Subgroups — C₅×#33778 #11956498

Order 1280.

598 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	C₅×#3168	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#3147	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×#2209	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2208	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2207	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2206	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2189	C₂	1	2	yes	maximal, complemented
10	C₅×#2186	C₂	1	2	yes	maximal, complemented
11	C₅×#2162	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	—	2	1	no	—
13	C₂×C₅×#135	C₂²	1	2	yes	—
14	C₅×#532	—	2	1	no	—
15	C₅×#529	—	2	1	no	—
16	C₂×C₅×Q₃₂	C₂²	1	2	yes	—
17	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
18	C₂×C₅×SD₃₂	C₂²	1	2	yes	—
19	C₂×C₅×D₁₆	C₂²	1	2	yes	—
20	C₅×#499	C₂²	1	1	yes	characteristic
21	C₅×#495	—	2	1	no	—
22	C₅×#495	C₂²	1	2	yes	—
23	C₅×#495	C₂²	1	1	yes	characteristic
24	C₅×#494	C₂²	1	1	yes	characteristic
25	C₅×#493	C₂²	1	1	yes	characteristic
26	C₅×#492	—	2	1	no	—
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
32	C₄×C₅×SD₁₆	—	2	1	no	—
33	C₄×C₅×D₈	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
35	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
36	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
37	C₅×#358	C₂²	1	2	yes	—
38	C₅×#358	C₂²	1	2	yes	—
39	C₅×#357	C₂²	1	2	yes	—
40	C₅×#357	C₂²	1	2	yes	—
41	C₅×C₂²⋊C₁₆	C₂²	1	2	yes	—
42	C₄×C₅×C₁₆	C₂²	1	2	yes	—
43	#33778	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
44	C₂×C₅×#41	—	2	2	no	—
45	C₅×#135	—	4	2	no	—
46	C₅×#135	—	4	2	no	—
47	C₅×#135	—	4	4	no	—
48	C₂×C₅×Q₁₆	—	2	1	no	—
49	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
50	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
51	C₂×C₅×SD₁₆	—	2	1	no	—
52	C₂×C₅×SD₁₆	—	2	2	no	—
53	C₂×C₅×SD₁₆	—	2	2	no	—
54	C₂×C₅×D₈	—	2	1	no	—
55	C₂×C₅×D₈	C₂³	1	2	yes	—
56	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
57	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
58	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
59	C₅×C₄⋊Q₈	—	2	1	no	—
60	C₅×#127	—	2	1	no	—
61	C₅×#126	—	4	1	no	—
62	C₅×#125	—	2	1	no	—
63	C₅×#124	—	2	1	no	—
64	C₅×#124	—	2	2	no	—
65	C₅×#123	—	4	1	no	—
66	C₅×C₂²⋊Q₈	—	2	1	no	—
67	C₅×#121	—	2	1	no	—
68	C₅×#121	—	4	1	no	—
69	C₅×#121	—	4	1	no	—
70	C₄×C₅×Q₈	—	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	C₅×#117	—	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	#3147	C₂×C₅	1	1	yes	characteristic, complemented
96	#2249	C₂×C₅	1	2	yes	complemented
97	#2242	C₂×C₅	1	2	yes	complemented
98	#2209	C₂×C₅	1	1	yes	characteristic, complemented
99	#2208	C₂×C₅	1	1	yes	characteristic, complemented
100	#2207	C₂×C₅	1	1	yes	characteristic, complemented
101	#2206	C₂×C₅	1	1	yes	characteristic, complemented
102	#2189	C₂×C₅	1	2	yes	complemented
103	#2186	C₂×C₅	1	2	yes	complemented
104	#2162	C₂×C₅	1	1	yes	characteristic, complemented
105	C₅×#41	—	4	4	no	—
106	C₅×#41	—	4	4	no	—
107	C₂×C₅×Q₈	—	2	1	no	—
108	C₂×C₅×Q₈	—	2	2	no	—
109	C₂×C₅×D₄	—	2	1	no	—
110	C₂×C₅×D₄	—	2	2	no	—
111	C₂×C₅×D₄	—	4	1	no	—
112	C₂×C₅×D₄	—	4	2	no	—
113	C₂×C₅×D₄	—	4	1	no	—
114	C₂×C₅×D₄	—	4	1	no	—
115	C₂²×C₄×C₅	—	4	1	no	—
116	C₂²×C₄×C₅	—	4	2	no	—
117	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
119	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
120	C₅×Q₁₆	—	2	2	no	—
121	C₅×Q₁₆	—	2	2	no	—
122	C₅×Q₁₆	—	2	1	no	—
123	C₅×Q₁₆	—	2	1	no	—
124	C₅×Q₁₆	—	4	2	no	—
125	C₅×SD₁₆	—	4	4	no	—
126	C₅×SD₁₆	—	4	2	no	—
127	C₅×SD₁₆	—	4	4	no	—
128	C₅×D₈	—	2	2	no	—
129	C₅×D₈	—	2	2	no	—
130	C₅×D₈	—	2	1	no	—
131	C₅×D₈	—	2	1	no	—
132	C₅×D₈	—	4	2	no	—
133	C₂×C₅×C₈	—	2	2	no	—
134	C₂×C₅×C₈	—	2	1	no	—
135	C₂×C₅×C₈	—	2	1	no	—
136	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
138	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
139	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
140	C₅×C₄⋊C₄	—	2	1	no	—
141	C₅×C₄⋊C₄	—	2	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×C₄⋊C₄	—	4	1	no	—
146	C₅×C₄⋊C₄	—	4	1	no	—
147	C₅×C₄⋊C₄	—	4	1	no	—
148	C₅×C₂²⋊C₄	—	4	1	no	—
149	C₅×C₂²⋊C₄	—	4	1	no	—
150	C₅×C₂²⋊C₄	—	4	1	no	—
151	C₅×C₂²⋊C₄	—	4	1	no	—
152	C₅×C₂²⋊C₄	—	4	2	no	—
153	C₅×C₂²⋊C₄	—	4	2	no	—
154	C₅×C₂²⋊C₄	—	4	1	no	—
155	C₄²×C₅	—	4	1	no	—
156	C₄²×C₅	D₈	1	1	yes	characteristic
157	C₄²×C₅	D₈	1	1	yes	characteristic
158	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
160	C₅×C₁₆	—	2	2	no	—
161	C₅×C₁₆	—	2	2	no	—
162	C₂×#135	—	2	1	no	—
163	C₂×#135	C₂²×C₅	1	2	yes	—
164	#532	—	2	1	no	—
165	#529	—	2	1	no	—
166	C₂×Q₃₂	C₂²×C₅	1	2	yes	—
167	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
168	C₂×SD₃₂	C₂²×C₅	1	2	yes	—
169	C₂×D₁₆	C₂²×C₅	1	2	yes	—
170	#499	C₂²×C₅	1	1	yes	characteristic
171	#495	—	2	1	no	—
172	#495	C₂²×C₅	1	2	yes	—
173	#495	C₂²×C₅	1	1	yes	characteristic
174	#494	C₂²×C₅	1	1	yes	characteristic
175	#493	C₂²×C₅	1	1	yes	characteristic
176	#492	—	2	1	no	—
177	#488	—	2	1	no	—
178	#467	C₂²×C₅	1	1	yes	characteristic
179	#466	C₂²×C₅	1	1	yes	characteristic
180	#465	—	2	1	no	—
181	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
182	C₄×SD₁₆	—	2	1	no	—
183	C₄×D₈	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
185	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
187	#358	C₂²×C₅	1	2	yes	—
188	#358	C₂²×C₅	1	2	yes	—
189	#357	C₂²×C₅	1	2	yes	—
190	#357	C₂²×C₅	1	2	yes	—
191	C₂²⋊C₁₆	C₂²×C₅	1	2	yes	—
192	C₄×C₁₆	C₂²×C₅	1	2	yes	—
193	C₂³×C₅	—	4	1	no	—
194	C₂³×C₅	—	4	2	no	—
195	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
196	C₅×Q₈	—	4	2	no	—
197	C₅×Q₈	—	4	1	no	—
198	C₅×Q₈	—	4	2	no	—
199	C₅×Q₈	—	4	1	no	—
200	C₅×D₄	—	4	2	no	—
201	C₅×D₄	—	4	1	no	—
202	C₅×D₄	—	4	2	no	—
203	C₅×D₄	—	4	1	no	—
204	C₅×D₄	—	8	2	no	—
205	C₅×D₄	—	8	2	no	—
206	C₅×D₄	—	8	4	no	—
207	C₅×D₄	—	8	2	no	—
208	C₂×C₄×C₅	—	2	1	no	—
209	C₂×C₄×C₅	—	2	1	no	—
210	C₂×C₄×C₅	—	2	2	no	—
211	C₂×C₄×C₅	—	4	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	—	8	4	no	—
217	C₂×C₄×C₅	—	8	2	no	—
218	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
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	C₂²×D₄	1	1	yes	characteristic
224	C₅×C₈	—	2	1	no	—
225	C₅×C₈	—	2	1	no	—
226	C₅×C₈	AGL(1,ℤ/8)	1	2	yes	—
227	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
228	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
229	C₂×#41	—	2	2	no	—
230	#135	—	4	2	no	—
231	#135	—	4	2	no	—
232	#135	—	4	4	no	—
233	C₂×Q₁₆	—	2	1	no	—
234	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
235	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
236	C₂×SD₁₆	—	2	2	no	—
237	C₂×SD₁₆	—	2	2	no	—
238	C₂×SD₁₆	—	2	1	no	—
239	C₂×D₈	—	2	1	no	—
240	C₂×D₈	C₂³×C₅	1	2	yes	—
241	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
242	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
243	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
244	C₄⋊Q₈	—	2	1	no	—
245	#127	—	2	1	no	—
246	#126	—	4	1	no	—
247	#125	—	2	1	no	—
248	#124	—	2	1	no	—
249	#124	—	2	2	no	—
250	#123	—	4	1	no	—
251	C₂²⋊Q₈	—	2	1	no	—
252	#121	—	2	1	no	—
253	#121	—	4	1	no	—
254	#121	—	4	1	no	—
255	C₄×Q₈	—	2	1	no	—
256	C₄×D₄	—	2	1	no	—
257	C₄×D₄	—	4	1	no	—
258	C₄×D₄	—	4	1	no	—
259	C₄×D₄	—	4	1	no	—
260	#117	—	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	—	2	1	no	—
282	C₂²×C₅	—	8	1	no	—
283	C₂²×C₅	—	8	2	no	—
284	C₂²×C₅	—	8	2	no	—
285	C₂²×C₅	—	8	1	no	—
286	C₂²×C₅	—	8	2	no	—
287	C₂²×C₅	—	8	1	no	—
288	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
289	C₄×C₅	—	2	1	no	—
290	C₄×C₅	—	2	1	no	—
291	C₄×C₅	—	2	1	no	—
292	C₄×C₅	—	2	1	no	—
293	C₄×C₅	—	8	1	no	—
294	C₄×C₅	—	8	1	no	—
295	C₄×C₅	—	8	2	no	—
296	C₄×C₅	—	8	1	no	—
297	C₄×C₅	#508	1	2	yes	—
298	C₄×C₅	#535	1	1	yes	characteristic
299	C₄×C₅	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
300	#41	—	4	4	no	—
301	#41	—	4	4	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	2	no	—
308	C₂×D₄	—	4	1	no	—
309	C₂×D₄	—	4	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
313	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
314	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
315	Q₁₆	—	2	1	no	—
316	Q₁₆	—	2	2	no	—
317	Q₁₆	—	2	1	no	—
318	Q₁₆	—	2	2	no	—
319	Q₁₆	—	4	2	no	—
320	SD₁₆	—	4	4	no	—
321	SD₁₆	—	4	4	no	—
322	SD₁₆	—	4	2	no	—
323	D₈	—	2	1	no	—
324	D₈	—	2	2	no	—
325	D₈	—	2	1	no	—
326	D₈	—	2	2	no	—
327	D₈	—	4	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	2	1	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	C₄⋊C₄	—	4	1	no	—
342	C₄⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	2	no	—
348	C₂²⋊C₄	—	4	2	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	—	4	1	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	C₂×C₅×D₈	1	1	yes	characteristic
366	Q₈	—	4	2	no	—
367	Q₈	—	4	1	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	1	no	—
370	D₄	—	4	2	no	—
371	D₄	—	4	1	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	1	no	—
374	D₄	—	8	2	no	—
375	D₄	—	8	4	no	—
376	D₄	—	8	2	no	—
377	D₄	—	8	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	4	1	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	8	4	no	—
387	C₂×C₄	—	8	2	no	—
388	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
389	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
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	C₂²×C₅×D₄	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	C₅×AGL(1,ℤ/8)	1	2	yes	—
397	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
398	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
399	C₅	#33778	1	1	yes	characteristic, direct product factor, Sylow
400	C₂²	—	2	1	no	—
401	C₂²	—	2	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	2	no	—
405	C₂²	—	8	2	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	2	no	—
408	C₂²	—	8	1	no	—
409	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	8	1	no	—
415	C₄	—	8	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	8	1	no	—
418	C₄	C₅×#508	1	2	yes	—
419	C₄	C₅×#535	1	1	yes	characteristic
420	C₄	C₂×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
421	C₂	—	4	1	no	—
422	C₂	—	16	1	no	—
423	C₂	—	16	2	no	—
424	C₂	C₅×#3205	1	1	yes	characteristic
425	C₂	C₂×C₅×#508	1	1	yes	characteristic
426	C₂	C₅×#3414	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
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. C₅×#3147	C₂	semidirect
3. C₅×#2249	C₂	semidirect
4. C₅×#2242	C₂	semidirect
5. C₅×#2209	C₂	semidirect
6. C₅×#2208	C₂	semidirect
7. C₅×#2207	C₂	semidirect
8. C₅×#2206	C₂	semidirect
9. C₅×#2189	C₂	semidirect
10. C₅×#2186	C₂	semidirect
11. C₅×#2162	C₂	semidirect
43. #33778	C₅	direct (N × H)
94. #3168	C₂×C₅	semidirect
95. #3147	C₂×C₅	semidirect
96. #2249	C₂×C₅	semidirect
97. #2242	C₂×C₅	semidirect
98. #2209	C₂×C₅	semidirect
99. #2208	C₂×C₅	semidirect
100. #2207	C₂×C₅	semidirect
101. #2206	C₂×C₅	semidirect
102. #2189	C₂×C₅	semidirect
103. #2186	C₂×C₅	semidirect
104. #2162	C₂×C₅	semidirect
399. C₅	#33778	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
C₅×#3147	2
C₅×#2249	2
C₅×#2242	2
C₅×#2209	2
C₅×#2208	2
C₅×#2207	2
C₅×#2206	2
C₅×#2189	2
C₅×#2186	2
C₅×#2162	2
#33778	5

Subgroups — C5×#33778 #11956498

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33778 #11956498