Subgroups — C₅×#19459 #11942179

Order 1280.

638 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3209	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3110	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#474	C₂	1	1	yes	maximal, characteristic
4	C₅×#2974	C₂	1	1	yes	maximal, characteristic
5	C₅×#1699	C₂	1	2	yes	maximal, complemented
6	C₅×#1689	C₂	1	2	yes	maximal, complemented
7	C₅×#1679	C₂	1	2	yes	maximal, complemented
8	C₅×#1669	C₂	1	2	yes	maximal, complemented
9	C₅×#1573	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1556	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1552	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₅×#494	C₂²	1	2	yes	complemented
16	C₅×#487	C₂²	1	2	yes	complemented
17	C₅×#484	—	2	1	no	—
18	C₅×#474	—	2	1	no	—
19	C₅×#474	—	2	1	no	—
20	C₅×#474	C₂²	1	2	yes	—
21	C₅×#474	C₂²	1	2	yes	—
22	C₅×#474	C₂²	1	1	yes	characteristic
23	C₅×#474	C₂²	1	1	yes	characteristic
24	C₅×#462	—	2	2	no	—
25	C₅×#461	C₂²	1	1	yes	characteristic
26	C₅×#461	C₂²	1	1	yes	characteristic
27	C₅×#451	—	2	1	no	—
28	C₅×#451	—	2	1	no	—
29	C₅×#450	—	2	1	no	—
30	C₅×#440	—	2	1	no	—
31	C₅×#440	—	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×#432	C₂²	1	1	yes	characteristic
36	C₅×#432	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	1	yes	characteristic
38	C₂×C₅×#107	—	2	1	no	—
39	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₅×#102	—	2	1	no	—
41	C₅×#407	—	2	1	no	—
42	C₂×C₅×C₂²⋊C₈	—	2	1	no	—
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×#332	C₂²	1	2	yes	complemented
49	#19459	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
50	C₂²×C₅×Q₈	—	2	1	no	—
51	C₂²×C₅×D₄	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₅	—	2	1	no	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×Q₁₆	—	2	2	no	—
55	C₂×C₅×SD₁₆	—	2	1	no	—
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×M₁₆	—	2	2	no	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₅×C₄⋊Q₈	—	2	1	no	—
61	C₅×C₄⋊Q₈	—	2	1	no	—
62	C₅×C₄⋊Q₈	—	2	1	no	—
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₅×#125	—	2	1	no	—
67	C₅×C₂²⋊Q₈	—	2	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₄×C₅×Q₈	—	2	1	no	—
70	C₄×C₅×Q₈	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	1	no	—
73	C₄×C₅×D₄	D₄	1	1	yes	characteristic
74	C₄×C₅×D₄	D₄	1	1	yes	characteristic
75	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
77	C₅×#117	—	2	1	no	—
78	C₂×C₅×C₄⋊C₄	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
81	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
83	C₅×#107	—	2	2	no	—
84	C₅×#107	—	2	2	no	—
85	C₅×#107	—	2	1	no	—
86	C₅×#107	—	2	1	no	—
87	C₅×C₄⋊C₈	—	2	1	no	—
88	C₅×C₄⋊C₈	D₄	1	2	yes	—
89	C₅×C₄⋊C₈	C₂³	1	2	yes	—
90	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
91	C₅×C₄⋊C₈	C₂³	1	2	yes	—
92	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
93	C₅×#103	—	2	2	no	—
94	C₅×#103	—	2	2	no	—
95	C₅×#103	—	2	1	no	—
96	C₅×#103	—	2	1	no	—
97	C₅×#102	—	2	2	no	—
98	C₅×#102	—	2	2	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	1	no	—
101	C₅×C₂²⋊C₈	—	2	1	no	—
102	C₅×C₂²⋊C₈	—	2	1	no	—
103	C₅×C₂²⋊C₈	—	2	2	no	—
104	C₅×C₂²⋊C₈	—	2	2	no	—
105	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
106	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
107	C₅×#97	—	2	1	no	—
108	C₅×#97	—	2	1	no	—
109	C₄×C₅×C₈	C₂³	1	2	yes	—
110	#3209	C₂×C₅	1	1	yes	characteristic, complemented
111	#3110	C₂×C₅	1	1	yes	characteristic
112	C₂×#474	C₂×C₅	1	1	yes	characteristic
113	#2974	C₂×C₅	1	1	yes	characteristic
114	#1699	C₂×C₅	1	2	yes	complemented
115	#1689	C₂×C₅	1	2	yes	complemented
116	#1679	C₂×C₅	1	2	yes	complemented
117	#1669	C₂×C₅	1	2	yes	complemented
118	#1573	C₂×C₅	1	1	yes	characteristic, complemented
119	#1556	C₂×C₅	1	1	yes	characteristic, complemented
120	#1552	C₂×C₅	1	1	yes	characteristic, complemented
121	C₂⁴×C₅	—	2	1	no	—
122	C₂×C₅×Q₈	—	2	1	no	—
123	C₂×C₅×Q₈	—	2	1	no	—
124	C₂×C₅×Q₈	—	2	2	no	—
125	C₂×C₅×Q₈	—	4	1	no	—
126	C₂×C₅×Q₈	—	8	2	no	—
127	C₂×C₅×D₄	—	2	2	no	—
128	C₂×C₅×D₄	—	2	1	no	—
129	C₂×C₅×D₄	—	4	1	no	—
130	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
131	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₅	—	2	1	no	—
133	C₂²×C₄×C₅	—	2	1	no	—
134	C₂²×C₄×C₅	—	2	1	no	—
135	C₂²×C₄×C₅	—	2	1	no	—
136	C₂²×C₄×C₅	—	2	1	no	—
137	C₂²×C₄×C₅	—	4	1	no	—
138	C₂²×C₄×C₅	—	8	2	no	—
139	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	#41	1	1	yes	characteristic
142	C₅×Q₁₆	—	8	2	no	—
143	C₅×Q₁₆	—	8	2	no	—
144	C₅×SD₁₆	—	4	2	no	—
145	C₅×SD₁₆	—	4	2	no	—
146	C₅×M₁₆	—	8	2	no	—
147	C₂×C₅×C₈	—	2	2	no	—
148	C₂×C₅×C₈	—	2	2	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	—	2	1	no	—
151	C₂×C₅×C₈	—	4	2	no	—
152	C₂×C₅×C₈	—	8	2	no	—
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
155	C₅×C₄⋊C₄	—	2	1	no	—
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	2	no	—
160	C₅×C₄⋊C₄	—	2	1	no	—
161	C₅×C₄⋊C₄	—	2	1	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	—	4	1	no	—
164	C₅×C₄⋊C₄	—	4	1	no	—
165	C₅×C₄⋊C₄	—	4	1	no	—
166	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
167	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
168	C₅×C₂²⋊C₄	—	2	1	no	—
169	C₅×C₂²⋊C₄	—	2	1	no	—
170	C₅×C₂²⋊C₄	—	2	1	no	—
171	C₅×C₂²⋊C₄	—	2	1	no	—
172	C₅×C₂²⋊C₄	—	4	1	no	—
173	C₄²×C₅	—	4	1	no	—
174	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
175	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₅	#41	1	1	yes	characteristic
177	C₄²×C₅	C₂⁴	1	1	yes	characteristic
178	#533	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
181	#494	C₂²×C₅	1	2	yes	complemented
182	#487	C₂²×C₅	1	2	yes	complemented
183	#484	—	2	1	no	—
184	#474	—	2	1	no	—
185	#474	—	2	1	no	—
186	#474	C₂²×C₅	1	1	yes	characteristic
187	#474	C₂²×C₅	1	1	yes	characteristic
188	#474	C₂²×C₅	1	2	yes	—
189	#474	C₂²×C₅	1	2	yes	—
190	#462	—	2	2	no	—
191	#461	C₂²×C₅	1	1	yes	characteristic
192	#461	C₂²×C₅	1	1	yes	characteristic
193	#451	—	2	1	no	—
194	#451	—	2	1	no	—
195	#450	—	2	1	no	—
196	#440	—	2	1	no	—
197	#440	—	2	1	no	—
198	#436	C₂²×C₅	1	2	yes	—
199	#435	—	2	2	no	—
200	C₈×D₄	C₂²×C₅	1	2	yes	—
201	#432	C₂²×C₅	1	1	yes	characteristic
202	#432	C₂²×C₅	1	1	yes	characteristic
203	#431	C₂²×C₅	1	1	yes	characteristic
204	C₂×#107	—	2	1	no	—
205	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
206	C₂×#102	—	2	1	no	—
207	#407	—	2	1	no	—
208	C₂×C₂²⋊C₈	—	2	1	no	—
209	#335	C₂²×C₅	1	2	yes	complemented
210	#334	C₂²×C₅	1	2	yes	complemented
211	#332	C₂²×C₅	1	2	yes	complemented
212	#332	C₂²×C₅	1	2	yes	complemented
213	#332	C₂²×C₅	1	2	yes	complemented
214	#332	C₂²×C₅	1	2	yes	complemented
215	C₂³×C₅	—	2	1	no	—
216	C₂³×C₅	—	2	1	no	—
217	C₂³×C₅	—	4	2	no	—
218	C₂³×C₅	—	4	2	no	—
219	C₂³×C₅	—	8	1	no	—
220	C₂³×C₅	#121	1	1	yes	characteristic
221	C₅×Q₈	—	4	1	no	—
222	C₅×Q₈	—	4	1	no	—
223	C₅×Q₈	—	4	2	no	—
224	C₅×Q₈	—	4	2	no	—
225	C₅×Q₈	—	4	2	no	—
226	C₅×Q₈	—	8	2	no	—
227	C₅×D₄	—	2	1	no	—
228	C₅×D₄	—	2	1	no	—
229	C₅×D₄	—	2	1	no	—
230	C₅×D₄	—	4	2	no	—
231	C₅×D₄	#137	1	2	yes	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	1	no	—
241	C₂×C₄×C₅	—	4	1	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	8	1	no	—
244	C₂×C₄×C₅	—	8	1	no	—
245	C₂×C₄×C₅	—	8	1	no	—
246	C₂×C₄×C₅	—	8	2	no	—
247	C₂×C₄×C₅	#121	1	1	yes	characteristic
248	C₂×C₄×C₅	#121	1	1	yes	characteristic
249	C₂×C₄×C₅	#121	1	1	yes	characteristic
250	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
253	C₅×C₈	—	2	2	no	—
254	C₅×C₈	—	2	2	no	—
255	C₅×C₈	—	4	1	no	—
256	C₅×C₈	—	4	2	no	—
257	C₅×C₈	—	4	1	no	—
258	C₅×C₈	—	4	2	no	—
259	C₂²×Q₈	—	2	1	no	—
260	C₂²×D₄	C₅×D₄	1	1	yes	characteristic
261	C₂³×C₄	—	2	1	no	—
262	C₂×Q₁₆	—	2	2	no	—
263	C₂×Q₁₆	—	2	2	no	—
264	C₂×SD₁₆	—	2	1	no	—
265	C₂×SD₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	2	no	—
267	C₂²×C₈	—	2	1	no	—
268	C₂²×C₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	—	2	1	no	—
271	C₄⋊Q₈	—	2	1	no	—
272	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
273	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
275	#125	—	2	1	no	—
276	C₂²⋊Q₈	—	2	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₄×Q₈	—	2	1	no	—
279	C₄×Q₈	—	2	1	no	—
280	C₄×D₄	—	2	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	C₅×D₄	1	1	yes	characteristic
283	C₄×D₄	C₅×D₄	1	1	yes	characteristic
284	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
285	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
286	#117	—	2	1	no	—
287	C₂×C₄⋊C₄	—	2	1	no	—
288	C₂×C₄⋊C₄	—	2	1	no	—
289	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
292	#107	—	2	2	no	—
293	#107	—	2	2	no	—
294	#107	—	2	1	no	—
295	#107	—	2	1	no	—
296	C₄⋊C₈	—	2	1	no	—
297	C₄⋊C₈	C₅×D₄	1	2	yes	—
298	C₄⋊C₈	C₂³×C₅	1	2	yes	—
299	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
300	C₄⋊C₈	C₂³×C₅	1	2	yes	—
301	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
302	#103	—	2	2	no	—
303	#103	—	2	2	no	—
304	#103	—	2	1	no	—
305	#103	—	2	1	no	—
306	#102	—	2	2	no	—
307	#102	—	2	2	no	—
308	#102	—	2	1	no	—
309	#102	—	2	1	no	—
310	C₂²⋊C₈	—	2	1	no	—
311	C₂²⋊C₈	—	2	1	no	—
312	C₂²⋊C₈	—	2	2	no	—
313	C₂²⋊C₈	—	2	2	no	—
314	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
315	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
316	#97	—	2	1	no	—
317	#97	—	2	1	no	—
318	C₄×C₈	C₂³×C₅	1	2	yes	—
319	C₂²×C₅	—	2	1	no	—
320	C₂²×C₅	—	2	1	no	—
321	C₂²×C₅	—	2	2	no	—
322	C₂²×C₅	—	4	1	no	—
323	C₂²×C₅	—	4	1	no	—
324	C₂²×C₅	—	4	1	no	—
325	C₂²×C₅	—	4	1	no	—
326	C₂²×C₅	—	4	1	no	—
327	C₂²×C₅	—	8	4	no	—
328	C₂²×C₅	#473	1	2	yes	—
329	C₂²×C₅	C₂×#121	1	1	yes	characteristic
330	C₄×C₅	—	2	1	no	—
331	C₄×C₅	—	2	1	no	—
332	C₄×C₅	—	2	1	no	—
333	C₄×C₅	—	2	1	no	—
334	C₄×C₅	—	4	1	no	—
335	C₄×C₅	—	4	1	no	—
336	C₄×C₅	—	8	2	no	—
337	C₄×C₅	—	8	1	no	—
338	C₄×C₅	—	8	1	no	—
339	C₄×C₅	C₂×#137	1	1	yes	characteristic
340	C₄×C₅	#575	1	1	yes	characteristic
341	C₄×C₅	#576	1	2	yes	—
342	C₂⁴	—	2	1	no	—
343	C₂×Q₈	—	2	1	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	4	1	no	—
347	C₂×Q₈	—	8	2	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	8	2	no	—
360	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²×C₄	C₅×#41	1	1	yes	characteristic
363	Q₁₆	—	8	2	no	—
364	Q₁₆	—	8	2	no	—
365	SD₁₆	—	4	2	no	—
366	SD₁₆	—	4	2	no	—
367	M₁₆	—	8	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	8	2	no	—
374	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
375	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	1	no	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	4	1	no	—
384	C₄⋊C₄	—	4	1	no	—
385	C₄⋊C₄	—	4	1	no	—
386	C₄⋊C₄	—	4	1	no	—
387	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
388	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
389	C₂²⋊C₄	—	2	1	no	—
390	C₂²⋊C₄	—	2	1	no	—
391	C₂²⋊C₄	—	2	1	no	—
392	C₂²⋊C₄	—	2	1	no	—
393	C₂²⋊C₄	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
396	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
397	C₄²	C₅×#41	1	1	yes	characteristic
398	C₄²	C₂⁴×C₅	1	1	yes	characteristic
399	C₂×C₅	—	2	2	no	—
400	C₂×C₅	—	4	2	no	—
401	C₂×C₅	—	8	1	no	—
402	C₂×C₅	#3041	1	1	yes	characteristic
403	C₂×C₅	#3056	1	1	yes	characteristic
404	C₂×C₅	C₂×#473	1	1	yes	characteristic
405	C₂³	—	2	1	no	—
406	C₂³	—	2	1	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	8	1	no	—
410	C₂³	C₅×#121	1	1	yes	characteristic
411	Q₈	—	4	1	no	—
412	Q₈	—	4	1	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	8	2	no	—
417	D₄	—	2	1	no	—
418	D₄	—	2	1	no	—
419	D₄	—	2	1	no	—
420	D₄	—	4	2	no	—
421	D₄	C₅×#137	1	2	yes	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	8	1	no	—
434	C₂×C₄	—	8	1	no	—
435	C₂×C₄	—	8	1	no	—
436	C₂×C₄	—	8	2	no	—
437	C₂×C₄	C₅×#121	1	1	yes	characteristic
438	C₂×C₄	C₅×#121	1	1	yes	characteristic
439	C₂×C₄	C₅×#121	1	1	yes	characteristic
440	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
441	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
442	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
443	C₈	—	2	2	no	—
444	C₈	—	2	2	no	—
445	C₈	—	4	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	4	1	no	—
448	C₈	—	4	2	no	—
449	C₅	#19459	1	1	yes	characteristic, direct product factor, Sylow
450	C₂²	—	2	1	no	—
451	C₂²	—	2	1	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	4	1	no	—
454	C₂²	—	4	1	no	—
455	C₂²	—	4	1	no	—
456	C₂²	—	4	1	no	—
457	C₂²	—	4	1	no	—
458	C₂²	—	8	4	no	—
459	C₂²	C₅×#473	1	2	yes	—
460	C₂²	C₂×C₅×#121	1	1	yes	characteristic
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	2	1	no	—
464	C₄	—	2	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	8	2	no	—
468	C₄	—	8	1	no	—
469	C₄	—	8	1	no	—
470	C₄	C₂×C₅×#137	1	1	yes	characteristic
471	C₄	C₅×#575	1	1	yes	characteristic
472	C₄	C₅×#576	1	2	yes	—
473	C₂	—	2	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	8	1	no	—
476	C₂	C₅×#3041	1	1	yes	characteristic
477	C₂	C₅×#3056	1	1	yes	characteristic
478	C₂	C₂×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	D₄
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×#3209	C₂	semidirect
5. C₅×#1699	C₂	semidirect
6. C₅×#1689	C₂	semidirect
7. C₅×#1679	C₂	semidirect
8. C₅×#1669	C₂	semidirect
9. C₅×#1573	C₂	semidirect
10. C₅×#1556	C₂	semidirect
11. C₅×#1552	C₂	semidirect
15. C₅×#494	C₂²	semidirect
16. C₅×#487	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×#332	C₂²	semidirect
49. #19459	C₅	direct (N × H)
110. #3209	C₂×C₅	semidirect
114. #1699	C₂×C₅	semidirect
115. #1689	C₂×C₅	semidirect
116. #1679	C₂×C₅	semidirect
117. #1669	C₂×C₅	semidirect
118. #1573	C₂×C₅	semidirect
119. #1556	C₂×C₅	semidirect
120. #1552	C₂×C₅	semidirect
181. #494	C₂²×C₅	semidirect
182. #487	C₂²×C₅	semidirect
209. #335	C₂²×C₅	semidirect
210. #334	C₂²×C₅	semidirect
211. #332	C₂²×C₅	semidirect
212. #332	C₂²×C₅	semidirect
213. #332	C₂²×C₅	semidirect
214. #332	C₂²×C₅	semidirect
449. C₅	#19459	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×#3209	2
C₅×#3110	2
C₂×C₅×#474	2
C₅×#2974	2
C₅×#1699	2
C₅×#1689	2
C₅×#1679	2
C₅×#1669	2
C₅×#1573	2
C₅×#1556	2
C₅×#1552	2
#19459	5

Subgroups — C5×#19459 #11942179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19459 #11942179