Subgroups — C₅×#19129 #11941849

Order 1280.

620 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3170	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3107	C₂	1	2	yes	maximal
3	C₅×C₈×#41	C₂	1	1	yes	maximal, characteristic
4	C₅×#1680	C₂	1	2	yes	maximal, complemented
5	C₅×#1679	C₂	1	2	yes	maximal, complemented
6	C₅×#1674	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#1673	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#1670	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1669	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1544	C₂	1	2	yes	maximal, complemented
12	C₅×#533	C₂²	1	2	yes	—
13	C₄×C₅×#41	C₂²	1	1	yes	characteristic
14	C₅×#500	C₂²	1	1	yes	characteristic
15	C₅×#494	C₂²	1	1	yes	characteristic
16	C₅×#487	C₂²	1	2	yes	—
17	C₅×#485	—	2	2	no	—
18	C₅×#475	C₂²	1	2	yes	—
19	C₅×#474	C₂²	1	2	yes	—
20	C₅×#467	—	2	1	no	—
21	C₅×#467	—	2	1	no	—
22	C₅×#462	C₂²	1	2	yes	—
23	C₅×#461	C₂²	1	2	yes	—
24	C₅×#452	—	2	2	no	—
25	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
26	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
27	C₄×C₅×Q₁₆	—	2	1	no	—
28	C₄×C₅×Q₁₆	—	2	1	no	—
29	C₄×C₅×Q₁₆	—	2	2	no	—
30	C₄×C₅×SD₁₆	—	2	2	no	—
31	C₅×C₈×D₄	—	2	1	no	—
32	C₅×C₈×D₄	—	2	1	no	—
33	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
34	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₅×#431	—	2	1	no	—
36	C₅×#431	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	2	yes	—
38	C₂×C₄×C₅×C₈	—	2	1	no	—
39	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
40	C₅×#335	C₂²	1	1	yes	characteristic
41	C₅×#335	C₂²	1	1	yes	characteristic
42	C₅×#334	C₂²	1	2	yes	—
43	C₅×#332	C₂²	1	2	yes	—
44	C₅×#332	C₂²	1	2	yes	—
45	C₅×#332	C₂²	1	2	yes	—
46	C₅×#332	C₂²	1	2	yes	—
47	#19129	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	D₄	1	1	yes	characteristic
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×Q₁₆	—	2	1	no	—
51	C₂×C₅×Q₁₆	—	2	1	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂²×C₅×C₈	—	2	1	no	—
54	C₂²×C₅×C₈	—	2	1	no	—
55	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
56	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
57	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
58	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
59	C₅×#125	—	2	2	no	—
60	C₅×C₂²⋊Q₈	—	2	2	no	—
61	C₅×C₂²⋊Q₈	—	2	2	no	—
62	C₄×C₅×Q₈	—	2	2	no	—
63	C₄×C₅×Q₈	—	2	2	no	—
64	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
65	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₄×C₅×D₄	—	2	1	no	—
67	C₄×C₅×D₄	—	2	1	no	—
68	C₄×C₅×D₄	D₄	1	1	yes	characteristic
69	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₅×#117	—	2	1	no	—
71	C₅×#117	—	2	2	no	—
72	C₅×#117	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#107	—	2	1	no	—
76	C₅×#107	—	2	1	no	—
77	C₅×#107	—	2	2	no	—
78	C₅×#106	—	2	2	no	—
79	C₅×C₄⋊C₈	—	2	1	no	—
80	C₅×C₄⋊C₈	—	2	1	no	—
81	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
82	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
83	C₅×C₄⋊C₈	C₂³	1	2	yes	—
84	C₅×C₄⋊C₈	C₂³	1	2	yes	—
85	C₅×#103	—	2	2	no	—
86	C₅×#103	—	2	2	no	—
87	C₅×#103	—	2	2	no	—
88	C₅×#103	—	2	2	no	—
89	C₅×#103	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×C₂²⋊C₈	—	2	1	no	—
92	C₅×C₂²⋊C₈	—	2	2	no	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₄×C₅×C₈	—	2	1	no	—
96	C₄×C₅×C₈	—	2	1	no	—
97	C₄×C₅×C₈	—	2	1	no	—
98	C₄×C₅×C₈	—	2	2	no	—
99	C₄×C₅×C₈	D₄	1	1	yes	characteristic
100	C₄×C₅×C₈	D₄	1	1	yes	characteristic
101	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
103	#3170	C₂×C₅	1	1	yes	characteristic, complemented
104	#3107	C₂×C₅	1	2	yes	—
105	C₈×#41	C₂×C₅	1	1	yes	characteristic
106	#1680	C₂×C₅	1	2	yes	complemented
107	#1679	C₂×C₅	1	2	yes	complemented
108	#1674	C₂×C₅	1	1	yes	characteristic, complemented
109	#1673	C₂×C₅	1	1	yes	characteristic, complemented
110	#1670	C₂×C₅	1	1	yes	characteristic, complemented
111	#1669	C₂×C₅	1	1	yes	characteristic, complemented
112	#1564	C₂×C₅	1	1	yes	characteristic, complemented
113	#1544	C₂×C₅	1	2	yes	complemented
114	C₅×#41	—	2	2	no	—
115	C₅×#41	—	2	2	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	2	2	no	—
118	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₅	#41	1	1	yes	characteristic
127	C₅×Q₁₆	—	4	2	no	—
128	C₅×Q₁₆	—	4	4	no	—
129	C₅×Q₁₆	—	4	2	no	—
130	C₅×SD₁₆	—	4	4	no	—
131	C₂×C₅×C₈	—	2	2	no	—
132	C₂×C₅×C₈	—	2	1	no	—
133	C₂×C₅×C₈	—	2	1	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	—	2	2	no	—
136	C₂×C₅×C₈	—	4	1	no	—
137	C₂×C₅×C₈	—	4	2	no	—
138	C₂×C₅×C₈	—	4	2	no	—
139	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
140	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
141	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₅×C₄⋊C₄	—	2	1	no	—
144	C₅×C₄⋊C₄	—	2	1	no	—
145	C₅×C₄⋊C₄	—	2	2	no	—
146	C₅×C₄⋊C₄	—	2	2	no	—
147	C₅×C₄⋊C₄	—	2	2	no	—
148	C₅×C₄⋊C₄	—	2	2	no	—
149	C₅×C₄⋊C₄	—	4	2	no	—
150	C₅×C₄⋊C₄	—	4	2	no	—
151	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
152	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
153	C₅×C₂²⋊C₄	—	2	1	no	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	4	2	no	—
157	C₄²×C₅	—	2	1	no	—
158	C₄²×C₅	—	2	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	4	2	no	—
161	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₅	#41	1	1	yes	characteristic
164	C₄²×C₅	C₂⁴	1	1	yes	characteristic
165	#533	C₂²×C₅	1	2	yes	—
166	C₄×#41	C₂²×C₅	1	1	yes	characteristic
167	#500	C₂²×C₅	1	1	yes	characteristic
168	#494	C₂²×C₅	1	1	yes	characteristic
169	#487	C₂²×C₅	1	2	yes	—
170	#485	—	2	2	no	—
171	#475	C₂²×C₅	1	2	yes	—
172	#474	C₂²×C₅	1	2	yes	—
173	#467	—	2	1	no	—
174	#467	—	2	1	no	—
175	#462	C₂²×C₅	1	2	yes	—
176	#461	C₂²×C₅	1	2	yes	—
177	#452	—	2	2	no	—
178	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₄×Q₁₆	—	2	2	no	—
181	C₄×Q₁₆	—	2	1	no	—
182	C₄×Q₁₆	—	2	1	no	—
183	C₄×SD₁₆	—	2	2	no	—
184	C₈×D₄	—	2	1	no	—
185	C₈×D₄	—	2	1	no	—
186	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
187	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
188	#431	—	2	1	no	—
189	#431	C₂²×C₅	1	1	yes	characteristic
190	#431	C₂²×C₅	1	2	yes	—
191	C₂×C₄×C₈	—	2	1	no	—
192	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
193	#335	C₂²×C₅	1	1	yes	characteristic
194	#335	C₂²×C₅	1	1	yes	characteristic
195	#334	C₂²×C₅	1	2	yes	—
196	#332	C₂²×C₅	1	2	yes	—
197	#332	C₂²×C₅	1	2	yes	—
198	#332	C₂²×C₅	1	2	yes	—
199	#332	C₂²×C₅	1	2	yes	—
200	C₂³×C₅	—	2	1	no	—
201	C₂³×C₅	#121	1	1	yes	characteristic
202	C₅×Q₈	—	2	1	no	—
203	C₅×Q₈	—	4	2	no	—
204	C₅×Q₈	—	4	2	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₅×Q₈	#135	1	2	yes	—
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	#135	1	2	yes	—
211	C₂×C₄×C₅	—	2	4	no	—
212	C₂×C₄×C₅	—	2	1	no	—
213	C₂×C₄×C₅	—	2	1	no	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	1	no	—
216	C₂×C₄×C₅	—	2	1	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	2	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	4	2	no	—
225	C₂×C₄×C₅	#121	1	1	yes	characteristic
226	C₂×C₄×C₅	#121	1	1	yes	characteristic
227	C₂×C₄×C₅	#121	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₅×C₈	—	2	1	no	—
232	C₅×C₈	—	2	1	no	—
233	C₅×C₈	—	2	1	no	—
234	C₅×C₈	—	4	1	no	—
235	C₅×C₈	—	4	2	no	—
236	C₅×C₈	—	4	2	no	—
237	C₅×C₈	—	4	1	no	—
238	C₅×C₈	#135	1	2	yes	—
239	C₂×#41	C₅×D₄	1	1	yes	characteristic
240	C₂×Q₁₆	—	2	2	no	—
241	C₂×Q₁₆	—	2	1	no	—
242	C₂×Q₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	2	2	no	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	1	no	—
246	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
247	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
248	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
249	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
250	#125	—	2	2	no	—
251	C₂²⋊Q₈	—	2	2	no	—
252	C₂²⋊Q₈	—	2	2	no	—
253	C₄×Q₈	—	2	2	no	—
254	C₄×Q₈	—	2	2	no	—
255	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
256	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	C₅×D₄	1	1	yes	characteristic
260	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
261	#117	—	2	1	no	—
262	#117	—	2	2	no	—
263	#117	C₅×D₄	1	1	yes	characteristic
264	C₂×C₄²	—	2	1	no	—
265	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
266	#107	—	2	1	no	—
267	#107	—	2	1	no	—
268	#107	—	2	2	no	—
269	#106	—	2	2	no	—
270	C₄⋊C₈	—	2	1	no	—
271	C₄⋊C₈	—	2	1	no	—
272	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₄⋊C₈	C₂³×C₅	1	2	yes	—
275	C₄⋊C₈	C₂³×C₅	1	2	yes	—
276	#103	—	2	2	no	—
277	#103	—	2	2	no	—
278	#103	—	2	2	no	—
279	#103	—	2	2	no	—
280	#103	—	2	2	no	—
281	#102	—	2	2	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	1	no	—
285	C₂²⋊C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	—	2	1	no	—
289	C₄×C₈	—	2	2	no	—
290	C₄×C₈	C₅×D₄	1	1	yes	characteristic
291	C₄×C₈	C₅×D₄	1	1	yes	characteristic
292	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
294	C₂²×C₅	—	2	1	no	—
295	C₂²×C₅	—	2	1	no	—
296	C₂²×C₅	—	2	2	no	—
297	C₂²×C₅	—	2	1	no	—
298	C₂²×C₅	—	4	1	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	C₂×#121	1	1	yes	characteristic
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	4	1	no	—
306	C₄×C₅	—	4	1	no	—
307	C₄×C₅	—	8	2	no	—
308	C₄×C₅	—	8	2	no	—
309	C₄×C₅	#473	1	2	yes	—
310	C₄×C₅	C₂×#135	1	1	yes	characteristic
311	C₄×C₅	C₂×#135	1	1	yes	characteristic
312	C₄×C₅	C₂×#135	1	1	yes	characteristic
313	C₄×C₅	#575	1	1	yes	characteristic
314	#41	—	2	2	no	—
315	#41	—	2	2	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₅×#41	1	1	yes	characteristic
327	Q₁₆	—	4	2	no	—
328	Q₁₆	—	4	4	no	—
329	Q₁₆	—	4	2	no	—
330	SD₁₆	—	4	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	1	no	—
337	C₂×C₈	—	4	2	no	—
338	C₂×C₈	—	4	2	no	—
339	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
340	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
341	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
342	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	C₄⋊C₄	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	—	4	2	no	—
357	C₄²	—	2	1	no	—
358	C₄²	—	2	1	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	4	2	no	—
361	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
362	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
363	C₄²	C₅×#41	1	1	yes	characteristic
364	C₄²	C₂⁴×C₅	1	1	yes	characteristic
365	C₂×C₅	—	4	1	no	—
366	C₂×C₅	—	4	2	no	—
367	C₂×C₅	#3035	1	1	yes	characteristic
368	C₂×C₅	#3050	1	1	yes	characteristic
369	C₂×C₅	C₂×#473	1	1	yes	characteristic
370	C₂³	—	2	1	no	—
371	C₂³	C₅×#121	1	1	yes	characteristic
372	Q₈	—	2	1	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	C₅×#135	1	2	yes	—
378	D₄	—	2	4	no	—
379	D₄	—	2	1	no	—
380	D₄	C₅×#135	1	2	yes	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	C₅×#121	1	1	yes	characteristic
396	C₂×C₄	C₅×#121	1	1	yes	characteristic
397	C₂×C₄	C₅×#121	1	1	yes	characteristic
398	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
400	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	4	1	no	—
405	C₈	—	4	2	no	—
406	C₈	—	4	2	no	—
407	C₈	—	4	1	no	—
408	C₈	C₅×#135	1	2	yes	—
409	C₅	#19129	1	1	yes	characteristic, direct product factor, Sylow
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	C₂×C₅×#121	1	1	yes	characteristic
417	C₄	—	2	1	no	—
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	1	no	—
421	C₄	—	4	1	no	—
422	C₄	—	4	1	no	—
423	C₄	—	8	2	no	—
424	C₄	—	8	2	no	—
425	C₄	C₅×#473	1	2	yes	—
426	C₄	C₂×C₅×#135	1	1	yes	characteristic
427	C₄	C₂×C₅×#135	1	1	yes	characteristic
428	C₄	C₂×C₅×#135	1	1	yes	characteristic
429	C₄	C₅×#575	1	1	yes	characteristic
430	C₂	—	4	1	no	—
431	C₂	—	4	2	no	—
432	C₂	C₅×#3035	1	1	yes	characteristic
433	C₂	C₅×#3050	1	1	yes	characteristic
434	C₂	C₂×C₅×#473	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
socle	C₂²×C₅	C₂×#121
prime radical	C₂×C₅×#41	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3170	C₂	semidirect
4. C₅×#1680	C₂	semidirect
5. C₅×#1679	C₂	semidirect
6. C₅×#1674	C₂	semidirect
7. C₅×#1673	C₂	semidirect
8. C₅×#1670	C₂	semidirect
9. C₅×#1669	C₂	semidirect
10. C₅×#1564	C₂	semidirect
11. C₅×#1544	C₂	semidirect
47. #19129	C₅	direct (N × H)
103. #3170	C₂×C₅	semidirect
106. #1680	C₂×C₅	semidirect
107. #1679	C₂×C₅	semidirect
108. #1674	C₂×C₅	semidirect
109. #1673	C₂×C₅	semidirect
110. #1670	C₂×C₅	semidirect
111. #1669	C₂×C₅	semidirect
112. #1564	C₂×C₅	semidirect
113. #1544	C₂×C₅	semidirect
409. C₅	#19129	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×#3170	2
C₅×#3107	2
C₅×C₈×#41	2
C₅×#1680	2
C₅×#1679	2
C₅×#1674	2
C₅×#1673	2
C₅×#1670	2
C₅×#1669	2
C₅×#1564	2
C₅×#1544	2
#19129	5

Subgroups — C5×#19129 #11941849

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19129 #11941849