Subgroups — C₅×#33836 #11956556

Order 1280.

664 conjugacy classes of subgroups.

The subgroup lattice has 568 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×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×D₄×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#3285	C₂	1	1	yes	maximal, characteristic
5	C₅×#2251	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2219	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#2217	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#2211	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#2209	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#2189	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#2188	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2188	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#2185	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#2176	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₅×#135	C₂²	1	1	yes	characteristic
17	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂²×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₅×D₄×Q₈	—	2	1	no	—
21	C₅×#548	—	2	1	no	—
22	C₅×#510	—	2	4	no	—
23	C₂×C₅×Q₃₂	—	2	4	no	—
24	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
25	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
26	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
27	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
28	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
29	C₂×C₅×Q₃₂	C₂²	1	1	yes	characteristic
30	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
31	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
32	C₂×C₅×SD₃₂	C₂²	1	1	yes	characteristic
33	C₂×C₅×M₃₂	C₂²	1	1	yes	characteristic
34	C₂²×C₅×C₁₆	C₂²	1	1	yes	characteristic
35	C₅×#495	C₂²	1	1	yes	characteristic
36	C₅×#494	C₂²	1	1	yes	characteristic
37	C₅×#467	C₂²	1	1	yes	characteristic
38	C₅×#467	C₂²	1	1	yes	characteristic
39	C₅×#467	C₂²	1	1	yes	characteristic
40	C₅×#466	C₂²	1	1	yes	characteristic
41	C₅×#464	—	2	1	no	—
42	C₅×#462	—	2	1	no	—
43	C₅×#452	—	2	1	no	—
44	C₅×#451	—	2	1	no	—
45	C₅×#451	—	2	1	no	—
46	C₅×#448	—	2	1	no	—
47	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
48	C₄×C₅×Q₁₆	C₂²	1	1	yes	characteristic
49	C₅×C₈×D₄	C₂²	1	1	yes	characteristic
50	C₅×#367	C₂²	1	1	yes	characteristic
51	C₅×C₄⋊C₁₆	C₂²	1	1	yes	characteristic
52	C₅×#358	C₂²	1	1	yes	characteristic
53	C₅×#358	C₂²	1	1	yes	characteristic
54	C₅×#358	C₂²	1	1	yes	characteristic
55	C₅×#358	C₂²	1	1	yes	characteristic
56	C₅×#358	C₂²	1	1	yes	characteristic
57	C₅×#357	C₂²	1	1	yes	characteristic
58	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
59	C₅×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
60	C₅×#346	C₂²	1	1	yes	characteristic
61	#33836	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
62	C₂×C₅×#41	—	2	1	no	—
63	C₂²×C₅×Q₈	—	2	1	no	—
64	C₂²×C₅×Q₈	—	2	1	no	—
65	C₂²×C₅×Q₈	—	2	1	no	—
66	C₅×#135	—	2	2	no	—
67	C₅×#135	—	4	1	no	—
68	C₂×C₅×Q₁₆	—	2	2	no	—
69	C₂×C₅×Q₁₆	—	2	2	no	—
70	C₂×C₅×Q₁₆	—	2	2	no	—
71	C₂×C₅×Q₁₆	—	2	1	no	—
72	C₂×C₅×Q₁₆	—	2	1	no	—
73	C₂×C₅×Q₁₆	—	2	1	no	—
74	C₂×C₅×Q₁₆	—	2	1	no	—
75	C₂×C₅×Q₁₆	—	4	1	no	—
76	C₂×C₅×Q₁₆	—	4	1	no	—
77	C₂×C₅×Q₁₆	—	4	1	no	—
78	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
79	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
80	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
81	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
82	C₂×C₅×Q₁₆	C₂³	1	1	yes	characteristic
83	C₂×C₅×SD₁₆	—	2	1	no	—
84	C₂×C₅×SD₁₆	—	2	1	no	—
85	C₂×C₅×D₈	C₂³	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
87	C₂²×C₅×C₈	C₂³	1	1	yes	characteristic
88	C₅×C₄⋊Q₈	—	2	1	no	—
89	C₅×C₄⋊Q₈	—	4	1	no	—
90	C₅×#124	—	2	1	no	—
91	C₅×#124	—	4	1	no	—
92	C₅×C₂²⋊Q₈	—	2	1	no	—
93	C₅×C₂²⋊Q₈	—	2	1	no	—
94	C₅×C₂²⋊Q₈	—	2	1	no	—
95	C₅×C₂²⋊Q₈	—	4	1	no	—
96	C₅×C₂²⋊Q₈	—	4	1	no	—
97	C₅×C₂²⋊Q₈	—	4	1	no	—
98	C₅×#121	—	2	1	no	—
99	C₅×#121	—	4	1	no	—
100	C₄×C₅×Q₈	—	2	1	no	—
101	C₄×C₅×Q₈	—	2	1	no	—
102	C₄×C₅×D₄	—	4	1	no	—
103	C₄×C₅×D₄	—	4	1	no	—
104	C₄×C₅×D₄	D₄	1	1	yes	characteristic
105	C₅×Q₃₂	—	2	2	no	—
106	C₅×Q₃₂	—	2	2	no	—
107	C₅×Q₃₂	—	2	2	no	—
108	C₅×Q₃₂	—	2	2	no	—
109	C₅×Q₃₂	—	4	1	no	—
110	C₅×Q₃₂	D₄	1	4	yes	complemented
111	C₅×SD₃₂	—	2	2	no	—
112	C₅×SD₃₂	—	2	2	no	—
113	C₅×SD₃₂	—	4	1	no	—
114	C₅×M₃₂	—	2	2	no	—
115	C₂×C₅×C₁₆	—	2	2	no	—
116	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
118	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
119	C₂×C₅×C₁₆	C₂³	1	1	yes	characteristic
120	C₅×#107	C₂³	1	1	yes	characteristic
121	C₅×#107	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊C₈	D₄	1	1	yes	characteristic
123	C₅×#103	—	2	1	no	—
124	C₅×#103	—	2	1	no	—
125	C₅×#103	—	2	1	no	—
126	C₅×#103	—	2	1	no	—
127	C₅×#103	—	2	1	no	—
128	C₅×#102	—	2	1	no	—
129	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
130	C₅×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₄×C₅×C₈	C₂³	1	1	yes	characteristic
132	C₂×#510	C₂×C₅	1	1	yes	characteristic, complemented
133	C₂²×Q₃₂	C₂×C₅	1	1	yes	characteristic, complemented
134	D₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
135	#3285	C₂×C₅	1	1	yes	characteristic
136	#2251	C₂×C₅	1	1	yes	characteristic, complemented
137	#2219	C₂×C₅	1	1	yes	characteristic, complemented
138	#2217	C₂×C₅	1	1	yes	characteristic, complemented
139	#2211	C₂×C₅	1	1	yes	characteristic, complemented
140	#2209	C₂×C₅	1	1	yes	characteristic, complemented
141	#2189	C₂×C₅	1	1	yes	characteristic, complemented
142	#2188	C₂×C₅	1	1	yes	characteristic, complemented
143	#2188	C₂×C₅	1	1	yes	characteristic, complemented
144	#2185	C₂×C₅	1	1	yes	characteristic, complemented
145	#2176	C₂×C₅	1	1	yes	characteristic, complemented
146	#2168	C₂×C₅	1	1	yes	characteristic, complemented
147	C₅×#41	—	4	2	no	—
148	C₅×#41	—	8	1	no	—
149	C₂×C₅×Q₈	—	2	1	no	—
150	C₂×C₅×Q₈	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	1	no	—
153	C₂×C₅×Q₈	—	2	1	no	—
154	C₂×C₅×Q₈	—	4	2	no	—
155	C₂×C₅×Q₈	—	4	2	no	—
156	C₂×C₅×Q₈	—	4	2	no	—
157	C₂×C₅×Q₈	—	4	1	no	—
158	C₂×C₅×Q₈	—	4	1	no	—
159	C₂×C₅×Q₈	—	4	1	no	—
160	C₂×C₅×Q₈	—	8	1	no	—
161	C₂×C₅×Q₈	—	8	1	no	—
162	C₂×C₅×Q₈	—	8	1	no	—
163	C₂×C₅×D₄	—	2	1	no	—
164	C₂×C₅×D₄	—	4	1	no	—
165	C₂×C₅×D₄	—	4	1	no	—
166	C₂×C₅×D₄	D₈	1	1	yes	characteristic
167	C₂²×C₄×C₅	—	4	1	no	—
168	C₂²×C₄×C₅	—	4	1	no	—
169	C₂²×C₄×C₅	—	4	1	no	—
170	C₂²×C₄×C₅	—	4	1	no	—
171	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
173	C₅×Q₁₆	—	2	1	no	—
174	C₅×Q₁₆	—	2	1	no	—
175	C₅×Q₁₆	—	2	1	no	—
176	C₅×Q₁₆	—	2	1	no	—
177	C₅×Q₁₆	—	2	1	no	—
178	C₅×Q₁₆	—	2	1	no	—
179	C₅×Q₁₆	—	2	1	no	—
180	C₅×Q₁₆	—	2	1	no	—
181	C₅×Q₁₆	—	4	2	no	—
182	C₅×Q₁₆	—	4	2	no	—
183	C₅×Q₁₆	—	4	2	no	—
184	C₅×Q₁₆	—	8	1	no	—
185	C₅×Q₁₆	C₂×D₄	1	2	yes	—
186	C₅×Q₁₆	C₂×D₄	1	2	yes	—
187	C₅×SD₁₆	—	4	2	no	—
188	C₅×SD₁₆	—	8	1	no	—
189	C₅×D₈	—	2	1	no	—
190	C₅×D₈	—	2	1	no	—
191	C₂×C₅×C₈	—	2	1	no	—
192	C₂×C₅×C₈	—	2	1	no	—
193	C₂×C₅×C₈	—	2	1	no	—
194	C₂×C₅×C₈	—	2	1	no	—
195	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
196	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
197	C₂×C₅×C₈	C₂×D₄	1	1	yes	characteristic
198	C₂×C₅×C₈	C₂⁴	1	1	yes	characteristic
199	C₅×C₄⋊C₄	—	2	1	no	—
200	C₅×C₄⋊C₄	—	2	1	no	—
201	C₅×C₄⋊C₄	—	4	1	no	—
202	C₅×C₄⋊C₄	—	4	1	no	—
203	C₅×C₄⋊C₄	—	4	1	no	—
204	C₅×C₄⋊C₄	—	4	1	no	—
205	C₅×C₄⋊C₄	—	4	1	no	—
206	C₅×C₄⋊C₄	—	4	1	no	—
207	C₅×C₄⋊C₄	—	4	1	no	—
208	C₅×C₄⋊C₄	D₈	1	1	yes	characteristic
209	C₅×C₂²⋊C₄	—	4	1	no	—
210	C₅×C₂²⋊C₄	—	4	1	no	—
211	C₅×C₂²⋊C₄	—	4	1	no	—
212	C₅×C₂²⋊C₄	—	4	1	no	—
213	C₅×C₂²⋊C₄	—	4	1	no	—
214	C₅×C₂²⋊C₄	—	4	1	no	—
215	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
216	C₅×C₂²⋊C₄	D₈	1	1	yes	characteristic
217	C₄²×C₅	—	4	1	no	—
218	C₄²×C₅	—	4	1	no	—
219	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
220	C₅×C₁₆	—	2	1	no	—
221	C₅×C₁₆	—	2	1	no	—
222	C₅×C₁₆	—	2	1	no	—
223	C₅×C₁₆	C₂×D₄	1	2	yes	—
224	C₂×#135	C₂²×C₅	1	1	yes	characteristic
225	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂²×Q₁₆	C₂²×C₅	1	1	yes	characteristic
228	D₄×Q₈	—	2	1	no	—
229	#548	—	2	1	no	—
230	#510	—	2	4	no	—
231	C₂×Q₃₂	—	2	4	no	—
232	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
233	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
234	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
235	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
236	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
237	C₂×Q₃₂	C₂²×C₅	1	1	yes	characteristic
238	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
239	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
240	C₂×SD₃₂	C₂²×C₅	1	1	yes	characteristic
241	C₂×M₃₂	C₂²×C₅	1	1	yes	characteristic
242	C₂²×C₁₆	C₂²×C₅	1	1	yes	characteristic
243	#495	C₂²×C₅	1	1	yes	characteristic
244	#494	C₂²×C₅	1	1	yes	characteristic
245	#467	C₂²×C₅	1	1	yes	characteristic
246	#467	C₂²×C₅	1	1	yes	characteristic
247	#467	C₂²×C₅	1	1	yes	characteristic
248	#466	C₂²×C₅	1	1	yes	characteristic
249	#464	—	2	1	no	—
250	#462	—	2	1	no	—
251	#452	—	2	1	no	—
252	#451	—	2	1	no	—
253	#451	—	2	1	no	—
254	#448	—	2	1	no	—
255	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
256	C₄×Q₁₆	C₂²×C₅	1	1	yes	characteristic
257	C₈×D₄	C₂²×C₅	1	1	yes	characteristic
258	#367	C₂²×C₅	1	1	yes	characteristic
259	C₄⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
260	#358	C₂²×C₅	1	1	yes	characteristic
261	#358	C₂²×C₅	1	1	yes	characteristic
262	#358	C₂²×C₅	1	1	yes	characteristic
263	#358	C₂²×C₅	1	1	yes	characteristic
264	#358	C₂²×C₅	1	1	yes	characteristic
265	#357	C₂²×C₅	1	1	yes	characteristic
266	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
267	C₂²⋊C₁₆	C₂²×C₅	1	1	yes	characteristic
268	#346	C₂²×C₅	1	1	yes	characteristic
269	C₂³×C₅	—	4	1	no	—
270	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
271	C₂³×C₅	C₂×D₈	1	1	yes	characteristic
272	C₅×Q₈	—	2	2	no	—
273	C₅×Q₈	—	2	2	no	—
274	C₅×Q₈	—	4	1	no	—
275	C₅×Q₈	—	4	1	no	—
276	C₅×Q₈	—	4	1	no	—
277	C₅×Q₈	—	4	1	no	—
278	C₅×Q₈	—	4	1	no	—
279	C₅×Q₈	—	4	1	no	—
280	C₅×Q₈	—	4	1	no	—
281	C₅×Q₈	—	4	1	no	—
282	C₅×Q₈	—	8	2	no	—
283	C₅×Q₈	—	8	2	no	—
284	C₅×Q₈	—	8	2	no	—
285	C₅×D₄	—	2	2	no	—
286	C₅×D₄	—	4	1	no	—
287	C₅×D₄	—	4	1	no	—
288	C₅×D₄	—	8	2	no	—
289	C₅×D₄	—	8	2	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	1	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	4	1	no	—
295	C₂×C₄×C₅	—	4	1	no	—
296	C₂×C₄×C₅	—	4	1	no	—
297	C₂×C₄×C₅	—	4	1	no	—
298	C₂×C₄×C₅	—	4	1	no	—
299	C₂×C₄×C₅	—	4	1	no	—
300	C₂×C₄×C₅	—	4	1	no	—
301	C₂×C₄×C₅	—	8	2	no	—
302	C₂×C₄×C₅	—	8	2	no	—
303	C₂×C₄×C₅	—	8	2	no	—
304	C₂×C₄×C₅	—	8	2	no	—
305	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×D₈	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	C₂²×D₄	1	1	yes	characteristic
314	C₅×C₈	H(5,𝔽₂)	1	1	yes	characteristic
315	C₂×#41	—	2	1	no	—
316	C₂²×Q₈	—	2	1	no	—
317	C₂²×Q₈	—	2	1	no	—
318	C₂²×Q₈	—	2	1	no	—
319	#135	—	2	2	no	—
320	#135	—	4	1	no	—
321	C₂×Q₁₆	—	2	2	no	—
322	C₂×Q₁₆	—	2	2	no	—
323	C₂×Q₁₆	—	2	2	no	—
324	C₂×Q₁₆	—	2	1	no	—
325	C₂×Q₁₆	—	2	1	no	—
326	C₂×Q₁₆	—	2	1	no	—
327	C₂×Q₁₆	—	2	1	no	—
328	C₂×Q₁₆	—	4	1	no	—
329	C₂×Q₁₆	—	4	1	no	—
330	C₂×Q₁₆	—	4	1	no	—
331	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
332	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
333	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
334	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
335	C₂×Q₁₆	C₂³×C₅	1	1	yes	characteristic
336	C₂×SD₁₆	—	2	1	no	—
337	C₂×SD₁₆	—	2	1	no	—
338	C₂×D₈	C₂³×C₅	1	1	yes	characteristic
339	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
340	C₂²×C₈	C₂³×C₅	1	1	yes	characteristic
341	C₄⋊Q₈	—	2	1	no	—
342	C₄⋊Q₈	—	4	1	no	—
343	#124	—	2	1	no	—
344	#124	—	4	1	no	—
345	C₂²⋊Q₈	—	2	1	no	—
346	C₂²⋊Q₈	—	2	1	no	—
347	C₂²⋊Q₈	—	2	1	no	—
348	C₂²⋊Q₈	—	4	1	no	—
349	C₂²⋊Q₈	—	4	1	no	—
350	C₂²⋊Q₈	—	4	1	no	—
351	#121	—	2	1	no	—
352	#121	—	4	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×D₄	—	4	1	no	—
356	C₄×D₄	—	4	1	no	—
357	C₄×D₄	C₅×D₄	1	1	yes	characteristic
358	Q₃₂	—	2	2	no	—
359	Q₃₂	—	2	2	no	—
360	Q₃₂	—	2	2	no	—
361	Q₃₂	—	2	2	no	—
362	Q₃₂	—	4	1	no	—
363	Q₃₂	C₅×D₄	1	4	yes	complemented
364	SD₃₂	—	2	2	no	—
365	SD₃₂	—	2	2	no	—
366	SD₃₂	—	4	1	no	—
367	M₃₂	—	2	2	no	—
368	C₂×C₁₆	—	2	2	no	—
369	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
370	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
371	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
372	C₂×C₁₆	C₂³×C₅	1	1	yes	characteristic
373	#107	C₂³×C₅	1	1	yes	characteristic
374	#107	C₂³×C₅	1	1	yes	characteristic
375	C₄⋊C₈	C₅×D₄	1	1	yes	characteristic
376	#103	—	2	1	no	—
377	#103	—	2	1	no	—
378	#103	—	2	1	no	—
379	#103	—	2	1	no	—
380	#103	—	2	1	no	—
381	#102	—	2	1	no	—
382	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
383	C₂²⋊C₈	C₅×D₄	1	1	yes	characteristic
384	C₄×C₈	C₂³×C₅	1	1	yes	characteristic
385	C₂²×C₅	—	2	1	no	—
386	C₂²×C₅	—	2	1	no	—
387	C₂²×C₅	—	2	1	no	—
388	C₂²×C₅	—	2	1	no	—
389	C₂²×C₅	—	2	1	no	—
390	C₂²×C₅	—	8	1	no	—
391	C₂²×C₅	—	8	1	no	—
392	C₂²×C₅	—	8	1	no	—
393	C₂²×C₅	#510	1	2	yes	complemented
394	C₂²×C₅	C₂²×D₈	1	1	yes	characteristic
395	C₄×C₅	—	2	1	no	—
396	C₄×C₅	—	2	1	no	—
397	C₄×C₅	—	2	1	no	—
398	C₄×C₅	—	2	1	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	2	no	—
401	C₄×C₅	—	8	1	no	—
402	C₄×C₅	—	8	1	no	—
403	C₄×C₅	—	8	1	no	—
404	C₄×C₅	—	8	1	no	—
405	C₄×C₅	—	8	1	no	—
406	C₄×C₅	D₄²	1	1	yes	characteristic
407	C₄×C₅	#576	1	1	yes	characteristic
408	#41	—	4	2	no	—
409	#41	—	8	1	no	—
410	C₂×Q₈	—	2	1	no	—
411	C₂×Q₈	—	2	1	no	—
412	C₂×Q₈	—	2	1	no	—
413	C₂×Q₈	—	2	1	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	4	2	no	—
416	C₂×Q₈	—	4	2	no	—
417	C₂×Q₈	—	4	2	no	—
418	C₂×Q₈	—	4	1	no	—
419	C₂×Q₈	—	4	1	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	—	8	1	no	—
422	C₂×Q₈	—	8	1	no	—
423	C₂×Q₈	—	8	1	no	—
424	C₂×D₄	—	2	1	no	—
425	C₂×D₄	—	4	1	no	—
426	C₂×D₄	—	4	1	no	—
427	C₂×D₄	C₅×D₈	1	1	yes	characteristic
428	C₂²×C₄	—	4	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
433	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
434	Q₁₆	—	2	1	no	—
435	Q₁₆	—	2	1	no	—
436	Q₁₆	—	2	1	no	—
437	Q₁₆	—	2	1	no	—
438	Q₁₆	—	2	1	no	—
439	Q₁₆	—	2	1	no	—
440	Q₁₆	—	2	1	no	—
441	Q₁₆	—	2	1	no	—
442	Q₁₆	—	4	2	no	—
443	Q₁₆	—	4	2	no	—
444	Q₁₆	—	4	2	no	—
445	Q₁₆	—	8	1	no	—
446	Q₁₆	C₂×C₅×D₄	1	2	yes	—
447	Q₁₆	C₂×C₅×D₄	1	2	yes	—
448	SD₁₆	—	4	2	no	—
449	SD₁₆	—	8	1	no	—
450	D₈	—	2	1	no	—
451	D₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
457	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
458	C₂×C₈	C₂×C₅×D₄	1	1	yes	characteristic
459	C₂×C₈	C₂⁴×C₅	1	1	yes	characteristic
460	C₄⋊C₄	—	2	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₄⋊C₄	—	4	1	no	—
465	C₄⋊C₄	—	4	1	no	—
466	C₄⋊C₄	—	4	1	no	—
467	C₄⋊C₄	—	4	1	no	—
468	C₄⋊C₄	—	4	1	no	—
469	C₄⋊C₄	C₅×D₈	1	1	yes	characteristic
470	C₂²⋊C₄	—	4	1	no	—
471	C₂²⋊C₄	—	4	1	no	—
472	C₂²⋊C₄	—	4	1	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	4	1	no	—
476	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
477	C₂²⋊C₄	C₅×D₈	1	1	yes	characteristic
478	C₄²	—	4	1	no	—
479	C₄²	—	4	1	no	—
480	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
481	C₁₆	—	2	1	no	—
482	C₁₆	—	2	1	no	—
483	C₁₆	—	2	1	no	—
484	C₁₆	C₂×C₅×D₄	1	2	yes	—
485	C₂×C₅	—	2	2	no	—
486	C₂×C₅	—	4	1	no	—
487	C₂×C₅	—	16	1	no	—
488	C₂×C₅	D₄×D₈	1	1	yes	characteristic
489	C₂×C₅	C₂×#510	1	1	yes	characteristic
490	C₂×C₅	#3417	1	1	yes	characteristic
491	C₂³	—	4	1	no	—
492	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
493	C₂³	C₂×C₅×D₈	1	1	yes	characteristic
494	Q₈	—	2	2	no	—
495	Q₈	—	2	2	no	—
496	Q₈	—	4	1	no	—
497	Q₈	—	4	1	no	—
498	Q₈	—	4	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	4	1	no	—
502	Q₈	—	4	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	8	2	no	—
505	Q₈	—	8	2	no	—
506	Q₈	—	8	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	2	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	8	2	no	—
524	C₂×C₄	—	8	2	no	—
525	C₂×C₄	—	8	2	no	—
526	C₂×C₄	—	8	2	no	—
527	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
528	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
529	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
530	C₂×C₄	C₂×C₅×D₈	1	1	yes	characteristic
531	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
532	C₈	—	2	1	no	—
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	C₂²×C₅×D₄	1	1	yes	characteristic
536	C₈	C₅×H(5,𝔽₂)	1	1	yes	characteristic
537	C₅	#33836	1	1	yes	characteristic, direct product factor, Sylow
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	2	1	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	8	1	no	—
544	C₂²	—	8	1	no	—
545	C₂²	—	8	1	no	—
546	C₂²	C₅×#510	1	2	yes	complemented
547	C₂²	C₂²×C₅×D₈	1	1	yes	characteristic
548	C₄	—	2	1	no	—
549	C₄	—	2	1	no	—
550	C₄	—	2	1	no	—
551	C₄	—	2	1	no	—
552	C₄	—	4	2	no	—
553	C₄	—	4	2	no	—
554	C₄	—	8	1	no	—
555	C₄	—	8	1	no	—
556	C₄	—	8	1	no	—
557	C₄	—	8	1	no	—
558	C₄	—	8	1	no	—
559	C₄	C₅×D₄²	1	1	yes	characteristic
560	C₄	C₅×#576	1	1	yes	characteristic
561	C₂	—	2	2	no	—
562	C₂	—	4	1	no	—
563	C₂	—	16	1	no	—
564	C₂	C₅×D₄×D₈	1	1	yes	characteristic
565	C₂	C₂×C₅×#510	1	1	yes	characteristic
566	C₂	C₅×#3417	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂²×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴×C₅
prime radical	C₅×#3285	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×D₄ ◁ C₅×C₈×D₄ ◁ 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×Q₃₂	C₂	semidirect
3. C₅×D₄×Q₁₆	C₂	semidirect
5. C₅×#2251	C₂	semidirect
6. C₅×#2219	C₂	semidirect
7. C₅×#2217	C₂	semidirect
8. C₅×#2211	C₂	semidirect
9. C₅×#2209	C₂	semidirect
10. C₅×#2189	C₂	semidirect
11. C₅×#2188	C₂	semidirect
12. C₅×#2188	C₂	semidirect
13. C₅×#2185	C₂	semidirect
14. C₅×#2176	C₂	semidirect
15. C₅×#2168	C₂	semidirect
61. #33836	C₅	direct (N × H)
110. C₅×Q₃₂	D₄	semidirect
132. C₂×#510	C₂×C₅	semidirect
133. C₂²×Q₃₂	C₂×C₅	semidirect
134. D₄×Q₁₆	C₂×C₅	semidirect
136. #2251	C₂×C₅	semidirect
137. #2219	C₂×C₅	semidirect
138. #2217	C₂×C₅	semidirect
139. #2211	C₂×C₅	semidirect
140. #2209	C₂×C₅	semidirect
141. #2189	C₂×C₅	semidirect
142. #2188	C₂×C₅	semidirect
143. #2188	C₂×C₅	semidirect
144. #2185	C₂×C₅	semidirect
145. #2176	C₂×C₅	semidirect
146. #2168	C₂×C₅	semidirect
363. Q₃₂	C₅×D₄	semidirect
393. C₂²×C₅	#510	semidirect
537. C₅	#33836	direct (N × H)
546. 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×Q₃₂	2
C₅×D₄×Q₁₆	2
C₅×#3285	2
C₅×#2251	2
C₅×#2219	2
C₅×#2217	2
C₅×#2211	2
C₅×#2209	2
C₅×#2189	2
C₅×#2188	2
C₅×#2185	2
C₅×#2176	2
C₅×#2168	2
#33836	5

Subgroups — C5×#33836 #11956556

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#33836 #11956556