Subgroups — C₅×#19219 #11941939

Order 1280.

630 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3212	C₂	1	2	yes	maximal, complemented
2	C₅×#3169	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2966	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1702	C₂	1	2	yes	maximal, complemented
5	C₅×#1701	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×#1668	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1667	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#1564	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1553	C₂	1	2	yes	maximal, complemented
12	C₅×#532	C₂²	1	2	yes	—
13	C₅×#529	C₂²	1	1	yes	characteristic
14	C₅×#500	C₂²	1	1	yes	characteristic
15	C₅×#495	—	2	2	no	—
16	C₅×#493	C₂²	1	1	yes	characteristic
17	C₅×#488	—	2	2	no	—
18	C₅×#486	C₂²	1	2	yes	—
19	C₅×#466	—	2	1	no	—
20	C₅×#466	—	2	1	no	—
21	C₅×#462	C₂²	1	2	yes	—
22	C₅×#461	C₂²	1	2	yes	—
23	C₅×#460	C₂²	1	2	yes	—
24	C₅×#459	C₂²	1	2	yes	—
25	C₅×#452	—	2	2	no	—
26	C₅×#449	—	2	2	no	—
27	C₅×#446	C₂²	1	1	yes	characteristic
28	C₅×C₈×Q₈	C₂²	1	1	yes	characteristic
29	C₄×C₅×D₈	—	2	1	no	—
30	C₄×C₅×D₈	—	2	1	no	—
31	C₅×#436	C₂²	1	1	yes	characteristic
32	C₅×#435	—	2	1	no	—
33	C₅×C₈×D₄	—	2	1	no	—
34	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
35	C₅×#433	—	2	1	no	—
36	C₅×#432	C₂²	1	1	yes	characteristic
37	C₅×#431	C₂²	1	2	yes	—
38	C₅×#405	—	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×#331	C₂²	1	2	yes	—
46	C₅×#331	C₂²	1	2	yes	—
47	#19219	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
48	C₂×C₅×#41	—	2	2	no	—
49	C₂×C₅×Q₁₆	—	2	2	no	—
50	C₂×C₅×SD₁₆	—	2	2	no	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×D₈	—	2	2	no	—
53	C₂×C₅×D₈	—	2	1	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×M₁₆	—	2	1	no	—
56	C₂²×C₅×C₈	—	2	1	no	—
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₅×#127	C₂³	1	2	yes	—
61	C₅×#126	—	2	1	no	—
62	C₅×#125	D₄	1	1	yes	characteristic
63	C₅×#124	—	2	2	no	—
64	C₅×#124	D₄	1	1	yes	characteristic
65	C₅×#123	—	2	1	no	—
66	C₅×C₂²⋊Q₈	D₄	1	1	yes	characteristic
67	C₅×#121	—	2	2	no	—
68	C₅×#121	—	2	2	no	—
69	C₅×#121	D₄	1	1	yes	characteristic
70	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	2	2	no	—
73	C₄×C₅×D₄	—	2	2	no	—
74	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₅×#117	—	2	1	no	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#107	—	2	1	no	—
78	C₅×#107	—	2	1	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×#102	—	2	2	no	—
88	C₅×#102	—	2	2	no	—
89	C₅×#102	—	2	2	no	—
90	C₅×#102	—	2	2	no	—
91	C₅×C₂²⋊C₈	—	2	2	no	—
92	C₅×C₂²⋊C₈	—	2	1	no	—
93	C₅×C₂²⋊C₈	—	2	1	no	—
94	C₅×C₂²⋊C₈	—	2	1	no	—
95	C₅×#97	—	2	1	no	—
96	C₅×#97	—	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	#3212	C₂×C₅	1	2	yes	complemented
104	#3169	C₂×C₅	1	1	yes	characteristic, complemented
105	#2966	C₂×C₅	1	1	yes	characteristic, complemented
106	#1702	C₂×C₅	1	2	yes	complemented
107	#1701	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	#1668	C₂×C₅	1	1	yes	characteristic, complemented
111	#1667	C₂×C₅	1	1	yes	characteristic, complemented
112	#1564	C₂×C₅	1	1	yes	characteristic, complemented
113	#1553	C₂×C₅	1	2	yes	complemented
114	C₅×#41	—	8	2	no	—
115	C₅×#41	—	8	2	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	2	no	—
120	C₂×C₅×D₄	—	2	2	no	—
121	C₂×C₅×D₄	—	2	2	no	—
122	C₂×C₅×D₄	—	4	2	no	—
123	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	4	2	no	—
126	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	#41	1	1	yes	characteristic
129	C₅×Q₁₆	—	8	2	no	—
130	C₅×SD₁₆	—	8	2	no	—
131	C₅×SD₁₆	—	8	2	no	—
132	C₅×D₈	—	4	2	no	—
133	C₅×D₈	—	4	2	no	—
134	C₅×D₈	—	8	2	no	—
135	C₅×M₁₆	—	4	2	no	—
136	C₂×C₅×C₈	—	2	2	no	—
137	C₂×C₅×C₈	—	2	1	no	—
138	C₂×C₅×C₈	—	2	1	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	4	1	no	—
142	C₂×C₅×C₈	—	4	2	no	—
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
147	C₅×C₄⋊C₄	—	2	1	no	—
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	2	1	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	—	2	2	no	—
153	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
154	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	1	no	—
157	C₅×C₂²⋊C₄	—	2	1	no	—
158	C₅×C₂²⋊C₄	—	2	1	no	—
159	C₅×C₂²⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	4	2	no	—
161	C₅×C₂²⋊C₄	—	4	2	no	—
162	C₄²×C₅	—	2	1	no	—
163	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅	#41	1	1	yes	characteristic
166	C₄²×C₅	C₂⁴	1	1	yes	characteristic
167	#532	C₂²×C₅	1	2	yes	—
168	#529	C₂²×C₅	1	1	yes	characteristic
169	#500	C₂²×C₅	1	1	yes	characteristic
170	#495	—	2	2	no	—
171	#493	C₂²×C₅	1	1	yes	characteristic
172	#488	—	2	2	no	—
173	#486	C₂²×C₅	1	2	yes	—
174	#466	—	2	1	no	—
175	#466	—	2	1	no	—
176	#462	C₂²×C₅	1	2	yes	—
177	#461	C₂²×C₅	1	2	yes	—
178	#460	C₂²×C₅	1	2	yes	—
179	#459	C₂²×C₅	1	2	yes	—
180	#452	—	2	2	no	—
181	#449	—	2	2	no	—
182	#446	C₂²×C₅	1	1	yes	characteristic
183	C₈×Q₈	C₂²×C₅	1	1	yes	characteristic
184	C₄×D₈	—	2	1	no	—
185	C₄×D₈	—	2	1	no	—
186	#436	C₂²×C₅	1	1	yes	characteristic
187	#435	—	2	1	no	—
188	C₈×D₄	—	2	1	no	—
189	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
190	#433	—	2	1	no	—
191	#432	C₂²×C₅	1	1	yes	characteristic
192	#431	C₂²×C₅	1	2	yes	—
193	#405	—	2	1	no	—
194	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
195	#335	C₂²×C₅	1	1	yes	characteristic
196	#335	C₂²×C₅	1	1	yes	characteristic
197	#334	C₂²×C₅	1	2	yes	—
198	#332	C₂²×C₅	1	2	yes	—
199	#332	C₂²×C₅	1	2	yes	—
200	#331	C₂²×C₅	1	2	yes	—
201	#331	C₂²×C₅	1	2	yes	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	—	4	2	no	—
204	C₂³×C₅	#121	1	1	yes	characteristic
205	C₅×Q₈	—	2	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	—	4	2	no	—
208	C₅×Q₈	—	4	2	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	—	2	1	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	—	4	2	no	—
214	C₅×D₄	—	4	2	no	—
215	C₅×D₄	—	4	2	no	—
216	C₅×D₄	—	8	2	no	—
217	C₅×D₄	—	8	4	no	—
218	C₂×C₄×C₅	—	2	1	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	2	1	no	—
221	C₂×C₄×C₅	—	2	1	no	—
222	C₂×C₄×C₅	—	2	1	no	—
223	C₂×C₄×C₅	—	2	1	no	—
224	C₂×C₄×C₅	—	2	1	no	—
225	C₂×C₄×C₅	—	4	1	no	—
226	C₂×C₄×C₅	—	4	1	no	—
227	C₂×C₄×C₅	—	4	1	no	—
228	C₂×C₄×C₅	—	4	2	no	—
229	C₂×C₄×C₅	—	8	4	no	—
230	C₂×C₄×C₅	#121	1	1	yes	characteristic
231	C₂×C₄×C₅	#121	1	1	yes	characteristic
232	C₂×C₄×C₅	#121	1	1	yes	characteristic
233	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
236	C₅×C₈	—	2	1	no	—
237	C₅×C₈	—	2	1	no	—
238	C₅×C₈	—	2	1	no	—
239	C₅×C₈	—	4	1	no	—
240	C₅×C₈	—	4	1	no	—
241	C₅×C₈	—	4	2	no	—
242	C₅×C₈	—	4	2	no	—
243	C₅×C₈	#135	1	2	yes	—
244	C₂×#41	—	2	2	no	—
245	C₂×Q₁₆	—	2	2	no	—
246	C₂×SD₁₆	—	2	2	no	—
247	C₂×SD₁₆	—	2	2	no	—
248	C₂×D₈	—	2	2	no	—
249	C₂×D₈	—	2	1	no	—
250	C₂×D₈	—	2	1	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₂²×C₈	—	2	1	no	—
253	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
254	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
255	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
256	#127	C₂³×C₅	1	2	yes	—
257	#126	—	2	1	no	—
258	#125	C₅×D₄	1	1	yes	characteristic
259	#124	—	2	2	no	—
260	#124	C₅×D₄	1	1	yes	characteristic
261	#123	—	2	1	no	—
262	C₂²⋊Q₈	C₅×D₄	1	1	yes	characteristic
263	#121	—	2	2	no	—
264	#121	—	2	2	no	—
265	#121	C₅×D₄	1	1	yes	characteristic
266	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
267	C₄×D₄	—	2	1	no	—
268	C₄×D₄	—	2	2	no	—
269	C₄×D₄	—	2	2	no	—
270	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
271	#117	—	2	1	no	—
272	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
273	#107	—	2	1	no	—
274	#107	—	2	1	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	2	yes	—
280	C₄⋊C₈	C₂³×C₅	1	2	yes	—
281	#103	—	2	2	no	—
282	#103	—	2	2	no	—
283	#102	—	2	2	no	—
284	#102	—	2	2	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	C₂²⋊C₈	—	2	1	no	—
289	C₂²⋊C₈	—	2	1	no	—
290	C₂²⋊C₈	—	2	1	no	—
291	#97	—	2	1	no	—
292	#97	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₄×C₈	—	2	2	no	—
295	C₄×C₈	C₅×D₄	1	1	yes	characteristic
296	C₄×C₈	C₅×D₄	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
299	C₂²×C₅	—	2	1	no	—
300	C₂²×C₅	—	2	1	no	—
301	C₂²×C₅	—	2	1	no	—
302	C₂²×C₅	—	4	1	no	—
303	C₂²×C₅	—	4	1	no	—
304	C₂²×C₅	—	4	1	no	—
305	C₂²×C₅	—	8	2	no	—
306	C₂²×C₅	—	8	2	no	—
307	C₂²×C₅	—	8	2	no	—
308	C₂²×C₅	C₂×#121	1	1	yes	characteristic
309	C₄×C₅	—	2	1	no	—
310	C₄×C₅	—	2	1	no	—
311	C₄×C₅	—	2	1	no	—
312	C₄×C₅	—	2	1	no	—
313	C₄×C₅	—	4	1	no	—
314	C₄×C₅	—	4	1	no	—
315	C₄×C₅	—	4	1	no	—
316	C₄×C₅	—	8	2	no	—
317	C₄×C₅	C₂×#135	1	1	yes	characteristic
318	C₄×C₅	#575	1	1	yes	characteristic
319	C₄×C₅	#576	1	1	yes	characteristic
320	C₄×C₅	#576	1	1	yes	characteristic
321	#41	—	8	2	no	—
322	#41	—	8	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	4	2	no	—
330	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	4	2	no	—
333	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
335	C₂²×C₄	C₅×#41	1	1	yes	characteristic
336	Q₁₆	—	8	2	no	—
337	SD₁₆	—	8	2	no	—
338	SD₁₆	—	8	2	no	—
339	D₈	—	4	2	no	—
340	D₈	—	4	2	no	—
341	D₈	—	8	2	no	—
342	M₁₆	—	4	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	1	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	1	no	—
348	C₂×C₈	—	4	1	no	—
349	C₂×C₈	—	4	2	no	—
350	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
352	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
353	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	2	1	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
361	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	1	no	—
364	C₂²⋊C₄	—	2	1	no	—
365	C₂²⋊C₄	—	2	1	no	—
366	C₂²⋊C₄	—	2	1	no	—
367	C₂²⋊C₄	—	4	2	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₄²	—	2	1	no	—
370	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
371	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
372	C₄²	C₅×#41	1	1	yes	characteristic
373	C₄²	C₂⁴×C₅	1	1	yes	characteristic
374	C₂×C₅	—	4	1	no	—
375	C₂×C₅	—	8	1	no	—
376	C₂×C₅	—	16	2	no	—
377	C₂×C₅	#3035	1	1	yes	characteristic
378	C₂×C₅	#3058	1	1	yes	characteristic
379	C₂×C₅	#3067	1	1	yes	characteristic
380	C₂³	—	2	1	no	—
381	C₂³	—	4	2	no	—
382	C₂³	C₅×#121	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	—	2	1	no	—
385	Q₈	—	4	2	no	—
386	Q₈	—	4	2	no	—
387	D₄	—	2	1	no	—
388	D₄	—	2	1	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	4	2	no	—
394	D₄	—	8	2	no	—
395	D₄	—	8	4	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	1	no	—
404	C₂×C₄	—	4	1	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	C₅×#121	1	1	yes	characteristic
409	C₂×C₄	C₅×#121	1	1	yes	characteristic
410	C₂×C₄	C₅×#121	1	1	yes	characteristic
411	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
413	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	2	1	no	—
416	C₈	—	2	1	no	—
417	C₈	—	4	1	no	—
418	C₈	—	4	1	no	—
419	C₈	—	4	2	no	—
420	C₈	—	4	2	no	—
421	C₈	C₅×#135	1	2	yes	—
422	C₅	#19219	1	1	yes	characteristic, direct product factor, Sylow
423	C₂²	—	2	1	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	4	1	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	—	8	2	no	—
432	C₂²	C₂×C₅×#121	1	1	yes	characteristic
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	2	1	no	—
437	C₄	—	4	1	no	—
438	C₄	—	4	1	no	—
439	C₄	—	4	1	no	—
440	C₄	—	8	2	no	—
441	C₄	C₂×C₅×#135	1	1	yes	characteristic
442	C₄	C₅×#575	1	1	yes	characteristic
443	C₄	C₅×#576	1	1	yes	characteristic
444	C₄	C₅×#576	1	1	yes	characteristic
445	C₂	—	4	1	no	—
446	C₂	—	8	1	no	—
447	C₂	—	16	2	no	—
448	C₂	C₅×#3035	1	1	yes	characteristic
449	C₂	C₅×#3058	1	1	yes	characteristic
450	C₂	C₅×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅
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×#3212	C₂	semidirect
2. C₅×#3169	C₂	semidirect
3. C₅×#2966	C₂	semidirect
4. C₅×#1702	C₂	semidirect
5. C₅×#1701	C₂	semidirect
6. C₅×#1674	C₂	semidirect
7. C₅×#1673	C₂	semidirect
8. C₅×#1668	C₂	semidirect
9. C₅×#1667	C₂	semidirect
10. C₅×#1564	C₂	semidirect
11. C₅×#1553	C₂	semidirect
47. #19219	C₅	direct (N × H)
103. #3212	C₂×C₅	semidirect
104. #3169	C₂×C₅	semidirect
105. #2966	C₂×C₅	semidirect
106. #1702	C₂×C₅	semidirect
107. #1701	C₂×C₅	semidirect
108. #1674	C₂×C₅	semidirect
109. #1673	C₂×C₅	semidirect
110. #1668	C₂×C₅	semidirect
111. #1667	C₂×C₅	semidirect
112. #1564	C₂×C₅	semidirect
113. #1553	C₂×C₅	semidirect
422. C₅	#19219	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×#3212	2
C₅×#3169	2
C₅×#2966	2
C₅×#1702	2
C₅×#1701	2
C₅×#1674	2
C₅×#1673	2
C₅×#1668	2
C₅×#1667	2
C₅×#1564	2
C₅×#1553	2
#19219	5

Subgroups — C5×#19219 #11941939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#19219 #11941939