Subgroups — C₅×#33777 #11956497

Order 1280.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#2249	C₂	1	2	yes	maximal, complemented
4	C₅×#2242	C₂	1	2	yes	maximal, complemented
5	C₅×#2211	C₂	1	2	yes	maximal, complemented
6	C₅×#2210	C₂	1	2	yes	maximal, complemented
7	C₅×#2188	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2187	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2185	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2184	C₂	1	1	yes	maximal, characteristic
11	C₅×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
13	C₂²×C₅×SD₁₆	—	2	1	no	—
14	C₂²×C₅×D₈	C₂²	1	1	yes	characteristic
15	C₅×#529	—	2	1	no	—
16	C₂×C₅×#124	—	2	1	no	—
17	C₂×C₅×Q₃₂	C₂²	1	2	yes	complemented
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₅×D₁₆	C₂²	1	2	yes	—
21	C₅×#499	C₂²	1	1	yes	characteristic, complemented
22	C₅×#495	—	2	1	no	—
23	C₅×#495	—	2	1	no	—
24	C₅×#495	C₂²	1	2	yes	—
25	C₅×#495	C₂²	1	2	yes	—
26	C₅×#495	C₂²	1	1	yes	characteristic, complemented
27	C₅×#488	—	2	1	no	—
28	C₅×#467	C₂²	1	1	yes	characteristic
29	C₅×#466	C₂²	1	1	yes	characteristic
30	C₅×#465	—	2	1	no	—
31	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	2	yes	complemented
36	C₅×#358	C₂²	1	2	yes	complemented
37	C₅×#358	C₂²	1	2	yes	complemented
38	C₅×#357	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	2	yes	—
40	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄×C₅×C₁₆	C₂²	1	2	yes	complemented
43	#33777	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂²×C₅×Q₈	—	2	1	no	—
45	C₂²×C₅×D₄	—	2	1	no	—
46	C₂×C₅×Q₁₆	—	2	1	no	—
47	C₂×C₅×Q₁₆	—	4	2	no	—
48	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
49	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
50	C₂×C₅×SD₁₆	—	2	1	no	—
51	C₂×C₅×SD₁₆	—	2	2	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	4	4	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	—	4	2	no	—
56	C₂×C₅×D₈	C₂³	1	2	yes	—
57	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
59	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
60	C₅×#126	—	4	1	no	—
61	C₅×#125	—	2	1	no	—
62	C₅×#124	—	2	1	no	—
63	C₅×#124	—	2	2	no	—
64	C₅×#124	—	2	2	no	—
65	C₅×#124	—	4	1	no	—
66	C₅×#124	—	4	1	no	—
67	C₅×#123	—	4	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×#121	—	2	1	no	—
70	C₄×C₅×Q₈	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	4	1	no	—
73	C₅×#117	—	4	1	no	—
74	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
75	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
76	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
77	C₅×Q₃₂	—	4	2	no	—
78	C₅×SD₃₂	—	4	2	no	—
79	C₅×SD₃₂	—	4	2	no	—
80	C₅×D₁₆	—	4	2	no	—
81	C₂×C₅×C₁₆	C₂³	1	2	yes	—
82	C₂×C₅×C₁₆	C₂³	1	2	yes	—
83	C₅×#107	C₂³	1	1	yes	characteristic
84	C₅×#107	C₂³	1	1	yes	characteristic
85	C₅×#106	—	2	1	no	—
86	C₅×#103	—	2	1	no	—
87	C₅×#103	—	2	1	no	—
88	C₅×#102	—	2	1	no	—
89	C₅×#102	—	2	1	no	—
90	C₄×C₅×C₈	D₄	1	1	yes	characteristic
91	C₄×C₅×C₈	D₄	1	1	yes	characteristic
92	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
94	#3168	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂×#495	C₂×C₅	1	1	yes	characteristic, complemented
96	#2249	C₂×C₅	1	2	yes	complemented
97	#2242	C₂×C₅	1	2	yes	complemented
98	#2211	C₂×C₅	1	2	yes	complemented
99	#2210	C₂×C₅	1	2	yes	complemented
100	#2188	C₂×C₅	1	1	yes	characteristic, complemented
101	#2187	C₂×C₅	1	1	yes	characteristic, complemented
102	#2185	C₂×C₅	1	1	yes	characteristic, complemented
103	#2184	C₂×C₅	1	1	yes	characteristic
104	#2162	C₂×C₅	1	1	yes	characteristic, complemented
105	C₂⁴×C₅	—	4	1	no	—
106	C₂×C₅×Q₈	—	2	1	no	—
107	C₂×C₅×Q₈	—	2	2	no	—
108	C₂×C₅×Q₈	—	4	2	no	—
109	C₂×C₅×Q₈	—	4	2	no	—
110	C₂×C₅×Q₈	—	4	1	no	—
111	C₂×C₅×D₄	—	2	1	no	—
112	C₂×C₅×D₄	—	2	2	no	—
113	C₂×C₅×D₄	—	4	2	no	—
114	C₂×C₅×D₄	—	4	2	no	—
115	C₂×C₅×D₄	—	4	1	no	—
116	C₂×C₅×D₄	—	4	1	no	—
117	C₂²×C₄×C₅	—	4	1	no	—
118	C₂²×C₄×C₅	—	4	1	no	—
119	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
122	C₅×Q₁₆	—	2	2	no	—
123	C₅×Q₁₆	—	2	2	no	—
124	C₅×Q₁₆	—	2	2	no	—
125	C₅×Q₁₆	—	4	2	no	—
126	C₅×SD₁₆	—	4	4	no	—
127	C₅×SD₁₆	—	4	2	no	—
128	C₅×SD₁₆	—	4	4	no	—
129	C₅×D₈	—	2	2	no	—
130	C₅×D₈	—	2	2	no	—
131	C₅×D₈	—	2	2	no	—
132	C₅×D₈	—	4	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	2	no	—
135	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
139	C₅×C₄⋊C₄	—	2	1	no	—
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	4	1	no	—
142	C₅×C₄⋊C₄	—	4	1	no	—
143	C₅×C₄⋊C₄	—	4	1	no	—
144	C₅×C₄⋊C₄	—	4	1	no	—
145	C₅×C₂²⋊C₄	—	4	1	no	—
146	C₅×C₂²⋊C₄	—	4	2	no	—
147	C₅×C₂²⋊C₄	—	4	2	no	—
148	C₅×C₂²⋊C₄	—	4	2	no	—
149	C₅×C₂²⋊C₄	—	4	2	no	—
150	C₅×C₂²⋊C₄	—	4	1	no	—
151	C₅×C₂²⋊C₄	—	4	1	no	—
152	C₅×C₂²⋊C₄	—	4	1	no	—
153	C₅×C₂²⋊C₄	—	4	1	no	—
154	C₄²×C₅	—	4	1	no	—
155	C₄²×C₅	D₈	1	1	yes	characteristic
156	C₄²×C₅	D₈	1	1	yes	characteristic
157	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₅×C₁₆	—	2	2	no	—
160	C₅×C₁₆	—	2	2	no	—
161	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
162	C₂²×SD₁₆	—	2	1	no	—
163	C₂²×D₈	C₂²×C₅	1	1	yes	characteristic
164	#529	—	2	1	no	—
165	C₂×#124	—	2	1	no	—
166	C₂×Q₃₂	C₂²×C₅	1	2	yes	complemented
167	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
168	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
169	C₂×D₁₆	C₂²×C₅	1	2	yes	—
170	#499	C₂²×C₅	1	1	yes	characteristic, complemented
171	#495	—	2	1	no	—
172	#495	—	2	1	no	—
173	#495	C₂²×C₅	1	2	yes	—
174	#495	C₂²×C₅	1	2	yes	—
175	#495	C₂²×C₅	1	1	yes	characteristic, complemented
176	#488	—	2	1	no	—
177	#467	C₂²×C₅	1	1	yes	characteristic
178	#466	C₂²×C₅	1	1	yes	characteristic
179	#465	—	2	1	no	—
180	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
181	C₄×SD₁₆	—	2	1	no	—
182	C₄×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
184	C₄⋊C₁₆	C₂²×C₅	1	2	yes	complemented
185	#358	C₂²×C₅	1	2	yes	complemented
186	#358	C₂²×C₅	1	2	yes	complemented
187	#357	C₂²×C₅	1	2	yes	—
188	#357	C₂²×C₅	1	2	yes	—
189	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
190	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
191	C₄×C₁₆	C₂²×C₅	1	2	yes	complemented
192	C₂³×C₅	—	4	1	no	—
193	C₂³×C₅	—	4	2	no	—
194	C₂³×C₅	—	8	2	no	—
195	C₂³×C₅	—	8	2	no	—
196	C₂³×C₅	—	8	2	no	—
197	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	4	1	no	—
200	C₅×Q₈	—	4	2	no	—
201	C₅×Q₈	—	4	1	no	—
202	C₅×Q₈	—	8	2	no	—
203	C₅×D₄	—	4	2	no	—
204	C₅×D₄	—	4	1	no	—
205	C₅×D₄	—	4	2	no	—
206	C₅×D₄	—	4	1	no	—
207	C₅×D₄	—	8	2	no	—
208	C₅×D₄	—	8	2	no	—
209	C₂×C₄×C₅	—	2	2	no	—
210	C₂×C₄×C₅	—	2	1	no	—
211	C₂×C₄×C₅	—	2	1	no	—
212	C₂×C₄×C₅	—	4	1	no	—
213	C₂×C₄×C₅	—	4	1	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	—	8	2	no	—
218	C₂×C₄×C₅	—	8	2	no	—
219	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
220	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
221	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
222	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
223	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
224	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	—	2	1	no	—
227	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
228	C₅×C₈	H(5,𝔽₂)	1	2	yes	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×D₄	—	2	1	no	—
231	C₂×Q₁₆	—	2	1	no	—
232	C₂×Q₁₆	—	4	2	no	—
233	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
234	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	2	no	—
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	1	no	—
238	C₂×SD₁₆	—	4	4	no	—
239	C₂×D₈	—	2	1	no	—
240	C₂×D₈	—	4	2	no	—
241	C₂×D₈	C₂³×C₅	1	2	yes	—
242	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
243	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
244	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
245	#126	—	4	1	no	—
246	#125	—	2	1	no	—
247	#124	—	2	2	no	—
248	#124	—	2	2	no	—
249	#124	—	2	1	no	—
250	#124	—	4	1	no	—
251	#124	—	4	1	no	—
252	#123	—	4	1	no	—
253	C₂²⋊Q₈	—	2	1	no	—
254	#121	—	2	1	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	4	1	no	—
258	#117	—	4	1	no	—
259	C₂×C₂²⋊C₄	—	4	1	no	—
260	C₂×C₂²⋊C₄	—	4	1	no	—
261	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
262	Q₃₂	—	4	2	no	—
263	SD₃₂	—	4	2	no	—
264	SD₃₂	—	4	2	no	—
265	D₁₆	—	4	2	no	—
266	C₂×C₁₆	C₂³×C₅	1	2	yes	—
267	C₂×C₁₆	C₂³×C₅	1	2	yes	—
268	#107	C₂³×C₅	1	1	yes	characteristic
269	#107	C₂³×C₅	1	1	yes	characteristic
270	#106	—	2	1	no	—
271	#103	—	2	1	no	—
272	#103	—	2	1	no	—
273	#102	—	2	1	no	—
274	#102	—	2	1	no	—
275	C₄×C₈	C₅×D₄	1	1	yes	characteristic
276	C₄×C₈	C₅×D₄	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
278	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
279	C₂²×C₅	—	2	1	no	—
280	C₂²×C₅	—	2	1	no	—
281	C₂²×C₅	—	8	1	no	—
282	C₂²×C₅	—	8	2	no	—
283	C₂²×C₅	—	8	1	no	—
284	C₂²×C₅	—	8	2	no	—
285	C₂²×C₅	—	8	2	no	—
286	C₂²×C₅	—	8	1	no	—
287	C₂²×C₅	—	16	4	no	—
288	C₂²×C₅	#508	1	2	yes	—
289	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	2	1	no	—
294	C₄×C₅	—	2	1	no	—
295	C₄×C₅	—	8	1	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	—	8	2	no	—
298	C₄×C₅	—	8	1	no	—
299	C₄×C₅	#535	1	1	yes	characteristic
300	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₂⁴	—	4	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×D₄	—	2	1	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂²×C₄	—	4	1	no	—
314	C₂²×C₄	—	4	1	no	—
315	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
316	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
318	Q₁₆	—	2	2	no	—
319	Q₁₆	—	2	2	no	—
320	Q₁₆	—	2	2	no	—
321	Q₁₆	—	4	2	no	—
322	SD₁₆	—	4	4	no	—
323	SD₁₆	—	4	4	no	—
324	SD₁₆	—	4	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	2	2	no	—
327	D₈	—	2	2	no	—
328	D₈	—	4	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
332	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
333	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
334	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
335	C₄⋊C₄	—	2	1	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	—	4	1	no	—
340	C₄⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₂²⋊C₄	—	4	2	no	—
344	C₂²⋊C₄	—	4	2	no	—
345	C₂²⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₄²	—	4	1	no	—
351	C₄²	C₅×D₈	1	1	yes	characteristic
352	C₄²	C₅×D₈	1	1	yes	characteristic
353	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
354	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
355	C₁₆	—	2	2	no	—
356	C₁₆	—	2	2	no	—
357	C₂×C₅	—	2	2	no	—
358	C₂×C₅	—	16	1	no	—
359	C₂×C₅	—	16	2	no	—
360	C₂×C₅	#3205	1	1	yes	characteristic
361	C₂×C₅	C₂×#508	1	1	yes	characteristic
362	C₂×C₅	#3414	1	1	yes	characteristic
363	C₂³	—	4	1	no	—
364	C₂³	—	4	2	no	—
365	C₂³	—	8	2	no	—
366	C₂³	—	8	2	no	—
367	C₂³	—	8	2	no	—
368	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	4	1	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	1	no	—
373	Q₈	—	8	2	no	—
374	D₄	—	4	2	no	—
375	D₄	—	4	1	no	—
376	D₄	—	4	2	no	—
377	D₄	—	4	1	no	—
378	D₄	—	8	2	no	—
379	D₄	—	8	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	1	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	8	2	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
391	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
392	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
393	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
394	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
395	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
399	C₈	C₅×H(5,𝔽₂)	1	2	yes	—
400	C₅	#33777	1	1	yes	characteristic, direct product factor, Sylow
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	2	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	—	16	4	no	—
410	C₂²	C₅×#508	1	2	yes	—
411	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	1	no	—
416	C₄	—	2	1	no	—
417	C₄	—	8	1	no	—
418	C₄	—	8	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	1	no	—
421	C₄	C₅×#535	1	1	yes	characteristic
422	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
423	C₂	—	2	2	no	—
424	C₂	—	16	2	no	—
425	C₂	—	16	1	no	—
426	C₂	C₅×#3205	1	1	yes	characteristic
427	C₂	C₂×C₅×#508	1	1	yes	characteristic
428	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#2184	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂×C₄²×C₅ ◁ C₂×C₄×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3168	C₂	semidirect
2. C₂×C₅×#495	C₂	semidirect
3. C₅×#2249	C₂	semidirect
4. C₅×#2242	C₂	semidirect
5. C₅×#2211	C₂	semidirect
6. C₅×#2210	C₂	semidirect
7. C₅×#2188	C₂	semidirect
8. C₅×#2187	C₂	semidirect
9. C₅×#2185	C₂	semidirect
11. C₅×#2162	C₂	semidirect
17. C₂×C₅×Q₃₂	C₂²	semidirect
19. C₂×C₅×SD₃₂	C₂²	semidirect
21. C₅×#499	C₂²	semidirect
26. C₅×#495	C₂²	semidirect
31. C₄×C₅×Q₁₆	C₂²	semidirect
33. C₄×C₅×D₈	C₂²	semidirect
35. C₅×C₄⋊C₁₆	C₂²	semidirect
36. C₅×#358	C₂²	semidirect
37. C₅×#358	C₂²	semidirect
42. C₄×C₅×C₁₆	C₂²	semidirect
43. #33777	C₅	direct (N × H)
94. #3168	C₂×C₅	semidirect
95. C₂×#495	C₂×C₅	semidirect
96. #2249	C₂×C₅	semidirect
97. #2242	C₂×C₅	semidirect
98. #2211	C₂×C₅	semidirect
99. #2210	C₂×C₅	semidirect
100. #2188	C₂×C₅	semidirect
101. #2187	C₂×C₅	semidirect
102. #2185	C₂×C₅	semidirect
104. #2162	C₂×C₅	semidirect
166. C₂×Q₃₂	C₂²×C₅	semidirect
168. C₂×SD₃₂	C₂²×C₅	semidirect
170. #499	C₂²×C₅	semidirect
175. #495	C₂²×C₅	semidirect
180. C₄×Q₁₆	C₂²×C₅	semidirect
182. C₄×D₈	C₂²×C₅	semidirect
184. C₄⋊C₁₆	C₂²×C₅	semidirect
185. #358	C₂²×C₅	semidirect
186. #358	C₂²×C₅	semidirect
191. C₄×C₁₆	C₂²×C₅	semidirect
400. C₅	#33777	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×#3168	2
C₂×C₅×#495	2
C₅×#2249	2
C₅×#2242	2
C₅×#2211	2
C₅×#2210	2
C₅×#2188	2
C₅×#2187	2
C₅×#2185	2
C₅×#2184	2
C₅×#2162	2
#33777	5

Subgroups — C5×#33777 #11956497

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33777 #11956497