Subgroups — C₅×#19169 #11941889

Order 1280.

728 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3141	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3100	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×D₄×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1701	C₂	1	2	yes	maximal, complemented
6	C₅×#1699	C₂	1	2	yes	maximal, complemented
7	C₅×#1681	C₂	1	2	yes	maximal, complemented
8	C₅×#1679	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1549	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1547	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×SD₁₆	—	2	1	no	—
13	C₂²×C₅×M₁₆	—	2	1	no	—
14	C₅×#532	C₂²	1	1	yes	characteristic
15	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₅×#489	—	2	2	no	—
18	C₅×#487	C₂²	1	2	yes	complemented
19	C₅×#486	C₂²	1	2	yes	complemented
20	C₅×#480	—	2	1	no	—
21	C₅×#474	C₂²	1	1	yes	characteristic
22	C₅×#474	C₂²	1	1	yes	characteristic
23	C₅×#461	—	2	1	no	—
24	C₅×#461	—	2	1	no	—
25	C₅×#461	C₂²	1	2	yes	—
26	C₅×#461	C₂²	1	2	yes	—
27	C₅×#459	C₂²	1	1	yes	characteristic
28	C₅×#459	C₂²	1	1	yes	characteristic
29	C₅×#447	—	2	1	no	—
30	C₄×C₅×D₈	—	2	1	no	—
31	C₄×C₅×D₈	—	2	1	no	—
32	C₅×#436	C₂²	1	2	yes	—
33	C₅×#435	—	2	2	no	—
34	C₅×C₈×D₄	C₂²	1	2	yes	—
35	C₅×#431	C₂²	1	1	yes	characteristic
36	C₅×#423	C₂²	1	1	yes	characteristic
37	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₅×#417	—	2	1	no	—
39	C₅×#417	—	2	1	no	—
40	C₂×C₅×#103	—	2	1	no	—
41	C₅×#407	—	2	1	no	—
42	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
43	C₅×#335	C₂²	1	2	yes	complemented
44	C₅×#334	C₂²	1	2	yes	complemented
45	C₅×#332	C₂²	1	2	yes	complemented
46	C₅×#332	C₂²	1	2	yes	complemented
47	C₅×#332	C₂²	1	2	yes	complemented
48	C₅×#331	C₂²	1	2	yes	complemented
49	#19169	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂×C₅×#41	—	2	1	no	—
51	C₂²×C₅×Q₈	—	2	1	no	—
52	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
53	C₂³×C₄×C₅	—	2	1	no	—
54	C₂×C₅×SD₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	2	no	—
56	C₂×C₅×SD₁₆	—	4	4	no	—
57	C₂×C₅×D₈	—	2	1	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×M₁₆	—	2	1	no	—
60	C₂×C₅×M₁₆	—	2	2	no	—
61	C₂×C₅×M₁₆	—	4	4	no	—
62	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
63	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
64	C₂²×C₅×C₈	—	2	1	no	—
65	C₂²×C₅×C₈	—	2	2	no	—
66	C₅×C₄⋊Q₈	—	2	1	no	—
67	C₅×C₄⋊Q₈	—	2	1	no	—
68	C₅×C₄⋊Q₈	—	2	1	no	—
69	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
70	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
71	C₅×#127	C₂³	1	1	yes	characteristic
72	C₅×#124	—	2	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₄×C₅×D₄	—	2	1	no	—
76	C₄×C₅×D₄	—	2	1	no	—
77	C₄×C₅×D₄	—	2	1	no	—
78	C₄×C₅×D₄	—	2	1	no	—
79	C₄×C₅×D₄	D₄	1	1	yes	characteristic
80	C₄×C₅×D₄	D₄	1	1	yes	characteristic
81	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
82	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₄⋊C₄	—	2	1	no	—
84	C₂×C₅×C₄⋊C₄	—	2	1	no	—
85	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
87	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
88	C₅×#107	—	2	1	no	—
89	C₅×#107	—	2	1	no	—
90	C₅×C₄⋊C₈	—	2	1	no	—
91	C₅×C₄⋊C₈	—	2	1	no	—
92	C₅×C₄⋊C₈	C₂³	1	2	yes	—
93	C₅×C₄⋊C₈	C₂³	1	2	yes	—
94	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
95	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	2	no	—
98	C₅×#103	—	2	2	no	—
99	C₅×#103	—	2	2	no	—
100	C₅×#102	—	2	1	no	—
101	C₅×#102	—	2	1	no	—
102	C₅×#102	—	2	2	no	—
103	C₅×#102	—	2	2	no	—
104	C₅×#102	—	2	1	no	—
105	C₅×#102	—	2	1	no	—
106	C₅×C₂²⋊C₈	—	2	1	no	—
107	C₅×C₂²⋊C₈	—	2	2	no	—
108	C₅×C₂²⋊C₈	—	2	2	no	—
109	C₅×#97	D₄	1	2	yes	—
110	C₄×C₅×C₈	—	2	1	no	—
111	C₄×C₅×C₈	C₂³	1	2	yes	—
112	#3141	C₂×C₅	1	1	yes	characteristic, complemented
113	#3100	C₂×C₅	1	1	yes	characteristic
114	C₂×#461	C₂×C₅	1	1	yes	characteristic, complemented
115	D₄×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
116	#1701	C₂×C₅	1	2	yes	complemented
117	#1699	C₂×C₅	1	2	yes	complemented
118	#1681	C₂×C₅	1	2	yes	complemented
119	#1679	C₂×C₅	1	2	yes	complemented
120	#1565	C₂×C₅	1	1	yes	characteristic, complemented
121	#1549	C₂×C₅	1	1	yes	characteristic, complemented
122	#1547	C₂×C₅	1	1	yes	characteristic, complemented
123	C₂⁴×C₅	—	2	1	no	—
124	C₅×#41	—	4	2	no	—
125	C₅×#41	—	4	2	no	—
126	C₂×C₅×Q₈	—	2	1	no	—
127	C₂×C₅×Q₈	—	2	2	no	—
128	C₂×C₅×Q₈	—	4	2	no	—
129	C₂×C₅×Q₈	—	4	2	no	—
130	C₂×C₅×Q₈	—	4	1	no	—
131	C₂×C₅×D₄	—	2	2	no	—
132	C₂×C₅×D₄	—	2	1	no	—
133	C₂×C₅×D₄	—	2	1	no	—
134	C₂×C₅×D₄	—	2	1	no	—
135	C₂×C₅×D₄	—	2	1	no	—
136	C₂×C₅×D₄	—	4	1	no	—
137	C₂×C₅×D₄	—	4	1	no	—
138	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	2	1	no	—
142	C₂²×C₄×C₅	—	2	1	no	—
143	C₂²×C₄×C₅	—	2	1	no	—
144	C₂²×C₄×C₅	—	2	1	no	—
145	C₂²×C₄×C₅	—	4	2	no	—
146	C₂²×C₄×C₅	—	4	2	no	—
147	C₂²×C₄×C₅	—	4	1	no	—
148	C₂²×C₄×C₅	—	4	1	no	—
149	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	#41	1	1	yes	characteristic
152	C₅×SD₁₆	—	4	4	no	—
153	C₅×SD₁₆	—	4	4	no	—
154	C₅×D₈	—	4	2	no	—
155	C₅×D₈	—	4	2	no	—
156	C₅×M₁₆	—	2	2	no	—
157	C₅×M₁₆	—	2	2	no	—
158	C₅×M₁₆	—	4	4	no	—
159	C₅×M₁₆	—	4	2	no	—
160	C₂×C₅×C₈	—	2	2	no	—
161	C₂×C₅×C₈	—	2	2	no	—
162	C₂×C₅×C₈	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	—	4	4	no	—
165	C₂×C₅×C₈	—	4	2	no	—
166	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
167	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
168	C₅×C₄⋊C₄	—	2	1	no	—
169	C₅×C₄⋊C₄	—	2	2	no	—
170	C₅×C₄⋊C₄	—	2	1	no	—
171	C₅×C₄⋊C₄	—	2	2	no	—
172	C₅×C₄⋊C₄	—	2	1	no	—
173	C₅×C₄⋊C₄	—	4	1	no	—
174	C₅×C₄⋊C₄	—	4	1	no	—
175	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
176	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
177	C₅×C₂²⋊C₄	—	2	1	no	—
178	C₅×C₂²⋊C₄	—	2	1	no	—
179	C₅×C₂²⋊C₄	—	2	1	no	—
180	C₅×C₂²⋊C₄	—	2	1	no	—
181	C₅×C₂²⋊C₄	—	4	1	no	—
182	C₅×C₂²⋊C₄	—	4	1	no	—
183	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₅	#41	1	1	yes	characteristic
186	C₄²×C₅	C₂⁴	1	1	yes	characteristic
187	C₂²×SD₁₆	—	2	1	no	—
188	C₂²×M₁₆	—	2	1	no	—
189	#532	C₂²×C₅	1	1	yes	characteristic
190	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
192	#489	—	2	2	no	—
193	#487	C₂²×C₅	1	2	yes	complemented
194	#486	C₂²×C₅	1	2	yes	complemented
195	#480	—	2	1	no	—
196	#474	C₂²×C₅	1	1	yes	characteristic
197	#474	C₂²×C₅	1	1	yes	characteristic
198	#461	—	2	1	no	—
199	#461	—	2	1	no	—
200	#461	C₂²×C₅	1	2	yes	—
201	#461	C₂²×C₅	1	2	yes	—
202	#459	C₂²×C₅	1	1	yes	characteristic
203	#459	C₂²×C₅	1	1	yes	characteristic
204	#447	—	2	1	no	—
205	C₄×D₈	—	2	1	no	—
206	C₄×D₈	—	2	1	no	—
207	#436	C₂²×C₅	1	2	yes	—
208	#435	—	2	2	no	—
209	C₈×D₄	C₂²×C₅	1	2	yes	—
210	#431	C₂²×C₅	1	1	yes	characteristic
211	#423	C₂²×C₅	1	1	yes	characteristic
212	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
213	#417	—	2	1	no	—
214	#417	—	2	1	no	—
215	C₂×#103	—	2	1	no	—
216	#407	—	2	1	no	—
217	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
218	#335	C₂²×C₅	1	2	yes	complemented
219	#334	C₂²×C₅	1	2	yes	complemented
220	#332	C₂²×C₅	1	2	yes	complemented
221	#332	C₂²×C₅	1	2	yes	complemented
222	#332	C₂²×C₅	1	2	yes	complemented
223	#331	C₂²×C₅	1	2	yes	complemented
224	C₂³×C₅	—	2	1	no	—
225	C₂³×C₅	—	2	1	no	—
226	C₂³×C₅	—	4	2	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	—	4	1	no	—
229	C₂³×C₅	—	8	1	no	—
230	C₂³×C₅	#121	1	1	yes	characteristic
231	C₅×Q₈	—	4	1	no	—
232	C₅×Q₈	—	4	2	no	—
233	C₅×Q₈	—	4	1	no	—
234	C₅×Q₈	—	4	2	no	—
235	C₅×Q₈	—	8	2	no	—
236	C₅×D₄	—	2	1	no	—
237	C₅×D₄	—	2	1	no	—
238	C₅×D₄	—	2	1	no	—
239	C₅×D₄	—	4	2	no	—
240	C₅×D₄	—	4	1	no	—
241	C₅×D₄	—	4	1	no	—
242	C₅×D₄	—	4	1	no	—
243	C₅×D₄	—	4	1	no	—
244	C₅×D₄	—	8	1	no	—
245	C₅×D₄	—	8	2	no	—
246	C₅×D₄	AGL(1,ℤ/8)	1	2	yes	—
247	C₂×C₄×C₅	—	2	1	no	—
248	C₂×C₄×C₅	—	2	1	no	—
249	C₂×C₄×C₅	—	2	1	no	—
250	C₂×C₄×C₅	—	2	1	no	—
251	C₂×C₄×C₅	—	4	1	no	—
252	C₂×C₄×C₅	—	4	2	no	—
253	C₂×C₄×C₅	—	4	1	no	—
254	C₂×C₄×C₅	—	4	1	no	—
255	C₂×C₄×C₅	—	4	1	no	—
256	C₂×C₄×C₅	—	4	1	no	—
257	C₂×C₄×C₅	—	4	2	no	—
258	C₂×C₄×C₅	—	4	2	no	—
259	C₂×C₄×C₅	—	4	1	no	—
260	C₂×C₄×C₅	—	4	2	no	—
261	C₂×C₄×C₅	—	8	2	no	—
262	C₂×C₄×C₅	—	8	2	no	—
263	C₂×C₄×C₅	#121	1	1	yes	characteristic
264	C₂×C₄×C₅	#121	1	1	yes	characteristic
265	C₂×C₄×C₅	#121	1	1	yes	characteristic
266	C₂×C₄×C₅	#135	1	2	yes	—
267	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
268	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
271	C₅×C₈	—	2	2	no	—
272	C₅×C₈	—	2	2	no	—
273	C₅×C₈	—	4	2	no	—
274	C₅×C₈	—	4	2	no	—
275	C₅×C₈	—	4	1	no	—
276	C₅×C₈	—	4	1	no	—
277	C₂×#41	—	2	1	no	—
278	C₂²×Q₈	—	2	1	no	—
279	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
280	C₂³×C₄	—	2	1	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	2	2	no	—
283	C₂×SD₁₆	—	4	4	no	—
284	C₂×D₈	—	2	1	no	—
285	C₂×D₈	—	2	1	no	—
286	C₂×M₁₆	—	2	1	no	—
287	C₂×M₁₆	—	2	2	no	—
288	C₂×M₁₆	—	4	4	no	—
289	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
290	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
291	C₂²×C₈	—	2	1	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₄⋊Q₈	—	2	1	no	—
294	C₄⋊Q₈	—	2	1	no	—
295	C₄⋊Q₈	—	2	1	no	—
296	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
297	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
298	#127	C₂³×C₅	1	1	yes	characteristic
299	#124	—	2	1	no	—
300	#121	—	2	1	no	—
301	#121	—	2	1	no	—
302	C₄×D₄	—	2	1	no	—
303	C₄×D₄	—	2	1	no	—
304	C₄×D₄	—	2	1	no	—
305	C₄×D₄	—	2	1	no	—
306	C₄×D₄	C₅×D₄	1	1	yes	characteristic
307	C₄×D₄	C₅×D₄	1	1	yes	characteristic
308	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
309	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	—	2	1	no	—
314	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
315	#107	—	2	1	no	—
316	#107	—	2	1	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	2	1	no	—
319	C₄⋊C₈	C₂³×C₅	1	2	yes	—
320	C₄⋊C₈	C₂³×C₅	1	2	yes	—
321	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
322	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
323	#103	—	2	2	no	—
324	#103	—	2	2	no	—
325	#103	—	2	2	no	—
326	#103	—	2	2	no	—
327	#102	—	2	1	no	—
328	#102	—	2	1	no	—
329	#102	—	2	2	no	—
330	#102	—	2	2	no	—
331	#102	—	2	1	no	—
332	#102	—	2	1	no	—
333	C₂²⋊C₈	—	2	1	no	—
334	C₂²⋊C₈	—	2	2	no	—
335	C₂²⋊C₈	—	2	2	no	—
336	#97	C₅×D₄	1	2	yes	—
337	C₄×C₈	—	2	1	no	—
338	C₄×C₈	C₂³×C₅	1	2	yes	—
339	C₂²×C₅	—	2	1	no	—
340	C₂²×C₅	—	2	1	no	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	—	4	1	no	—
343	C₂²×C₅	—	4	1	no	—
344	C₂²×C₅	—	4	1	no	—
345	C₂²×C₅	—	4	1	no	—
346	C₂²×C₅	—	4	1	no	—
347	C₂²×C₅	—	8	4	no	—
348	C₂²×C₅	—	8	1	no	—
349	C₂²×C₅	—	8	1	no	—
350	C₂²×C₅	—	8	1	no	—
351	C₂²×C₅	#463	1	2	yes	—
352	C₂²×C₅	C₂×#121	1	1	yes	characteristic
353	C₄×C₅	—	2	1	no	—
354	C₄×C₅	—	2	1	no	—
355	C₄×C₅	—	2	1	no	—
356	C₄×C₅	—	4	1	no	—
357	C₄×C₅	—	4	1	no	—
358	C₄×C₅	—	8	1	no	—
359	C₄×C₅	—	8	2	no	—
360	C₄×C₅	#463	1	2	yes	—
361	C₄×C₅	C₂×#135	1	1	yes	characteristic
362	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
363	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
364	C₄×C₅	#575	1	1	yes	characteristic
365	C₂⁴	—	2	1	no	—
366	#41	—	4	2	no	—
367	#41	—	4	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	4	2	no	—
371	C₂×Q₈	—	4	2	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	1	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	1	no	—
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	—	4	1	no	—
379	C₂×D₄	—	4	1	no	—
380	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
381	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	4	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂²×C₄	C₅×#41	1	1	yes	characteristic
394	SD₁₆	—	4	4	no	—
395	SD₁₆	—	4	4	no	—
396	D₈	—	4	2	no	—
397	D₈	—	4	2	no	—
398	M₁₆	—	2	2	no	—
399	M₁₆	—	2	2	no	—
400	M₁₆	—	4	4	no	—
401	M₁₆	—	4	2	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	4	4	no	—
407	C₂×C₈	—	4	2	no	—
408	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
409	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	—	4	1	no	—
417	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
418	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	2	1	no	—
422	C₂²⋊C₄	—	2	1	no	—
423	C₂²⋊C₄	—	4	1	no	—
424	C₂²⋊C₄	—	4	1	no	—
425	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
426	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
427	C₄²	C₅×#41	1	1	yes	characteristic
428	C₄²	C₂⁴×C₅	1	1	yes	characteristic
429	C₂×C₅	—	2	2	no	—
430	C₂×C₅	—	4	2	no	—
431	C₂×C₅	—	8	1	no	—
432	C₂×C₅	—	16	1	no	—
433	C₂×C₅	C₂×#463	1	1	yes	characteristic
434	C₂×C₅	#3055	1	1	yes	characteristic
435	C₂×C₅	#3069	1	1	yes	characteristic
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	8	1	no	—
442	C₂³	C₅×#121	1	1	yes	characteristic
443	Q₈	—	4	1	no	—
444	Q₈	—	4	2	no	—
445	Q₈	—	4	1	no	—
446	Q₈	—	4	2	no	—
447	Q₈	—	8	2	no	—
448	D₄	—	2	1	no	—
449	D₄	—	2	1	no	—
450	D₄	—	2	1	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	1	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	1	no	—
455	D₄	—	4	1	no	—
456	D₄	—	8	1	no	—
457	D₄	—	8	2	no	—
458	D₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	1	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	2	no	—
474	C₂×C₄	—	8	2	no	—
475	C₂×C₄	C₅×#121	1	1	yes	characteristic
476	C₂×C₄	C₅×#121	1	1	yes	characteristic
477	C₂×C₄	C₅×#121	1	1	yes	characteristic
478	C₂×C₄	C₅×#135	1	2	yes	—
479	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
480	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	4	2	no	—
486	C₈	—	4	2	no	—
487	C₈	—	4	1	no	—
488	C₈	—	4	1	no	—
489	C₅	#19169	1	1	yes	characteristic, direct product factor, Sylow
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	1	no	—
494	C₂²	—	4	1	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	8	4	no	—
499	C₂²	—	8	1	no	—
500	C₂²	—	8	1	no	—
501	C₂²	—	8	1	no	—
502	C₂²	C₅×#463	1	2	yes	—
503	C₂²	C₂×C₅×#121	1	1	yes	characteristic
504	C₄	—	2	1	no	—
505	C₄	—	2	1	no	—
506	C₄	—	2	1	no	—
507	C₄	—	4	1	no	—
508	C₄	—	4	1	no	—
509	C₄	—	8	1	no	—
510	C₄	—	8	2	no	—
511	C₄	C₅×#463	1	2	yes	—
512	C₄	C₂×C₅×#135	1	1	yes	characteristic
513	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
514	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
515	C₄	C₅×#575	1	1	yes	characteristic
516	C₂	—	2	2	no	—
517	C₂	—	4	2	no	—
518	C₂	—	8	1	no	—
519	C₂	—	16	1	no	—
520	C₂	C₂×C₅×#463	1	1	yes	characteristic
521	C₂	C₅×#3055	1	1	yes	characteristic
522	C₂	C₅×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₅×#3100	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3141	C₂	semidirect
3. C₂×C₅×#461	C₂	semidirect
4. C₅×D₄×M₁₆	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1699	C₂	semidirect
7. C₅×#1681	C₂	semidirect
8. C₅×#1679	C₂	semidirect
9. C₅×#1565	C₂	semidirect
10. C₅×#1549	C₂	semidirect
11. C₅×#1547	C₂	semidirect
18. C₅×#487	C₂²	semidirect
19. C₅×#486	C₂²	semidirect
43. C₅×#335	C₂²	semidirect
44. C₅×#334	C₂²	semidirect
45. C₅×#332	C₂²	semidirect
46. C₅×#332	C₂²	semidirect
47. C₅×#332	C₂²	semidirect
48. C₅×#331	C₂²	semidirect
49. #19169	C₅	direct (N × H)
112. #3141	C₂×C₅	semidirect
114. C₂×#461	C₂×C₅	semidirect
115. D₄×M₁₆	C₂×C₅	semidirect
116. #1701	C₂×C₅	semidirect
117. #1699	C₂×C₅	semidirect
118. #1681	C₂×C₅	semidirect
119. #1679	C₂×C₅	semidirect
120. #1565	C₂×C₅	semidirect
121. #1549	C₂×C₅	semidirect
122. #1547	C₂×C₅	semidirect
193. #487	C₂²×C₅	semidirect
194. #486	C₂²×C₅	semidirect
218. #335	C₂²×C₅	semidirect
219. #334	C₂²×C₅	semidirect
220. #332	C₂²×C₅	semidirect
221. #332	C₂²×C₅	semidirect
222. #332	C₂²×C₅	semidirect
223. #331	C₂²×C₅	semidirect
489. C₅	#19169	direct (N × H)

Maximal subgroups

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

subgroup	index
C₅×#3141	2
C₅×#3100	2
C₂×C₅×#461	2
C₅×D₄×M₁₆	2
C₅×#1701	2
C₅×#1699	2
C₅×#1681	2
C₅×#1679	2
C₅×#1565	2
C₅×#1549	2
C₅×#1547	2
#19169	5

Subgroups — C5×#19169 #11941889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19169 #11941889