Subgroups — C₅×#33579 #11956299

Order 1280.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#508	C₂	1	2	yes	maximal, complemented
2	C₅×#3147	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#2211	C₂	1	2	yes	maximal, complemented
5	C₅×#2210	C₂	1	2	yes	maximal, complemented
6	C₅×#2209	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×C₄⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2138	C₂	1	2	yes	maximal, complemented
12	C₂×C₅×#135	—	2	1	no	—
13	C₂×C₅×#135	C₂²	1	2	yes	—
14	C₂×C₅×#135	C₂²	1	1	yes	characteristic
15	C₅×#532	—	2	1	no	—
16	C₄×C₅×#41	—	2	1	no	—
17	C₅×#508	—	2	8	no	—
18	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
20	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
21	C₂×C₅×D₁₆	C₂²	1	2	yes	—
22	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
23	C₅×#495	—	2	1	no	—
24	C₅×#495	C₂²	1	2	yes	—
25	C₅×#494	C₂²	1	1	yes	characteristic
26	C₅×#493	C₂²	1	1	yes	characteristic
27	C₅×#492	—	2	1	no	—
28	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
29	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
30	C₄×C₅×SD₁₆	—	2	1	no	—
31	C₄×C₅×SD₁₆	—	2	1	no	—
32	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₅×#427	C₂²	1	1	yes	characteristic
35	C₅×#416	—	2	1	no	—
36	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
37	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
38	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
39	C₅×C₄⋊C₁₆	C₂²	1	2	yes	—
40	C₅×#358	C₂²	1	2	yes	—
41	C₅×#358	C₂²	1	2	yes	—
42	C₅×#357	C₂²	1	2	yes	—
43	C₅×#357	C₂²	1	2	yes	—
44	#33579	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
45	C₂×C₅×#41	—	2	1	no	—
46	C₂×C₅×#41	—	2	2	no	—
47	C₅×#135	—	2	4	no	—
48	C₅×#135	—	2	2	no	—
49	C₅×#135	—	2	4	no	—
50	C₅×#135	—	4	4	no	—
51	C₅×#135	D₄	1	4	yes	complemented
52	C₂×C₅×Q₁₆	—	2	1	no	—
53	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
54	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
55	C₂×C₅×SD₁₆	—	2	1	no	—
56	C₂×C₅×SD₁₆	—	2	2	no	—
57	C₂×C₅×SD₁₆	—	2	2	no	—
58	C₂×C₅×D₈	—	2	1	no	—
59	C₂×C₅×D₈	C₂³	1	2	yes	—
60	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
63	C₅×C₄⋊Q₈	—	2	1	no	—
64	C₅×#127	—	2	1	no	—
65	C₅×#124	—	2	2	no	—
66	C₅×#121	—	4	1	no	—
67	C₅×#121	—	4	1	no	—
68	C₄×C₅×Q₈	—	2	1	no	—
69	C₄×C₅×Q₈	—	2	1	no	—
70	C₄×C₅×D₄	—	2	1	no	—
71	C₄×C₅×D₄	—	2	1	no	—
72	C₄×C₅×D₄	—	4	1	no	—
73	C₄×C₅×D₄	—	4	1	no	—
74	C₄×C₅×D₄	—	4	1	no	—
75	C₄×C₅×D₄	—	4	1	no	—
76	C₅×#117	—	2	1	no	—
77	C₅×#117	—	4	1	no	—
78	C₂×C₄²×C₅	—	4	1	no	—
79	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
80	C₅×Q₃₂	—	2	4	no	—
81	C₅×SD₃₂	—	2	4	no	—
82	C₅×SD₃₂	—	2	4	no	—
83	C₅×D₁₆	—	2	4	no	—
84	C₂×C₅×C₁₆	—	2	4	no	—
85	C₂×C₅×C₁₆	C₂³	1	2	yes	—
86	C₂×C₅×C₁₆	C₂³	1	2	yes	—
87	C₅×#107	C₂³	1	1	yes	characteristic
88	C₅×#107	C₂³	1	1	yes	characteristic
89	C₅×#106	—	2	1	no	—
90	C₅×#103	—	2	1	no	—
91	C₅×#103	—	2	1	no	—
92	C₅×#102	—	2	1	no	—
93	C₅×#102	—	2	1	no	—
94	C₄×C₅×C₈	D₄	1	1	yes	characteristic
95	C₄×C₅×C₈	D₄	1	1	yes	characteristic
96	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂×#508	C₂×C₅	1	2	yes	complemented
99	#3147	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄×#135	C₂×C₅	1	1	yes	characteristic, complemented
101	#2211	C₂×C₅	1	2	yes	complemented
102	#2210	C₂×C₅	1	2	yes	complemented
103	#2209	C₂×C₅	1	1	yes	characteristic, complemented
104	#2208	C₂×C₅	1	1	yes	characteristic, complemented
105	#2207	C₂×C₅	1	1	yes	characteristic, complemented
106	#2206	C₂×C₅	1	1	yes	characteristic, complemented
107	C₂×C₄⋊C₁₆	C₂×C₅	1	1	yes	characteristic, complemented
108	#2138	C₂×C₅	1	2	yes	complemented
109	C₅×#41	—	2	4	no	—
110	C₅×#41	—	4	2	no	—
111	C₅×#41	—	4	4	no	—
112	C₅×#41	—	4	4	no	—
113	C₂×C₅×Q₈	—	2	1	no	—
114	C₂×C₅×Q₈	—	2	2	no	—
115	C₂×C₅×D₄	—	2	1	no	—
116	C₂×C₅×D₄	—	2	2	no	—
117	C₂×C₅×D₄	—	4	1	no	—
118	C₂×C₅×D₄	—	4	2	no	—
119	C₂×C₅×D₄	—	4	1	no	—
120	C₂×C₅×D₄	—	4	1	no	—
121	C₂²×C₄×C₅	—	4	1	no	—
122	C₂²×C₄×C₅	—	4	1	no	—
123	C₂²×C₄×C₅	—	4	1	no	—
124	C₂²×C₄×C₅	—	4	2	no	—
125	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
126	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
127	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
128	C₅×Q₁₆	—	2	2	no	—
129	C₅×Q₁₆	—	2	1	no	—
130	C₅×Q₁₆	—	2	2	no	—
131	C₅×Q₁₆	—	4	2	no	—
132	C₅×Q₁₆	C₂×D₄	1	2	yes	—
133	C₅×SD₁₆	—	2	4	no	—
134	C₅×SD₁₆	—	4	4	no	—
135	C₅×SD₁₆	—	4	4	no	—
136	C₅×D₈	—	2	2	no	—
137	C₅×D₈	—	2	1	no	—
138	C₅×D₈	—	2	2	no	—
139	C₅×D₈	—	4	2	no	—
140	C₅×D₈	C₂×D₄	1	2	yes	—
141	C₂×C₅×C₈	—	2	2	no	—
142	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
144	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
145	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
146	C₂×C₅×C₈	#41	1	2	yes	—
147	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
148	C₅×C₄⋊C₄	—	2	1	no	—
149	C₅×C₄⋊C₄	—	2	1	no	—
150	C₅×C₄⋊C₄	—	4	1	no	—
151	C₅×C₄⋊C₄	—	4	1	no	—
152	C₅×C₄⋊C₄	—	4	1	no	—
153	C₅×C₄⋊C₄	—	4	1	no	—
154	C₅×C₂²⋊C₄	—	4	1	no	—
155	C₅×C₂²⋊C₄	—	4	1	no	—
156	C₅×C₂²⋊C₄	—	4	1	no	—
157	C₅×C₂²⋊C₄	—	4	2	no	—
158	C₅×C₂²⋊C₄	—	4	2	no	—
159	C₄²×C₅	—	4	1	no	—
160	C₄²×C₅	—	4	1	no	—
161	C₄²×C₅	—	4	1	no	—
162	C₄²×C₅	D₈	1	1	yes	characteristic
163	C₄²×C₅	D₈	1	1	yes	characteristic
164	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
165	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
166	C₅×C₁₆	—	2	2	no	—
167	C₅×C₁₆	—	2	2	no	—
168	C₂×#135	—	2	1	no	—
169	C₂×#135	C₂²×C₅	1	2	yes	—
170	C₂×#135	C₂²×C₅	1	1	yes	characteristic
171	#532	—	2	1	no	—
172	C₄×#41	—	2	1	no	—
173	#508	—	2	8	no	—
174	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
175	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
176	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
177	C₂×D₁₆	C₂²×C₅	1	2	yes	—
178	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
179	#495	—	2	1	no	—
180	#495	C₂²×C₅	1	2	yes	—
181	#494	C₂²×C₅	1	1	yes	characteristic
182	#493	C₂²×C₅	1	1	yes	characteristic
183	#492	—	2	1	no	—
184	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
185	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₄×SD₁₆	—	2	1	no	—
187	C₄×SD₁₆	—	2	1	no	—
188	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
189	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
190	#427	C₂²×C₅	1	1	yes	characteristic
191	#416	—	2	1	no	—
192	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
193	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
194	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
195	C₄⋊C₁₆	C₂²×C₅	1	2	yes	—
196	#358	C₂²×C₅	1	2	yes	—
197	#358	C₂²×C₅	1	2	yes	—
198	#357	C₂²×C₅	1	2	yes	—
199	#357	C₂²×C₅	1	2	yes	—
200	C₂³×C₅	—	4	1	no	—
201	C₂³×C₅	—	4	2	no	—
202	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
203	C₅×Q₈	—	2	2	no	—
204	C₅×Q₈	—	4	1	no	—
205	C₅×Q₈	—	4	2	no	—
206	C₅×Q₈	—	4	2	no	—
207	C₅×D₄	—	2	2	no	—
208	C₅×D₄	—	4	4	no	—
209	C₅×D₄	—	4	2	no	—
210	C₅×D₄	—	4	1	no	—
211	C₅×D₄	—	4	2	no	—
212	C₅×D₄	—	8	2	no	—
213	C₅×D₄	—	8	4	no	—
214	C₅×D₄	—	8	2	no	—
215	C₂×C₄×C₅	—	2	2	no	—
216	C₂×C₄×C₅	—	4	1	no	—
217	C₂×C₄×C₅	—	4	1	no	—
218	C₂×C₄×C₅	—	4	4	no	—
219	C₂×C₄×C₅	—	4	1	no	—
220	C₂×C₄×C₅	—	4	1	no	—
221	C₂×C₄×C₅	—	4	2	no	—
222	C₂×C₄×C₅	—	8	2	no	—
223	C₂×C₄×C₅	—	8	4	no	—
224	C₂×C₄×C₅	—	8	2	no	—
225	C₂×C₄×C₅	#121	1	2	yes	—
226	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
227	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
228	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
229	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
230	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
231	C₂×C₄×C₅	AGL(1,ℤ/8)	1	2	yes	—
232	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₅×C₈	—	2	1	no	—
234	C₅×C₈	—	2	1	no	—
235	C₅×C₈	#121	1	2	yes	—
236	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
237	C₅×C₈	C₂×#41	1	1	yes	characteristic
238	C₂×#41	—	2	1	no	—
239	C₂×#41	—	2	2	no	—
240	#135	—	2	4	no	—
241	#135	—	2	2	no	—
242	#135	—	2	4	no	—
243	#135	—	4	4	no	—
244	#135	C₅×D₄	1	4	yes	complemented
245	C₂×Q₁₆	—	2	1	no	—
246	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
247	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
248	C₂×SD₁₆	—	2	1	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×SD₁₆	—	2	2	no	—
251	C₂×D₈	—	2	1	no	—
252	C₂×D₈	C₂³×C₅	1	2	yes	—
253	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
254	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
256	C₄⋊Q₈	—	2	1	no	—
257	#127	—	2	1	no	—
258	#124	—	2	2	no	—
259	#121	—	4	1	no	—
260	#121	—	4	1	no	—
261	C₄×Q₈	—	2	1	no	—
262	C₄×Q₈	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	4	1	no	—
266	C₄×D₄	—	4	1	no	—
267	C₄×D₄	—	4	1	no	—
268	C₄×D₄	—	4	1	no	—
269	#117	—	2	1	no	—
270	#117	—	4	1	no	—
271	C₂×C₄²	—	4	1	no	—
272	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
273	Q₃₂	—	2	4	no	—
274	SD₃₂	—	2	4	no	—
275	SD₃₂	—	2	4	no	—
276	D₁₆	—	2	4	no	—
277	C₂×C₁₆	—	2	4	no	—
278	C₂×C₁₆	C₂³×C₅	1	2	yes	—
279	C₂×C₁₆	C₂³×C₅	1	2	yes	—
280	#107	C₂³×C₅	1	1	yes	characteristic
281	#107	C₂³×C₅	1	1	yes	characteristic
282	#106	—	2	1	no	—
283	#103	—	2	1	no	—
284	#103	—	2	1	no	—
285	#102	—	2	1	no	—
286	#102	—	2	1	no	—
287	C₄×C₈	C₅×D₄	1	1	yes	characteristic
288	C₄×C₈	C₅×D₄	1	1	yes	characteristic
289	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
290	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
291	C₂²×C₅	—	2	1	no	—
292	C₂²×C₅	—	2	1	no	—
293	C₂²×C₅	—	4	2	no	—
294	C₂²×C₅	—	8	1	no	—
295	C₂²×C₅	—	8	1	no	—
296	C₂²×C₅	—	8	2	no	—
297	C₂²×C₅	—	8	2	no	—
298	C₂²×C₅	—	8	2	no	—
299	C₂²×C₅	#459	1	2	yes	—
300	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
301	C₄×C₅	—	2	1	no	—
302	C₄×C₅	—	2	1	no	—
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	4	2	no	—
305	C₄×C₅	—	8	1	no	—
306	C₄×C₅	—	8	1	no	—
307	C₄×C₅	—	8	2	no	—
308	C₄×C₅	#459	1	2	yes	—
309	C₄×C₅	#508	1	2	yes	complemented
310	C₄×C₅	C₂×#121	1	1	yes	characteristic
311	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	#41	—	2	4	no	—
313	#41	—	4	2	no	—
314	#41	—	4	4	no	—
315	#41	—	4	4	no	—
316	C₂×Q₈	—	2	1	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×D₄	—	2	1	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	1	no	—
321	C₂×D₄	—	4	2	no	—
322	C₂×D₄	—	4	1	no	—
323	C₂×D₄	—	4	1	no	—
324	C₂²×C₄	—	4	1	no	—
325	C₂²×C₄	—	4	1	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
329	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
330	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
331	Q₁₆	—	2	2	no	—
332	Q₁₆	—	2	1	no	—
333	Q₁₆	—	2	2	no	—
334	Q₁₆	—	4	2	no	—
335	Q₁₆	C₂×C₅×D₄	1	2	yes	—
336	SD₁₆	—	2	4	no	—
337	SD₁₆	—	4	4	no	—
338	SD₁₆	—	4	4	no	—
339	D₈	—	2	2	no	—
340	D₈	—	2	1	no	—
341	D₈	—	2	2	no	—
342	D₈	—	4	2	no	—
343	D₈	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
347	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
348	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
349	C₂×C₈	C₅×#41	1	2	yes	—
350	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
351	C₄⋊C₄	—	2	1	no	—
352	C₄⋊C₄	—	2	1	no	—
353	C₄⋊C₄	—	4	1	no	—
354	C₄⋊C₄	—	4	1	no	—
355	C₄⋊C₄	—	4	1	no	—
356	C₄⋊C₄	—	4	1	no	—
357	C₂²⋊C₄	—	4	1	no	—
358	C₂²⋊C₄	—	4	1	no	—
359	C₂²⋊C₄	—	4	1	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₄²	—	4	1	no	—
363	C₄²	—	4	1	no	—
364	C₄²	—	4	1	no	—
365	C₄²	C₅×D₈	1	1	yes	characteristic
366	C₄²	C₅×D₈	1	1	yes	characteristic
367	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
368	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
369	C₁₆	—	2	2	no	—
370	C₁₆	—	2	2	no	—
371	C₂×C₅	—	2	2	no	—
372	C₂×C₅	—	8	2	no	—
373	C₂×C₅	—	16	2	no	—
374	C₂×C₅	C₂×#459	1	1	yes	characteristic
375	C₂×C₅	C₂×#508	1	1	yes	characteristic
376	C₂×C₅	#3414	1	1	yes	characteristic
377	C₂³	—	4	1	no	—
378	C₂³	—	4	2	no	—
379	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	4	2	no	—
384	D₄	—	2	2	no	—
385	D₄	—	4	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	1	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	4	no	—
391	D₄	—	8	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	8	4	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	C₅×#121	1	2	yes	—
403	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
404	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
405	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
406	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
407	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
408	C₂×C₄	C₅×AGL(1,ℤ/8)	1	2	yes	—
409	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
410	C₈	—	2	1	no	—
411	C₈	—	2	1	no	—
412	C₈	C₅×#121	1	2	yes	—
413	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
414	C₈	C₂×C₅×#41	1	1	yes	characteristic
415	C₅	#33579	1	1	yes	characteristic, direct product factor, Sylow
416	C₂²	—	2	1	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	4	2	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	2	no	—
422	C₂²	—	8	2	no	—
423	C₂²	—	8	2	no	—
424	C₂²	C₅×#459	1	2	yes	—
425	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	4	2	no	—
430	C₄	—	8	2	no	—
431	C₄	—	8	1	no	—
432	C₄	—	8	1	no	—
433	C₄	C₅×#459	1	2	yes	—
434	C₄	C₅×#508	1	2	yes	complemented
435	C₄	C₂×C₅×#121	1	1	yes	characteristic
436	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
437	C₂	—	2	2	no	—
438	C₂	—	8	2	no	—
439	C₂	—	16	2	no	—
440	C₂	C₂×C₅×#459	1	1	yes	characteristic
441	C₂	C₂×C₅×#508	1	1	yes	characteristic
442	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
socle	C₂²×C₅	C₂²×D₈
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×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. C₂×C₅×#508	C₂	semidirect
2. C₅×#3147	C₂	semidirect
3. C₄×C₅×#135	C₂	semidirect
4. C₅×#2211	C₂	semidirect
5. C₅×#2210	C₂	semidirect
6. C₅×#2209	C₂	semidirect
7. C₅×#2208	C₂	semidirect
8. C₅×#2207	C₂	semidirect
9. C₅×#2206	C₂	semidirect
10. C₂×C₅×C₄⋊C₁₆	C₂	semidirect
11. C₅×#2138	C₂	semidirect
44. #33579	C₅	direct (N × H)
51. C₅×#135	D₄	semidirect
98. C₂×#508	C₂×C₅	semidirect
99. #3147	C₂×C₅	semidirect
100. C₄×#135	C₂×C₅	semidirect
101. #2211	C₂×C₅	semidirect
102. #2210	C₂×C₅	semidirect
103. #2209	C₂×C₅	semidirect
104. #2208	C₂×C₅	semidirect
105. #2207	C₂×C₅	semidirect
106. #2206	C₂×C₅	semidirect
107. C₂×C₄⋊C₁₆	C₂×C₅	semidirect
108. #2138	C₂×C₅	semidirect
244. #135	C₅×D₄	semidirect
309. C₄×C₅	#508	semidirect
415. C₅	#33579	direct (N × H)
434. C₄	C₅×#508	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#508	2
C₅×#3147	2
C₄×C₅×#135	2
C₅×#2211	2
C₅×#2210	2
C₅×#2209	2
C₅×#2208	2
C₅×#2207	2
C₅×#2206	2
C₂×C₅×C₄⋊C₁₆	2
C₅×#2138	2
#33579	5

Subgroups — C5×#33579 #11956299

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33579 #11956299