Subgroups — C₅×#22219 #11944939

Order 1280.

990 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#486	C₂	1	1	yes	maximal, characteristic
2	C₄×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#127	C₂	1	1	yes	maximal, characteristic
4	C₅×#1990	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#1957	C₂	1	1	yes	maximal, characteristic
6	C₅×#1926	C₂	1	4	yes	maximal, complemented
7	C₅×#1864	C₂	1	4	yes	maximal, complemented
8	C₅×#1844	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
11	C₂×C₅×#127	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Q₈	—	2	1	no	—
13	C₂×C₄×C₅×D₄	—	2	1	no	—
14	C₂×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
16	C₅×#486	C₄	1	8	yes	complemented
17	C₂×C₅×#106	C₂²	1	4	yes	—
18	C₂×C₅×#102	C₂²	1	4	yes	—
19	C₂×C₅×#102	C₂²	1	4	yes	—
20	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
22	C₅×#391	—	2	1	no	—
23	C₅×#390	—	2	1	no	—
24	C₅×#390	—	2	1	no	—
25	C₅×#390	C₂²	1	2	yes	—
26	C₅×#389	—	2	1	no	—
27	C₅×#389	C₂²	1	2	yes	—
28	C₅×#384	C₂²	1	1	yes	characteristic
29	C₅×#384	C₂²	1	1	yes	characteristic
30	C₄×C₅×C₄⋊C₄	—	2	1	no	—
31	C₄×C₅×C₄⋊C₄	C₂²	1	2	yes	—
32	C₄³×C₅	C₂²	1	1	yes	characteristic
33	C₅×#340	C₂²	1	4	yes	—
34	C₅×#336	C₂²	1	2	yes	—
35	C₅×#336	C₂²	1	2	yes	—
36	#22219	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₅×Q₈	—	2	1	no	—
38	C₂²×C₅×D₄	—	2	1	no	—
39	C₂²×C₅×D₄	—	2	1	no	—
40	C₂²×C₅×D₄	C₂³	1	2	yes	—
41	C₂³×C₄×C₅	—	2	2	no	—
42	C₂²×C₅×C₈	C₂³	1	2	yes	—
43	C₂²×C₅×C₈	C₂³	1	2	yes	—
44	C₅×C₄⋊Q₈	—	2	2	no	—
45	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
46	C₅×#127	—	2	2	no	—
47	C₅×#127	C₂×C₄	1	4	yes	—
48	C₄×C₅×Q₈	—	4	4	no	—
49	C₄×C₅×D₄	—	4	4	no	—
50	C₄×C₅×D₄	—	4	4	no	—
51	C₄×C₅×D₄	—	4	4	no	—
52	C₂×C₅×C₄⋊C₄	—	2	1	no	—
53	C₂×C₅×C₄⋊C₄	—	2	1	no	—
54	C₂×C₅×C₄⋊C₄	—	2	1	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	2	no	—
58	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
59	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
60	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
62	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
63	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
64	C₂×C₄²×C₅	—	2	2	no	—
65	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₅×#106	—	4	4	no	—
73	C₅×#102	—	4	4	no	—
74	C₅×#102	C₂×C₄	1	16	yes	complemented
75	C₄×C₅×C₈	—	2	2	no	—
76	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
77	C₅×#95	—	2	2	no	—
78	C₅×#95	—	2	2	no	—
79	C₂×#486	C₂×C₅	1	1	yes	characteristic
80	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
81	C₄×#127	C₂×C₅	1	1	yes	characteristic
82	#1990	C₂×C₅	1	1	yes	characteristic, complemented
83	#1957	C₂×C₅	1	1	yes	characteristic
84	#1926	C₂×C₅	1	4	yes	complemented
85	#1864	C₂×C₅	1	4	yes	complemented
86	#1844	C₂×C₅	1	1	yes	characteristic, complemented
87	#1744	C₂×C₅	1	1	yes	characteristic, complemented
88	C₂⁴×C₅	—	2	2	no	—
89	C₂×C₅×Q₈	—	2	4	no	—
90	C₂×C₅×Q₈	—	4	2	no	—
91	C₂×C₅×Q₈	—	4	2	no	—
92	C₂×C₅×D₄	—	2	4	no	—
93	C₂×C₅×D₄	—	2	4	no	—
94	C₂×C₅×D₄	—	2	2	no	—
95	C₂×C₅×D₄	—	2	4	no	—
96	C₂×C₅×D₄	—	2	4	no	—
97	C₂×C₅×D₄	—	4	2	no	—
98	C₂×C₅×D₄	—	4	2	no	—
99	C₂×C₅×D₄	—	4	2	no	—
100	C₂×C₅×D₄	—	4	2	no	—
101	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
102	C₂²×C₄×C₅	—	2	2	no	—
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	—	4	4	no	—
106	C₂²×C₄×C₅	—	4	4	no	—
107	C₂²×C₄×C₅	—	4	4	no	—
108	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
115	C₂×C₅×C₈	—	2	2	no	—
116	C₂×C₅×C₈	—	2	2	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
121	C₅×C₄⋊C₄	—	2	4	no	—
122	C₅×C₄⋊C₄	—	2	2	no	—
123	C₅×C₄⋊C₄	—	2	4	no	—
124	C₅×C₄⋊C₄	—	2	4	no	—
125	C₅×C₄⋊C₄	—	4	4	no	—
126	C₅×C₄⋊C₄	—	4	2	no	—
127	C₅×C₄⋊C₄	—	4	2	no	—
128	C₅×C₄⋊C₄	—	4	2	no	—
129	C₅×C₄⋊C₄	—	4	2	no	—
130	C₅×C₄⋊C₄	C₂²×C₄	1	4	yes	—
131	C₅×C₂²⋊C₄	—	4	4	no	—
132	C₅×C₂²⋊C₄	—	4	4	no	—
133	C₅×C₂²⋊C₄	—	4	4	no	—
134	C₄²×C₅	—	2	2	no	—
135	C₄²×C₅	—	2	2	no	—
136	C₄²×C₅	—	2	2	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	4	4	no	—
140	C₄²×C₅	SD₁₆	1	4	yes	—
141	C₄²×C₅	C₂²×C₄	1	2	yes	—
142	C₄²×C₅	#41	1	2	yes	—
143	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
144	C₂×#127	C₂²×C₅	1	1	yes	characteristic
145	C₂×C₄×Q₈	—	2	1	no	—
146	C₂×C₄×D₄	—	2	1	no	—
147	C₂×C₄×D₄	—	2	1	no	—
148	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
149	#486	C₄×C₅	1	8	yes	complemented
150	C₂×#106	C₂²×C₅	1	4	yes	—
151	C₂×#102	C₂²×C₅	1	4	yes	—
152	C₂×#102	C₂²×C₅	1	4	yes	—
153	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
155	#391	—	2	1	no	—
156	#390	—	2	1	no	—
157	#390	—	2	1	no	—
158	#390	C₂²×C₅	1	2	yes	—
159	#389	—	2	1	no	—
160	#389	C₂²×C₅	1	2	yes	—
161	#384	C₂²×C₅	1	1	yes	characteristic
162	#384	C₂²×C₅	1	1	yes	characteristic
163	C₄×C₄⋊C₄	—	2	1	no	—
164	C₄×C₄⋊C₄	C₂²×C₅	1	2	yes	—
165	C₄³	C₂²×C₅	1	1	yes	characteristic
166	#340	C₂²×C₅	1	4	yes	—
167	#336	C₂²×C₅	1	2	yes	—
168	#336	C₂²×C₅	1	2	yes	—
169	C₂³×C₅	—	2	4	no	—
170	C₂³×C₅	—	4	2	no	—
171	C₂³×C₅	—	4	2	no	—
172	C₂³×C₅	—	4	2	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	—	4	2	no	—
176	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
177	C₅×Q₈	—	4	8	no	—
178	C₅×D₄	—	2	8	no	—
179	C₅×D₄	—	4	4	no	—
180	C₅×D₄	—	4	8	no	—
181	C₅×D₄	—	4	8	no	—
182	C₂×C₄×C₅	—	2	1	no	—
183	C₂×C₄×C₅	—	2	1	no	—
184	C₂×C₄×C₅	—	2	1	no	—
185	C₂×C₄×C₅	—	2	1	no	—
186	C₂×C₄×C₅	—	2	4	no	—
187	C₂×C₄×C₅	—	2	1	no	—
188	C₂×C₄×C₅	—	2	1	no	—
189	C₂×C₄×C₅	—	2	1	no	—
190	C₂×C₄×C₅	—	2	1	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	4	2	no	—
194	C₂×C₄×C₅	—	4	2	no	—
195	C₂×C₄×C₅	—	4	2	no	—
196	C₂×C₄×C₅	—	4	2	no	—
197	C₂×C₄×C₅	—	4	2	no	—
198	C₂×C₄×C₅	—	4	2	no	—
199	C₂×C₄×C₅	—	4	2	no	—
200	C₂×C₄×C₅	—	4	2	no	—
201	C₂×C₄×C₅	—	8	8	no	—
202	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
206	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
207	C₂×C₄×C₅	#135	1	2	yes	—
208	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
209	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
210	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
211	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
213	C₂×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
214	C₅×C₈	—	2	4	no	—
215	C₅×C₈	—	4	2	no	—
216	C₂²×Q₈	—	2	1	no	—
217	C₂²×D₄	—	2	1	no	—
218	C₂²×D₄	—	2	1	no	—
219	C₂²×D₄	C₂³×C₅	1	2	yes	—
220	C₂³×C₄	—	2	2	no	—
221	C₂²×C₈	C₂³×C₅	1	2	yes	—
222	C₂²×C₈	C₂³×C₅	1	2	yes	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
225	#127	—	2	2	no	—
226	#127	C₂×C₄×C₅	1	4	yes	—
227	C₄×Q₈	—	4	4	no	—
228	C₄×D₄	—	4	4	no	—
229	C₄×D₄	—	4	4	no	—
230	C₄×D₄	—	4	4	no	—
231	C₂×C₄⋊C₄	—	2	1	no	—
232	C₂×C₄⋊C₄	—	2	1	no	—
233	C₂×C₄⋊C₄	—	2	1	no	—
234	C₂×C₄⋊C₄	—	2	1	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
239	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₄²	—	2	2	no	—
244	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
245	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
246	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
247	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
248	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
251	#106	—	4	4	no	—
252	#102	—	4	4	no	—
253	#102	C₂×C₄×C₅	1	16	yes	complemented
254	C₄×C₈	—	2	2	no	—
255	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	C₂²×C₅	—	4	4	no	—
259	C₂²×C₅	—	4	4	no	—
260	C₂²×C₅	—	4	4	no	—
261	C₂²×C₅	—	8	2	no	—
262	C₂²×C₅	—	8	2	no	—
263	C₂²×C₅	—	8	2	no	—
264	C₂²×C₅	—	8	2	no	—
265	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂²×C₅	#535	1	1	yes	characteristic
267	C₂²×C₅	#536	1	1	yes	characteristic
268	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
269	C₂²×C₅	C₂×#135	1	1	yes	characteristic
270	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
271	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
272	C₄×C₅	—	2	2	no	—
273	C₄×C₅	—	2	2	no	—
274	C₄×C₅	—	4	4	no	—
275	C₄×C₅	—	4	1	no	—
276	C₄×C₅	—	4	1	no	—
277	C₄×C₅	—	8	2	no	—
278	C₄×C₅	—	8	2	no	—
279	C₄×C₅	C₄×SD₁₆	1	4	yes	—
280	C₄×C₅	#442	1	4	yes	—
281	C₄×C₅	#520	1	2	yes	—
282	C₄×C₅	#542	1	2	yes	—
283	C₂⁴	—	2	2	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	4	2	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	4	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	—	4	2	no	—
295	C₂×D₄	—	4	2	no	—
296	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	4	no	—
320	C₄⋊C₄	—	4	4	no	—
321	C₄⋊C₄	—	4	2	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	C₂²×C₄×C₅	1	4	yes	—
326	C₂²⋊C₄	—	4	4	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	4	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	4	4	no	—
335	C₄²	C₅×SD₁₆	1	4	yes	—
336	C₄²	C₂²×C₄×C₅	1	2	yes	—
337	C₄²	C₅×#41	1	2	yes	—
338	C₂×C₅	—	8	4	no	—
339	C₂×C₅	#2326	1	1	yes	characteristic
340	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
341	C₂×C₅	C₂×#442	1	1	yes	characteristic
342	C₂×C₅	#3207	1	1	yes	characteristic
343	C₂×C₅	#3208	1	1	yes	characteristic
344	C₂×C₅	#3227	1	1	yes	characteristic
345	C₂×C₅	#3228	1	1	yes	characteristic
346	C₂³	—	2	4	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	—	4	2	no	—
352	C₂³	—	4	2	no	—
353	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
354	Q₈	—	4	8	no	—
355	D₄	—	2	8	no	—
356	D₄	—	4	8	no	—
357	D₄	—	4	8	no	—
358	D₄	—	4	4	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	8	8	no	—
379	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
380	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
381	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
382	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
383	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
384	C₂×C₄	C₅×#135	1	2	yes	—
385	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
386	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
387	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
388	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
389	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
390	C₂×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
391	C₈	—	2	4	no	—
392	C₈	—	4	2	no	—
393	C₅	#22219	1	1	yes	characteristic, direct product factor, Sylow
394	C₂²	—	4	4	no	—
395	C₂²	—	4	4	no	—
396	C₂²	—	4	4	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	8	2	no	—
401	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
402	C₂²	C₅×#535	1	1	yes	characteristic
403	C₂²	C₅×#536	1	1	yes	characteristic
404	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
405	C₂²	C₂×C₅×#135	1	1	yes	characteristic
406	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
407	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
408	C₄	—	2	2	no	—
409	C₄	—	2	2	no	—
410	C₄	—	4	4	no	—
411	C₄	—	4	1	no	—
412	C₄	—	4	1	no	—
413	C₄	—	8	2	no	—
414	C₄	—	8	2	no	—
415	C₄	C₄×C₅×SD₁₆	1	4	yes	—
416	C₄	C₅×#442	1	4	yes	—
417	C₄	C₅×#520	1	2	yes	—
418	C₄	C₅×#542	1	2	yes	—
419	C₂	—	8	4	no	—
420	C₂	C₅×#2326	1	1	yes	characteristic
421	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
422	C₂	C₂×C₅×#442	1	1	yes	characteristic
423	C₂	C₅×#3207	1	1	yes	characteristic
424	C₂	C₅×#3208	1	1	yes	characteristic
425	C₂	C₅×#3227	1	1	yes	characteristic
426	C₂	C₅×#3228	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₅	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂⁴×C₅
prime radical	C₂×C₅×#127	C₂²
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. C₄×C₅×C₄⋊Q₈	C₂	semidirect
4. C₅×#1990	C₂	semidirect
6. C₅×#1926	C₂	semidirect
7. C₅×#1864	C₂	semidirect
8. C₅×#1844	C₂	semidirect
9. C₅×#1744	C₂	semidirect
16. C₅×#486	C₄	semidirect
36. #22219	C₅	direct (N × H)
45. C₅×C₄⋊Q₈	C₂×C₄	semidirect
74. C₅×#102	C₂×C₄	semidirect
76. C₄×C₅×C₈	C₂×C₄	semidirect
80. C₄×C₄⋊Q₈	C₂×C₅	semidirect
82. #1990	C₂×C₅	semidirect
84. #1926	C₂×C₅	semidirect
85. #1864	C₂×C₅	semidirect
86. #1844	C₂×C₅	semidirect
87. #1744	C₂×C₅	semidirect
149. #486	C₄×C₅	semidirect
224. C₄⋊Q₈	C₂×C₄×C₅	semidirect
253. #102	C₂×C₄×C₅	semidirect
255. C₄×C₈	C₂×C₄×C₅	semidirect
393. C₅	#22219	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×#486	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#127	2
C₅×#1990	2
C₅×#1957	2
C₅×#1926	2
C₅×#1864	2
C₅×#1844	2
C₅×#1744	2
#22219	5

Subgroups — C5×#22219 #11944939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22219 #11944939