Subgroups — C₅×#21702 #11944422

Order 1280.

1094 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	C₂×C₅×#497	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#441	C₂	1	2	yes	maximal, complemented
3	C₂×C₅×#440	C₂	1	2	yes	maximal
4	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#124	C₂	1	1	yes	maximal, characteristic
6	C₅×#1969	C₂	1	2	yes	maximal, complemented
7	C₅×#1968	C₂	1	2	yes	maximal
8	C₅×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1959	C₂	1	1	yes	maximal, characteristic
10	C₅×#1847	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	2	yes	—
13	C₂²×C₅×SD₁₆	C₂²	1	2	yes	—
14	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₅×#124	C₂²	1	1	yes	characteristic
16	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
18	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₅×#497	C₄	1	8	yes	complemented
20	C₅×#441	—	2	8	no	—
21	C₅×#440	—	2	8	no	—
22	C₂×C₅×#107	C₂²	1	2	yes	—
23	C₂×C₅×#106	C₂²	1	2	yes	—
24	C₂×C₅×#103	C₂²	1	2	yes	—
25	C₂×C₅×#103	C₂²	1	2	yes	—
26	C₂×C₅×#103	C₂²	1	2	yes	—
27	C₂×C₅×#102	C₂²	1	2	yes	—
28	C₂×C₅×#97	C₂²	1	1	yes	characteristic
29	C₂×C₅×#97	C₂²	1	1	yes	characteristic
30	C₂×C₅×#97	C₂²	1	2	yes	—
31	C₂×C₄×C₅×C₈	C₂²	1	2	yes	—
32	C₅×#391	C₂²	1	1	yes	characteristic
33	C₅×#391	C₂²	1	2	yes	—
34	C₅×#390	C₂²	1	1	yes	characteristic
35	C₅×#389	—	2	2	no	—
36	C₅×#388	—	2	2	no	—
37	C₅×#384	C₂²	1	1	yes	characteristic
38	C₅×#382	C₂²	1	1	yes	characteristic
39	C₄×C₅×C₄⋊C₄	—	2	2	no	—
40	C₄×C₅×C₂²⋊C₄	—	2	2	no	—
41	C₄³×C₅	C₂²	1	1	yes	characteristic
42	#21702	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
43	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
44	C₂²×C₅×Q₈	C₂³	1	2	yes	—
45	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₅	—	2	1	no	—
47	C₂×C₅×Q₁₆	—	2	4	no	—
48	C₂×C₅×Q₁₆	—	2	4	no	—
49	C₂×C₅×Q₁₆	C₂×C₄	1	8	yes	complemented
50	C₂×C₅×SD₁₆	—	2	4	no	—
51	C₂×C₅×SD₁₆	—	2	4	no	—
52	C₂×C₅×SD₁₆	C₂×C₄	1	8	yes	—
53	C₂²×C₅×C₈	C₂³	1	2	yes	—
54	C₂²×C₅×C₈	C₂³	1	2	yes	—
55	C₅×C₄⋊Q₈	—	2	2	no	—
56	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
57	C₅×#124	—	2	2	no	—
58	C₅×#124	C₂×C₄	1	4	yes	—
59	C₄×C₅×Q₈	—	2	4	no	—
60	C₄×C₅×Q₈	—	2	4	no	—
61	C₄×C₅×Q₈	—	2	4	no	—
62	C₄×C₅×D₄	—	2	4	no	—
63	C₂×C₅×C₄⋊C₄	—	2	2	no	—
64	C₂×C₅×C₄⋊C₄	—	2	2	no	—
65	C₂×C₅×C₄⋊C₄	—	2	1	no	—
66	C₂×C₅×C₄⋊C₄	—	2	2	no	—
67	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
69	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
73	C₂×C₄²×C₅	—	2	1	no	—
74	C₂×C₄²×C₅	—	2	2	no	—
75	C₂×C₄²×C₅	D₄	1	2	yes	—
76	C₂×C₄²×C₅	D₄	1	2	yes	—
77	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₅×#107	—	2	4	no	—
81	C₅×#106	—	2	4	no	—
82	C₅×#103	—	2	4	no	—
83	C₅×#103	—	2	4	no	—
84	C₅×#103	—	2	4	no	—
85	C₅×#102	—	2	4	no	—
86	C₅×#97	—	2	2	no	—
87	C₅×#97	C₂×C₄	1	4	yes	complemented
88	C₅×#97	D₄	1	8	yes	—
89	C₄×C₅×C₈	—	2	4	no	—
90	C₅×#95	—	2	2	no	—
91	C₅×#95	—	2	2	no	—
92	C₅×#95	—	2	4	no	—
93	C₂×#497	C₂×C₅	1	1	yes	characteristic
94	C₂×#441	C₂×C₅	1	2	yes	complemented
95	C₂×#440	C₂×C₅	1	2	yes	—
96	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
97	C₄×#124	C₂×C₅	1	1	yes	characteristic
98	#1969	C₂×C₅	1	2	yes	complemented
99	#1968	C₂×C₅	1	2	yes	—
100	#1960	C₂×C₅	1	1	yes	characteristic, complemented
101	#1959	C₂×C₅	1	1	yes	characteristic
102	#1847	C₂×C₅	1	1	yes	characteristic, complemented
103	C₄×#97	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂⁴×C₅	—	2	1	no	—
105	C₂×C₅×Q₈	—	2	1	no	—
106	C₂×C₅×Q₈	—	2	2	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×Q₈	—	2	2	no	—
110	C₂×C₅×Q₈	—	2	2	no	—
111	C₂×C₅×Q₈	—	2	2	no	—
112	C₂×C₅×Q₈	—	2	2	no	—
113	C₂×C₅×Q₈	C₂²×C₄	1	2	yes	—
114	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
115	C₂×C₅×D₄	—	2	2	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	2	1	no	—
118	C₂×C₅×D₄	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₅	—	2	1	no	—
120	C₂²×C₄×C₅	—	2	2	no	—
121	C₂²×C₄×C₅	—	2	1	no	—
122	C₂²×C₄×C₅	—	2	2	no	—
123	C₂²×C₄×C₅	—	2	1	no	—
124	C₂²×C₄×C₅	—	4	4	no	—
125	C₂²×C₄×C₅	—	4	2	no	—
126	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₅×Q₁₆	—	2	16	no	—
132	C₅×SD₁₆	—	2	16	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
136	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
137	C₂×C₅×C₈	C₂×D₄	1	4	yes	—
138	C₂×C₅×C₈	#41	1	4	yes	—
139	C₅×C₄⋊C₄	—	2	8	no	—
140	C₅×C₄⋊C₄	—	2	2	no	—
141	C₅×C₄⋊C₄	—	2	2	no	—
142	C₅×C₄⋊C₄	—	2	2	no	—
143	C₅×C₄⋊C₄	—	2	2	no	—
144	C₅×C₄⋊C₄	—	4	4	no	—
145	C₅×C₄⋊C₄	—	4	2	no	—
146	C₅×C₄⋊C₄	—	4	4	no	—
147	C₅×C₂²⋊C₄	—	2	8	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₅×C₂²⋊C₄	—	4	4	no	—
150	C₄²×C₅	—	2	4	no	—
151	C₄²×C₅	—	2	2	no	—
152	C₄²×C₅	—	4	2	no	—
153	C₄²×C₅	—	4	4	no	—
154	C₄²×C₅	—	4	2	no	—
155	C₄²×C₅	C₂²×C₄	1	2	yes	—
156	C₄²×C₅	C₂×D₄	1	4	yes	—
157	C₄²×C₅	#41	1	2	yes	—
158	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
159	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
160	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×#124	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
163	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
165	#497	C₄×C₅	1	8	yes	complemented
166	#441	—	2	8	no	—
167	#440	—	2	8	no	—
168	C₂×#107	C₂²×C₅	1	2	yes	—
169	C₂×#106	C₂²×C₅	1	2	yes	—
170	C₂×#103	C₂²×C₅	1	2	yes	—
171	C₂×#103	C₂²×C₅	1	2	yes	—
172	C₂×#103	C₂²×C₅	1	2	yes	—
173	C₂×#102	C₂²×C₅	1	2	yes	—
174	C₂×#97	C₂²×C₅	1	1	yes	characteristic
175	C₂×#97	C₂²×C₅	1	1	yes	characteristic
176	C₂×#97	C₂²×C₅	1	2	yes	—
177	C₂×C₄×C₈	C₂²×C₅	1	2	yes	—
178	#391	C₂²×C₅	1	2	yes	—
179	#391	C₂²×C₅	1	1	yes	characteristic
180	#390	C₂²×C₅	1	1	yes	characteristic
181	#389	—	2	2	no	—
182	#388	—	2	2	no	—
183	#384	C₂²×C₅	1	1	yes	characteristic
184	#382	C₂²×C₅	1	1	yes	characteristic
185	C₄×C₄⋊C₄	—	2	2	no	—
186	C₄×C₂²⋊C₄	—	2	2	no	—
187	C₄³	C₂²×C₅	1	1	yes	characteristic
188	C₂³×C₅	—	2	2	no	—
189	C₂³×C₅	—	4	1	no	—
190	C₂³×C₅	—	4	1	no	—
191	C₂³×C₅	—	4	2	no	—
192	C₂³×C₅	—	4	2	no	—
193	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₅×Q₈	—	2	4	no	—
195	C₅×Q₈	—	2	4	no	—
196	C₅×Q₈	—	2	4	no	—
197	C₅×Q₈	—	4	2	no	—
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	4	2	no	—
200	C₅×D₄	—	2	4	no	—
201	C₅×D₄	—	4	2	no	—
202	C₂×C₄×C₅	—	2	2	no	—
203	C₂×C₄×C₅	—	2	2	no	—
204	C₂×C₄×C₅	—	2	2	no	—
205	C₂×C₄×C₅	—	2	2	no	—
206	C₂×C₄×C₅	—	2	2	no	—
207	C₂×C₄×C₅	—	2	2	no	—
208	C₂×C₄×C₅	—	2	2	no	—
209	C₂×C₄×C₅	—	2	4	no	—
210	C₂×C₄×C₅	—	4	1	no	—
211	C₂×C₄×C₅	—	4	2	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	2	no	—
214	C₂×C₄×C₅	—	4	1	no	—
215	C₂×C₄×C₅	—	4	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	2	no	—
218	C₂×C₄×C₅	—	4	4	no	—
219	C₂×C₄×C₅	—	4	2	no	—
220	C₂×C₄×C₅	—	8	4	no	—
221	C₂×C₄×C₅	C₄×D₄	1	4	yes	—
222	C₂×C₄×C₅	#127	1	2	yes	—
223	C₂×C₄×C₅	#127	1	2	yes	—
224	C₂×C₄×C₅	#137	1	4	yes	—
225	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₅	C₂×#41	1	2	yes	—
228	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
229	C₅×C₈	—	2	4	no	—
230	C₅×C₈	C₄×D₄	1	8	yes	—
231	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
232	C₂²×Q₈	C₂³×C₅	1	2	yes	—
233	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
234	C₂³×C₄	—	2	1	no	—
235	C₂×Q₁₆	—	2	4	no	—
236	C₂×Q₁₆	—	2	4	no	—
237	C₂×Q₁₆	C₂×C₄×C₅	1	8	yes	complemented
238	C₂×SD₁₆	—	2	4	no	—
239	C₂×SD₁₆	—	2	4	no	—
240	C₂×SD₁₆	C₂×C₄×C₅	1	8	yes	—
241	C₂²×C₈	C₂³×C₅	1	2	yes	—
242	C₂²×C₈	C₂³×C₅	1	2	yes	—
243	C₄⋊Q₈	—	2	2	no	—
244	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
245	#124	—	2	2	no	—
246	#124	C₂×C₄×C₅	1	4	yes	—
247	C₄×Q₈	—	2	4	no	—
248	C₄×Q₈	—	2	4	no	—
249	C₄×Q₈	—	2	4	no	—
250	C₄×D₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	1	no	—
253	C₂×C₄⋊C₄	—	2	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	C₅×D₄	1	2	yes	—
264	C₂×C₄²	C₅×D₄	1	2	yes	—
265	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
268	#107	—	2	4	no	—
269	#106	—	2	4	no	—
270	#103	—	2	4	no	—
271	#103	—	2	4	no	—
272	#103	—	2	4	no	—
273	#102	—	2	4	no	—
274	#97	—	2	2	no	—
275	#97	C₂×C₄×C₅	1	4	yes	complemented
276	#97	C₅×D₄	1	8	yes	—
277	C₄×C₈	—	2	4	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	4	no	—
281	C₂²×C₅	—	4	2	no	—
282	C₂²×C₅	—	4	4	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	8	1	no	—
285	C₂²×C₅	—	8	2	no	—
286	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
287	C₂²×C₅	C₂×#127	1	1	yes	characteristic
288	C₂²×C₅	#532	1	1	yes	characteristic
289	C₂²×C₅	C₂×#137	1	2	yes	—
290	C₂²×C₅	#575	1	2	yes	—
291	C₄×C₅	—	2	2	no	—
292	C₄×C₅	—	2	2	no	—
293	C₄×C₅	—	2	4	no	—
294	C₄×C₅	—	2	4	no	—
295	C₄×C₅	—	4	2	no	—
296	C₄×C₅	—	4	4	no	—
297	C₄×C₅	—	8	1	no	—
298	C₄×C₅	—	8	2	no	—
299	C₄×C₅	—	8	1	no	—
300	C₄×C₅	C₂×C₄×D₄	1	2	yes	—
301	C₄×C₅	#532	1	2	yes	—
302	C₂⁴	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	2	no	—
306	C₂×Q₈	—	2	2	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	2	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	C₂²×C₄×C₅	1	2	yes	—
312	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
313	C₂×D₄	—	2	2	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	1	no	—
316	C₂×D₄	C₂²×C₄×C₅	1	2	yes	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
325	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
328	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
329	Q₁₆	—	2	16	no	—
330	SD₁₆	—	2	16	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
334	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
335	C₂×C₈	C₂×C₅×D₄	1	4	yes	—
336	C₂×C₈	C₅×#41	1	4	yes	—
337	C₄⋊C₄	—	2	8	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	4	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₂²⋊C₄	—	2	8	no	—
346	C₂²⋊C₄	—	4	2	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	4	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	—	4	2	no	—
353	C₄²	C₂²×C₄×C₅	1	2	yes	—
354	C₄²	C₂×C₅×D₄	1	4	yes	—
355	C₄²	C₅×#41	1	2	yes	—
356	C₂×C₅	—	8	2	no	—
357	C₂×C₅	C₄×#127	1	1	yes	characteristic
358	C₂×C₅	C₄×#137	1	2	yes	—
359	C₂×C₅	#3152	1	1	yes	characteristic
360	C₂×C₅	#3153	1	1	yes	characteristic
361	C₂×C₅	#3181	1	2	yes	—
362	C₂³	—	2	2	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
368	Q₈	—	2	4	no	—
369	Q₈	—	2	4	no	—
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	4	no	—
395	C₂×C₄	C₄×C₅×D₄	1	4	yes	—
396	C₂×C₄	C₅×#127	1	2	yes	—
397	C₂×C₄	C₅×#127	1	2	yes	—
398	C₂×C₄	C₅×#137	1	4	yes	—
399	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
401	C₂×C₄	C₂×C₅×#41	1	2	yes	—
402	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
403	C₈	—	2	4	no	—
404	C₈	C₄×C₅×D₄	1	8	yes	—
405	C₅	#21702	1	1	yes	characteristic, direct product factor, Sylow
406	C₂²	—	4	2	no	—
407	C₂²	—	4	4	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	8	1	no	—
410	C₂²	—	8	2	no	—
411	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
412	C₂²	C₂×C₅×#127	1	1	yes	characteristic
413	C₂²	C₅×#532	1	1	yes	characteristic
414	C₂²	C₂×C₅×#137	1	2	yes	—
415	C₂²	C₅×#575	1	2	yes	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	2	4	no	—
419	C₄	—	2	4	no	—
420	C₄	—	4	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	8	1	no	—
423	C₄	—	8	1	no	—
424	C₄	—	8	2	no	—
425	C₄	C₂×C₄×C₅×D₄	1	2	yes	—
426	C₄	C₅×#532	1	2	yes	—
427	C₂	—	8	2	no	—
428	C₂	C₄×C₅×#127	1	1	yes	characteristic
429	C₂	C₄×C₅×#137	1	2	yes	—
430	C₂	C₅×#3152	1	1	yes	characteristic
431	C₂	C₅×#3153	1	1	yes	characteristic
432	C₂	C₅×#3181	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂²×C₅×D₄	C₂³
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅ ◁ C₄³×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#441	C₂	semidirect
4. C₄×C₅×C₄⋊Q₈	C₂	semidirect
6. C₅×#1969	C₂	semidirect
8. C₅×#1960	C₂	semidirect
10. C₅×#1847	C₂	semidirect
11. C₄×C₅×#97	C₂	semidirect
19. C₅×#497	C₄	semidirect
42. #21702	C₅	direct (N × H)
49. C₂×C₅×Q₁₆	C₂×C₄	semidirect
56. C₅×C₄⋊Q₈	C₂×C₄	semidirect
87. C₅×#97	C₂×C₄	semidirect
94. C₂×#441	C₂×C₅	semidirect
96. C₄×C₄⋊Q₈	C₂×C₅	semidirect
98. #1969	C₂×C₅	semidirect
100. #1960	C₂×C₅	semidirect
102. #1847	C₂×C₅	semidirect
103. C₄×#97	C₂×C₅	semidirect
165. #497	C₄×C₅	semidirect
237. C₂×Q₁₆	C₂×C₄×C₅	semidirect
244. C₄⋊Q₈	C₂×C₄×C₅	semidirect
275. #97	C₂×C₄×C₅	semidirect
405. C₅	#21702	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₅×#497	2
C₂×C₅×#441	2
C₂×C₅×#440	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#124	2
C₅×#1969	2
C₅×#1968	2
C₅×#1960	2
C₅×#1959	2
C₅×#1847	2
C₄×C₅×#97	2
#21702	5

Subgroups — C5×#21702 #11944422

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#21702 #11944422