Subgroups — C₅×#19245 #11941965

Order 1280.

606 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3246	C₂	1	1	yes	maximal, characteristic
2	C₅×#3209	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3141	C₂	1	1	yes	maximal, characteristic
4	C₅×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1702	C₂	1	2	yes	maximal, complemented
6	C₅×#1700	C₂	1	2	yes	maximal, complemented
7	C₅×#1682	C₂	1	2	yes	maximal, complemented
8	C₅×#1680	C₂	1	2	yes	maximal, complemented
9	C₅×#1565	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1540	C₂	1	1	yes	maximal, characteristic
11	C₂×C₅×#332	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#533	C₂²	1	1	yes	characteristic
13	C₅×#532	C₂²	1	1	yes	characteristic
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₅×#494	—	2	1	no	—
16	C₅×#489	—	2	2	no	—
17	C₅×#487	—	2	1	no	—
18	C₅×#487	C₂²	1	2	yes	—
19	C₅×#486	C₂²	1	2	yes	—
20	C₅×#476	—	2	1	no	—
21	C₅×#475	C₂²	1	2	yes	—
22	C₅×#465	—	2	2	no	—
23	C₅×#462	C₂²	1	2	yes	—
24	C₅×#462	C₂²	1	2	yes	—
25	C₅×#461	—	2	1	no	—
26	C₅×#460	C₂²	1	2	yes	—
27	C₅×#451	—	2	2	no	—
28	C₅×#446	—	2	2	no	—
29	C₅×#446	C₂²	1	2	yes	—
30	C₅×C₈×Q₈	C₂²	1	2	yes	—
31	C₅×#431	C₂²	1	1	yes	characteristic
32	C₅×#424	—	2	1	no	—
33	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
35	C₅×#417	—	2	1	no	—
36	C₅×#417	—	2	1	no	—
37	C₅×#405	—	2	1	no	—
38	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
39	C₅×#335	C₂²	1	2	yes	—
40	C₅×#334	C₂²	1	2	yes	—
41	C₅×#332	C₂²	1	2	yes	—
42	C₅×#332	C₂²	1	2	yes	—
43	C₅×#332	C₂²	1	1	yes	characteristic
44	C₅×#332	C₂²	1	1	yes	characteristic
45	C₅×#331	C₂²	1	1	yes	characteristic
46	C₅×#331	C₂²	1	1	yes	characteristic
47	#19245	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	1	no	—
49	C₂²×C₅×Q₈	—	2	1	no	—
50	C₂×C₅×Q₁₆	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
54	C₂×C₅×M₁₆	D₄	1	1	yes	characteristic
55	C₂²×C₅×C₈	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₅×C₄⋊Q₈	—	2	1	no	—
58	C₅×C₄⋊Q₈	—	2	1	no	—
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
61	C₅×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
63	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₅×#127	C₂³	1	1	yes	characteristic
65	C₅×#125	—	2	1	no	—
66	C₅×#124	—	2	1	no	—
67	C₅×C₂²⋊Q₈	—	2	1	no	—
68	C₅×C₂²⋊Q₈	D₄	1	2	yes	—
69	C₅×#121	—	2	1	no	—
70	C₅×#121	—	2	1	no	—
71	C₄×C₅×Q₈	—	2	1	no	—
72	C₄×C₅×Q₈	C₂³	1	2	yes	—
73	C₄×C₅×D₄	—	2	1	no	—
74	C₄×C₅×D₄	—	2	1	no	—
75	C₅×#117	—	2	1	no	—
76	C₂×C₅×C₄⋊C₄	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	—	2	1	no	—
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₅×#106	—	2	2	no	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×C₄⋊C₈	—	2	1	no	—
83	C₅×C₄⋊C₈	—	2	1	no	—
84	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
86	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
87	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊C₈	C₂³	1	2	yes	—
89	C₅×#103	—	2	2	no	—
90	C₅×#103	—	2	2	no	—
91	C₅×#103	—	2	2	no	—
92	C₅×#103	—	2	2	no	—
93	C₅×#103	—	2	2	no	—
94	C₅×#102	—	2	2	no	—
95	C₅×#102	—	2	2	no	—
96	C₅×#102	—	2	2	no	—
97	C₅×C₂²⋊C₈	—	2	1	no	—
98	C₅×#97	—	2	2	no	—
99	C₅×#97	D₄	1	2	yes	—
100	C₄×C₅×C₈	—	2	2	no	—
101	C₄×C₅×C₈	—	2	1	no	—
102	C₄×C₅×C₈	C₂³	1	2	yes	—
103	#3246	C₂×C₅	1	1	yes	characteristic
104	#3209	C₂×C₅	1	1	yes	characteristic, complemented
105	#3141	C₂×C₅	1	1	yes	characteristic
106	#2962	C₂×C₅	1	1	yes	characteristic, complemented
107	#1702	C₂×C₅	1	2	yes	complemented
108	#1700	C₂×C₅	1	2	yes	complemented
109	#1682	C₂×C₅	1	2	yes	complemented
110	#1680	C₂×C₅	1	2	yes	complemented
111	#1565	C₂×C₅	1	1	yes	characteristic, complemented
112	#1540	C₂×C₅	1	1	yes	characteristic
113	C₂×#332	C₂×C₅	1	1	yes	characteristic, complemented
114	C₅×#41	—	4	2	no	—
115	C₅×#41	—	4	2	no	—
116	C₂×C₅×Q₈	—	2	1	no	—
117	C₂×C₅×Q₈	—	2	1	no	—
118	C₂×C₅×Q₈	—	2	2	no	—
119	C₂×C₅×Q₈	—	4	1	no	—
120	C₂×C₅×Q₈	—	8	1	no	—
121	C₂×C₅×Q₈	—	8	1	no	—
122	C₂×C₅×Q₈	C₂×D₄	1	2	yes	—
123	C₂×C₅×D₄	—	2	1	no	—
124	C₂×C₅×D₄	—	2	1	no	—
125	C₂×C₅×D₄	—	2	1	no	—
126	C₂×C₅×D₄	—	4	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₅	#41	1	1	yes	characteristic
132	C₅×Q₁₆	—	8	2	no	—
133	C₅×Q₁₆	—	8	2	no	—
134	C₅×SD₁₆	—	8	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₂×C₅×C₈	—	2	2	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	1	no	—
140	C₂×C₅×C₈	—	2	1	no	—
141	C₂×C₅×C₈	—	2	1	no	—
142	C₂×C₅×C₈	—	4	2	no	—
143	C₂×C₅×C₈	—	8	1	no	—
144	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₅×C₄⋊C₄	—	2	1	no	—
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	2	no	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	2	2	no	—
154	C₅×C₄⋊C₄	—	2	1	no	—
155	C₅×C₄⋊C₄	—	4	1	no	—
156	C₅×C₄⋊C₄	—	4	1	no	—
157	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
158	C₅×C₂²⋊C₄	—	2	2	no	—
159	C₅×C₂²⋊C₄	—	4	1	no	—
160	C₅×C₂²⋊C₄	—	4	1	no	—
161	C₄²×C₅	—	2	2	no	—
162	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅	#41	1	1	yes	characteristic
165	C₄²×C₅	C₂⁴	1	1	yes	characteristic
166	#533	C₂²×C₅	1	1	yes	characteristic
167	#532	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
169	#494	—	2	1	no	—
170	#489	—	2	2	no	—
171	#487	—	2	1	no	—
172	#487	C₂²×C₅	1	2	yes	—
173	#486	C₂²×C₅	1	2	yes	—
174	#476	—	2	1	no	—
175	#475	C₂²×C₅	1	2	yes	—
176	#465	—	2	2	no	—
177	#462	C₂²×C₅	1	2	yes	—
178	#462	C₂²×C₅	1	2	yes	—
179	#461	—	2	1	no	—
180	#460	C₂²×C₅	1	2	yes	—
181	#451	—	2	2	no	—
182	#446	—	2	2	no	—
183	#446	C₂²×C₅	1	2	yes	—
184	C₈×Q₈	C₂²×C₅	1	2	yes	—
185	#431	C₂²×C₅	1	1	yes	characteristic
186	#424	—	2	1	no	—
187	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
189	#417	—	2	1	no	—
190	#417	—	2	1	no	—
191	#405	—	2	1	no	—
192	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
193	#335	C₂²×C₅	1	2	yes	—
194	#334	C₂²×C₅	1	2	yes	—
195	#332	C₂²×C₅	1	2	yes	—
196	#332	C₂²×C₅	1	2	yes	—
197	#332	C₂²×C₅	1	1	yes	characteristic
198	#332	C₂²×C₅	1	1	yes	characteristic
199	#331	C₂²×C₅	1	1	yes	characteristic
200	#331	C₂²×C₅	1	1	yes	characteristic
201	C₂³×C₅	—	4	1	no	—
202	C₂³×C₅	#121	1	1	yes	characteristic
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	—	2	2	no	—
205	C₅×Q₈	—	4	1	no	—
206	C₅×Q₈	—	4	1	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×Q₈	—	8	1	no	—
210	C₅×Q₈	—	8	2	no	—
211	C₅×D₄	—	4	1	no	—
212	C₅×D₄	—	4	1	no	—
213	C₅×D₄	—	4	1	no	—
214	C₅×D₄	—	4	1	no	—
215	C₅×D₄	—	8	1	no	—
216	C₅×D₄	—	8	2	no	—
217	C₂×C₄×C₅	—	2	1	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	2	no	—
220	C₂×C₄×C₅	—	2	2	no	—
221	C₂×C₄×C₅	—	4	1	no	—
222	C₂×C₄×C₅	—	4	1	no	—
223	C₂×C₄×C₅	—	4	2	no	—
224	C₂×C₄×C₅	—	8	2	no	—
225	C₂×C₄×C₅	—	8	2	no	—
226	C₂×C₄×C₅	#121	1	1	yes	characteristic
227	C₂×C₄×C₅	#121	1	1	yes	characteristic
228	C₂×C₄×C₅	#121	1	1	yes	characteristic
229	C₂×C₄×C₅	#135	1	2	yes	—
230	C₂×C₄×C₅	#137	1	2	yes	—
231	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	4	1	no	—
237	C₅×C₈	—	4	1	no	—
238	C₅×C₈	—	4	2	no	—
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	4	1	no	—
241	C₂×#41	—	2	1	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	—	2	2	no	—
245	C₂×SD₁₆	—	2	2	no	—
246	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
247	C₂×M₁₆	C₅×D₄	1	1	yes	characteristic
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₄⋊Q₈	—	2	1	no	—
251	C₄⋊Q₈	—	2	1	no	—
252	C₄⋊Q₈	—	2	1	no	—
253	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
254	C₄⋊Q₈	C₅×D₄	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
256	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
257	#127	C₂³×C₅	1	1	yes	characteristic
258	#125	—	2	1	no	—
259	#124	—	2	1	no	—
260	C₂²⋊Q₈	—	2	1	no	—
261	C₂²⋊Q₈	C₅×D₄	1	2	yes	—
262	#121	—	2	1	no	—
263	#121	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	C₂³×C₅	1	2	yes	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	2	1	no	—
268	#117	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
272	#106	—	2	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	C₄⋊C₈	—	2	1	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
278	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
279	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
280	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
281	C₄⋊C₈	C₂³×C₅	1	2	yes	—
282	#103	—	2	2	no	—
283	#103	—	2	2	no	—
284	#103	—	2	2	no	—
285	#103	—	2	2	no	—
286	#103	—	2	2	no	—
287	#102	—	2	2	no	—
288	#102	—	2	2	no	—
289	#102	—	2	2	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	2	2	no	—
292	#97	C₅×D₄	1	2	yes	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	—	2	1	no	—
295	C₄×C₈	C₂³×C₅	1	2	yes	—
296	C₂²×C₅	—	2	1	no	—
297	C₂²×C₅	—	2	1	no	—
298	C₂²×C₅	—	8	1	no	—
299	C₂²×C₅	—	8	1	no	—
300	C₂²×C₅	—	8	1	no	—
301	C₂²×C₅	#464	1	2	yes	—
302	C₂²×C₅	C₂×#121	1	1	yes	characteristic
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	2	1	no	—
305	C₄×C₅	—	2	1	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	2	no	—
308	C₄×C₅	—	8	1	no	—
309	C₄×C₅	—	8	2	no	—
310	C₄×C₅	#464	1	2	yes	—
311	C₄×C₅	C₂×#135	1	1	yes	characteristic
312	C₄×C₅	C₂×#137	1	1	yes	characteristic
313	C₄×C₅	#576	1	1	yes	characteristic
314	C₄×C₅	#577	1	1	yes	characteristic
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	1	no	—
321	C₂×Q₈	—	8	1	no	—
322	C₂×Q₈	—	8	1	no	—
323	C₂×Q₈	C₂×C₅×D₄	1	2	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	1	no	—
327	C₂×D₄	—	4	1	no	—
328	C₂²×C₄	—	4	1	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂²×C₄	C₅×#41	1	1	yes	characteristic
333	Q₁₆	—	8	2	no	—
334	Q₁₆	—	8	2	no	—
335	SD₁₆	—	8	2	no	—
336	M₁₆	—	2	2	no	—
337	M₁₆	—	2	2	no	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	2	1	no	—
341	C₂×C₈	—	2	1	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	4	2	no	—
344	C₂×C₈	—	8	1	no	—
345	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
346	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	1	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₄⋊C₄	—	4	1	no	—
358	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
359	C₂²⋊C₄	—	2	2	no	—
360	C₂²⋊C₄	—	4	1	no	—
361	C₂²⋊C₄	—	4	1	no	—
362	C₄²	—	2	2	no	—
363	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
364	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
365	C₄²	C₅×#41	1	1	yes	characteristic
366	C₄²	C₂⁴×C₅	1	1	yes	characteristic
367	C₂×C₅	—	2	2	no	—
368	C₂×C₅	—	16	1	no	—
369	C₂×C₅	C₂×#464	1	1	yes	characteristic
370	C₂×C₅	#3062	1	1	yes	characteristic
371	C₂×C₅	#3069	1	1	yes	characteristic
372	C₂³	—	4	1	no	—
373	C₂³	C₅×#121	1	1	yes	characteristic
374	Q₈	—	2	2	no	—
375	Q₈	—	2	2	no	—
376	Q₈	—	4	1	no	—
377	Q₈	—	4	1	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	8	1	no	—
381	Q₈	—	8	2	no	—
382	D₄	—	4	1	no	—
383	D₄	—	4	1	no	—
384	D₄	—	4	1	no	—
385	D₄	—	4	1	no	—
386	D₄	—	8	1	no	—
387	D₄	—	8	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	C₅×#121	1	1	yes	characteristic
398	C₂×C₄	C₅×#121	1	1	yes	characteristic
399	C₂×C₄	C₅×#121	1	1	yes	characteristic
400	C₂×C₄	C₅×#135	1	2	yes	—
401	C₂×C₄	C₅×#137	1	2	yes	—
402	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
403	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
404	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	—	4	1	no	—
408	C₈	—	4	1	no	—
409	C₈	—	4	2	no	—
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₅	#19245	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	8	1	no	—
416	C₂²	—	8	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	C₅×#464	1	2	yes	—
419	C₂²	C₂×C₅×#121	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	2	no	—
427	C₄	C₅×#464	1	2	yes	—
428	C₄	C₂×C₅×#135	1	1	yes	characteristic
429	C₄	C₂×C₅×#137	1	1	yes	characteristic
430	C₄	C₅×#576	1	1	yes	characteristic
431	C₄	C₅×#577	1	1	yes	characteristic
432	C₂	—	2	2	no	—
433	C₂	—	16	1	no	—
434	C₂	C₂×C₅×#464	1	1	yes	characteristic
435	C₂	C₅×#3062	1	1	yes	characteristic
436	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×#532	C₂²
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
2. C₅×#3209	C₂	semidirect
4. C₅×#2962	C₂	semidirect
5. C₅×#1702	C₂	semidirect
6. C₅×#1700	C₂	semidirect
7. C₅×#1682	C₂	semidirect
8. C₅×#1680	C₂	semidirect
9. C₅×#1565	C₂	semidirect
11. C₂×C₅×#332	C₂	semidirect
47. #19245	C₅	direct (N × H)
104. #3209	C₂×C₅	semidirect
106. #2962	C₂×C₅	semidirect
107. #1702	C₂×C₅	semidirect
108. #1700	C₂×C₅	semidirect
109. #1682	C₂×C₅	semidirect
110. #1680	C₂×C₅	semidirect
111. #1565	C₂×C₅	semidirect
113. C₂×#332	C₂×C₅	semidirect
412. C₅	#19245	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×#3246	2
C₅×#3209	2
C₅×#3141	2
C₅×#2962	2
C₅×#1702	2
C₅×#1700	2
C₅×#1682	2
C₅×#1680	2
C₅×#1565	2
C₅×#1540	2
C₂×C₅×#332	2
#19245	5

Subgroups — C5×#19245 #11941965

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19245 #11941965