Subgroups — C₅×#60590 #11983310

Order 1280.

2194 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×C₅×H(5,𝔽₂)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3122	C₂	1	4	yes	maximal, complemented
4	C₅×#3119	C₂	1	4	yes	maximal, complemented
5	C₅×#3115	C₂	1	2	yes	maximal, complemented
6	C₅×#3109	C₂	1	2	yes	maximal, complemented
7	C₅×#3106	C₂	1	2	yes	maximal, complemented
8	C₅×#3100	C₂	1	2	yes	maximal, complemented
9	C₅×#3096	C₂	1	2	yes	maximal, complemented
10	C₅×#3077	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3076	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3038	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3008	C₂	1	2	yes	maximal, complemented
15	C₅×#2948	C₂	1	2	yes	maximal, complemented
16	C₅×#2946	C₂	1	2	yes	maximal, complemented
17	C₅×#2925	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
19	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂²×C₅×D₈	C₂²	1	2	yes	—
21	C₅×#559	—	2	1	no	—
22	C₅×#559	—	2	1	no	—
23	C₅×#550	—	2	1	no	—
24	C₅×#550	—	2	1	no	—
25	C₅×#546	—	2	2	no	—
26	C₅×#546	—	2	2	no	—
27	C₅×#540	C₂²	1	4	yes	complemented
28	C₅×#535	C₂²	1	2	yes	—
29	C₅×#533	C₂²	1	1	yes	characteristic, complemented
30	C₅×#532	C₂²	1	2	yes	complemented
31	C₅×#532	C₂²	1	2	yes	complemented
32	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
33	C₅×#520	—	2	1	no	—
34	C₅×#520	C₂²	1	1	yes	characteristic
35	C₅×#520	C₂²	1	1	yes	characteristic
36	C₅×#520	C₂²	1	2	yes	complemented
37	C₅×#518	—	2	2	no	—
38	C₅×#518	—	2	1	no	—
39	C₅×#518	C₂²	1	1	yes	characteristic
40	C₅×#518	C₂²	1	2	yes	complemented
41	C₅×#518	C₂²	1	2	yes	complemented
42	C₄×C₅×#41	—	2	1	no	—
43	C₄×C₅×#41	C₂²	1	1	yes	characteristic
44	C₄×C₅×#41	C₂²	1	1	yes	characteristic
45	C₄×C₅×#41	C₂²	1	2	yes	complemented
46	C₂×C₄×C₅×D₄	—	2	1	no	—
47	C₂×C₄×C₅×D₄	—	2	2	no	—
48	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
49	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
50	C₅×#482	C₂²	1	4	yes	complemented
51	C₅×#482	C₂²	1	4	yes	complemented
52	C₅×#481	C₂²	1	4	yes	complemented
53	C₅×#480	C₂²	1	4	yes	complemented
54	C₅×#479	C₂²	1	2	yes	complemented
55	C₅×#478	C₂²	1	2	yes	complemented
56	C₅×#478	C₂²	1	4	yes	complemented
57	C₅×#477	C₂²	1	1	yes	characteristic, complemented
58	C₅×#476	C₂²	1	1	yes	characteristic, complemented
59	C₅×#476	C₂²	1	2	yes	complemented
60	C₅×#475	C₂²	1	1	yes	characteristic, complemented
61	C₅×#474	C₂²	1	1	yes	characteristic, complemented
62	C₅×#474	C₂²	1	2	yes	complemented
63	C₅×#460	C₂²	1	2	yes	complemented
64	C₅×#460	C₂²	1	2	yes	complemented
65	C₅×#459	C₂²	1	2	yes	complemented
66	C₅×#459	C₂²	1	2	yes	complemented
67	C₅×#459	C₂²	1	4	yes	complemented
68	C₅×#459	C₂²	1	2	yes	complemented
69	C₅×#459	C₂²	1	2	yes	complemented
70	C₅×#449	C₂²	1	4	yes	complemented
71	C₅×#449	C₂²	1	4	yes	complemented
72	C₅×#447	C₂²	1	4	yes	complemented
73	C₅×#447	C₂²	1	4	yes	complemented
74	C₅×#442	C₂²	1	4	yes	complemented
75	C₅×#442	C₂²	1	4	yes	complemented
76	C₅×#442	C₂²	1	4	yes	complemented
77	C₅×#440	C₂²	1	4	yes	complemented
78	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
79	C₄×C₅×D₈	C₂²	1	4	yes	complemented
80	C₄×C₅×D₈	C₂²	1	4	yes	complemented
81	C₄×C₅×D₈	C₂²	1	4	yes	complemented
82	C₅×#433	C₂²	1	4	yes	complemented
83	C₅×#432	C₂²	1	2	yes	complemented
84	C₅×#431	C₂²	1	2	yes	complemented
85	C₅×#428	C₂²	1	2	yes	complemented
86	C₅×#427	C₂²	1	2	yes	complemented
87	C₅×#423	C₂²	1	1	yes	characteristic, complemented
88	C₂×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
89	C₅×#418	C₂²	1	2	yes	—
90	C₅×#418	C₂²	1	2	yes	complemented
91	C₅×#416	C₂²	1	2	yes	—
92	C₂×C₅×#102	C₂²	1	2	yes	complemented
93	C₅×#408	C₂²	1	2	yes	—
94	C₅×#405	C₂²	1	2	yes	complemented
95	#60590	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₅×H(5,𝔽₂)	—	2	4	no	—
97	C₅×H(5,𝔽₂)	—	2	4	no	—
98	C₂×C₅×#41	—	2	1	no	—
99	C₂×C₅×#41	—	2	2	no	—
100	C₂×C₅×#41	—	2	2	no	—
101	C₂×C₅×#41	C₂³	1	2	yes	—
102	C₂×C₅×#41	C₂³	1	1	yes	characteristic
103	C₂×C₅×#41	C₂³	1	1	yes	characteristic
104	C₂²×C₅×D₄	—	2	2	no	—
105	C₂²×C₅×D₄	—	2	1	no	—
106	C₂²×C₅×D₄	—	2	1	no	—
107	C₂²×C₅×D₄	—	2	1	no	—
108	C₂²×C₅×D₄	C₂³	1	2	yes	—
109	C₂²×C₅×D₄	C₂³	1	2	yes	—
110	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₅	—	2	1	no	—
112	C₂³×C₄×C₅	—	2	2	no	—
113	C₅×AGL(1,ℤ/8)	—	2	8	no	—
114	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₅×D₈	—	2	8	no	—
116	C₂×C₅×D₈	C₂³	1	4	yes	—
117	C₂×C₅×D₈	C₂³	1	4	yes	—
118	C₂×C₅×D₈	C₂³	1	4	yes	—
119	C₂×C₅×M₁₆	C₂³	1	2	yes	—
120	C₂²×C₅×C₈	C₂³	1	2	yes	—
121	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
122	C₅×C₄⋊Q₈	C₂³	1	1	yes	characteristic
123	C₅×#127	—	2	2	no	—
124	C₅×#127	—	2	1	no	—
125	C₅×#127	—	2	1	no	—
126	C₅×#127	C₂³	1	2	yes	—
127	C₅×#127	C₂³	1	2	yes	—
128	C₅×#125	C₂³	1	2	yes	—
129	C₅×#124	—	2	2	no	—
130	C₅×#124	—	2	2	no	—
131	C₅×#124	—	2	2	no	—
132	C₅×#123	—	2	4	no	—
133	C₅×#123	—	2	4	no	—
134	C₅×C₂²⋊Q₈	—	2	1	no	—
135	C₅×C₂²⋊Q₈	—	2	1	no	—
136	C₅×#121	—	2	2	no	—
137	C₅×#121	—	2	2	no	—
138	C₅×#121	—	2	4	no	—
139	C₅×#121	—	2	4	no	—
140	C₅×#121	C₂³	1	4	yes	—
141	C₅×#121	C₂³	1	4	yes	—
142	C₅×#120	—	2	4	no	—
143	C₄×C₅×Q₈	—	2	1	no	—
144	C₄×C₅×Q₈	—	2	1	no	—
145	C₄×C₅×Q₈	—	2	1	no	—
146	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
147	C₄×C₅×Q₈	D₄	1	1	yes	characteristic
148	C₄×C₅×Q₈	C₂³	1	2	yes	—
149	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
150	C₄×C₅×Q₈	C₂³	1	1	yes	characteristic
151	C₄×C₅×D₄	—	2	2	no	—
152	C₄×C₅×D₄	—	2	1	no	—
153	C₄×C₅×D₄	—	2	1	no	—
154	C₄×C₅×D₄	—	2	2	no	—
155	C₄×C₅×D₄	—	2	1	no	—
156	C₄×C₅×D₄	—	2	2	no	—
157	C₄×C₅×D₄	—	2	1	no	—
158	C₄×C₅×D₄	—	2	2	no	—
159	C₄×C₅×D₄	—	2	1	no	—
160	C₄×C₅×D₄	—	2	2	no	—
161	C₄×C₅×D₄	—	2	2	no	—
162	C₄×C₅×D₄	—	2	2	no	—
163	C₄×C₅×D₄	—	2	2	no	—
164	C₄×C₅×D₄	—	2	2	no	—
165	C₄×C₅×D₄	—	2	2	no	—
166	C₄×C₅×D₄	—	2	1	no	—
167	C₄×C₅×D₄	—	2	2	no	—
168	C₄×C₅×D₄	—	2	1	no	—
169	C₄×C₅×D₄	—	2	2	no	—
170	C₄×C₅×D₄	—	2	2	no	—
171	C₄×C₅×D₄	—	2	2	no	—
172	C₄×C₅×D₄	D₄	1	2	yes	—
173	C₄×C₅×D₄	D₄	1	1	yes	characteristic
174	C₄×C₅×D₄	D₄	1	2	yes	—
175	C₄×C₅×D₄	D₄	1	1	yes	characteristic
176	C₄×C₅×D₄	C₂³	1	4	yes	—
177	C₄×C₅×D₄	C₂³	1	2	yes	—
178	C₄×C₅×D₄	C₂³	1	2	yes	—
179	C₄×C₅×D₄	C₂³	1	2	yes	—
180	C₄×C₅×D₄	C₂³	1	4	yes	—
181	C₄×C₅×D₄	C₂³	1	2	yes	—
182	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
183	C₄×C₅×D₄	C₂³	1	2	yes	—
184	C₄×C₅×D₄	C₂³	1	1	yes	characteristic
185	C₅×#117	—	2	1	no	—
186	C₅×#117	—	2	2	no	—
187	C₅×#117	—	2	1	no	—
188	C₅×#117	—	2	2	no	—
189	C₅×#117	C₂³	1	2	yes	—
190	C₅×#117	C₂³	1	1	yes	characteristic
191	C₅×#117	C₂³	1	2	yes	—
192	C₅×#117	C₂³	1	1	yes	characteristic
193	C₅×#117	C₂³	1	2	yes	—
194	C₂×C₅×C₄⋊C₄	—	2	1	no	—
195	C₂×C₅×C₄⋊C₄	—	2	2	no	—
196	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
197	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
199	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
200	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
201	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
202	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
203	C₂×C₅×C₂²⋊C₄	—	2	4	no	—
204	C₂×C₄²×C₅	—	2	1	no	—
205	C₂×C₄²×C₅	—	2	2	no	—
206	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
207	C₂×C₄²×C₅	C₂³	1	2	yes	—
208	C₅×#107	C₂³	1	2	yes	—
209	C₅×#107	C₂³	1	2	yes	—
210	C₅×#107	C₂³	1	4	yes	—
211	C₅×#106	C₂³	1	2	yes	—
212	C₅×#106	C₂³	1	2	yes	—
213	C₅×#106	C₂³	1	4	yes	—
214	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
215	C₅×C₄⋊C₈	C₂³	1	1	yes	characteristic
216	C₅×C₄⋊C₈	C₂³	1	2	yes	—
217	C₅×C₄⋊C₈	C₂³	1	2	yes	—
218	C₅×C₄⋊C₈	C₂³	1	2	yes	—
219	C₅×#103	C₂³	1	2	yes	—
220	C₅×#103	C₂³	1	2	yes	—
221	C₅×#102	C₂³	1	4	yes	—
222	C₅×#102	C₂³	1	4	yes	—
223	C₅×#102	C₂³	1	2	yes	—
224	C₅×#102	C₂³	1	2	yes	—
225	C₅×#102	C₂³	1	4	yes	—
226	C₅×#102	C₂³	1	4	yes	—
227	C₅×#102	C₂³	1	4	yes	—
228	C₅×#102	C₂³	1	4	yes	—
229	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
230	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
231	C₅×#97	C₂³	1	4	yes	—
232	C₄×C₅×C₈	C₂³	1	4	yes	—
233	#3508	C₂×C₅	1	1	yes	characteristic, complemented
234	C₄×H(5,𝔽₂)	C₂×C₅	1	1	yes	characteristic, complemented
235	#3122	C₂×C₅	1	4	yes	complemented
236	#3119	C₂×C₅	1	4	yes	complemented
237	#3115	C₂×C₅	1	2	yes	complemented
238	#3109	C₂×C₅	1	2	yes	complemented
239	#3106	C₂×C₅	1	2	yes	complemented
240	#3100	C₂×C₅	1	2	yes	complemented
241	#3096	C₂×C₅	1	2	yes	complemented
242	#3077	C₂×C₅	1	1	yes	characteristic, complemented
243	#3076	C₂×C₅	1	1	yes	characteristic, complemented
244	#3038	C₂×C₅	1	1	yes	characteristic, complemented
245	C₂×#459	C₂×C₅	1	1	yes	characteristic, complemented
246	#3008	C₂×C₅	1	2	yes	complemented
247	#2948	C₂×C₅	1	2	yes	complemented
248	#2946	C₂×C₅	1	2	yes	complemented
249	#2925	C₂×C₅	1	1	yes	characteristic, complemented
250	C₂⁴×C₅	—	2	2	no	—
251	C₂⁴×C₅	—	2	1	no	—
252	C₂⁴×C₅	—	2	2	no	—
253	C₅×#41	—	2	8	no	—
254	C₅×#41	—	2	4	no	—
255	C₅×#41	—	2	4	no	—
256	C₅×#41	—	2	2	no	—
257	C₅×#41	—	2	2	no	—
258	C₅×#41	—	2	2	no	—
259	C₅×#41	—	8	4	no	—
260	C₅×#41	—	8	4	no	—
261	C₅×#41	#41	1	4	yes	complemented
262	C₂×C₅×Q₈	—	2	1	no	—
263	C₂×C₅×Q₈	—	2	1	no	—
264	C₂×C₅×Q₈	C₂×D₄	1	1	yes	characteristic
265	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₅×D₄	—	2	16	no	—
267	C₂×C₅×D₄	—	2	8	no	—
268	C₂×C₅×D₄	—	2	2	no	—
269	C₂×C₅×D₄	—	2	1	no	—
270	C₂×C₅×D₄	—	2	4	no	—
271	C₂×C₅×D₄	—	2	4	no	—
272	C₂×C₅×D₄	—	2	4	no	—
273	C₂×C₅×D₄	—	2	4	no	—
274	C₂×C₅×D₄	—	2	2	no	—
275	C₂×C₅×D₄	—	2	1	no	—
276	C₂×C₅×D₄	—	2	2	no	—
277	C₂×C₅×D₄	—	2	2	no	—
278	C₂×C₅×D₄	—	2	2	no	—
279	C₂×C₅×D₄	—	2	2	no	—
280	C₂×C₅×D₄	—	2	2	no	—
281	C₂×C₅×D₄	—	2	2	no	—
282	C₂×C₅×D₄	—	2	4	no	—
283	C₂×C₅×D₄	—	2	4	no	—
284	C₂×C₅×D₄	—	8	2	no	—
285	C₂×C₅×D₄	—	8	2	no	—
286	C₂×C₅×D₄	C₂×D₄	1	2	yes	—
287	C₂×C₅×D₄	C₂×D₄	1	1	yes	characteristic
288	C₂×C₅×D₄	#41	1	4	yes	complemented
289	C₂×C₅×D₄	C₂⁴	1	4	yes	—
290	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
291	C₂×C₅×D₄	C₂⁴	1	2	yes	—
292	C₂²×C₄×C₅	—	2	2	no	—
293	C₂²×C₄×C₅	—	2	1	no	—
294	C₂²×C₄×C₅	—	2	2	no	—
295	C₂²×C₄×C₅	—	2	1	no	—
296	C₂²×C₄×C₅	—	2	1	no	—
297	C₂²×C₄×C₅	—	2	2	no	—
298	C₂²×C₄×C₅	—	2	2	no	—
299	C₂²×C₄×C₅	—	2	1	no	—
300	C₂²×C₄×C₅	—	2	2	no	—
301	C₂²×C₄×C₅	—	2	2	no	—
302	C₂²×C₄×C₅	—	2	2	no	—
303	C₂²×C₄×C₅	—	2	4	no	—
304	C₂²×C₄×C₅	—	2	4	no	—
305	C₂²×C₄×C₅	—	8	2	no	—
306	C₂²×C₄×C₅	—	8	4	no	—
307	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
308	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
309	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
310	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₅	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
313	C₅×SD₁₆	—	2	8	no	—
314	C₅×D₈	—	2	8	no	—
315	C₅×D₈	—	2	8	no	—
316	C₅×D₈	—	2	8	no	—
317	C₅×M₁₆	—	2	4	no	—
318	C₂×C₅×C₈	—	2	4	no	—
319	C₂×C₅×C₈	C₂⁴	1	2	yes	—
320	C₂×C₅×C₈	C₂⁴	1	2	yes	—
321	C₂×C₅×C₈	C₂⁴	1	4	yes	—
322	C₅×C₄⋊C₄	—	2	2	no	—
323	C₅×C₄⋊C₄	—	2	1	no	—
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	2	1	no	—
326	C₅×C₄⋊C₄	—	2	1	no	—
327	C₅×C₄⋊C₄	—	2	1	no	—
328	C₅×C₄⋊C₄	—	2	1	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	2	2	no	—
331	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
332	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
333	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
334	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
335	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
336	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
337	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
338	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
340	C₅×C₂²⋊C₄	—	2	2	no	—
341	C₅×C₂²⋊C₄	—	2	1	no	—
342	C₅×C₂²⋊C₄	—	2	2	no	—
343	C₅×C₂²⋊C₄	—	2	2	no	—
344	C₅×C₂²⋊C₄	—	2	1	no	—
345	C₅×C₂²⋊C₄	—	2	2	no	—
346	C₅×C₂²⋊C₄	—	2	2	no	—
347	C₅×C₂²⋊C₄	—	2	2	no	—
348	C₅×C₂²⋊C₄	—	2	2	no	—
349	C₅×C₂²⋊C₄	—	2	1	no	—
350	C₅×C₂²⋊C₄	—	2	4	no	—
351	C₅×C₂²⋊C₄	—	2	4	no	—
352	C₅×C₂²⋊C₄	—	2	4	no	—
353	C₅×C₂²⋊C₄	—	2	4	no	—
354	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
355	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₄²×C₅	—	2	1	no	—
358	C₄²×C₅	—	2	2	no	—
359	C₄²×C₅	—	2	1	no	—
360	C₄²×C₅	—	2	2	no	—
361	C₄²×C₅	—	2	1	no	—
362	C₄²×C₅	—	2	2	no	—
363	C₄²×C₅	C₂×D₄	1	2	yes	—
364	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₅	C₂×D₄	1	2	yes	—
366	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₅	C₂⁴	1	1	yes	characteristic
368	C₄²×C₅	C₂⁴	1	2	yes	—
369	C₄²×C₅	C₂⁴	1	1	yes	characteristic
370	C₂×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic
371	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
372	C₂²×D₈	C₂²×C₅	1	2	yes	—
373	#559	—	2	1	no	—
374	#559	—	2	1	no	—
375	#550	—	2	1	no	—
376	#550	—	2	1	no	—
377	#546	—	2	2	no	—
378	#546	—	2	2	no	—
379	#540	C₂²×C₅	1	4	yes	complemented
380	#535	C₂²×C₅	1	2	yes	—
381	#533	C₂²×C₅	1	1	yes	characteristic, complemented
382	#532	C₂²×C₅	1	2	yes	complemented
383	#532	C₂²×C₅	1	2	yes	complemented
384	C₂×#127	C₂²×C₅	1	1	yes	characteristic, complemented
385	#520	—	2	1	no	—
386	#520	C₂²×C₅	1	1	yes	characteristic
387	#520	C₂²×C₅	1	1	yes	characteristic
388	#520	C₂²×C₅	1	2	yes	complemented
389	#518	—	2	2	no	—
390	#518	—	2	1	no	—
391	#518	C₂²×C₅	1	1	yes	characteristic
392	#518	C₂²×C₅	1	2	yes	complemented
393	#518	C₂²×C₅	1	2	yes	complemented
394	C₄×#41	—	2	1	no	—
395	C₄×#41	C₂²×C₅	1	1	yes	characteristic
396	C₄×#41	C₂²×C₅	1	1	yes	characteristic
397	C₄×#41	C₂²×C₅	1	2	yes	complemented
398	C₂×C₄×D₄	—	2	1	no	—
399	C₂×C₄×D₄	—	2	2	no	—
400	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
401	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
402	#482	C₂²×C₅	1	4	yes	complemented
403	#482	C₂²×C₅	1	4	yes	complemented
404	#481	C₂²×C₅	1	4	yes	complemented
405	#480	C₂²×C₅	1	4	yes	complemented
406	#479	C₂²×C₅	1	2	yes	complemented
407	#478	C₂²×C₅	1	2	yes	complemented
408	#478	C₂²×C₅	1	4	yes	complemented
409	#477	C₂²×C₅	1	1	yes	characteristic, complemented
410	#476	C₂²×C₅	1	1	yes	characteristic, complemented
411	#476	C₂²×C₅	1	2	yes	complemented
412	#475	C₂²×C₅	1	1	yes	characteristic, complemented
413	#474	C₂²×C₅	1	1	yes	characteristic, complemented
414	#474	C₂²×C₅	1	2	yes	complemented
415	#460	C₂²×C₅	1	2	yes	complemented
416	#460	C₂²×C₅	1	2	yes	complemented
417	#459	C₂²×C₅	1	2	yes	complemented
418	#459	C₂²×C₅	1	2	yes	complemented
419	#459	C₂²×C₅	1	2	yes	complemented
420	#459	C₂²×C₅	1	4	yes	complemented
421	#459	C₂²×C₅	1	2	yes	complemented
422	#449	C₂²×C₅	1	4	yes	complemented
423	#449	C₂²×C₅	1	4	yes	complemented
424	#447	C₂²×C₅	1	4	yes	complemented
425	#447	C₂²×C₅	1	4	yes	complemented
426	#442	C₂²×C₅	1	4	yes	complemented
427	#442	C₂²×C₅	1	4	yes	complemented
428	#442	C₂²×C₅	1	4	yes	complemented
429	#440	C₂²×C₅	1	4	yes	complemented
430	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
431	C₄×D₈	C₂²×C₅	1	4	yes	complemented
432	C₄×D₈	C₂²×C₅	1	4	yes	complemented
433	C₄×D₈	C₂²×C₅	1	4	yes	complemented
434	#433	C₂²×C₅	1	4	yes	complemented
435	#432	C₂²×C₅	1	2	yes	complemented
436	#431	C₂²×C₅	1	2	yes	complemented
437	#428	C₂²×C₅	1	2	yes	complemented
438	#427	C₂²×C₅	1	2	yes	complemented
439	#423	C₂²×C₅	1	1	yes	characteristic, complemented
440	C₂×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
441	#418	C₂²×C₅	1	2	yes	—
442	#418	C₂²×C₅	1	2	yes	complemented
443	#416	C₂²×C₅	1	2	yes	—
444	C₂×#102	C₂²×C₅	1	2	yes	complemented
445	#408	C₂²×C₅	1	2	yes	—
446	#405	C₂²×C₅	1	2	yes	complemented
447	C₂³×C₅	—	2	8	no	—
448	C₂³×C₅	—	2	2	no	—
449	C₂³×C₅	—	2	1	no	—
450	C₂³×C₅	—	2	4	no	—
451	C₂³×C₅	—	2	4	no	—
452	C₂³×C₅	—	4	4	no	—
453	C₂³×C₅	—	8	1	no	—
454	C₂³×C₅	—	8	2	no	—
455	C₂³×C₅	—	8	1	no	—
456	C₂³×C₅	—	8	2	no	—
457	C₂³×C₅	—	8	2	no	—
458	C₂³×C₅	—	8	2	no	—
459	C₂³×C₅	C₂²×D₄	1	2	yes	—
460	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
461	C₅×Q₈	—	2	2	no	—
462	C₅×Q₈	—	2	1	no	—
463	C₅×Q₈	—	4	2	no	—
464	C₅×Q₈	—	4	2	no	—
465	C₅×Q₈	C₂×#41	1	2	yes	—
466	C₅×D₄	—	2	8	no	—
467	C₅×D₄	—	2	8	no	—
468	C₅×D₄	—	2	4	no	—
469	C₅×D₄	—	2	4	no	—
470	C₅×D₄	—	2	2	no	—
471	C₅×D₄	—	2	4	no	—
472	C₅×D₄	—	2	2	no	—
473	C₅×D₄	—	2	1	no	—
474	C₅×D₄	—	2	4	no	—
475	C₅×D₄	—	2	4	no	—
476	C₅×D₄	—	4	4	no	—
477	C₅×D₄	—	4	4	no	—
478	C₅×D₄	—	4	4	no	—
479	C₅×D₄	—	8	2	no	—
480	C₅×D₄	—	8	2	no	—
481	C₅×D₄	—	8	4	no	—
482	C₅×D₄	—	8	4	no	—
483	C₅×D₄	C₂×#41	1	2	yes	—
484	C₅×D₄	C₂×#41	1	4	yes	—
485	C₂×C₄×C₅	—	2	8	no	—
486	C₂×C₄×C₅	—	2	1	no	—
487	C₂×C₄×C₅	—	2	4	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	—	2	4	no	—
490	C₂×C₄×C₅	—	2	2	no	—
491	C₂×C₄×C₅	—	2	2	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	2	no	—
494	C₂×C₄×C₅	—	2	1	no	—
495	C₂×C₄×C₅	—	2	2	no	—
496	C₂×C₄×C₅	—	2	2	no	—
497	C₂×C₄×C₅	—	4	1	no	—
498	C₂×C₄×C₅	—	4	2	no	—
499	C₂×C₄×C₅	—	4	2	no	—
500	C₂×C₄×C₅	—	4	4	no	—
501	C₂×C₄×C₅	—	8	2	no	—
502	C₂×C₄×C₅	—	8	1	no	—
503	C₂×C₄×C₅	—	8	2	no	—
504	C₂×C₄×C₅	—	8	2	no	—
505	C₂×C₄×C₅	—	8	2	no	—
506	C₂×C₄×C₅	—	8	4	no	—
507	C₂×C₄×C₅	—	8	4	no	—
508	C₂×C₄×C₅	—	8	1	no	—
509	C₂×C₄×C₅	—	8	2	no	—
510	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
511	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
512	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
513	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
514	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
515	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
516	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
517	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
518	C₂×C₄×C₅	C₂×#41	1	2	yes	—
519	C₂×C₄×C₅	C₂×#41	1	2	yes	—
520	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
521	C₅×C₈	—	2	2	no	—
522	C₅×C₈	—	2	2	no	—
523	C₅×C₈	—	2	4	no	—
524	H(5,𝔽₂)	—	2	4	no	—
525	H(5,𝔽₂)	—	2	4	no	—
526	C₂×#41	—	2	1	no	—
527	C₂×#41	—	2	2	no	—
528	C₂×#41	—	2	2	no	—
529	C₂×#41	C₂³×C₅	1	2	yes	—
530	C₂×#41	C₂³×C₅	1	1	yes	characteristic
531	C₂×#41	C₂³×C₅	1	1	yes	characteristic
532	C₂²×D₄	—	2	2	no	—
533	C₂²×D₄	—	2	1	no	—
534	C₂²×D₄	—	2	1	no	—
535	C₂²×D₄	—	2	1	no	—
536	C₂²×D₄	C₂³×C₅	1	2	yes	—
537	C₂²×D₄	C₂³×C₅	1	2	yes	—
538	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
539	C₂³×C₄	—	2	1	no	—
540	C₂³×C₄	—	2	2	no	—
541	AGL(1,ℤ/8)	—	2	8	no	—
542	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
543	C₂×D₈	—	2	8	no	—
544	C₂×D₈	C₂³×C₅	1	4	yes	—
545	C₂×D₈	C₂³×C₅	1	4	yes	—
546	C₂×D₈	C₂³×C₅	1	4	yes	—
547	C₂×M₁₆	C₂³×C₅	1	2	yes	—
548	C₂²×C₈	C₂³×C₅	1	2	yes	—
549	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
550	C₄⋊Q₈	C₂³×C₅	1	1	yes	characteristic
551	#127	—	2	2	no	—
552	#127	—	2	1	no	—
553	#127	—	2	1	no	—
554	#127	C₂³×C₅	1	2	yes	—
555	#127	C₂³×C₅	1	2	yes	—
556	#125	C₂³×C₅	1	2	yes	—
557	#124	—	2	2	no	—
558	#124	—	2	2	no	—
559	#124	—	2	2	no	—
560	#123	—	2	4	no	—
561	#123	—	2	4	no	—
562	C₂²⋊Q₈	—	2	1	no	—
563	C₂²⋊Q₈	—	2	1	no	—
564	#121	—	2	2	no	—
565	#121	—	2	2	no	—
566	#121	—	2	4	no	—
567	#121	—	2	4	no	—
568	#121	C₂³×C₅	1	4	yes	—
569	#121	C₂³×C₅	1	4	yes	—
570	#120	—	2	4	no	—
571	C₄×Q₈	—	2	1	no	—
572	C₄×Q₈	—	2	1	no	—
573	C₄×Q₈	—	2	1	no	—
574	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
575	C₄×Q₈	C₅×D₄	1	1	yes	characteristic
576	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
577	C₄×Q₈	C₂³×C₅	1	1	yes	characteristic
578	C₄×Q₈	C₂³×C₅	1	2	yes	—
579	C₄×D₄	—	2	2	no	—
580	C₄×D₄	—	2	1	no	—
581	C₄×D₄	—	2	1	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	—	2	1	no	—
584	C₄×D₄	—	2	2	no	—
585	C₄×D₄	—	2	1	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	1	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	2	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	—	2	2	no	—
593	C₄×D₄	—	2	2	no	—
594	C₄×D₄	—	2	1	no	—
595	C₄×D₄	—	2	2	no	—
596	C₄×D₄	—	2	1	no	—
597	C₄×D₄	—	2	2	no	—
598	C₄×D₄	—	2	2	no	—
599	C₄×D₄	—	2	2	no	—
600	C₄×D₄	C₅×D₄	1	2	yes	—
601	C₄×D₄	C₅×D₄	1	1	yes	characteristic
602	C₄×D₄	C₅×D₄	1	2	yes	—
603	C₄×D₄	C₅×D₄	1	1	yes	characteristic
604	C₄×D₄	C₂³×C₅	1	2	yes	—
605	C₄×D₄	C₂³×C₅	1	2	yes	—
606	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
607	C₄×D₄	C₂³×C₅	1	2	yes	—
608	C₄×D₄	C₂³×C₅	1	2	yes	—
609	C₄×D₄	C₂³×C₅	1	1	yes	characteristic
610	C₄×D₄	C₂³×C₅	1	2	yes	—
611	C₄×D₄	C₂³×C₅	1	4	yes	—
612	C₄×D₄	C₂³×C₅	1	4	yes	—
613	#117	—	2	1	no	—
614	#117	—	2	2	no	—
615	#117	—	2	1	no	—
616	#117	—	2	2	no	—
617	#117	C₂³×C₅	1	1	yes	characteristic
618	#117	C₂³×C₅	1	2	yes	—
619	#117	C₂³×C₅	1	2	yes	—
620	#117	C₂³×C₅	1	1	yes	characteristic
621	#117	C₂³×C₅	1	2	yes	—
622	C₂×C₄⋊C₄	—	2	1	no	—
623	C₂×C₄⋊C₄	—	2	2	no	—
624	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
625	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
626	C₂×C₂²⋊C₄	—	2	1	no	—
627	C₂×C₂²⋊C₄	—	2	2	no	—
628	C₂×C₂²⋊C₄	—	2	2	no	—
629	C₂×C₂²⋊C₄	—	2	2	no	—
630	C₂×C₂²⋊C₄	—	2	2	no	—
631	C₂×C₂²⋊C₄	—	2	4	no	—
632	C₂×C₄²	—	2	1	no	—
633	C₂×C₄²	—	2	2	no	—
634	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
635	C₂×C₄²	C₂³×C₅	1	2	yes	—
636	#107	C₂³×C₅	1	2	yes	—
637	#107	C₂³×C₅	1	2	yes	—
638	#107	C₂³×C₅	1	4	yes	—
639	#106	C₂³×C₅	1	2	yes	—
640	#106	C₂³×C₅	1	2	yes	—
641	#106	C₂³×C₅	1	4	yes	—
642	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
643	C₄⋊C₈	C₂³×C₅	1	1	yes	characteristic
644	C₄⋊C₈	C₂³×C₅	1	2	yes	—
645	C₄⋊C₈	C₂³×C₅	1	2	yes	—
646	C₄⋊C₈	C₂³×C₅	1	2	yes	—
647	#103	C₂³×C₅	1	2	yes	—
648	#103	C₂³×C₅	1	2	yes	—
649	#102	C₂³×C₅	1	4	yes	—
650	#102	C₂³×C₅	1	4	yes	—
651	#102	C₂³×C₅	1	2	yes	—
652	#102	C₂³×C₅	1	2	yes	—
653	#102	C₂³×C₅	1	4	yes	—
654	#102	C₂³×C₅	1	4	yes	—
655	#102	C₂³×C₅	1	4	yes	—
656	#102	C₂³×C₅	1	4	yes	—
657	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
658	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
659	#97	C₂³×C₅	1	4	yes	—
660	C₄×C₈	C₂³×C₅	1	4	yes	—
661	C₂²×C₅	—	2	1	no	—
662	C₂²×C₅	—	2	1	no	—
663	C₂²×C₅	—	2	2	no	—
664	C₂²×C₅	—	2	2	no	—
665	C₂²×C₅	—	2	4	no	—
666	C₂²×C₅	—	2	2	no	—
667	C₂²×C₅	—	2	2	no	—
668	C₂²×C₅	—	4	2	no	—
669	C₂²×C₅	—	4	1	no	—
670	C₂²×C₅	—	4	2	no	—
671	C₂²×C₅	—	4	1	no	—
672	C₂²×C₅	—	4	4	no	—
673	C₂²×C₅	—	4	4	no	—
674	C₂²×C₅	—	4	4	no	—
675	C₂²×C₅	—	8	4	no	—
676	C₂²×C₅	—	8	8	no	—
677	C₂²×C₅	—	16	4	no	—
678	C₂²×C₅	#525	1	2	yes	—
679	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
680	C₄×C₅	—	2	1	no	—
681	C₄×C₅	—	2	2	no	—
682	C₄×C₅	—	2	1	no	—
683	C₄×C₅	—	2	2	no	—
684	C₄×C₅	—	2	2	no	—
685	C₄×C₅	—	2	2	no	—
686	C₄×C₅	—	2	1	no	—
687	C₄×C₅	—	4	1	no	—
688	C₄×C₅	—	4	2	no	—
689	C₄×C₅	—	4	1	no	—
690	C₄×C₅	—	4	2	no	—
691	C₄×C₅	—	4	2	no	—
692	C₄×C₅	#525	1	2	yes	—
693	C₄×C₅	#576	1	2	yes	—
694	C₄×C₅	C₂²×#41	1	1	yes	characteristic
695	C₄×C₅	C₂²×#41	1	1	yes	characteristic
696	C₂⁴	—	2	2	no	—
697	C₂⁴	—	2	1	no	—
698	C₂⁴	—	2	2	no	—
699	#41	—	2	8	no	—
700	#41	—	2	4	no	—
701	#41	—	2	4	no	—
702	#41	—	2	2	no	—
703	#41	—	2	2	no	—
704	#41	—	2	2	no	—
705	#41	—	8	4	no	—
706	#41	—	8	4	no	—
707	#41	C₅×#41	1	4	yes	complemented
708	C₂×Q₈	—	2	1	no	—
709	C₂×Q₈	—	2	1	no	—
710	C₂×Q₈	C₂×C₅×D₄	1	1	yes	characteristic
711	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
712	C₂×D₄	—	2	16	no	—
713	C₂×D₄	—	2	8	no	—
714	C₂×D₄	—	2	2	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	4	no	—
717	C₂×D₄	—	2	4	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	2	4	no	—
720	C₂×D₄	—	2	2	no	—
721	C₂×D₄	—	2	1	no	—
722	C₂×D₄	—	2	2	no	—
723	C₂×D₄	—	2	2	no	—
724	C₂×D₄	—	2	2	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	2	no	—
728	C₂×D₄	—	2	4	no	—
729	C₂×D₄	—	2	4	no	—
730	C₂×D₄	—	8	2	no	—
731	C₂×D₄	—	8	2	no	—
732	C₂×D₄	C₂×C₅×D₄	1	2	yes	—
733	C₂×D₄	C₂×C₅×D₄	1	1	yes	characteristic
734	C₂×D₄	C₅×#41	1	4	yes	complemented
735	C₂×D₄	C₂⁴×C₅	1	4	yes	—
736	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
737	C₂×D₄	C₂⁴×C₅	1	2	yes	—
738	C₂²×C₄	—	2	2	no	—
739	C₂²×C₄	—	2	1	no	—
740	C₂²×C₄	—	2	2	no	—
741	C₂²×C₄	—	2	1	no	—
742	C₂²×C₄	—	2	1	no	—
743	C₂²×C₄	—	2	2	no	—
744	C₂²×C₄	—	2	2	no	—
745	C₂²×C₄	—	2	1	no	—
746	C₂²×C₄	—	2	2	no	—
747	C₂²×C₄	—	2	2	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	4	no	—
751	C₂²×C₄	—	8	2	no	—
752	C₂²×C₄	—	8	4	no	—
753	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
754	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
755	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
756	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
757	C₂²×C₄	C₂⁴×C₅	1	2	yes	—
758	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
759	SD₁₆	—	2	8	no	—
760	D₈	—	2	8	no	—
761	D₈	—	2	8	no	—
762	D₈	—	2	8	no	—
763	M₁₆	—	2	4	no	—
764	C₂×C₈	—	2	4	no	—
765	C₂×C₈	C₂⁴×C₅	1	2	yes	—
766	C₂×C₈	C₂⁴×C₅	1	4	yes	—
767	C₂×C₈	C₂⁴×C₅	1	2	yes	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	1	no	—
770	C₄⋊C₄	—	2	2	no	—
771	C₄⋊C₄	—	2	1	no	—
772	C₄⋊C₄	—	2	1	no	—
773	C₄⋊C₄	—	2	1	no	—
774	C₄⋊C₄	—	2	1	no	—
775	C₄⋊C₄	—	2	2	no	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
778	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
779	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
780	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
781	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
782	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
783	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
784	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
785	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	1	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	1	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	2	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	2	no	—
795	C₂²⋊C₄	—	2	1	no	—
796	C₂²⋊C₄	—	2	4	no	—
797	C₂²⋊C₄	—	2	4	no	—
798	C₂²⋊C₄	—	2	4	no	—
799	C₂²⋊C₄	—	2	4	no	—
800	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
801	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
802	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
803	C₄²	—	2	1	no	—
804	C₄²	—	2	2	no	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	2	no	—
807	C₄²	—	2	1	no	—
808	C₄²	—	2	2	no	—
809	C₄²	C₂×C₅×D₄	1	2	yes	—
810	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
811	C₄²	C₂×C₅×D₄	1	2	yes	—
812	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
813	C₄²	C₂⁴×C₅	1	2	yes	—
814	C₄²	C₂⁴×C₅	1	1	yes	characteristic
815	C₄²	C₂⁴×C₅	1	1	yes	characteristic
816	C₂×C₅	—	2	2	no	—
817	C₂×C₅	—	4	2	no	—
818	C₂×C₅	—	4	4	no	—
819	C₂×C₅	—	4	2	no	—
820	C₂×C₅	—	8	4	no	—
821	C₂×C₅	C₂×#525	1	1	yes	characteristic
822	C₂×C₅	C₂×#576	1	1	yes	characteristic
823	C₂×C₅	#3585	1	1	yes	characteristic
824	C₂³	—	2	8	no	—
825	C₂³	—	2	2	no	—
826	C₂³	—	2	1	no	—
827	C₂³	—	2	4	no	—
828	C₂³	—	2	4	no	—
829	C₂³	—	4	4	no	—
830	C₂³	—	8	1	no	—
831	C₂³	—	8	2	no	—
832	C₂³	—	8	1	no	—
833	C₂³	—	8	2	no	—
834	C₂³	—	8	2	no	—
835	C₂³	—	8	2	no	—
836	C₂³	C₂²×C₅×D₄	1	2	yes	—
837	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
838	Q₈	—	2	2	no	—
839	Q₈	—	2	1	no	—
840	Q₈	—	4	2	no	—
841	Q₈	—	4	2	no	—
842	Q₈	C₂×C₅×#41	1	2	yes	—
843	D₄	—	2	8	no	—
844	D₄	—	2	8	no	—
845	D₄	—	2	4	no	—
846	D₄	—	2	4	no	—
847	D₄	—	2	2	no	—
848	D₄	—	2	4	no	—
849	D₄	—	2	2	no	—
850	D₄	—	2	1	no	—
851	D₄	—	2	4	no	—
852	D₄	—	2	4	no	—
853	D₄	—	4	4	no	—
854	D₄	—	4	4	no	—
855	D₄	—	4	4	no	—
856	D₄	—	8	2	no	—
857	D₄	—	8	2	no	—
858	D₄	—	8	4	no	—
859	D₄	—	8	4	no	—
860	D₄	C₂×C₅×#41	1	2	yes	—
861	D₄	C₂×C₅×#41	1	4	yes	—
862	C₂×C₄	—	2	8	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	4	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	2	4	no	—
867	C₂×C₄	—	2	2	no	—
868	C₂×C₄	—	2	2	no	—
869	C₂×C₄	—	2	1	no	—
870	C₂×C₄	—	2	2	no	—
871	C₂×C₄	—	2	1	no	—
872	C₂×C₄	—	2	2	no	—
873	C₂×C₄	—	2	2	no	—
874	C₂×C₄	—	4	1	no	—
875	C₂×C₄	—	4	2	no	—
876	C₂×C₄	—	4	2	no	—
877	C₂×C₄	—	4	4	no	—
878	C₂×C₄	—	8	2	no	—
879	C₂×C₄	—	8	2	no	—
880	C₂×C₄	—	8	2	no	—
881	C₂×C₄	—	8	4	no	—
882	C₂×C₄	—	8	4	no	—
883	C₂×C₄	—	8	2	no	—
884	C₂×C₄	—	8	1	no	—
885	C₂×C₄	—	8	1	no	—
886	C₂×C₄	—	8	2	no	—
887	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
888	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
889	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
890	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
891	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
892	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
893	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
894	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
895	C₂×C₄	C₂×C₅×#41	1	2	yes	—
896	C₂×C₄	C₂×C₅×#41	1	2	yes	—
897	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
898	C₈	—	2	2	no	—
899	C₈	—	2	2	no	—
900	C₈	—	2	4	no	—
901	C₅	#60590	1	1	yes	characteristic, direct product factor, Sylow
902	C₂²	—	2	1	no	—
903	C₂²	—	2	1	no	—
904	C₂²	—	2	2	no	—
905	C₂²	—	2	4	no	—
906	C₂²	—	2	2	no	—
907	C₂²	—	2	2	no	—
908	C₂²	—	2	2	no	—
909	C₂²	—	4	2	no	—
910	C₂²	—	4	1	no	—
911	C₂²	—	4	2	no	—
912	C₂²	—	4	1	no	—
913	C₂²	—	4	4	no	—
914	C₂²	—	4	4	no	—
915	C₂²	—	4	4	no	—
916	C₂²	—	8	4	no	—
917	C₂²	—	8	8	no	—
918	C₂²	—	16	4	no	—
919	C₂²	C₅×#525	1	2	yes	—
920	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
921	C₄	—	2	2	no	—
922	C₄	—	2	2	no	—
923	C₄	—	2	2	no	—
924	C₄	—	2	1	no	—
925	C₄	—	2	1	no	—
926	C₄	—	2	2	no	—
927	C₄	—	2	1	no	—
928	C₄	—	4	1	no	—
929	C₄	—	4	2	no	—
930	C₄	—	4	2	no	—
931	C₄	—	4	1	no	—
932	C₄	—	4	2	no	—
933	C₄	C₅×#525	1	2	yes	—
934	C₄	C₅×#576	1	2	yes	—
935	C₄	C₂²×C₅×#41	1	1	yes	characteristic
936	C₄	C₂²×C₅×#41	1	1	yes	characteristic
937	C₂	—	2	2	no	—
938	C₂	—	4	2	no	—
939	C₂	—	4	4	no	—
940	C₂	—	4	2	no	—
941	C₂	—	8	4	no	—
942	C₂	C₂×C₅×#525	1	1	yes	characteristic
943	C₂	C₂×C₅×#576	1	1	yes	characteristic
944	C₂	C₅×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3508	C₂	semidirect
2. C₄×C₅×H(5,𝔽₂)	C₂	semidirect
3. C₅×#3122	C₂	semidirect
4. C₅×#3119	C₂	semidirect
5. C₅×#3115	C₂	semidirect
6. C₅×#3109	C₂	semidirect
7. C₅×#3106	C₂	semidirect
8. C₅×#3100	C₂	semidirect
9. C₅×#3096	C₂	semidirect
10. C₅×#3077	C₂	semidirect
11. C₅×#3076	C₂	semidirect
12. C₅×#3038	C₂	semidirect
13. C₂×C₅×#459	C₂	semidirect
14. C₅×#3008	C₂	semidirect
15. C₅×#2948	C₂	semidirect
16. C₅×#2946	C₂	semidirect
17. C₅×#2925	C₂	semidirect
27. C₅×#540	C₂²	semidirect
29. C₅×#533	C₂²	semidirect
30. C₅×#532	C₂²	semidirect
31. C₅×#532	C₂²	semidirect
32. C₂×C₅×#127	C₂²	semidirect
36. C₅×#520	C₂²	semidirect
40. C₅×#518	C₂²	semidirect
41. C₅×#518	C₂²	semidirect
45. C₄×C₅×#41	C₂²	semidirect
49. C₂×C₄×C₅×D₄	C₂²	semidirect
50. C₅×#482	C₂²	semidirect
51. C₅×#482	C₂²	semidirect
52. C₅×#481	C₂²	semidirect
53. C₅×#480	C₂²	semidirect
54. C₅×#479	C₂²	semidirect
55. C₅×#478	C₂²	semidirect
56. C₅×#478	C₂²	semidirect
57. C₅×#477	C₂²	semidirect
58. C₅×#476	C₂²	semidirect
59. C₅×#476	C₂²	semidirect
60. C₅×#475	C₂²	semidirect
61. C₅×#474	C₂²	semidirect
62. C₅×#474	C₂²	semidirect
63. C₅×#460	C₂²	semidirect
64. C₅×#460	C₂²	semidirect
65. C₅×#459	C₂²	semidirect
66. C₅×#459	C₂²	semidirect
67. C₅×#459	C₂²	semidirect
68. C₅×#459	C₂²	semidirect
69. C₅×#459	C₂²	semidirect
70. C₅×#449	C₂²	semidirect
71. C₅×#449	C₂²	semidirect
72. C₅×#447	C₂²	semidirect
73. C₅×#447	C₂²	semidirect
74. C₅×#442	C₂²	semidirect
75. C₅×#442	C₂²	semidirect
76. C₅×#442	C₂²	semidirect
77. C₅×#440	C₂²	semidirect
78. C₄×C₅×SD₁₆	C₂²	semidirect
79. C₄×C₅×D₈	C₂²	semidirect
80. C₄×C₅×D₈	C₂²	semidirect
81. C₄×C₅×D₈	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
83. C₅×#432	C₂²	semidirect
84. C₅×#431	C₂²	semidirect
85. C₅×#428	C₂²	semidirect
86. C₅×#427	C₂²	semidirect
87. C₅×#423	C₂²	semidirect
88. C₂×C₅×C₄⋊C₈	C₂²	semidirect
90. C₅×#418	C₂²	semidirect
92. C₂×C₅×#102	C₂²	semidirect
94. C₅×#405	C₂²	semidirect
95. #60590	C₅	direct (N × H)
233. #3508	C₂×C₅	semidirect
234. C₄×H(5,𝔽₂)	C₂×C₅	semidirect
235. #3122	C₂×C₅	semidirect
236. #3119	C₂×C₅	semidirect
237. #3115	C₂×C₅	semidirect
238. #3109	C₂×C₅	semidirect
239. #3106	C₂×C₅	semidirect
240. #3100	C₂×C₅	semidirect
241. #3096	C₂×C₅	semidirect
242. #3077	C₂×C₅	semidirect
243. #3076	C₂×C₅	semidirect
244. #3038	C₂×C₅	semidirect
245. C₂×#459	C₂×C₅	semidirect
246. #3008	C₂×C₅	semidirect
247. #2948	C₂×C₅	semidirect
248. #2946	C₂×C₅	semidirect
249. #2925	C₂×C₅	semidirect
261. C₅×#41	#41	semidirect
288. C₂×C₅×D₄	#41	semidirect
379. #540	C₂²×C₅	semidirect
381. #533	C₂²×C₅	semidirect
382. #532	C₂²×C₅	semidirect
383. #532	C₂²×C₅	semidirect
384. C₂×#127	C₂²×C₅	semidirect
388. #520	C₂²×C₅	semidirect
392. #518	C₂²×C₅	semidirect
393. #518	C₂²×C₅	semidirect
397. C₄×#41	C₂²×C₅	semidirect
401. C₂×C₄×D₄	C₂²×C₅	semidirect
402. #482	C₂²×C₅	semidirect
403. #482	C₂²×C₅	semidirect
404. #481	C₂²×C₅	semidirect
405. #480	C₂²×C₅	semidirect
406. #479	C₂²×C₅	semidirect
407. #478	C₂²×C₅	semidirect
408. #478	C₂²×C₅	semidirect
409. #477	C₂²×C₅	semidirect
410. #476	C₂²×C₅	semidirect
411. #476	C₂²×C₅	semidirect
412. #475	C₂²×C₅	semidirect
413. #474	C₂²×C₅	semidirect
414. #474	C₂²×C₅	semidirect
415. #460	C₂²×C₅	semidirect
416. #460	C₂²×C₅	semidirect
417. #459	C₂²×C₅	semidirect
418. #459	C₂²×C₅	semidirect
419. #459	C₂²×C₅	semidirect
420. #459	C₂²×C₅	semidirect
421. #459	C₂²×C₅	semidirect
422. #449	C₂²×C₅	semidirect
423. #449	C₂²×C₅	semidirect
424. #447	C₂²×C₅	semidirect
425. #447	C₂²×C₅	semidirect
426. #442	C₂²×C₅	semidirect
427. #442	C₂²×C₅	semidirect
428. #442	C₂²×C₅	semidirect
429. #440	C₂²×C₅	semidirect
430. C₄×SD₁₆	C₂²×C₅	semidirect
431. C₄×D₈	C₂²×C₅	semidirect
432. C₄×D₈	C₂²×C₅	semidirect
433. C₄×D₈	C₂²×C₅	semidirect
434. #433	C₂²×C₅	semidirect
435. #432	C₂²×C₅	semidirect
436. #431	C₂²×C₅	semidirect
437. #428	C₂²×C₅	semidirect
438. #427	C₂²×C₅	semidirect
439. #423	C₂²×C₅	semidirect
440. C₂×C₄⋊C₈	C₂²×C₅	semidirect
442. #418	C₂²×C₅	semidirect
444. C₂×#102	C₂²×C₅	semidirect
446. #405	C₂²×C₅	semidirect
707. #41	C₅×#41	semidirect
734. C₂×D₄	C₅×#41	semidirect
901. C₅	#60590	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×#3508	2
C₄×C₅×H(5,𝔽₂)	2
C₅×#3122	2
C₅×#3119	2
C₅×#3115	2
C₅×#3109	2
C₅×#3106	2
C₅×#3100	2
C₅×#3096	2
C₅×#3077	2
C₅×#3076	2
C₅×#3038	2
C₂×C₅×#459	2
C₅×#3008	2
C₅×#2948	2
C₅×#2946	2
C₅×#2925	2
#60590	5

Subgroups — C5×#60590 #11983310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60590 #11983310