂×C₅	—	2	1	no	—
483	C₂×C₅	—	2	1	no	—
484	C₂×C₅	—	2	1	no	—
485	C₂×C₅	—	2	1	no	—
486	C₂×C₅	—	8	2	no	—
487	C₂×C₅	#1439	1	1	yes	characteristic
488	C₂×C₅	#2098	1	2	yes	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	4	no	—
492	C₂³	—	4	1	no	—
493	C₂³	—	4	1	no	—
494	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
495	C₂³	C₅×#121	1	1	yes	characteristic
496	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
497	C₂³	C₅×#123	1	1	yes	characteristic
498	C₂³	C₅×#123	1	1	yes	characteristic
499	C₂³	C₅×#123	1	1	yes	characteristic
500	C₂³	C₅×#126	1	1	yes	characteristic
501	Q₈	—	2	2	no	—
502	Q₈	—	2	2	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	D₄	—	2	2	no	—
506	D₄	—	2	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	4	2	no	—
509	D₄	—	4	2	no	—
510	D₄	—	4	2	no	—
511	D₄	—	4	1	no	—
512	D₄	—	4	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	2	no	—
519	C₂×C₄	—	4	2	no	—
520	C₂×C₄	—	4	2	no	—
521	C₂×C₄	—	4	2	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
525	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
526	C₂×C₄	C₅×#117	1	1	yes	characteristic
527	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
528	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
529	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
530	C₂×C₄	C₅×#120	1	1	yes	characteristic
531	C₂×C₄	C₅×#120	1	1	yes	characteristic
532	C₂×C₄	C₅×#120	1	1	yes	characteristic
533	C₂×C₄	C₅×#121	1	1	yes	characteristic
534	C₂×C₄	C₅×#121	1	1	yes	characteristic
535	C₂×C₄	C₅×#121	1	1	yes	characteristic
536	C₂×C₄	C₅×#121	1	1	yes	characteristic
537	C₂×C₄	C₅×#121	1	1	yes	characteristic
538	C₂×C₄	C₅×#121	1	1	yes	characteristic
539	C₂×C₄	C₅×#121	1	1	yes	characteristic
540	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
541	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
542	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
543	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
544	C₂×C₄	C₅×C₂²⋊Q₈	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×#124	1	1	yes	characteristic
548	C₂×C₄	C₅×#124	1	1	yes	characteristic
549	C₂×C₄	C₅×#124	1	1	yes	characteristic
550	C₂×C₄	C₅×#126	1	1	yes	characteristic
551	C₂×C₄	C₅×#127	1	1	yes	characteristic
552	C₈	—	4	2	no	—
553	C₈	—	4	2	no	—
554	C₈	—	4	2	no	—
555	C₈	—	4	2	no	—
556	C₅	#11084	1	1	yes	characteristic, direct product factor, Sylow
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	8	2	no	—
568	C₂²	C₅×#385	1	1	yes	characteristic
569	C₂²	C₅×#386	1	1	yes	characteristic
570	C₂²	C₅×#388	1	1	yes	characteristic
571	C₂²	C₅×#394	1	1	yes	characteristic
572	C₂²	C₅×#396	1	1	yes	characteristic
573	C₂²	C₅×#397	1	1	yes	characteristic
574	C₂²	C₅×#399	1	1	yes	characteristic
575	C₄	—	4	4	no	—
576	C₄	—	4	2	no	—
577	C₄	—	8	2	no	—
578	C₄	C₅×#380	1	1	yes	characteristic
579	C₄	C₅×#385	1	1	yes	characteristic
580	C₄	C₅×#388	1	1	yes	characteristic
581	C₄	C₅×#390	1	1	yes	characteristic
582	C₄	C₅×#392	1	1	yes	characteristic
583	C₄	C₅×#393	1	1	yes	characteristic
584	C₄	C₅×#394	1	1	yes	characteristic
585	C₄	C₅×#396	1	1	yes	characteristic
586	C₂	—	2	1	no	—
587	C₂	—	2	1	no	—
588	C₂	—	2	1	no	—
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	2	1	no	—
592	C₂	—	8	2	no	—
593	C₂	C₅×#1439	1	1	yes	characteristic
594	C₂	C₅×#2098	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	#127
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂²×C₅	#399
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂²×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
1. C₂×C₅×#424	C₂	semidirect
5. C₅×#1738	C₂	semidirect
6. C₂×C₅×H(3,ℤ/4)	C₂	semidirect
7. C₅×#1729	C₂	semidirect
21. C₅×#421	C₄	semidirect
30. #11084	C₅	direct (N × H)
94. C₂×#424	C₂×C₅	semidirect
98. #1738	C₂×C₅	semidirect
99. C₂×H(3,ℤ/4)	C₂×C₅	semidirect
100. #1729	C₂×C₅	semidirect
213. #421	C₄×C₅	semidirect
556. C₅	#11084	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×#424	2
C₂×C₅×#421	2
C₂×C₅×#408	2
C₅×#1738	2
C₂×C₅×H(3,ℤ/4)	2
C₅×#1729	2
#11084	5

Subgroups — C5×#11084 #11933804

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11084 #11933804