Subgroups — C₅×#33606 #11956326

Order 1280.

686 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#510	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₅×M₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3050	C₂	1	1	yes	maximal, characteristic
4	C₂×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#2220	C₂	1	2	yes	maximal, complemented
6	C₅×#2219	C₂	1	2	yes	maximal, complemented
7	C₅×#2217	C₂	1	2	yes	maximal, complemented
8	C₅×#2216	C₂	1	2	yes	maximal, complemented
9	C₅×#2159	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2141	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2139	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₅×#135	C₂²	1	1	yes	characteristic
13	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
14	C₂³×C₅×C₈	C₂²	1	1	yes	characteristic
15	C₅×#525	—	2	1	no	—
16	C₂×C₅×C₂²⋊Q₈	—	2	1	no	—
17	C₅×#510	—	2	4	no	—
18	C₂×C₅×Q₃₂	C₂²	1	2	yes	complemented
19	C₂×C₅×SD₃₂	C₂²	1	2	yes	complemented
20	C₂×C₅×M₃₂	—	2	4	no	—
21	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
22	C₂×C₅×M₃₂	C₂²	1	2	yes	—
23	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
24	C₂²×C₅×C₁₆	C₂²	1	2	yes	—
25	C₅×#467	—	2	1	no	—
26	C₅×#467	—	2	1	no	—
27	C₅×#467	C₂²	1	2	yes	—
28	C₅×#467	C₂²	1	2	yes	—
29	C₅×#467	C₂²	1	1	yes	characteristic
30	C₅×#467	C₂²	1	1	yes	characteristic
31	C₅×#466	C₂²	1	1	yes	characteristic
32	C₅×#466	C₂²	1	1	yes	characteristic
33	C₅×#465	—	2	1	no	—
34	C₅×#465	—	2	1	no	—
35	C₅×#427	C₂²	1	1	yes	characteristic
36	C₂×C₅×#107	C₂²	1	1	yes	characteristic
37	C₅×#416	—	2	1	no	—
38	C₂×C₅×#103	—	2	1	no	—
39	C₅×#367	C₂²	1	2	yes	complemented
40	C₅×#366	C₂²	1	2	yes	complemented
41	C₅×#358	C₂²	1	2	yes	complemented
42	C₅×#358	C₂²	1	2	yes	complemented
43	C₅×#358	C₂²	1	2	yes	complemented
44	C₅×#357	C₂²	1	2	yes	complemented
45	#33606	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
46	C₂×C₅×#41	—	2	1	no	—
47	C₂²×C₅×Q₈	—	2	1	no	—
48	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
49	C₅×#135	—	2	2	no	—
50	C₅×#135	—	2	2	no	—
51	C₂×C₅×Q₁₆	—	2	2	no	—
52	C₂×C₅×Q₁₆	—	2	1	no	—
53	C₂×C₅×Q₁₆	—	2	2	no	—
54	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
55	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
56	C₂×C₅×SD₁₆	—	2	1	no	—
57	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
58	C₂²×C₅×C₈	—	2	2	no	—
59	C₂²×C₅×C₈	—	2	2	no	—
60	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
61	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
62	C₂²×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
64	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₅×#123	—	4	1	no	—
67	C₅×C₂²⋊Q₈	—	2	1	no	—
68	C₅×C₂²⋊Q₈	—	2	1	no	—
69	C₅×C₂²⋊Q₈	—	2	2	no	—
70	C₅×C₂²⋊Q₈	—	2	2	no	—
71	C₅×C₂²⋊Q₈	—	4	1	no	—
72	C₅×C₂²⋊Q₈	—	4	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#120	—	4	1	no	—
76	C₄×C₅×D₄	—	4	1	no	—
77	C₄×C₅×D₄	—	4	1	no	—
78	C₅×#117	—	2	1	no	—
79	C₂×C₅×C₄⋊C₄	—	2	1	no	—
80	C₂×C₅×C₄⋊C₄	—	4	1	no	—
81	C₂×C₅×C₂²⋊C₄	—	4	1	no	—
82	C₅×Q₃₂	—	2	4	no	—
83	C₅×SD₃₂	—	2	4	no	—
84	C₅×M₃₂	—	2	2	no	—
85	C₅×M₃₂	—	2	4	no	—
86	C₅×M₃₂	D₄	1	4	yes	complemented
87	C₂×C₅×C₁₆	—	2	4	no	—
88	C₂×C₅×C₁₆	C₂³	1	2	yes	—
89	C₂×C₅×C₁₆	C₂³	1	2	yes	—
90	C₅×#107	—	2	1	no	—
91	C₅×#107	C₂³	1	2	yes	—
92	C₅×#107	C₂³	1	1	yes	characteristic
93	C₅×#107	C₂³	1	1	yes	characteristic
94	C₅×#106	—	2	1	no	—
95	C₅×#103	—	2	2	no	—
96	C₅×#103	—	2	2	no	—
97	C₅×#103	—	2	1	no	—
98	C₅×#103	—	2	1	no	—
99	C₅×#102	—	2	1	no	—
100	C₅×#102	—	2	1	no	—
101	C₂×#510	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂²×M₃₂	C₂×C₅	1	1	yes	characteristic, complemented
103	#3050	C₂×C₅	1	1	yes	characteristic
104	C₂×#467	C₂×C₅	1	1	yes	characteristic, complemented
105	#2220	C₂×C₅	1	2	yes	complemented
106	#2219	C₂×C₅	1	2	yes	complemented
107	#2217	C₂×C₅	1	2	yes	complemented
108	#2216	C₂×C₅	1	2	yes	complemented
109	#2159	C₂×C₅	1	1	yes	characteristic, complemented
110	#2141	C₂×C₅	1	1	yes	characteristic, complemented
111	#2139	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂⁴×C₅	D₈	1	1	yes	characteristic
113	C₅×#41	—	4	2	no	—
114	C₅×#41	—	4	2	no	—
115	C₂×C₅×Q₈	—	2	1	no	—
116	C₂×C₅×Q₈	—	2	2	no	—
117	C₂×C₅×Q₈	—	4	1	no	—
118	C₂×C₅×Q₈	—	4	2	no	—
119	C₂×C₅×Q₈	—	4	2	no	—
120	C₂×C₅×D₄	—	2	1	no	—
121	C₂×C₅×D₄	—	4	1	no	—
122	C₂×C₅×D₄	—	4	1	no	—
123	C₂×C₅×D₄	—	4	1	no	—
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	4	1	no	—
127	C₂²×C₄×C₅	—	4	1	no	—
128	C₂²×C₄×C₅	—	4	1	no	—
129	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
130	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
131	C₂²×C₄×C₅	D₈	1	1	yes	characteristic
132	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₅×Q₁₆	—	2	2	no	—
136	C₅×Q₁₆	—	2	1	no	—
137	C₅×Q₁₆	—	2	2	no	—
138	C₅×Q₁₆	—	2	1	no	—
139	C₅×Q₁₆	—	4	2	no	—
140	C₅×SD₁₆	—	4	2	no	—
141	C₅×D₈	—	2	1	no	—
142	C₅×D₈	—	2	1	no	—
143	C₂×C₅×C₈	—	2	2	no	—
144	C₂×C₅×C₈	—	2	2	no	—
145	C₂×C₅×C₈	—	2	2	no	—
146	C₂×C₅×C₈	—	2	1	no	—
147	C₂×C₅×C₈	—	2	1	no	—
148	C₂×C₅×C₈	—	2	1	no	—
149	C₂×C₅×C₈	—	2	1	no	—
150	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
151	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
152	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
153	C₂×C₅×C₈	C₂×D₄	1	2	yes	—
154	C₂×C₅×C₈	#41	1	2	yes	—
155	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
156	C₅×C₄⋊C₄	—	2	2	no	—
157	C₅×C₄⋊C₄	—	2	1	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	4	1	no	—
160	C₅×C₄⋊C₄	—	4	2	no	—
161	C₅×C₄⋊C₄	—	4	2	no	—
162	C₅×C₄⋊C₄	—	4	1	no	—
163	C₅×C₄⋊C₄	—	4	1	no	—
164	C₅×C₂²⋊C₄	—	4	2	no	—
165	C₅×C₂²⋊C₄	—	4	2	no	—
166	C₅×C₂²⋊C₄	—	4	1	no	—
167	C₅×C₂²⋊C₄	—	4	1	no	—
168	C₅×C₂²⋊C₄	—	4	1	no	—
169	C₅×C₂²⋊C₄	—	4	1	no	—
170	C₅×C₂²⋊C₄	—	4	1	no	—
171	C₄²×C₅	—	4	1	no	—
172	C₅×C₁₆	—	2	2	no	—
173	C₅×C₁₆	C₂×D₄	1	4	yes	—
174	C₂×#135	C₂²×C₅	1	1	yes	characteristic
175	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
176	C₂³×C₈	C₂²×C₅	1	1	yes	characteristic
177	#525	—	2	1	no	—
178	C₂×C₂²⋊Q₈	—	2	1	no	—
179	#510	—	2	4	no	—
180	C₂×Q₃₂	C₂²×C₅	1	2	yes	complemented
181	C₂×SD₃₂	C₂²×C₅	1	2	yes	complemented
182	C₂×M₃₂	—	2	4	no	—
183	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
184	C₂×M₃₂	C₂²×C₅	1	2	yes	—
185	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
186	C₂²×C₁₆	C₂²×C₅	1	2	yes	—
187	#467	—	2	1	no	—
188	#467	—	2	1	no	—
189	#467	C₂²×C₅	1	1	yes	characteristic
190	#467	C₂²×C₅	1	2	yes	—
191	#467	C₂²×C₅	1	1	yes	characteristic
192	#467	C₂²×C₅	1	2	yes	—
193	#466	C₂²×C₅	1	1	yes	characteristic
194	#466	C₂²×C₅	1	1	yes	characteristic
195	#465	—	2	1	no	—
196	#465	—	2	1	no	—
197	#427	C₂²×C₅	1	1	yes	characteristic
198	C₂×#107	C₂²×C₅	1	1	yes	characteristic
199	#416	—	2	1	no	—
200	C₂×#103	—	2	1	no	—
201	#367	C₂²×C₅	1	2	yes	complemented
202	#366	C₂²×C₅	1	2	yes	complemented
203	#358	C₂²×C₅	1	2	yes	complemented
204	#358	C₂²×C₅	1	2	yes	complemented
205	#358	C₂²×C₅	1	2	yes	complemented
206	#357	C₂²×C₅	1	2	yes	complemented
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	—	2	2	no	—
209	C₂³×C₅	—	4	1	no	—
210	C₂³×C₅	—	4	1	no	—
211	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
212	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
213	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
214	C₅×Q₈	—	4	1	no	—
215	C₅×Q₈	—	4	2	no	—
216	C₅×Q₈	—	4	2	no	—
217	C₅×Q₈	—	4	1	no	—
218	C₅×Q₈	—	8	2	no	—
219	C₅×D₄	—	4	1	no	—
220	C₅×D₄	—	4	1	no	—
221	C₅×D₄	—	8	2	no	—
222	C₅×D₄	—	8	2	no	—
223	C₅×D₄	—	8	2	no	—
224	C₂×C₄×C₅	—	2	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	2	1	no	—
227	C₂×C₄×C₅	—	2	1	no	—
228	C₂×C₄×C₅	—	2	1	no	—
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	4	1	no	—
232	C₂×C₄×C₅	—	4	1	no	—
233	C₂×C₄×C₅	—	4	2	no	—
234	C₂×C₄×C₅	—	4	1	no	—
235	C₂×C₄×C₅	—	4	2	no	—
236	C₂×C₄×C₅	—	8	2	no	—
237	C₂×C₄×C₅	—	8	2	no	—
238	C₂×C₄×C₅	—	8	2	no	—
239	C₂×C₄×C₅	#121	1	2	yes	—
240	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
243	C₂×C₄×C₅	#135	1	2	yes	—
244	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₅×C₈	—	2	1	no	—
246	C₅×C₈	—	2	1	no	—
247	C₅×C₈	#121	1	2	yes	—
248	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
249	C₅×C₈	C₂×#41	1	1	yes	characteristic
250	C₂×#41	—	2	1	no	—
251	C₂²×Q₈	—	2	1	no	—
252	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
253	#135	—	2	2	no	—
254	#135	—	2	2	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	—	2	1	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
259	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
260	C₂×SD₁₆	—	2	1	no	—
261	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	2	2	no	—
264	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
265	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
266	C₂²×C₈	C₅×D₄	1	1	yes	characteristic
267	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
270	#123	—	4	1	no	—
271	C₂²⋊Q₈	—	2	2	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	1	no	—
274	C₂²⋊Q₈	—	2	1	no	—
275	C₂²⋊Q₈	—	4	1	no	—
276	C₂²⋊Q₈	—	4	1	no	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	#120	—	4	1	no	—
280	C₄×D₄	—	4	1	no	—
281	C₄×D₄	—	4	1	no	—
282	#117	—	2	1	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	4	1	no	—
285	C₂×C₂²⋊C₄	—	4	1	no	—
286	Q₃₂	—	2	4	no	—
287	SD₃₂	—	2	4	no	—
288	M₃₂	—	2	2	no	—
289	M₃₂	—	2	4	no	—
290	M₃₂	C₅×D₄	1	4	yes	complemented
291	C₂×C₁₆	—	2	4	no	—
292	C₂×C₁₆	C₂³×C₅	1	2	yes	—
293	C₂×C₁₆	C₂³×C₅	1	2	yes	—
294	#107	—	2	1	no	—
295	#107	C₂³×C₅	1	2	yes	—
296	#107	C₂³×C₅	1	1	yes	characteristic
297	#107	C₂³×C₅	1	1	yes	characteristic
298	#106	—	2	1	no	—
299	#103	—	2	2	no	—
300	#103	—	2	2	no	—
301	#103	—	2	1	no	—
302	#103	—	2	1	no	—
303	#102	—	2	1	no	—
304	#102	—	2	1	no	—
305	C₂²×C₅	—	2	1	no	—
306	C₂²×C₅	—	2	1	no	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	—	2	1	no	—
309	C₂²×C₅	—	2	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	—	8	1	no	—
314	C₂²×C₅	—	8	1	no	—
315	C₂²×C₅	—	8	1	no	—
316	C₂²×C₅	#466	1	2	yes	—
317	C₂²×C₅	#510	1	2	yes	complemented
318	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
319	C₄×C₅	—	2	1	no	—
320	C₄×C₅	—	2	1	no	—
321	C₄×C₅	—	8	1	no	—
322	C₄×C₅	—	8	2	no	—
323	C₄×C₅	—	8	1	no	—
324	C₄×C₅	—	8	1	no	—
325	C₄×C₅	—	8	2	no	—
326	C₄×C₅	#466	1	2	yes	—
327	C₄×C₅	C₂×#121	1	1	yes	characteristic
328	C₄×C₅	C₂×#135	1	1	yes	characteristic
329	C₂⁴	C₅×D₈	1	1	yes	characteristic
330	#41	—	4	2	no	—
331	#41	—	4	2	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	4	1	no	—
335	C₂×Q₈	—	4	2	no	—
336	C₂×Q₈	—	4	2	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	4	1	no	—
340	C₂×D₄	—	4	1	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	4	1	no	—
346	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
347	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
348	C₂²×C₄	C₅×D₈	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
352	Q₁₆	—	2	2	no	—
353	Q₁₆	—	2	1	no	—
354	Q₁₆	—	2	2	no	—
355	Q₁₆	—	2	1	no	—
356	Q₁₆	—	4	2	no	—
357	SD₁₆	—	4	2	no	—
358	D₈	—	2	1	no	—
359	D₈	—	2	1	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
368	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂×C₈	C₂×C₅×D₄	1	2	yes	—
371	C₂×C₈	C₅×#41	1	2	yes	—
372	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	4	1	no	—
377	C₄⋊C₄	—	4	2	no	—
378	C₄⋊C₄	—	4	2	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	2	no	—
382	C₂²⋊C₄	—	4	2	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₂²⋊C₄	—	4	1	no	—
388	C₄²	—	4	1	no	—
389	C₁₆	—	2	2	no	—
390	C₁₆	C₂×C₅×D₄	1	4	yes	—
391	C₂×C₅	—	2	2	no	—
392	C₂×C₅	—	2	2	no	—
393	C₂×C₅	—	4	1	no	—
394	C₂×C₅	—	16	1	no	—
395	C₂×C₅	C₂×#466	1	1	yes	characteristic
396	C₂×C₅	C₂×#510	1	1	yes	characteristic
397	C₂×C₅	#3414	1	1	yes	characteristic
398	C₂³	—	2	2	no	—
399	C₂³	—	2	2	no	—
400	C₂³	—	4	1	no	—
401	C₂³	—	4	1	no	—
402	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
403	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
404	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
405	Q₈	—	4	1	no	—
406	Q₈	—	4	2	no	—
407	Q₈	—	4	2	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	8	2	no	—
410	D₄	—	4	1	no	—
411	D₄	—	4	1	no	—
412	D₄	—	8	2	no	—
413	D₄	—	8	2	no	—
414	D₄	—	8	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	8	2	no	—
428	C₂×C₄	—	8	2	no	—
429	C₂×C₄	—	8	2	no	—
430	C₂×C₄	C₅×#121	1	2	yes	—
431	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
432	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
433	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
434	C₂×C₄	C₅×#135	1	2	yes	—
435	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
436	C₈	—	2	1	no	—
437	C₈	—	2	1	no	—
438	C₈	C₅×#121	1	2	yes	—
439	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
440	C₈	C₂×C₅×#41	1	1	yes	characteristic
441	C₅	#33606	1	1	yes	characteristic, direct product factor, Sylow
442	C₂²	—	2	1	no	—
443	C₂²	—	2	1	no	—
444	C₂²	—	2	1	no	—
445	C₂²	—	2	1	no	—
446	C₂²	—	2	1	no	—
447	C₂²	—	2	1	no	—
448	C₂²	—	2	1	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	8	1	no	—
451	C₂²	—	8	1	no	—
452	C₂²	—	8	1	no	—
453	C₂²	C₅×#466	1	2	yes	—
454	C₂²	C₅×#510	1	2	yes	complemented
455	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
456	C₄	—	2	1	no	—
457	C₄	—	2	1	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	2	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	2	no	—
462	C₄	—	8	1	no	—
463	C₄	C₅×#466	1	2	yes	—
464	C₄	C₂×C₅×#121	1	1	yes	characteristic
465	C₄	C₂×C₅×#135	1	1	yes	characteristic
466	C₂	—	2	2	no	—
467	C₂	—	2	2	no	—
468	C₂	—	4	1	no	—
469	C₂	—	16	1	no	—
470	C₂	C₂×C₅×#466	1	1	yes	characteristic
471	C₂	C₂×C₅×#510	1	1	yes	characteristic
472	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×#3050	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂³×C₅×C₈ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#510	C₂	semidirect
2. C₂²×C₅×M₃₂	C₂	semidirect
4. C₂×C₅×#467	C₂	semidirect
5. C₅×#2220	C₂	semidirect
6. C₅×#2219	C₂	semidirect
7. C₅×#2217	C₂	semidirect
8. C₅×#2216	C₂	semidirect
9. C₅×#2159	C₂	semidirect
10. C₅×#2141	C₂	semidirect
11. C₅×#2139	C₂	semidirect
18. C₂×C₅×Q₃₂	C₂²	semidirect
19. C₂×C₅×SD₃₂	C₂²	semidirect
39. C₅×#367	C₂²	semidirect
40. C₅×#366	C₂²	semidirect
41. C₅×#358	C₂²	semidirect
42. C₅×#358	C₂²	semidirect
43. C₅×#358	C₂²	semidirect
44. C₅×#357	C₂²	semidirect
45. #33606	C₅	direct (N × H)
86. C₅×M₃₂	D₄	semidirect
101. C₂×#510	C₂×C₅	semidirect
102. C₂²×M₃₂	C₂×C₅	semidirect
104. C₂×#467	C₂×C₅	semidirect
105. #2220	C₂×C₅	semidirect
106. #2219	C₂×C₅	semidirect
107. #2217	C₂×C₅	semidirect
108. #2216	C₂×C₅	semidirect
109. #2159	C₂×C₅	semidirect
110. #2141	C₂×C₅	semidirect
111. #2139	C₂×C₅	semidirect
180. C₂×Q₃₂	C₂²×C₅	semidirect
181. C₂×SD₃₂	C₂²×C₅	semidirect
201. #367	C₂²×C₅	semidirect
202. #366	C₂²×C₅	semidirect
203. #358	C₂²×C₅	semidirect
204. #358	C₂²×C₅	semidirect
205. #358	C₂²×C₅	semidirect
206. #357	C₂²×C₅	semidirect
290. M₃₂	C₅×D₄	semidirect
317. C₂²×C₅	#510	semidirect
441. C₅	#33606	direct (N × H)
454. C₂²	C₅×#510	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#510	2
C₂²×C₅×M₃₂	2
C₅×#3050	2
C₂×C₅×#467	2
C₅×#2220	2
C₅×#2219	2
C₅×#2217	2
C₅×#2216	2
C₅×#2159	2
C₅×#2141	2
C₅×#2139	2
#33606	5

Subgroups — C5×#33606 #11956326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33606 #11956326