Subgroups — C₅×#22268 #11944988

Order 1280.

1054 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#492	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×#1957	C₂	1	1	yes	maximal, characteristic
5	C₅×#1956	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#1880	C₂	1	4	yes	maximal, complemented
7	C₅×#1877	C₂	1	4	yes	maximal, complemented
8	C₅×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#1744	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₅×SD₁₆	C₂²	1	4	yes	—
11	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₅×#127	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₄×C₅×D₄	—	2	1	no	—
15	C₂×C₄×C₅×D₄	—	2	1	no	—
16	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
17	C₅×#492	C₄	1	8	yes	complemented
18	C₂×C₅×#103	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	C₂²	1	2	yes	—
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	—	2	1	no	—
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	—	2	1	no	—
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	#22268	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
37	C₂²×C₅×Q₈	C₂³	1	2	yes	—
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	C₂×C₅×SD₁₆	—	4	4	no	—
43	C₂×C₅×SD₁₆	—	4	4	no	—
44	C₂×C₅×SD₁₆	C₂×C₄	1	16	yes	complemented
45	C₂²×C₅×C₈	C₂³	1	2	yes	—
46	C₂²×C₅×C₈	C₂³	1	2	yes	—
47	C₅×C₄⋊Q₈	—	2	2	no	—
48	C₅×C₄⋊Q₈	C₂×C₄	1	4	yes	complemented
49	C₅×#127	—	2	2	no	—
50	C₅×#127	C₂×C₄	1	4	yes	—
51	C₄×C₅×Q₈	—	4	4	no	—
52	C₄×C₅×D₄	—	4	4	no	—
53	C₄×C₅×D₄	—	4	4	no	—
54	C₄×C₅×D₄	—	4	4	no	—
55	C₂×C₅×C₄⋊C₄	—	2	1	no	—
56	C₂×C₅×C₄⋊C₄	—	2	1	no	—
57	C₂×C₅×C₄⋊C₄	—	2	1	no	—
58	C₂×C₅×C₄⋊C₄	—	2	1	no	—
59	C₂×C₅×C₄⋊C₄	—	2	1	no	—
60	C₂×C₅×C₄⋊C₄	—	2	1	no	—
61	C₂×C₅×C₄⋊C₄	—	2	2	no	—
62	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
63	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
64	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
65	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
66	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
67	C₂×C₄²×C₅	—	2	2	no	—
68	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
69	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₅×#103	—	4	4	no	—
76	C₅×#102	—	4	4	no	—
77	C₄×C₅×C₈	—	2	2	no	—
78	C₄×C₅×C₈	C₂×C₄	1	4	yes	complemented
79	C₅×#95	—	2	2	no	—
80	C₅×#95	—	2	2	no	—
81	C₂×#492	C₂×C₅	1	1	yes	characteristic
82	C₄×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
83	C₄×#127	C₂×C₅	1	1	yes	characteristic
84	#1957	C₂×C₅	1	1	yes	characteristic
85	#1956	C₂×C₅	1	1	yes	characteristic, complemented
86	#1880	C₂×C₅	1	4	yes	complemented
87	#1877	C₂×C₅	1	4	yes	complemented
88	#1834	C₂×C₅	1	1	yes	characteristic, complemented
89	#1744	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂⁴×C₅	—	2	2	no	—
91	C₂×C₅×Q₈	—	2	2	no	—
92	C₂×C₅×Q₈	—	2	4	no	—
93	C₂×C₅×Q₈	—	2	4	no	—
94	C₂×C₅×Q₈	C₂²×C₄	1	4	yes	—
95	C₂×C₅×D₄	—	2	4	no	—
96	C₂×C₅×D₄	—	2	4	no	—
97	C₂×C₅×D₄	—	2	2	no	—
98	C₂×C₅×D₄	—	2	4	no	—
99	C₂×C₅×D₄	—	2	4	no	—
100	C₂×C₅×D₄	—	4	2	no	—
101	C₂×C₅×D₄	—	4	2	no	—
102	C₂×C₅×D₄	—	4	2	no	—
103	C₂×C₅×D₄	—	4	2	no	—
104	C₂×C₅×D₄	C₂²×C₄	1	4	yes	—
105	C₂²×C₄×C₅	—	2	2	no	—
106	C₂²×C₄×C₅	—	2	2	no	—
107	C₂²×C₄×C₅	—	2	2	no	—
108	C₂²×C₄×C₅	—	4	4	no	—
109	C₂²×C₄×C₅	—	4	4	no	—
110	C₂²×C₄×C₅	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₅×SD₁₆	—	4	16	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	2	no	—
121	C₂×C₅×C₈	—	2	2	no	—
122	C₂×C₅×C₈	—	2	2	no	—
123	C₂×C₅×C₈	—	2	2	no	—
124	C₂×C₅×C₈	C₂²×C₄	1	4	yes	—
125	C₅×C₄⋊C₄	—	2	4	no	—
126	C₅×C₄⋊C₄	—	2	4	no	—
127	C₅×C₄⋊C₄	—	2	4	no	—
128	C₅×C₄⋊C₄	—	2	4	no	—
129	C₅×C₄⋊C₄	—	4	4	no	—
130	C₅×C₄⋊C₄	—	4	2	no	—
131	C₅×C₄⋊C₄	—	4	2	no	—
132	C₅×C₄⋊C₄	—	4	2	no	—
133	C₅×C₄⋊C₄	—	4	2	no	—
134	C₅×C₂²⋊C₄	—	4	4	no	—
135	C₅×C₂²⋊C₄	—	4	4	no	—
136	C₅×C₂²⋊C₄	—	4	4	no	—
137	C₄²×C₅	—	2	2	no	—
138	C₄²×C₅	—	2	2	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₄²×C₅	—	2	2	no	—
141	C₄²×C₅	—	2	2	no	—
142	C₄²×C₅	—	4	4	no	—
143	C₄²×C₅	SD₁₆	1	4	yes	complemented
144	C₄²×C₅	C₂²×C₄	1	2	yes	—
145	C₄²×C₅	#41	1	2	yes	—
146	C₂²×SD₁₆	C₂²×C₅	1	4	yes	—
147	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
148	C₂×#127	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
150	C₂×C₄×D₄	—	2	1	no	—
151	C₂×C₄×D₄	—	2	1	no	—
152	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
153	#492	C₄×C₅	1	8	yes	complemented
154	C₂×#103	C₂²×C₅	1	4	yes	—
155	C₂×#102	C₂²×C₅	1	4	yes	—
156	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
158	#391	C₂²×C₅	1	2	yes	—
159	#390	—	2	1	no	—
160	#390	—	2	1	no	—
161	#390	C₂²×C₅	1	2	yes	—
162	#389	—	2	1	no	—
163	#389	—	2	1	no	—
164	#384	C₂²×C₅	1	1	yes	characteristic
165	#384	C₂²×C₅	1	1	yes	characteristic
166	C₄×C₄⋊C₄	—	2	1	no	—
167	C₄×C₄⋊C₄	—	2	1	no	—
168	C₄³	C₂²×C₅	1	1	yes	characteristic
169	#340	C₂²×C₅	1	4	yes	—
170	#336	C₂²×C₅	1	2	yes	—
171	#336	C₂²×C₅	1	2	yes	—
172	C₂³×C₅	—	2	4	no	—
173	C₂³×C₅	—	4	2	no	—
174	C₂³×C₅	—	4	2	no	—
175	C₂³×C₅	—	4	2	no	—
176	C₂³×C₅	—	4	2	no	—
177	C₂³×C₅	—	4	2	no	—
178	C₂³×C₅	—	4	2	no	—
179	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
180	C₅×Q₈	—	2	8	no	—
181	C₅×Q₈	—	4	4	no	—
182	C₅×D₄	—	2	8	no	—
183	C₅×D₄	—	4	4	no	—
184	C₅×D₄	—	4	8	no	—
185	C₅×D₄	—	4	8	no	—
186	C₂×C₄×C₅	—	2	1	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	4	no	—
191	C₂×C₄×C₅	—	2	1	no	—
192	C₂×C₄×C₅	—	2	1	no	—
193	C₂×C₄×C₅	—	2	1	no	—
194	C₂×C₄×C₅	—	2	1	no	—
195	C₂×C₄×C₅	—	2	1	no	—
196	C₂×C₄×C₅	—	2	1	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	—	4	2	no	—
202	C₂×C₄×C₅	—	4	2	no	—
203	C₂×C₄×C₅	—	4	2	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	8	8	no	—
206	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
207	C₂×C₄×C₅	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
209	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₅	C₂×SD₁₆	1	2	yes	—
211	C₂×C₄×C₅	#135	1	2	yes	—
212	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₅	#137	1	2	yes	—
214	C₂×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
215	C₂×C₄×C₅	C₂×#41	1	1	yes	characteristic
216	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
217	C₂×C₄×C₅	H(5,𝔽₂)	1	2	yes	—
218	C₅×C₈	—	2	4	no	—
219	C₅×C₈	—	4	2	no	—
220	C₂²×Q₈	C₂³×C₅	1	2	yes	—
221	C₂²×D₄	—	2	1	no	—
222	C₂²×D₄	—	2	1	no	—
223	C₂²×D₄	C₂³×C₅	1	2	yes	—
224	C₂³×C₄	—	2	2	no	—
225	C₂×SD₁₆	—	4	4	no	—
226	C₂×SD₁₆	—	4	4	no	—
227	C₂×SD₁₆	C₂×C₄×C₅	1	16	yes	complemented
228	C₂²×C₈	C₂³×C₅	1	2	yes	—
229	C₂²×C₈	C₂³×C₅	1	2	yes	—
230	C₄⋊Q₈	—	2	2	no	—
231	C₄⋊Q₈	C₂×C₄×C₅	1	4	yes	complemented
232	#127	—	2	2	no	—
233	#127	C₂×C₄×C₅	1	4	yes	—
234	C₄×Q₈	—	4	4	no	—
235	C₄×D₄	—	4	4	no	—
236	C₄×D₄	—	4	4	no	—
237	C₄×D₄	—	4	4	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
246	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	2	no	—
248	C₂×C₂²⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
252	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
253	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
254	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
258	#103	—	4	4	no	—
259	#102	—	4	4	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	C₂×C₄×C₅	1	4	yes	complemented
262	#95	—	2	2	no	—
263	#95	—	2	2	no	—
264	C₂²×C₅	—	4	4	no	—
265	C₂²×C₅	—	4	4	no	—
266	C₂²×C₅	—	4	4	no	—
267	C₂²×C₅	—	8	2	no	—
268	C₂²×C₅	—	8	2	no	—
269	C₂²×C₅	—	8	2	no	—
270	C₂²×C₅	—	8	2	no	—
271	C₂²×C₅	C₂×C₄×D₄	1	1	yes	characteristic
272	C₂²×C₅	#535	1	1	yes	characteristic
273	C₂²×C₅	#535	1	1	yes	characteristic
274	C₂²×C₅	C₂²×SD₁₆	1	1	yes	characteristic
275	C₂²×C₅	C₂×#135	1	1	yes	characteristic
276	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
277	C₂²×C₅	C₂×#137	1	1	yes	characteristic
278	C₄×C₅	—	2	2	no	—
279	C₄×C₅	—	2	2	no	—
280	C₄×C₅	—	4	4	no	—
281	C₄×C₅	—	4	1	no	—
282	C₄×C₅	—	4	1	no	—
283	C₄×C₅	—	8	2	no	—
284	C₄×C₅	—	8	2	no	—
285	C₄×C₅	C₄×SD₁₆	1	4	yes	—
286	C₄×C₅	#440	1	4	yes	—
287	C₄×C₅	#518	1	2	yes	—
288	C₄×C₅	#540	1	2	yes	—
289	C₂⁴	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	2	4	no	—
293	C₂×Q₈	C₂²×C₄×C₅	1	4	yes	—
294	C₂×D₄	—	2	4	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	4	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	C₂²×C₄×C₅	1	4	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	4	4	no	—
309	C₂²×C₄	—	4	4	no	—
310	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
313	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
316	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
317	SD₁₆	—	4	16	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	C₂²×C₄×C₅	1	4	yes	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	2	4	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	4	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	2	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₂²⋊C₄	—	4	4	no	—
334	C₂²⋊C₄	—	4	4	no	—
335	C₂²⋊C₄	—	4	4	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	4	4	no	—
342	C₄²	C₅×SD₁₆	1	4	yes	complemented
343	C₄²	C₂²×C₄×C₅	1	2	yes	—
344	C₄²	C₅×#41	1	2	yes	—
345	C₂×C₅	—	8	4	no	—
346	C₂×C₅	#2328	1	1	yes	characteristic
347	C₂×C₅	C₂×C₄×SD₁₆	1	1	yes	characteristic
348	C₂×C₅	C₂×#440	1	1	yes	characteristic
349	C₂×C₅	#3206	1	1	yes	characteristic
350	C₂×C₅	#3207	1	1	yes	characteristic
351	C₂×C₅	#3208	1	1	yes	characteristic
352	C₂×C₅	#3210	1	1	yes	characteristic
353	C₂³	—	2	4	no	—
354	C₂³	—	4	2	no	—
355	C₂³	—	4	2	no	—
356	C₂³	—	4	2	no	—
357	C₂³	—	4	2	no	—
358	C₂³	—	4	2	no	—
359	C₂³	—	4	2	no	—
360	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
361	Q₈	—	2	8	no	—
362	Q₈	—	4	4	no	—
363	D₄	—	2	8	no	—
364	D₄	—	4	8	no	—
365	D₄	—	4	8	no	—
366	D₄	—	4	4	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	4	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	8	no	—
387	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
388	C₂×C₄	C₄×C₅×D₄	1	2	yes	—
389	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
390	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
391	C₂×C₄	C₂×C₅×SD₁₆	1	2	yes	—
392	C₂×C₄	C₅×#135	1	2	yes	—
393	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
394	C₂×C₄	C₅×#137	1	2	yes	—
395	C₂×C₄	C₂³×C₄×C₅	1	1	yes	characteristic
396	C₂×C₄	C₂×C₅×#41	1	1	yes	characteristic
397	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
398	C₂×C₄	C₅×H(5,𝔽₂)	1	2	yes	—
399	C₈	—	2	4	no	—
400	C₈	—	4	2	no	—
401	C₅	#22268	1	1	yes	characteristic, direct product factor, Sylow
402	C₂²	—	4	4	no	—
403	C₂²	—	4	4	no	—
404	C₂²	—	4	4	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	2	no	—
409	C₂²	C₂×C₄×C₅×D₄	1	1	yes	characteristic
410	C₂²	C₅×#535	1	1	yes	characteristic
411	C₂²	C₅×#535	1	1	yes	characteristic
412	C₂²	C₂²×C₅×SD₁₆	1	1	yes	characteristic
413	C₂²	C₂×C₅×#135	1	1	yes	characteristic
414	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
415	C₂²	C₂×C₅×#137	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	4	4	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₄×C₅×SD₁₆	1	4	yes	—
424	C₄	C₅×#440	1	4	yes	—
425	C₄	C₅×#518	1	2	yes	—
426	C₄	C₅×#540	1	2	yes	—
427	C₂	—	8	4	no	—
428	C₂	C₅×#2328	1	1	yes	characteristic
429	C₂	C₂×C₄×C₅×SD₁₆	1	1	yes	characteristic
430	C₂	C₂×C₅×#440	1	1	yes	characteristic
431	C₂	C₅×#3206	1	1	yes	characteristic
432	C₂	C₅×#3207	1	1	yes	characteristic
433	C₂	C₅×#3208	1	1	yes	characteristic
434	C₂	C₅×#3210	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
5. C₅×#1956	C₂	semidirect
6. C₅×#1880	C₂	semidirect
7. C₅×#1877	C₂	semidirect
8. C₅×#1834	C₂	semidirect
9. C₅×#1744	C₂	semidirect
17. C₅×#492	C₄	semidirect
36. #22268	C₅	direct (N × H)
44. C₂×C₅×SD₁₆	C₂×C₄	semidirect
48. C₅×C₄⋊Q₈	C₂×C₄	semidirect
78. C₄×C₅×C₈	C₂×C₄	semidirect
82. C₄×C₄⋊Q₈	C₂×C₅	semidirect
85. #1956	C₂×C₅	semidirect
86. #1880	C₂×C₅	semidirect
87. #1877	C₂×C₅	semidirect
88. #1834	C₂×C₅	semidirect
89. #1744	C₂×C₅	semidirect
143. C₄²×C₅	SD₁₆	semidirect
153. #492	C₄×C₅	semidirect
227. C₂×SD₁₆	C₂×C₄×C₅	semidirect
231. C₄⋊Q₈	C₂×C₄×C₅	semidirect
261. C₄×C₈	C₂×C₄×C₅	semidirect
342. C₄²	C₅×SD₁₆	semidirect
401. C₅	#22268	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×#492	2
C₄×C₅×C₄⋊Q₈	2
C₄×C₅×#127	2
C₅×#1957	2
C₅×#1956	2
C₅×#1880	2
C₅×#1877	2
C₅×#1834	2
C₅×#1744	2
#22268	5

Subgroups — C5×#22268 #11944988

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#22268 #11944988