Subgroups — C₅×#21139 #11943859

Order 1280.

780 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#2943	C₂	1	1	yes	maximal, characteristic
2	C₅×#2923	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2875	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#1929	C₂	1	2	yes	maximal, complemented
5	C₅×#1922	C₂	1	2	yes	maximal, complemented
6	C₅×#1876	C₂	1	2	yes	maximal
7	C₅×#1866	C₂	1	2	yes	maximal, complemented
8	C₅×#1778	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#104	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#1745	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂×C₅×#131	C₂²	1	2	yes	—
14	C₄×C₅×#41	C₂²	1	1	yes	characteristic
15	C₄×C₅×#41	C₂²	1	1	yes	characteristic
16	C₅×#442	C₄	1	2	yes	complemented
17	C₅×#441	C₄	1	2	yes	complemented
18	C₅×#440	C₄	1	2	yes	complemented
19	C₅×#440	C₄	1	2	yes	complemented
20	C₅×#433	—	2	1	no	—
21	C₅×#433	—	2	1	no	—
22	C₅×#432	—	2	2	no	—
23	C₂×C₅×#108	C₂²	1	2	yes	—
24	C₅×#427	C₂²	1	1	yes	characteristic
25	C₅×#424	C₂²	1	2	yes	—
26	C₂×C₅×#104	C₂²	1	2	yes	—
27	C₂×C₅×#104	C₂²	1	2	yes	—
28	C₅×#416	C₂²	1	1	yes	characteristic
29	C₅×#416	C₂²	1	1	yes	characteristic
30	C₅×#408	C₂²	1	2	yes	—
31	C₅×#405	—	2	2	no	—
32	C₅×#405	C₂²	1	2	yes	—
33	C₄×C₅×M₁₆	—	2	1	no	—
34	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
35	C₄×C₅×M₁₆	C₂²	1	1	yes	characteristic
36	C₂×C₅×#97	—	2	1	no	—
37	C₂×C₅×#97	C₂²	1	1	yes	characteristic
38	C₂×C₅×#97	C₂²	1	1	yes	characteristic
39	C₄³×C₅	C₂²	1	1	yes	characteristic
40	C₅×#341	C₂²	1	2	yes	—
41	C₅×#339	C₂²	1	2	yes	—
42	C₅×#339	C₂²	1	2	yes	—
43	C₅×#336	C₂²	1	2	yes	—
44	C₅×#336	C₂²	1	2	yes	—
45	#21139	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	C₂³	1	1	yes	characteristic
47	C₂×C₅×#41	C₂³	1	1	yes	characteristic
48	C₅×#135	—	2	4	no	—
49	C₂×C₅×Q₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₅×SD₁₆	C₂×C₄	1	1	yes	characteristic
52	C₂×C₅×D₈	C₂×C₄	1	1	yes	characteristic
53	C₅×#131	—	2	4	no	—
54	C₅×#131	—	2	4	no	—
55	C₂×C₅×M₁₆	—	2	2	no	—
56	C₂×C₅×M₁₆	C₂³	1	2	yes	—
57	C₂×C₅×M₁₆	C₂³	1	2	yes	—
58	C₂²×C₅×C₈	—	2	2	no	—
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	C₂³	1	2	yes	—
62	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
63	C₄×C₅×Q₈	C₂×C₄	1	2	yes	—
64	C₄×C₅×D₄	—	2	2	no	—
65	C₄×C₅×D₄	—	2	2	no	—
66	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
67	C₄×C₅×D₄	C₂×C₄	1	2	yes	—
68	C₅×#117	—	2	1	no	—
69	C₅×#117	—	2	1	no	—
70	C₅×#117	C₂³	1	1	yes	characteristic
71	C₅×#117	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₅	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	C₂³	1	2	yes	—
76	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
77	C₅×#108	—	2	4	no	—
78	C₅×#107	C₂×C₄	1	2	yes	—
79	C₅×#106	C₂×C₄	1	2	yes	—
80	C₅×C₄⋊C₈	—	2	2	no	—
81	C₅×C₄⋊C₈	—	2	2	no	—
82	C₅×#104	—	2	4	no	—
83	C₅×#104	—	2	4	no	—
84	C₅×#103	C₂×C₄	1	2	yes	—
85	C₅×#103	C₂×C₄	1	2	yes	—
86	C₅×#102	C₂×C₄	1	2	yes	—
87	C₅×#102	C₂×C₄	1	2	yes	—
88	C₅×C₂²⋊C₈	—	2	2	no	—
89	C₅×C₂²⋊C₈	—	2	2	no	—
90	C₅×#97	—	2	2	no	—
91	C₅×#97	—	2	1	no	—
92	C₅×#97	—	2	1	no	—
93	C₅×#97	C₂×C₄	1	2	yes	—
94	C₅×#97	C₂×C₄	1	2	yes	—
95	C₅×#97	D₄	1	1	yes	characteristic
96	C₅×#97	D₄	1	1	yes	characteristic
97	C₅×#97	D₄	1	2	yes	—
98	C₄×C₅×C₈	—	2	2	no	—
99	C₄×C₅×C₈	—	2	1	no	—
100	C₄×C₅×C₈	—	2	1	no	—
101	#2943	C₂×C₅	1	1	yes	characteristic
102	#2923	C₂×C₅	1	1	yes	characteristic, complemented
103	#2875	C₂×C₅	1	1	yes	characteristic, complemented
104	#1929	C₂×C₅	1	2	yes	complemented
105	#1922	C₂×C₅	1	2	yes	complemented
106	#1876	C₂×C₅	1	2	yes	—
107	#1866	C₂×C₅	1	2	yes	complemented
108	#1778	C₂×C₅	1	1	yes	characteristic, complemented
109	C₄×#104	C₂×C₅	1	1	yes	characteristic, complemented
110	C₄×#104	C₂×C₅	1	1	yes	characteristic, complemented
111	#1745	C₂×C₅	1	1	yes	characteristic, complemented
112	C₅×#41	—	2	2	no	—
113	C₅×#41	—	2	2	no	—
114	C₅×#41	—	2	2	no	—
115	C₅×#41	#41	1	4	yes	—
116	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₅×Q₈	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₅×D₄	—	2	1	no	—
119	C₂×C₅×D₄	—	2	1	no	—
120	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₅×D₄	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₅	—	2	1	no	—
123	C₂²×C₄×C₅	—	2	2	no	—
124	C₂²×C₄×C₅	—	2	1	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	#41	1	2	yes	—
128	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
129	C₅×Q₁₆	—	2	2	no	—
130	C₅×SD₁₆	—	2	2	no	—
131	C₅×SD₁₆	—	2	2	no	—
132	C₅×D₈	—	2	2	no	—
133	C₅×M₁₆	—	2	8	no	—
134	C₅×M₁₆	—	2	2	no	—
135	C₅×M₁₆	—	2	2	no	—
136	C₅×M₁₆	—	2	2	no	—
137	C₅×M₁₆	#41	1	4	yes	—
138	C₂×C₅×C₈	—	2	8	no	—
139	C₂×C₅×C₈	—	2	2	no	—
140	C₂×C₅×C₈	—	2	2	no	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	—	2	2	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₅×C₈	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₅×C₈	C₂²×C₄	1	2	yes	—
148	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
149	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
150	C₅×C₄⋊C₄	—	2	2	no	—
151	C₅×C₄⋊C₄	—	2	2	no	—
152	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
153	C₅×C₄⋊C₄	C₂²×C₄	1	2	yes	—
154	C₅×C₂²⋊C₄	—	2	1	no	—
155	C₅×C₂²⋊C₄	—	2	1	no	—
156	C₅×C₂²⋊C₄	—	2	2	no	—
157	C₅×C₂²⋊C₄	—	2	2	no	—
158	C₄²×C₅	—	2	2	no	—
159	C₄²×C₅	—	2	2	no	—
160	C₄²×C₅	—	2	1	no	—
161	C₄²×C₅	—	2	1	no	—
162	C₄²×C₅	—	2	2	no	—
163	C₄²×C₅	—	2	2	no	—
164	C₄²×C₅	—	4	4	no	—
165	C₄²×C₅	C₂²×C₄	1	2	yes	—
166	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
168	C₂×#135	C₂²×C₅	1	1	yes	characteristic
169	C₂×#131	C₂²×C₅	1	2	yes	—
170	C₄×#41	C₂²×C₅	1	1	yes	characteristic
171	C₄×#41	C₂²×C₅	1	1	yes	characteristic
172	#442	C₄×C₅	1	2	yes	complemented
173	#441	C₄×C₅	1	2	yes	complemented
174	#440	C₄×C₅	1	2	yes	complemented
175	#440	C₄×C₅	1	2	yes	complemented
176	#433	—	2	1	no	—
177	#433	—	2	1	no	—
178	#432	—	2	2	no	—
179	C₂×#108	C₂²×C₅	1	2	yes	—
180	#427	C₂²×C₅	1	1	yes	characteristic
181	#424	C₂²×C₅	1	2	yes	—
182	C₂×#104	C₂²×C₅	1	2	yes	—
183	C₂×#104	C₂²×C₅	1	2	yes	—
184	#416	C₂²×C₅	1	1	yes	characteristic
185	#416	C₂²×C₅	1	1	yes	characteristic
186	#408	C₂²×C₅	1	2	yes	—
187	#405	—	2	2	no	—
188	#405	C₂²×C₅	1	2	yes	—
189	C₄×M₁₆	—	2	1	no	—
190	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₄×M₁₆	C₂²×C₅	1	1	yes	characteristic
192	C₂×#97	—	2	1	no	—
193	C₂×#97	C₂²×C₅	1	1	yes	characteristic
194	C₂×#97	C₂²×C₅	1	1	yes	characteristic
195	C₄³	C₂²×C₅	1	1	yes	characteristic
196	#341	C₂²×C₅	1	2	yes	—
197	#339	C₂²×C₅	1	2	yes	—
198	#339	C₂²×C₅	1	2	yes	—
199	#336	C₂²×C₅	1	2	yes	—
200	#336	C₂²×C₅	1	2	yes	—
201	C₂³×C₅	—	2	1	no	—
202	C₂³×C₅	—	2	1	no	—
203	C₂³×C₅	C₂×#41	1	1	yes	characteristic
204	C₅×Q₈	—	2	1	no	—
205	C₅×Q₈	—	2	1	no	—
206	C₅×Q₈	—	2	1	no	—
207	C₅×Q₈	#117	1	2	yes	—
208	C₅×D₄	—	2	4	no	—
209	C₅×D₄	—	2	1	no	—
210	C₅×D₄	—	2	1	no	—
211	C₅×D₄	—	2	1	no	—
212	C₅×D₄	—	4	2	no	—
213	C₅×D₄	#117	1	2	yes	—
214	C₂×C₄×C₅	—	2	1	no	—
215	C₂×C₄×C₅	—	2	4	no	—
216	C₂×C₄×C₅	—	2	4	no	—
217	C₂×C₄×C₅	—	2	2	no	—
218	C₂×C₄×C₅	—	2	2	no	—
219	C₂×C₄×C₅	—	2	1	no	—
220	C₂×C₄×C₅	—	4	2	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	4	2	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	C₄×D₄	1	2	yes	—
227	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
228	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×#41	1	2	yes	—
231	C₂×C₄×C₅	C₂×#41	1	2	yes	—
232	C₅×C₈	—	2	1	no	—
233	C₅×C₈	—	2	1	no	—
234	C₅×C₈	—	2	2	no	—
235	C₅×C₈	—	2	2	no	—
236	C₅×C₈	—	2	4	no	—
237	C₅×C₈	—	2	2	no	—
238	C₅×C₈	—	4	2	no	—
239	C₂×#41	C₂³×C₅	1	1	yes	characteristic
240	C₂×#41	C₂³×C₅	1	1	yes	characteristic
241	#135	—	2	4	no	—
242	C₂×Q₁₆	C₂×C₄×C₅	1	1	yes	characteristic
243	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
244	C₂×SD₁₆	C₂×C₄×C₅	1	1	yes	characteristic
245	C₂×D₈	C₂×C₄×C₅	1	1	yes	characteristic
246	#131	—	2	4	no	—
247	#131	—	2	4	no	—
248	C₂×M₁₆	—	2	2	no	—
249	C₂×M₁₆	C₂³×C₅	1	2	yes	—
250	C₂×M₁₆	C₂³×C₅	1	2	yes	—
251	C₂²×C₈	—	2	2	no	—
252	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×C₈	C₂³×C₅	1	2	yes	—
255	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
256	C₄×Q₈	C₂×C₄×C₅	1	2	yes	—
257	C₄×D₄	—	2	2	no	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
260	C₄×D₄	C₂×C₄×C₅	1	2	yes	—
261	#117	—	2	1	no	—
262	#117	—	2	1	no	—
263	#117	C₂³×C₅	1	1	yes	characteristic
264	#117	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	2	2	no	—
268	C₂×C₄²	C₂³×C₅	1	2	yes	—
269	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
270	#108	—	2	4	no	—
271	#107	C₂×C₄×C₅	1	2	yes	—
272	#106	C₂×C₄×C₅	1	2	yes	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	2	2	no	—
275	#104	—	2	4	no	—
276	#104	—	2	4	no	—
277	#103	C₂×C₄×C₅	1	2	yes	—
278	#103	C₂×C₄×C₅	1	2	yes	—
279	#102	C₂×C₄×C₅	1	2	yes	—
280	#102	C₂×C₄×C₅	1	2	yes	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	#97	—	2	2	no	—
284	#97	—	2	1	no	—
285	#97	—	2	1	no	—
286	#97	C₂×C₄×C₅	1	2	yes	—
287	#97	C₂×C₄×C₅	1	2	yes	—
288	#97	C₅×D₄	1	1	yes	characteristic
289	#97	C₅×D₄	1	1	yes	characteristic
290	#97	C₅×D₄	1	2	yes	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	2	1	no	—
293	C₄×C₈	—	2	1	no	—
294	C₂²×C₅	—	2	2	no	—
295	C₂²×C₅	—	2	2	no	—
296	C₂²×C₅	—	4	2	no	—
297	C₂²×C₅	—	4	2	no	—
298	C₂²×C₅	—	4	1	no	—
299	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
300	C₂²×C₅	#529	1	2	yes	—
301	C₄×C₅	—	2	2	no	—
302	C₄×C₅	—	2	2	no	—
303	C₄×C₅	—	2	2	no	—
304	C₄×C₅	—	4	4	no	—
305	C₄×C₅	—	4	2	no	—
306	C₄×C₅	—	4	2	no	—
307	C₄×C₅	—	4	1	no	—
308	C₄×C₅	C₂×#117	1	1	yes	characteristic
309	C₄×C₅	C₄×#41	1	1	yes	characteristic
310	C₄×C₅	#525	1	2	yes	—
311	#41	—	2	2	no	—
312	#41	—	2	2	no	—
313	#41	—	2	2	no	—
314	#41	C₅×#41	1	4	yes	—
315	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
316	C₂×Q₈	C₂²×C₄×C₅	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
320	C₂×D₄	C₂²×C₄×C₅	1	1	yes	characteristic
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	1	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	C₅×#41	1	2	yes	—
327	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
328	Q₁₆	—	2	2	no	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	2	2	no	—
331	D₈	—	2	2	no	—
332	M₁₆	—	2	8	no	—
333	M₁₆	—	2	2	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	2	no	—
336	M₁₆	C₅×#41	1	4	yes	—
337	C₂×C₈	—	2	8	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	C₂²×C₄×C₅	1	2	yes	—
345	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₂×C₈	C₂²×C₄×C₅	1	1	yes	characteristic
347	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
348	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	2	no	—
351	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
352	C₄⋊C₄	C₂²×C₄×C₅	1	2	yes	—
353	C₂²⋊C₄	—	2	1	no	—
354	C₂²⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	2	no	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	4	4	no	—
364	C₄²	C₂²×C₄×C₅	1	2	yes	—
365	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
366	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
367	C₂×C₅	—	2	2	no	—
368	C₂×C₅	—	4	2	no	—
369	C₂×C₅	—	8	1	no	—
370	C₂×C₅	#2290	1	1	yes	characteristic
371	C₂×C₅	#2956	1	2	yes	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	C₂×C₅×#41	1	1	yes	characteristic
375	Q₈	—	2	1	no	—
376	Q₈	—	2	1	no	—
377	Q₈	—	2	1	no	—
378	Q₈	C₅×#117	1	2	yes	—
379	D₄	—	2	4	no	—
380	D₄	—	2	1	no	—
381	D₄	—	2	1	no	—
382	D₄	—	2	1	no	—
383	D₄	—	4	2	no	—
384	D₄	C₅×#117	1	2	yes	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	4	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
398	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
399	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
401	C₂×C₄	C₂×C₅×#41	1	2	yes	—
402	C₂×C₄	C₂×C₅×#41	1	2	yes	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	2	no	—
406	C₈	—	2	2	no	—
407	C₈	—	2	4	no	—
408	C₈	—	2	2	no	—
409	C₈	—	4	2	no	—
410	C₅	#21139	1	1	yes	characteristic, direct product factor, Sylow
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	4	2	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
417	C₂²	C₅×#529	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	2	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	1	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	2	no	—
425	C₄	C₂×C₅×#117	1	1	yes	characteristic
426	C₄	C₄×C₅×#41	1	1	yes	characteristic
427	C₄	C₅×#525	1	2	yes	—
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	C₅×#2290	1	1	yes	characteristic
432	C₂	C₅×#2956	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
socle	C₂²×C₅	C₂×C₄×D₄
prime radical	C₂×C₅×#135	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₅×#97 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₅×#2923	C₂	semidirect
3. C₅×#2875	C₂	semidirect
4. C₅×#1929	C₂	semidirect
5. C₅×#1922	C₂	semidirect
7. C₅×#1866	C₂	semidirect
8. C₅×#1778	C₂	semidirect
9. C₄×C₅×#104	C₂	semidirect
10. C₄×C₅×#104	C₂	semidirect
11. C₅×#1745	C₂	semidirect
16. C₅×#442	C₄	semidirect
17. C₅×#441	C₄	semidirect
18. C₅×#440	C₄	semidirect
19. C₅×#440	C₄	semidirect
45. #21139	C₅	direct (N × H)
102. #2923	C₂×C₅	semidirect
103. #2875	C₂×C₅	semidirect
104. #1929	C₂×C₅	semidirect
105. #1922	C₂×C₅	semidirect
107. #1866	C₂×C₅	semidirect
108. #1778	C₂×C₅	semidirect
109. C₄×#104	C₂×C₅	semidirect
110. C₄×#104	C₂×C₅	semidirect
111. #1745	C₂×C₅	semidirect
172. #442	C₄×C₅	semidirect
173. #441	C₄×C₅	semidirect
174. #440	C₄×C₅	semidirect
175. #440	C₄×C₅	semidirect
410. C₅	#21139	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×#2943	2
C₅×#2923	2
C₅×#2875	2
C₅×#1929	2
C₅×#1922	2
C₅×#1876	2
C₅×#1866	2
C₅×#1778	2
C₄×C₅×#104	2
C₅×#1745	2
#21139	5

Subgroups — C5×#21139 #11943859

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21139 #11943859