Subgroups — C₅×#11125 #11933845

Order 1280.

930 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×#104	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#416	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#408	C₂	1	1	yes	maximal, characteristic
5	C₂×C₅×#339	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1729	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₅×#336	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	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
12	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
13	C₂×C₅×#117	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₅×#108	—	2	2	no	—
16	C₂×C₅×#108	—	2	2	no	—
17	C₂×C₅×#108	—	2	2	no	—
18	C₂×C₅×#104	—	2	2	no	—
19	C₂×C₅×#104	—	2	2	no	—
20	C₂×C₅×#104	—	2	2	no	—
21	C₅×#416	—	2	2	no	—
22	C₅×#416	—	2	2	no	—
23	C₂×C₅×#103	C₄	1	1	yes	characteristic, complemented
24	C₂×C₅×#103	C₄	1	1	yes	characteristic, complemented
25	C₂×C₅×#102	C₄	1	1	yes	characteristic, complemented
26	C₂×C₅×#102	C₄	1	1	yes	characteristic, complemented
27	C₅×#408	—	2	2	no	—
28	C₅×#408	—	2	2	no	—
29	C₂×C₅×C₂²⋊C₈	—	2	2	no	—
30	C₅×#339	—	2	2	no	—
31	C₅×#336	—	2	2	no	—
32	C₅×#336	—	2	2	no	—
33	#11125	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
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	—	2	1	no	—
42	C₂×C₅×#41	—	2	1	no	—
43	C₂×C₅×#41	—	2	1	no	—
44	C₂×C₅×#41	D₄	1	2	yes	—
45	C₂×C₅×#41	Q₈	1	2	yes	—
46	C₂²×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₅×D₄	—	2	1	no	—
48	C₂²×C₅×D₄	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₅	—	2	1	no	—
50	C₂³×C₄×C₅	—	2	1	no	—
51	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
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	D₄	1	2	yes	—
63	C₂×C₅×M₁₆	D₄	1	2	yes	—
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	—	2	1	no	—
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	—	2	1	no	—
75	C₂²×C₅×C₈	—	2	1	no	—
76	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
77	C₂²×C₅×C₈	C₂×C₄	1	1	yes	characteristic
78	C₂²×C₅×C₈	D₄	1	2	yes	—
79	C₂²×C₅×C₈	D₄	1	2	yes	—
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	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
88	C₂×C₄²×C₅	—	2	1	no	—
89	C₂×C₄²×C₅	—	2	1	no	—
90	C₂×C₄²×C₅	—	2	1	no	—
91	C₂×C₄²×C₅	—	2	1	no	—
92	C₂×C₄²×C₅	—	2	1	no	—
93	C₂×C₄²×C₅	—	2	1	no	—
94	C₂×C₄²×C₅	D₄	1	2	yes	—
95	C₅×#108	—	2	8	no	—
96	C₅×#104	—	2	8	no	—
97	C₅×#103	—	2	2	no	—
98	C₅×#103	—	2	2	no	—
99	C₅×#102	—	2	2	no	—
100	C₅×#102	—	2	2	no	—
101	C₅×C₂²⋊C₈	—	2	8	no	—
102	C₂²×#108	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂²×#104	C₂×C₅	1	1	yes	characteristic
104	C₂×#416	C₂×C₅	1	1	yes	characteristic
105	C₂×#408	C₂×C₅	1	1	yes	characteristic
106	C₂×#339	C₂×C₅	1	1	yes	characteristic, complemented
107	#1729	C₂×C₅	1	1	yes	characteristic, complemented
108	C₂×#336	C₂×C₅	1	1	yes	characteristic, complemented
109	C₂⁴×C₅	—	2	1	no	—
110	C₂⁴×C₅	#41	1	1	yes	characteristic
111	C₅×#41	—	2	2	no	—
112	C₅×#41	—	2	2	no	—
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	—	4	1	no	—
120	C₅×#41	—	4	1	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	C₂×C₅×Q₈	—	2	1	no	—
128	C₂×C₅×Q₈	—	2	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	C₄⋊C₄	1	2	yes	—
133	C₂×C₅×D₄	—	2	2	no	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	2	1	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	—	4	1	no	—
141	C₂×C₅×D₄	—	4	1	no	—
142	C₂×C₅×D₄	—	4	1	no	—
143	C₂×C₅×D₄	—	4	1	no	—
144	C₂×C₅×D₄	C₄⋊C₄	1	2	yes	—
145	C₂²×C₄×C₅	—	2	4	no	—
146	C₂²×C₄×C₅	—	2	1	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	—	2	2	no	—
149	C₂²×C₄×C₅	—	2	2	no	—
150	C₂²×C₄×C₅	—	2	1	no	—
151	C₂²×C₄×C₅	—	2	1	no	—
152	C₂²×C₄×C₅	—	4	2	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	—	4	1	no	—
157	C₂²×C₄×C₅	—	4	1	no	—
158	C₂²×C₄×C₅	—	4	1	no	—
159	C₂²×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×D₄	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	C₂²×C₄×C₅	C₂×Q₈	1	1	yes	characteristic
168	C₂²×C₄×C₅	#41	1	1	yes	characteristic
169	C₂²×C₄×C₅	#41	1	1	yes	characteristic
170	C₂²×C₄×C₅	#41	1	1	yes	characteristic
171	C₂²×C₄×C₅	#41	1	1	yes	characteristic
172	C₂²×C₄×C₅	#41	1	1	yes	characteristic
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	—	4	1	no	—
178	C₅×M₁₆	—	4	1	no	—
179	C₅×M₁₆	—	4	1	no	—
180	C₅×M₁₆	—	4	1	no	—
181	C₂×C₅×C₈	—	2	1	no	—
182	C₂×C₅×C₈	—	2	1	no	—
183	C₂×C₅×C₈	—	2	1	no	—
184	C₂×C₅×C₈	—	2	1	no	—
185	C₂×C₅×C₈	—	2	2	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	—	2	2	no	—
192	C₂×C₅×C₈	—	2	2	no	—
193	C₂×C₅×C₈	—	2	2	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	—	4	1	no	—
198	C₂×C₅×C₈	—	4	1	no	—
199	C₂×C₅×C₈	—	4	1	no	—
200	C₂×C₅×C₈	—	4	1	no	—
201	C₂×C₅×C₈	—	4	1	no	—
202	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
203	C₂×C₅×C₈	C₂²⋊C₄	1	2	yes	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₂²⋊C₄	—	4	1	no	—
209	C₅×C₂²⋊C₄	—	4	1	no	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	2	no	—
212	C₄²×C₅	—	4	1	no	—
213	C₄²×C₅	—	4	1	no	—
214	C₄²×C₅	—	4	1	no	—
215	C₄²×C₅	—	4	1	no	—
216	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
217	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
218	C₂²×M₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
220	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
221	C₂×#117	C₂²×C₅	1	1	yes	characteristic
222	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
223	C₂×#108	—	2	2	no	—
224	C₂×#108	—	2	2	no	—
225	C₂×#108	—	2	2	no	—
226	C₂×#104	—	2	2	no	—
227	C₂×#104	—	2	2	no	—
228	C₂×#104	—	2	2	no	—
229	#416	—	2	2	no	—
230	#416	—	2	2	no	—
231	C₂×#103	C₄×C₅	1	1	yes	characteristic, complemented
232	C₂×#103	C₄×C₅	1	1	yes	characteristic, complemented
233	C₂×#102	C₄×C₅	1	1	yes	characteristic, complemented
234	C₂×#102	C₄×C₅	1	1	yes	characteristic, complemented
235	#408	—	2	2	no	—
236	#408	—	2	2	no	—
237	C₂×C₂²⋊C₈	—	2	2	no	—
238	#339	—	2	2	no	—
239	#336	—	2	2	no	—
240	#336	—	2	2	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	—	2	2	no	—
244	C₂³×C₅	—	4	1	no	—
245	C₂³×C₅	—	4	1	no	—
246	C₂³×C₅	—	4	2	no	—
247	C₂³×C₅	—	4	2	no	—
248	C₂³×C₅	C₄×D₄	1	1	yes	characteristic
249	C₂³×C₅	#121	1	1	yes	characteristic
250	C₂³×C₅	C₂²⋊Q₈	1	1	yes	characteristic
251	C₂³×C₅	#123	1	1	yes	characteristic
252	C₂³×C₅	#124	1	1	yes	characteristic
253	C₂³×C₅	#124	1	1	yes	characteristic
254	C₂³×C₅	#126	1	1	yes	characteristic
255	C₅×Q₈	—	2	2	no	—
256	C₅×Q₈	—	2	2	no	—
257	C₅×Q₈	—	4	1	no	—
258	C₅×Q₈	—	4	1	no	—
259	C₅×D₄	—	2	2	no	—
260	C₅×D₄	—	2	2	no	—
261	C₅×D₄	—	4	2	no	—
262	C₅×D₄	—	4	2	no	—
263	C₅×D₄	—	4	2	no	—
264	C₅×D₄	—	4	2	no	—
265	C₅×D₄	—	4	1	no	—
266	C₅×D₄	—	4	1	no	—
267	C₂×C₄×C₅	—	2	4	no	—
268	C₂×C₄×C₅	—	2	2	no	—
269	C₂×C₄×C₅	—	4	4	no	—
270	C₂×C₄×C₅	—	4	4	no	—
271	C₂×C₄×C₅	—	4	2	no	—
272	C₂×C₄×C₅	—	4	1	no	—
273	C₂×C₄×C₅	—	4	1	no	—
274	C₂×C₄×C₅	—	4	2	no	—
275	C₂×C₄×C₅	—	4	2	no	—
276	C₂×C₄×C₅	—	4	2	no	—
277	C₂×C₄×C₅	—	4	2	no	—
278	C₂×C₄×C₅	—	4	2	no	—
279	C₂×C₄×C₅	—	4	1	no	—
280	C₂×C₄×C₅	—	4	1	no	—
281	C₂×C₄×C₅	—	4	2	no	—
282	C₂×C₄×C₅	—	4	2	no	—
283	C₂×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
285	C₂×C₄×C₅	#117	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	#120	1	1	yes	characteristic
290	C₂×C₄×C₅	#120	1	1	yes	characteristic
291	C₂×C₄×C₅	#120	1	1	yes	characteristic
292	C₂×C₄×C₅	#121	1	1	yes	characteristic
293	C₂×C₄×C₅	#121	1	1	yes	characteristic
294	C₂×C₄×C₅	#121	1	1	yes	characteristic
295	C₂×C₄×C₅	#121	1	1	yes	characteristic
296	C₂×C₄×C₅	#121	1	1	yes	characteristic
297	C₂×C₄×C₅	#121	1	1	yes	characteristic
298	C₂×C₄×C₅	#121	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	C₂²⋊Q₈	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂²⋊Q₈	1	1	yes	characteristic
304	C₂×C₄×C₅	#123	1	1	yes	characteristic
305	C₂×C₄×C₅	#123	1	1	yes	characteristic
306	C₂×C₄×C₅	#123	1	1	yes	characteristic
307	C₂×C₄×C₅	#123	1	1	yes	characteristic
308	C₂×C₄×C₅	#124	1	1	yes	characteristic
309	C₂×C₄×C₅	#126	1	1	yes	characteristic
310	C₂×C₄×C₅	#127	1	1	yes	characteristic
311	C₅×C₈	—	2	2	no	—
312	C₅×C₈	—	2	2	no	—
313	C₅×C₈	—	4	2	no	—
314	C₅×C₈	—	4	2	no	—
315	C₅×C₈	—	4	2	no	—
316	C₂×#41	—	2	1	no	—
317	C₂×#41	—	2	1	no	—
318	C₂×#41	—	2	1	no	—
319	C₂×#41	—	2	1	no	—
320	C₂×#41	—	2	1	no	—
321	C₂×#41	—	2	1	no	—
322	C₂×#41	—	2	1	no	—
323	C₂×#41	—	2	1	no	—
324	C₂×#41	—	2	1	no	—
325	C₂×#41	—	2	1	no	—
326	C₂×#41	C₅×D₄	1	2	yes	—
327	C₂×#41	C₅×Q₈	1	2	yes	—
328	C₂²×Q₈	C₂×C₄×C₅	1	1	yes	characteristic
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂×C₄×C₅	1	1	yes	characteristic
331	C₂³×C₄	—	2	1	no	—
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
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	—	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	C₅×D₄	1	2	yes	—
345	C₂×M₁₆	C₅×D₄	1	2	yes	—
346	C₂²×C₈	—	2	1	no	—
347	C₂²×C₈	—	2	1	no	—
348	C₂²×C₈	—	2	1	no	—
349	C₂²×C₈	—	2	1	no	—
350	C₂²×C₈	—	2	1	no	—
351	C₂²×C₈	—	2	1	no	—
352	C₂²×C₈	—	2	1	no	—
353	C₂²×C₈	—	2	1	no	—
354	C₂²×C₈	—	2	1	no	—
355	C₂²×C₈	—	2	1	no	—
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	—	2	1	no	—
358	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
359	C₂²×C₈	C₂×C₄×C₅	1	1	yes	characteristic
360	C₂²×C₈	C₅×D₄	1	2	yes	—
361	C₂²×C₈	C₅×D₄	1	2	yes	—
362	C₂²×C₈	C₅×D₄	1	2	yes	—
363	#117	—	2	1	no	—
364	#117	—	2	1	no	—
365	#117	—	2	1	no	—
366	#117	—	2	1	no	—
367	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
368	C₂×C₄⋊C₄	C₂×C₄×C₅	1	1	yes	characteristic
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₄²	—	2	1	no	—
371	C₂×C₄²	—	2	1	no	—
372	C₂×C₄²	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	—	2	1	no	—
376	C₂×C₄²	C₅×D₄	1	2	yes	—
377	#108	—	2	8	no	—
378	#104	—	2	8	no	—
379	#103	—	2	2	no	—
380	#103	—	2	2	no	—
381	#102	—	2	2	no	—
382	#102	—	2	2	no	—
383	C₂²⋊C₈	—	2	8	no	—
384	C₂²×C₅	—	2	2	no	—
385	C₂²×C₅	—	2	2	no	—
386	C₂²×C₅	—	2	2	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	—	2	1	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	—	4	4	no	—
393	C₂²×C₅	—	4	2	no	—
394	C₂²×C₅	—	8	2	no	—
395	C₂²×C₅	—	8	1	no	—
396	C₂²×C₅	—	8	1	no	—
397	C₂²×C₅	#385	1	1	yes	characteristic
398	C₂²×C₅	#388	1	1	yes	characteristic
399	C₂²×C₅	#390	1	1	yes	characteristic
400	C₂²×C₅	#393	1	1	yes	characteristic
401	C₂²×C₅	#394	1	1	yes	characteristic
402	C₂²×C₅	#396	1	1	yes	characteristic
403	C₂²×C₅	#397	1	1	yes	characteristic
404	C₂²×C₅	#443	1	2	yes	—
405	C₂²×C₅	#444	1	2	yes	—
406	C₄×C₅	—	4	4	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	—	8	1	no	—
409	C₄×C₅	—	8	1	no	—
410	C₄×C₅	#380	1	1	yes	characteristic
411	C₄×C₅	#385	1	1	yes	characteristic
412	C₄×C₅	#386	1	1	yes	characteristic
413	C₄×C₅	#388	1	1	yes	characteristic
414	C₄×C₅	#392	1	1	yes	characteristic
415	C₄×C₅	#394	1	1	yes	characteristic
416	C₄×C₅	#396	1	1	yes	characteristic
417	C₄×C₅	#399	1	1	yes	characteristic
418	C₂⁴	—	2	1	no	—
419	C₂⁴	C₅×#41	1	1	yes	characteristic
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	—	2	2	no	—
428	#41	—	4	1	no	—
429	#41	—	4	1	no	—
430	#41	—	4	1	no	—
431	#41	—	4	1	no	—
432	#41	—	4	1	no	—
433	#41	—	4	1	no	—
434	#41	—	4	1	no	—
435	#41	—	4	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	2	1	no	—
439	C₂×Q₈	—	2	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	C₅×C₄⋊C₄	1	2	yes	—
442	C₂×D₄	—	2	2	no	—
443	C₂×D₄	—	2	2	no	—
444	C₂×D₄	—	2	1	no	—
445	C₂×D₄	—	2	1	no	—
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	4	1	no	—
450	C₂×D₄	—	4	1	no	—
451	C₂×D₄	—	4	1	no	—
452	C₂×D₄	—	4	1	no	—
453	C₂×D₄	C₅×C₄⋊C₄	1	2	yes	—
454	C₂²×C₄	—	2	4	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	4	2	no	—
462	C₂²×C₄	—	4	1	no	—
463	C₂²×C₄	—	4	1	no	—
464	C₂²×C₄	—	4	1	no	—
465	C₂²×C₄	—	4	1	no	—
466	C₂²×C₄	—	4	1	no	—
467	C₂²×C₄	—	4	1	no	—
468	C₂²×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
469	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
470	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
471	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
472	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
473	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
474	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
475	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₅×Q₈	1	1	yes	characteristic
477	C₂²×C₄	C₅×#41	1	1	yes	characteristic
478	C₂²×C₄	C₅×#41	1	1	yes	characteristic
479	C₂²×C₄	C₅×#41	1	1	yes	characteristic
480	C₂²×C₄	C₅×#41	1	1	yes	characteristic
481	C₂²×C₄	C₅×#41	1	1	yes	characteristic
482	M₁₆	—	2	2	no	—
483	M₁₆	—	2	2	no	—
484	M₁₆	—	2	2	no	—
485	M₁₆	—	2	2	no	—
486	M₁₆	—	4	1	no	—
487	M₁₆	—	4	1	no	—
488	M₁₆	—	4	1	no	—
489	M₁₆	—	4	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	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	—	2	2	no	—
500	C₂×C₈	—	2	2	no	—
501	C₂×C₈	—	2	2	no	—
502	C₂×C₈	—	2	2	no	—
503	C₂×C₈	—	4	1	no	—
504	C₂×C₈	—	4	1	no	—
505	C₂×C₈	—	4	1	no	—
506	C₂×C₈	—	4	1	no	—
507	C₂×C₈	—	4	1	no	—
508	C₂×C₈	—	4	1	no	—
509	C₂×C₈	—	4	1	no	—
510	C₂×C₈	—	4	1	no	—
511	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
512	C₂×C₈	C₅×C₂²⋊C₄	1	2	yes	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	4	1	no	—
518	C₂²⋊C₄	—	4	1	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	4	1	no	—
522	C₄²	—	4	1	no	—
523	C₄²	—	4	1	no	—
524	C₄²	—	4	1	no	—
525	C₂×C₅	—	2	1	no	—
526	C₂×C₅	—	2	1	no	—
527	C₂×C₅	—	2	1	no	—
528	C₂×C₅	—	2	1	no	—
529	C₂×C₅	—	8	2	no	—
530	C₂×C₅	#1439	1	1	yes	characteristic
531	C₂×C₅	#1866	1	2	yes	—
532	C₂×C₅	#1929	1	2	yes	—
533	C₂×C₅	#1974	1	1	yes	characteristic
534	C₂×C₅	#1975	1	1	yes	characteristic
535	C₂³	—	2	2	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	2	no	—
538	C₂³	—	4	1	no	—
539	C₂³	—	4	1	no	—
540	C₂³	—	4	2	no	—
541	C₂³	—	4	2	no	—
542	C₂³	C₄×C₅×D₄	1	1	yes	characteristic
543	C₂³	C₅×#121	1	1	yes	characteristic
544	C₂³	C₅×C₂²⋊Q₈	1	1	yes	characteristic
545	C₂³	C₅×#123	1	1	yes	characteristic
546	C₂³	C₅×#124	1	1	yes	characteristic
547	C₂³	C₅×#124	1	1	yes	characteristic
548	C₂³	C₅×#126	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	2	2	no	—
551	Q₈	—	4	1	no	—
552	Q₈	—	4	1	no	—
553	D₄	—	2	2	no	—
554	D₄	—	2	2	no	—
555	D₄	—	4	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	2	no	—
559	D₄	—	4	1	no	—
560	D₄	—	4	1	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	4	4	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	1	no	—
567	C₂×C₄	—	4	1	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
578	C₂×C₄	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
579	C₂×C₄	C₅×#117	1	1	yes	characteristic
580	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
581	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
582	C₂×C₄	C₄×C₅×D₄	1	1	yes	characteristic
583	C₂×C₄	C₅×#120	1	1	yes	characteristic
584	C₂×C₄	C₅×#120	1	1	yes	characteristic
585	C₂×C₄	C₅×#120	1	1	yes	characteristic
586	C₂×C₄	C₅×#121	1	1	yes	characteristic
587	C₂×C₄	C₅×#121	1	1	yes	characteristic
588	C₂×C₄	C₅×#121	1	1	yes	characteristic
589	C₂×C₄	C₅×#121	1	1	yes	characteristic
590	C₂×C₄	C₅×#121	1	1	yes	characteristic
591	C₂×C₄	C₅×#121	1	1	yes	characteristic
592	C₂×C₄	C₅×#121	1	1	yes	characteristic
593	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
594	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
595	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
596	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
597	C₂×C₄	C₅×C₂²⋊Q₈	1	1	yes	characteristic
598	C₂×C₄	C₅×#123	1	1	yes	characteristic
599	C₂×C₄	C₅×#123	1	1	yes	characteristic
600	C₂×C₄	C₅×#123	1	1	yes	characteristic
601	C₂×C₄	C₅×#123	1	1	yes	characteristic
602	C₂×C₄	C₅×#124	1	1	yes	characteristic
603	C₂×C₄	C₅×#126	1	1	yes	characteristic
604	C₂×C₄	C₅×#127	1	1	yes	characteristic
605	C₈	—	2	2	no	—
606	C₈	—	2	2	no	—
607	C₈	—	4	2	no	—
608	C₈	—	4	2	no	—
609	C₈	—	4	2	no	—
610	C₅	#11125	1	1	yes	characteristic, direct product factor, Sylow
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	1	no	—
616	C₂²	—	2	1	no	—
617	C₂²	—	2	1	no	—
618	C₂²	—	2	1	no	—
619	C₂²	—	4	4	no	—
620	C₂²	—	4	2	no	—
621	C₂²	—	8	2	no	—
622	C₂²	—	8	1	no	—
623	C₂²	—	8	1	no	—
624	C₂²	C₅×#385	1	1	yes	characteristic
625	C₂²	C₅×#388	1	1	yes	characteristic
626	C₂²	C₅×#390	1	1	yes	characteristic
627	C₂²	C₅×#393	1	1	yes	characteristic
628	C₂²	C₅×#394	1	1	yes	characteristic
629	C₂²	C₅×#396	1	1	yes	characteristic
630	C₂²	C₅×#397	1	1	yes	characteristic
631	C₂²	C₅×#443	1	2	yes	—
632	C₂²	C₅×#444	1	2	yes	—
633	C₄	—	4	4	no	—
634	C₄	—	4	2	no	—
635	C₄	—	8	1	no	—
636	C₄	—	8	1	no	—
637	C₄	C₅×#380	1	1	yes	characteristic
638	C₄	C₅×#385	1	1	yes	characteristic
639	C₄	C₅×#386	1	1	yes	characteristic
640	C₄	C₅×#388	1	1	yes	characteristic
641	C₄	C₅×#392	1	1	yes	characteristic
642	C₄	C₅×#394	1	1	yes	characteristic
643	C₄	C₅×#396	1	1	yes	characteristic
644	C₄	C₅×#399	1	1	yes	characteristic
645	C₂	—	2	1	no	—
646	C₂	—	2	1	no	—
647	C₂	—	2	1	no	—
648	C₂	—	2	1	no	—
649	C₂	—	8	2	no	—
650	C₂	C₅×#1439	1	1	yes	characteristic
651	C₂	C₅×#1866	1	2	yes	—
652	C₂	C₅×#1929	1	2	yes	—
653	C₂	C₅×#1974	1	1	yes	characteristic
654	C₂	C₅×#1975	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₅	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₅
Frattini, cosocle	C₂³×C₄	C₂³×C₅
socle	C₂³×C₅	C₄×D₄
prime radical	C₂²×C₅×#41	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₅×#108	C₂	semidirect
5. C₂×C₅×#339	C₂	semidirect
6. C₅×#1729	C₂	semidirect
7. C₂×C₅×#336	C₂	semidirect
23. C₂×C₅×#103	C₄	semidirect
24. C₂×C₅×#103	C₄	semidirect
25. C₂×C₅×#102	C₄	semidirect
26. C₂×C₅×#102	C₄	semidirect
33. #11125	C₅	direct (N × H)
102. C₂²×#108	C₂×C₅	semidirect
106. C₂×#339	C₂×C₅	semidirect
107. #1729	C₂×C₅	semidirect
108. C₂×#336	C₂×C₅	semidirect
231. C₂×#103	C₄×C₅	semidirect
232. C₂×#103	C₄×C₅	semidirect
233. C₂×#102	C₄×C₅	semidirect
234. C₂×#102	C₄×C₅	semidirect
610. C₅	#11125	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₅×#108	2
C₂²×C₅×#104	2
C₂×C₅×#416	2
C₂×C₅×#408	2
C₂×C₅×#339	2
C₅×#1729	2
C₂×C₅×#336	2
#11125	5

Subgroups — C5×#11125 #11933845

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#11125 #11933845