Subgroups — C₅×#60561 #11983281

Order 1280.

2428 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#532	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3115	C₂	1	4	yes	maximal, complemented
4	C₅×#3112	C₂	1	2	yes	maximal, complemented
5	C₅×#3109	C₂	1	2	yes	maximal, complemented
6	C₅×#3106	C₂	1	4	yes	maximal, complemented
7	C₅×#3103	C₂	1	2	yes	maximal, complemented
8	C₅×#3100	C₂	1	2	yes	maximal, complemented
9	C₅×#3094	C₂	1	2	yes	maximal, complemented
10	C₅×#3079	C₂	1	2	yes	maximal, complemented
11	C₅×#3038	C₂	1	2	yes	maximal, complemented
12	C₅×#3006	C₂	1	2	yes	maximal, complemented
13	C₄×C₅×AGL(1,ℤ/8)	C₂	1	4	yes	maximal, complemented
14	C₅×#2920	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₅×#41	—	2	1	no	—
16	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
17	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	4	yes	—
18	C₅×#532	—	2	1	no	—
19	C₅×#532	—	2	1	no	—
20	C₅×#532	—	2	1	no	—
21	C₅×#532	—	2	1	no	—
22	C₅×#532	C₂²	1	2	yes	—
23	C₅×#532	C₂²	1	2	yes	—
24	C₅×#532	C₂²	1	2	yes	complemented
25	C₅×#532	C₂²	1	2	yes	complemented
26	C₂×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₅×#127	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₅×#124	—	2	1	no	—
29	C₂×C₅×#121	—	2	1	no	—
30	C₂×C₅×#121	C₂²	1	2	yes	—
31	C₄×C₅×#41	—	2	1	no	—
32	C₄×C₅×#41	—	2	1	no	—
33	C₄×C₅×#41	—	2	1	no	—
34	C₄×C₅×#41	—	2	1	no	—
35	C₄×C₅×#41	C₂²	1	2	yes	—
36	C₄×C₅×#41	C₂²	1	2	yes	—
37	C₄×C₅×#41	C₂²	1	2	yes	complemented
38	C₄×C₅×#41	C₂²	1	2	yes	complemented
39	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
40	C₂×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₄×C₅×D₄	—	2	1	no	—
42	C₂×C₄×C₅×D₄	—	2	1	no	—
43	C₂×C₄×C₅×D₄	—	2	1	no	—
44	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
47	C₂×C₅×#117	—	2	1	no	—
48	C₂×C₅×#117	C₂²	1	1	yes	characteristic
49	C₂²×C₄²×C₅	—	2	1	no	—
50	C₂²×C₄²×C₅	C₂²	1	1	yes	characteristic
51	C₅×#482	C₂²	1	8	yes	complemented
52	C₅×#481	C₂²	1	4	yes	complemented
53	C₅×#480	C₂²	1	4	yes	complemented
54	C₅×#477	C₂²	1	4	yes	complemented
55	C₅×#476	C₂²	1	4	yes	complemented
56	C₅×#475	C₂²	1	4	yes	complemented
57	C₅×#474	C₂²	1	4	yes	complemented
58	C₅×#460	C₂²	1	4	yes	complemented
59	C₅×#460	C₂²	1	4	yes	complemented
60	C₅×#459	C₂²	1	4	yes	complemented
61	C₅×#459	C₂²	1	4	yes	complemented
62	C₅×#449	C₂²	1	8	yes	complemented
63	C₅×#448	C₂²	1	4	yes	complemented
64	C₅×#447	C₂²	1	4	yes	complemented
65	C₅×#442	C₂²	1	8	yes	complemented
66	C₅×#440	C₂²	1	8	yes	complemented
67	C₄×C₅×SD₁₆	C₂²	1	8	yes	complemented
68	C₄×C₅×D₈	C₂²	1	8	yes	complemented
69	C₅×#432	C₂²	1	2	yes	complemented
70	C₅×#432	C₂²	1	2	yes	complemented
71	C₅×#431	C₂²	1	2	yes	complemented
72	C₅×#431	C₂²	1	2	yes	complemented
73	C₅×#428	C₂²	1	4	yes	complemented
74	C₅×#423	C₂²	1	2	yes	complemented
75	C₅×#418	C₂²	1	4	yes	complemented
76	C₅×#417	C₂²	1	4	yes	—
77	C₅×#407	C₂²	1	2	yes	—
78	C₄×C₅×M₁₆	C₂²	1	2	yes	complemented
79	#60561	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂×C₅×#41	—	2	8	no	—
81	C₂×C₅×#41	—	2	1	no	—
82	C₂×C₅×#41	—	2	1	no	—
83	C₂×C₅×#41	—	2	2	no	—
84	C₂×C₅×#41	—	2	2	no	—
85	C₂×C₅×#41	—	2	2	no	—
86	C₂×C₅×#41	—	2	2	no	—
87	C₂×C₅×#41	—	4	8	no	—
88	C₂×C₅×#41	C₂³	1	2	yes	—
89	C₂×C₅×#41	C₂³	1	2	yes	—
90	C₂²×C₅×Q₈	—	2	1	no	—
91	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
92	C₂²×C₅×D₄	—	2	1	no	—
93	C₂²×C₅×D₄	—	2	2	no	—
94	C₂²×C₅×D₄	—	2	1	no	—
95	C₂²×C₅×D₄	—	2	1	no	—
96	C₂²×C₅×D₄	C₂³	1	2	yes	—
97	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₅	—	2	1	no	—
99	C₂³×C₄×C₅	—	2	1	no	—
100	C₂³×C₄×C₅	—	2	1	no	—
101	C₂³×C₄×C₅	—	2	2	no	—
102	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
103	C₂³×C₄×C₅	D₄	1	1	yes	characteristic
104	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
105	C₅×AGL(1,ℤ/8)	—	2	16	no	—
106	C₂×C₅×SD₁₆	C₂³	1	8	yes	—
107	C₂×C₅×D₈	C₂³	1	8	yes	—
108	C₂×C₅×M₁₆	C₂³	1	4	yes	—
109	C₅×C₄⋊Q₈	—	2	1	no	—
110	C₅×C₄⋊Q₈	—	2	1	no	—
111	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
112	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
113	C₅×#127	—	2	1	no	—
114	C₅×#127	—	2	1	no	—
115	C₅×#127	C₂³	1	2	yes	—
116	C₅×#127	C₂³	1	2	yes	—
117	C₅×#124	—	2	2	no	—
118	C₅×#124	—	2	2	no	—
119	C₅×#124	—	2	2	no	—
120	C₅×#124	—	2	2	no	—
121	C₅×#121	—	2	2	no	—
122	C₅×#121	—	2	2	no	—
123	C₅×#121	—	2	2	no	—
124	C₅×#121	—	2	2	no	—
125	C₅×#121	—	2	2	no	—
126	C₅×#121	—	2	2	no	—
127	C₅×#121	C₂³	1	4	yes	—
128	C₅×#121	C₂³	1	4	yes	—
129	C₄×C₅×Q₈	—	2	1	no	—
130	C₄×C₅×Q₈	—	2	1	no	—
131	C₄×C₅×Q₈	—	2	1	no	—
132	C₄×C₅×Q₈	—	2	1	no	—
133	C₄×C₅×Q₈	C₂³	1	2	yes	—
134	C₄×C₅×Q₈	C₂³	1	2	yes	—
135	C₄×C₅×Q₈	C₂³	1	2	yes	—
136	C₄×C₅×Q₈	C₂³	1	2	yes	—
137	C₄×C₅×D₄	—	2	2	no	—
138	C₄×C₅×D₄	—	2	2	no	—
139	C₄×C₅×D₄	—	2	2	no	—
140	C₄×C₅×D₄	—	2	2	no	—
141	C₄×C₅×D₄	—	2	2	no	—
142	C₄×C₅×D₄	—	2	2	no	—
143	C₄×C₅×D₄	—	2	2	no	—
144	C₄×C₅×D₄	—	2	2	no	—
145	C₄×C₅×D₄	—	2	2	no	—
146	C₄×C₅×D₄	—	2	2	no	—
147	C₄×C₅×D₄	—	2	2	no	—
148	C₄×C₅×D₄	—	2	2	no	—
149	C₄×C₅×D₄	—	2	1	no	—
150	C₄×C₅×D₄	—	2	1	no	—
151	C₄×C₅×D₄	—	2	1	no	—
152	C₄×C₅×D₄	—	2	1	no	—
153	C₄×C₅×D₄	—	2	2	no	—
154	C₄×C₅×D₄	—	2	2	no	—
155	C₄×C₅×D₄	C₂³	1	2	yes	—
156	C₄×C₅×D₄	C₂³	1	4	yes	—
157	C₄×C₅×D₄	C₂³	1	4	yes	—
158	C₄×C₅×D₄	C₂³	1	2	yes	—
159	C₄×C₅×D₄	C₂³	1	2	yes	—
160	C₄×C₅×D₄	C₂³	1	2	yes	—
161	C₅×#117	—	2	1	no	—
162	C₅×#117	—	2	1	no	—
163	C₅×#117	—	2	2	no	—
164	C₅×#117	—	2	2	no	—
165	C₅×#117	—	2	2	no	—
166	C₅×#117	—	2	2	no	—
167	C₅×#117	C₂³	1	2	yes	—
168	C₅×#117	C₂³	1	2	yes	—
169	C₂×C₅×C₄⋊C₄	—	2	1	no	—
170	C₂×C₅×C₄⋊C₄	—	2	1	no	—
171	C₂×C₅×C₄⋊C₄	—	2	1	no	—
172	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
173	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
174	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
176	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
177	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
178	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
179	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
180	C₂×C₄²×C₅	—	2	1	no	—
181	C₂×C₄²×C₅	—	2	1	no	—
182	C₂×C₄²×C₅	—	2	1	no	—
183	C₂×C₄²×C₅	—	2	2	no	—
184	C₂×C₄²×C₅	—	2	2	no	—
185	C₂×C₄²×C₅	—	2	2	no	—
186	C₂×C₄²×C₅	—	2	2	no	—
187	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
188	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
189	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
190	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
191	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
192	C₂×C₄²×C₅	D₄	1	1	yes	characteristic
193	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
194	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
195	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
196	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
197	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
198	C₂×C₄²×C₅	C₂³	1	1	yes	characteristic
199	C₅×#107	C₂³	1	8	yes	—
200	C₅×#106	C₂³	1	8	yes	—
201	C₅×C₄⋊C₈	C₂³	1	4	yes	—
202	C₅×C₄⋊C₈	C₂³	1	4	yes	—
203	C₅×#103	C₂³	1	8	yes	—
204	C₅×#102	C₂³	1	8	yes	—
205	C₅×#102	C₂³	1	8	yes	—
206	C₅×#102	C₂³	1	8	yes	—
207	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
208	C₅×C₂²⋊C₈	C₂³	1	4	yes	—
209	C₅×#97	C₂³	1	4	yes	—
210	C₄×C₅×C₈	C₂³	1	4	yes	—
211	C₂×#532	C₂×C₅	1	1	yes	characteristic, complemented
212	C₂×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
213	#3115	C₂×C₅	1	4	yes	complemented
214	#3112	C₂×C₅	1	2	yes	complemented
215	#3109	C₂×C₅	1	2	yes	complemented
216	#3106	C₂×C₅	1	4	yes	complemented
217	#3103	C₂×C₅	1	2	yes	complemented
218	#3100	C₂×C₅	1	2	yes	complemented
219	#3094	C₂×C₅	1	2	yes	complemented
220	#3079	C₂×C₅	1	2	yes	complemented
221	#3038	C₂×C₅	1	2	yes	complemented
222	#3006	C₂×C₅	1	2	yes	complemented
223	C₄×AGL(1,ℤ/8)	C₂×C₅	1	4	yes	complemented
224	#2920	C₂×C₅	1	1	yes	characteristic, complemented
225	C₂⁴×C₅	—	2	1	no	—
226	C₂⁴×C₅	—	2	2	no	—
227	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
228	C₅×#41	—	2	8	no	—
229	C₅×#41	—	2	8	no	—
230	C₅×#41	—	2	4	no	—
231	C₅×#41	—	2	4	no	—
232	C₅×#41	—	2	4	no	—
233	C₅×#41	—	4	8	no	—
234	C₅×#41	—	4	8	no	—
235	C₅×#41	—	4	8	no	—
236	C₅×#41	—	4	8	no	—
237	C₅×#41	#41	1	8	yes	complemented
238	C₂×C₅×Q₈	—	2	4	no	—
239	C₂×C₅×Q₈	—	2	1	no	—
240	C₂×C₅×Q₈	—	2	2	no	—
241	C₂×C₅×Q₈	—	2	2	no	—
242	C₂×C₅×Q₈	—	4	4	no	—
243	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
244	C₂×C₅×D₄	—	2	8	no	—
245	C₂×C₅×D₄	—	2	2	no	—
246	C₂×C₅×D₄	—	2	2	no	—
247	C₂×C₅×D₄	—	2	4	no	—
248	C₂×C₅×D₄	—	2	4	no	—
249	C₂×C₅×D₄	—	2	4	no	—
250	C₂×C₅×D₄	—	2	1	no	—
251	C₂×C₅×D₄	—	2	2	no	—
252	C₂×C₅×D₄	—	2	2	no	—
253	C₂×C₅×D₄	—	2	2	no	—
254	C₂×C₅×D₄	—	2	2	no	—
255	C₂×C₅×D₄	—	2	2	no	—
256	C₂×C₅×D₄	—	2	8	no	—
257	C₂×C₅×D₄	—	4	4	no	—
258	C₂×C₅×D₄	—	4	4	no	—
259	C₂×C₅×D₄	—	4	8	no	—
260	C₂×C₅×D₄	C₂⁴	1	4	yes	—
261	C₂×C₅×D₄	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₅	—	2	8	no	—
263	C₂²×C₄×C₅	—	2	1	no	—
264	C₂²×C₄×C₅	—	2	4	no	—
265	C₂²×C₄×C₅	—	2	2	no	—
266	C₂²×C₄×C₅	—	2	2	no	—
267	C₂²×C₄×C₅	—	2	4	no	—
268	C₂²×C₄×C₅	—	2	1	no	—
269	C₂²×C₄×C₅	—	2	1	no	—
270	C₂²×C₄×C₅	—	2	2	no	—
271	C₂²×C₄×C₅	—	2	2	no	—
272	C₂²×C₄×C₅	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	2	no	—
274	C₂²×C₄×C₅	—	2	4	no	—
275	C₂²×C₄×C₅	—	2	2	no	—
276	C₂²×C₄×C₅	—	2	4	no	—
277	C₂²×C₄×C₅	—	4	2	no	—
278	C₂²×C₄×C₅	—	4	4	no	—
279	C₂²×C₄×C₅	—	4	8	no	—
280	C₂²×C₄×C₅	—	4	4	no	—
281	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
282	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
283	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
285	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
286	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
287	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
290	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
293	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
294	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
295	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₅×SD₁₆	—	2	16	no	—
300	C₅×D₈	—	2	16	no	—
301	C₅×M₁₆	—	2	8	no	—
302	C₂×C₅×C₈	C₂⁴	1	8	yes	—
303	C₅×C₄⋊C₄	—	2	2	no	—
304	C₅×C₄⋊C₄	—	2	2	no	—
305	C₅×C₄⋊C₄	—	2	2	no	—
306	C₅×C₄⋊C₄	—	2	2	no	—
307	C₅×C₄⋊C₄	—	2	2	no	—
308	C₅×C₄⋊C₄	—	2	2	no	—
309	C₅×C₄⋊C₄	—	2	1	no	—
310	C₅×C₄⋊C₄	—	2	1	no	—
311	C₅×C₄⋊C₄	—	2	2	no	—
312	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
313	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
314	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
315	C₅×C₂²⋊C₄	—	2	2	no	—
316	C₅×C₂²⋊C₄	—	2	2	no	—
317	C₅×C₂²⋊C₄	—	2	2	no	—
318	C₅×C₂²⋊C₄	—	2	2	no	—
319	C₅×C₂²⋊C₄	—	2	2	no	—
320	C₅×C₂²⋊C₄	—	2	2	no	—
321	C₅×C₂²⋊C₄	—	2	4	no	—
322	C₅×C₂²⋊C₄	—	2	4	no	—
323	C₅×C₂²⋊C₄	—	2	4	no	—
324	C₅×C₂²⋊C₄	—	2	4	no	—
325	C₄²×C₅	—	2	2	no	—
326	C₄²×C₅	—	2	2	no	—
327	C₄²×C₅	—	2	2	no	—
328	C₄²×C₅	—	2	2	no	—
329	C₄²×C₅	—	2	2	no	—
330	C₄²×C₅	—	2	2	no	—
331	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
332	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
333	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
334	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
335	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
336	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
337	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
338	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
339	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
340	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
341	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
342	C₄²×C₅	C₂×D₄	1	1	yes	characteristic
343	C₄²×C₅	C₂⁴	1	1	yes	characteristic
344	C₄²×C₅	C₂⁴	1	1	yes	characteristic
345	C₄²×C₅	C₂⁴	1	1	yes	characteristic
346	C₄²×C₅	C₂⁴	1	1	yes	characteristic
347	C₂²×#41	—	2	1	no	—
348	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
349	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	4	yes	—
350	#532	—	2	1	no	—
351	#532	—	2	1	no	—
352	#532	—	2	1	no	—
353	#532	—	2	1	no	—
354	#532	C₂²×C₅	1	2	yes	—
355	#532	C₂²×C₅	1	2	yes	—
356	#532	C₂²×C₅	1	2	yes	complemented
357	#532	C₂²×C₅	1	2	yes	complemented
358	C₂×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
359	C₂×#127	C₂²×C₅	1	1	yes	characteristic, complemented
360	C₂×#124	—	2	1	no	—
361	C₂×#121	—	2	1	no	—
362	C₂×#121	C₂²×C₅	1	2	yes	—
363	C₄×#41	—	2	1	no	—
364	C₄×#41	—	2	1	no	—
365	C₄×#41	—	2	1	no	—
366	C₄×#41	—	2	1	no	—
367	C₄×#41	C₂²×C₅	1	2	yes	—
368	C₄×#41	C₂²×C₅	1	2	yes	—
369	C₄×#41	C₂²×C₅	1	2	yes	complemented
370	C₄×#41	C₂²×C₅	1	2	yes	complemented
371	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
372	C₂×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
373	C₂×C₄×D₄	—	2	1	no	—
374	C₂×C₄×D₄	—	2	1	no	—
375	C₂×C₄×D₄	—	2	1	no	—
376	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
377	C₂×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
378	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
379	C₂×#117	—	2	1	no	—
380	C₂×#117	C₂²×C₅	1	1	yes	characteristic
381	C₂²×C₄²	—	2	1	no	—
382	C₂²×C₄²	C₂²×C₅	1	1	yes	characteristic
383	#482	C₂²×C₅	1	8	yes	complemented
384	#481	C₂²×C₅	1	4	yes	complemented
385	#480	C₂²×C₅	1	4	yes	complemented
386	#477	C₂²×C₅	1	4	yes	complemented
387	#476	C₂²×C₅	1	4	yes	complemented
388	#475	C₂²×C₅	1	4	yes	complemented
389	#474	C₂²×C₅	1	4	yes	complemented
390	#460	C₂²×C₅	1	4	yes	complemented
391	#460	C₂²×C₅	1	4	yes	complemented
392	#459	C₂²×C₅	1	4	yes	complemented
393	#459	C₂²×C₅	1	4	yes	complemented
394	#449	C₂²×C₅	1	8	yes	complemented
395	#448	C₂²×C₅	1	4	yes	complemented
396	#447	C₂²×C₅	1	4	yes	complemented
397	#442	C₂²×C₅	1	8	yes	complemented
398	#440	C₂²×C₅	1	8	yes	complemented
399	C₄×SD₁₆	C₂²×C₅	1	8	yes	complemented
400	C₄×D₈	C₂²×C₅	1	8	yes	complemented
401	#432	C₂²×C₅	1	2	yes	complemented
402	#432	C₂²×C₅	1	2	yes	complemented
403	#431	C₂²×C₅	1	2	yes	complemented
404	#431	C₂²×C₅	1	2	yes	complemented
405	#428	C₂²×C₅	1	4	yes	complemented
406	#423	C₂²×C₅	1	2	yes	complemented
407	#418	C₂²×C₅	1	4	yes	complemented
408	#417	C₂²×C₅	1	4	yes	—
409	#407	C₂²×C₅	1	2	yes	—
410	C₄×M₁₆	C₂²×C₅	1	2	yes	complemented
411	C₂³×C₅	—	2	4	no	—
412	C₂³×C₅	—	2	2	no	—
413	C₂³×C₅	—	2	2	no	—
414	C₂³×C₅	—	2	2	no	—
415	C₂³×C₅	—	2	4	no	—
416	C₂³×C₅	—	4	1	no	—
417	C₂³×C₅	—	4	2	no	—
418	C₂³×C₅	—	4	4	no	—
419	C₂³×C₅	—	4	4	no	—
420	C₂³×C₅	—	4	2	no	—
421	C₂³×C₅	—	4	4	no	—
422	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
423	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
424	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
425	C₅×Q₈	—	2	4	no	—
426	C₅×Q₈	—	2	2	no	—
427	C₅×Q₈	—	4	4	no	—
428	C₅×Q₈	—	4	4	no	—
429	C₅×Q₈	C₂×#41	1	4	yes	complemented
430	C₅×D₄	—	2	8	no	—
431	C₅×D₄	—	2	4	no	—
432	C₅×D₄	—	2	8	no	—
433	C₅×D₄	—	2	2	no	—
434	C₅×D₄	—	2	8	no	—
435	C₅×D₄	—	4	4	no	—
436	C₅×D₄	—	4	4	no	—
437	C₅×D₄	—	4	8	no	—
438	C₅×D₄	—	4	8	no	—
439	C₅×D₄	—	4	4	no	—
440	C₅×D₄	—	4	4	no	—
441	C₅×D₄	—	4	4	no	—
442	C₅×D₄	C₂×#41	1	4	yes	complemented
443	C₂×C₄×C₅	—	2	4	no	—
444	C₂×C₄×C₅	—	2	8	no	—
445	C₂×C₄×C₅	—	2	2	no	—
446	C₂×C₄×C₅	—	2	2	no	—
447	C₂×C₄×C₅	—	2	2	no	—
448	C₂×C₄×C₅	—	2	2	no	—
449	C₂×C₄×C₅	—	2	8	no	—
450	C₂×C₄×C₅	—	2	2	no	—
451	C₂×C₄×C₅	—	2	2	no	—
452	C₂×C₄×C₅	—	2	2	no	—
453	C₂×C₄×C₅	—	2	2	no	—
454	C₂×C₄×C₅	—	2	2	no	—
455	C₂×C₄×C₅	—	2	2	no	—
456	C₂×C₄×C₅	—	2	2	no	—
457	C₂×C₄×C₅	—	2	2	no	—
458	C₂×C₄×C₅	—	2	2	no	—
459	C₂×C₄×C₅	—	2	2	no	—
460	C₂×C₄×C₅	—	2	2	no	—
461	C₂×C₄×C₅	—	2	2	no	—
462	C₂×C₄×C₅	—	2	4	no	—
463	C₂×C₄×C₅	—	4	1	no	—
464	C₂×C₄×C₅	—	4	1	no	—
465	C₂×C₄×C₅	—	4	1	no	—
466	C₂×C₄×C₅	—	4	4	no	—
467	C₂×C₄×C₅	—	4	8	no	—
468	C₂×C₄×C₅	—	4	2	no	—
469	C₂×C₄×C₅	—	4	4	no	—
470	C₂×C₄×C₅	—	4	2	no	—
471	C₂×C₄×C₅	—	4	4	no	—
472	C₂×C₄×C₅	—	4	4	no	—
473	C₂×C₄×C₅	—	4	8	no	—
474	C₂×C₄×C₅	—	4	4	no	—
475	C₂×C₄×C₅	AGL(1,ℤ/8)	1	4	yes	complemented
476	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₅	C₂×#41	1	4	yes	—
488	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
489	C₅×C₈	—	2	8	no	—
490	C₂×#41	—	2	8	no	—
491	C₂×#41	—	2	1	no	—
492	C₂×#41	—	2	1	no	—
493	C₂×#41	—	2	2	no	—
494	C₂×#41	—	2	2	no	—
495	C₂×#41	—	2	2	no	—
496	C₂×#41	—	2	2	no	—
497	C₂×#41	—	4	8	no	—
498	C₂×#41	C₂³×C₅	1	2	yes	—
499	C₂×#41	C₂³×C₅	1	2	yes	—
500	C₂²×Q₈	—	2	1	no	—
501	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
502	C₂²×D₄	—	2	1	no	—
503	C₂²×D₄	—	2	2	no	—
504	C₂²×D₄	—	2	1	no	—
505	C₂²×D₄	—	2	1	no	—
506	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
507	C₂²×D₄	C₂³×C₅	1	2	yes	—
508	C₂³×C₄	—	2	1	no	—
509	C₂³×C₄	—	2	2	no	—
510	C₂³×C₄	—	2	1	no	—
511	C₂³×C₄	—	2	1	no	—
512	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
513	C₂³×C₄	C₅×D₄	1	1	yes	characteristic
514	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
515	AGL(1,ℤ/8)	—	2	16	no	—
516	C₂×SD₁₆	C₂³×C₅	1	8	yes	—
517	C₂×D₈	C₂³×C₅	1	8	yes	—
518	C₂×M₁₆	C₂³×C₅	1	4	yes	—
519	C₄⋊Q₈	—	2	1	no	—
520	C₄⋊Q₈	—	2	1	no	—
521	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
522	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
523	#127	—	2	1	no	—
524	#127	—	2	1	no	—
525	#127	C₂³×C₅	1	2	yes	—
526	#127	C₂³×C₅	1	2	yes	—
527	#124	—	2	2	no	—
528	#124	—	2	2	no	—
529	#124	—	2	2	no	—
530	#124	—	2	2	no	—
531	#121	—	2	2	no	—
532	#121	—	2	2	no	—
533	#121	—	2	2	no	—
534	#121	—	2	2	no	—
535	#121	—	2	2	no	—
536	#121	—	2	2	no	—
537	#121	C₂³×C₅	1	4	yes	—
538	#121	C₂³×C₅	1	4	yes	—
539	C₄×Q₈	—	2	1	no	—
540	C₄×Q₈	—	2	1	no	—
541	C₄×Q₈	—	2	1	no	—
542	C₄×Q₈	—	2	1	no	—
543	C₄×Q₈	C₂³×C₅	1	2	yes	—
544	C₄×Q₈	C₂³×C₅	1	2	yes	—
545	C₄×Q₈	C₂³×C₅	1	2	yes	—
546	C₄×Q₈	C₂³×C₅	1	2	yes	—
547	C₄×D₄	—	2	2	no	—
548	C₄×D₄	—	2	2	no	—
549	C₄×D₄	—	2	2	no	—
550	C₄×D₄	—	2	2	no	—
551	C₄×D₄	—	2	2	no	—
552	C₄×D₄	—	2	2	no	—
553	C₄×D₄	—	2	2	no	—
554	C₄×D₄	—	2	2	no	—
555	C₄×D₄	—	2	2	no	—
556	C₄×D₄	—	2	2	no	—
557	C₄×D₄	—	2	2	no	—
558	C₄×D₄	—	2	2	no	—
559	C₄×D₄	—	2	1	no	—
560	C₄×D₄	—	2	1	no	—
561	C₄×D₄	—	2	1	no	—
562	C₄×D₄	—	2	1	no	—
563	C₄×D₄	—	2	2	no	—
564	C₄×D₄	—	2	2	no	—
565	C₄×D₄	C₂³×C₅	1	2	yes	—
566	C₄×D₄	C₂³×C₅	1	2	yes	—
567	C₄×D₄	C₂³×C₅	1	2	yes	—
568	C₄×D₄	C₂³×C₅	1	2	yes	—
569	C₄×D₄	C₂³×C₅	1	4	yes	—
570	C₄×D₄	C₂³×C₅	1	4	yes	—
571	#117	—	2	1	no	—
572	#117	—	2	1	no	—
573	#117	—	2	2	no	—
574	#117	—	2	2	no	—
575	#117	—	2	2	no	—
576	#117	—	2	2	no	—
577	#117	C₂³×C₅	1	2	yes	—
578	#117	C₂³×C₅	1	2	yes	—
579	C₂×C₄⋊C₄	—	2	1	no	—
580	C₂×C₄⋊C₄	—	2	1	no	—
581	C₂×C₄⋊C₄	—	2	1	no	—
582	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
583	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
584	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
585	C₂×C₂²⋊C₄	—	2	1	no	—
586	C₂×C₂²⋊C₄	—	2	1	no	—
587	C₂×C₂²⋊C₄	—	2	1	no	—
588	C₂×C₂²⋊C₄	—	2	2	no	—
589	C₂×C₂²⋊C₄	—	2	2	no	—
590	C₂×C₄²	—	2	1	no	—
591	C₂×C₄²	—	2	1	no	—
592	C₂×C₄²	—	2	1	no	—
593	C₂×C₄²	—	2	2	no	—
594	C₂×C₄²	—	2	2	no	—
595	C₂×C₄²	—	2	2	no	—
596	C₂×C₄²	—	2	2	no	—
597	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
598	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
599	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
600	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
601	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
602	C₂×C₄²	C₅×D₄	1	1	yes	characteristic
603	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
604	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
606	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
607	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
608	C₂×C₄²	C₂³×C₅	1	1	yes	characteristic
609	#107	C₂³×C₅	1	8	yes	—
610	#106	C₂³×C₅	1	8	yes	—
611	C₄⋊C₈	C₂³×C₅	1	4	yes	—
612	C₄⋊C₈	C₂³×C₅	1	4	yes	—
613	#103	C₂³×C₅	1	8	yes	—
614	#102	C₂³×C₅	1	8	yes	—
615	#102	C₂³×C₅	1	8	yes	—
616	#102	C₂³×C₅	1	8	yes	—
617	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
618	C₂²⋊C₈	C₂³×C₅	1	4	yes	—
619	#97	C₂³×C₅	1	4	yes	—
620	C₄×C₈	C₂³×C₅	1	4	yes	—
621	C₂²×C₅	—	2	1	no	—
622	C₂²×C₅	—	2	1	no	—
623	C₂²×C₅	—	2	1	no	—
624	C₂²×C₅	—	2	1	no	—
625	C₂²×C₅	—	2	1	no	—
626	C₂²×C₅	—	2	4	no	—
627	C₂²×C₅	—	2	1	no	—
628	C₂²×C₅	—	2	1	no	—
629	C₂²×C₅	—	4	4	no	—
630	C₂²×C₅	—	4	8	no	—
631	C₂²×C₅	—	4	2	no	—
632	C₂²×C₅	—	4	2	no	—
633	C₂²×C₅	—	4	4	no	—
634	C₂²×C₅	—	4	4	no	—
635	C₂²×C₅	—	4	4	no	—
636	C₂²×C₅	—	8	8	no	—
637	C₂²×C₅	#525	1	2	yes	—
638	C₂²×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
639	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
640	C₄×C₅	—	2	1	no	—
641	C₄×C₅	—	2	4	no	—
642	C₄×C₅	—	2	1	no	—
643	C₄×C₅	—	2	1	no	—
644	C₄×C₅	—	2	1	no	—
645	C₄×C₅	—	2	1	no	—
646	C₄×C₅	—	2	1	no	—
647	C₄×C₅	—	2	1	no	—
648	C₄×C₅	—	4	2	no	—
649	C₄×C₅	—	4	4	no	—
650	C₄×C₅	—	4	2	no	—
651	C₄×C₅	#525	1	2	yes	—
652	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
653	C₄×C₅	C₂×AGL(1,ℤ/8)	1	2	yes	—
654	C₄×C₅	#575	1	2	yes	—
655	C₄×C₅	C₂²×#41	1	2	yes	—
656	C₂⁴	—	2	1	no	—
657	C₂⁴	—	2	2	no	—
658	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
659	#41	—	2	8	no	—
660	#41	—	2	8	no	—
661	#41	—	2	4	no	—
662	#41	—	2	4	no	—
663	#41	—	2	4	no	—
664	#41	—	4	8	no	—
665	#41	—	4	8	no	—
666	#41	—	4	8	no	—
667	#41	—	4	8	no	—
668	#41	C₅×#41	1	8	yes	complemented
669	C₂×Q₈	—	2	4	no	—
670	C₂×Q₈	—	2	1	no	—
671	C₂×Q₈	—	2	2	no	—
672	C₂×Q₈	—	2	2	no	—
673	C₂×Q₈	—	4	4	no	—
674	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
675	C₂×D₄	—	2	8	no	—
676	C₂×D₄	—	2	2	no	—
677	C₂×D₄	—	2	2	no	—
678	C₂×D₄	—	2	4	no	—
679	C₂×D₄	—	2	4	no	—
680	C₂×D₄	—	2	4	no	—
681	C₂×D₄	—	2	1	no	—
682	C₂×D₄	—	2	2	no	—
683	C₂×D₄	—	2	2	no	—
684	C₂×D₄	—	2	2	no	—
685	C₂×D₄	—	2	2	no	—
686	C₂×D₄	—	2	2	no	—
687	C₂×D₄	—	2	8	no	—
688	C₂×D₄	—	4	4	no	—
689	C₂×D₄	—	4	4	no	—
690	C₂×D₄	—	4	8	no	—
691	C₂×D₄	C₂⁴×C₅	1	4	yes	—
692	C₂×D₄	C₂⁴×C₅	1	2	yes	—
693	C₂²×C₄	—	2	8	no	—
694	C₂²×C₄	—	2	1	no	—
695	C₂²×C₄	—	2	4	no	—
696	C₂²×C₄	—	2	2	no	—
697	C₂²×C₄	—	2	2	no	—
698	C₂²×C₄	—	2	4	no	—
699	C₂²×C₄	—	2	1	no	—
700	C₂²×C₄	—	2	1	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	2	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	4	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	4	2	no	—
709	C₂²×C₄	—	4	8	no	—
710	C₂²×C₄	—	4	4	no	—
711	C₂²×C₄	—	4	4	no	—
712	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
713	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
714	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
715	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
716	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
717	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
718	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
719	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
720	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
721	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
722	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
723	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
724	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
725	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
726	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
727	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
728	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
729	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
730	SD₁₆	—	2	16	no	—
731	D₈	—	2	16	no	—
732	M₁₆	—	2	8	no	—
733	C₂×C₈	C₂⁴×C₅	1	8	yes	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	2	no	—
736	C₄⋊C₄	—	2	2	no	—
737	C₄⋊C₄	—	2	2	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	1	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
744	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
745	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	2	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	—	2	2	no	—
751	C₂²⋊C₄	—	2	2	no	—
752	C₂²⋊C₄	—	2	4	no	—
753	C₂²⋊C₄	—	2	4	no	—
754	C₂²⋊C₄	—	2	4	no	—
755	C₂²⋊C₄	—	2	4	no	—
756	C₄²	—	2	2	no	—
757	C₄²	—	2	2	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
763	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
764	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
765	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
766	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
767	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
768	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
769	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
770	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
771	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
772	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
773	C₄²	C₂×C₅×D₄	1	1	yes	characteristic
774	C₄²	C₂⁴×C₅	1	1	yes	characteristic
775	C₄²	C₂⁴×C₅	1	1	yes	characteristic
776	C₄²	C₂⁴×C₅	1	1	yes	characteristic
777	C₄²	C₂⁴×C₅	1	1	yes	characteristic
778	C₂×C₅	—	2	2	no	—
779	C₂×C₅	—	2	2	no	—
780	C₂×C₅	—	4	1	no	—
781	C₂×C₅	—	4	4	no	—
782	C₂×C₅	—	8	4	no	—
783	C₂×C₅	C₂×#525	1	1	yes	characteristic
784	C₂×C₅	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
785	C₂×C₅	C₂×#575	1	1	yes	characteristic
786	C₂³	—	2	4	no	—
787	C₂³	—	2	2	no	—
788	C₂³	—	2	2	no	—
789	C₂³	—	2	2	no	—
790	C₂³	—	2	4	no	—
791	C₂³	—	4	1	no	—
792	C₂³	—	4	2	no	—
793	C₂³	—	4	4	no	—
794	C₂³	—	4	4	no	—
795	C₂³	—	4	2	no	—
796	C₂³	—	4	4	no	—
797	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
798	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
799	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
800	Q₈	—	2	4	no	—
801	Q₈	—	2	2	no	—
802	Q₈	—	4	4	no	—
803	Q₈	—	4	4	no	—
804	Q₈	C₂×C₅×#41	1	4	yes	complemented
805	D₄	—	2	8	no	—
806	D₄	—	2	4	no	—
807	D₄	—	2	8	no	—
808	D₄	—	2	2	no	—
809	D₄	—	2	8	no	—
810	D₄	—	4	4	no	—
811	D₄	—	4	4	no	—
812	D₄	—	4	8	no	—
813	D₄	—	4	8	no	—
814	D₄	—	4	4	no	—
815	D₄	—	4	4	no	—
816	D₄	—	4	4	no	—
817	D₄	C₂×C₅×#41	1	4	yes	complemented
818	C₂×C₄	—	2	4	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	8	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	2	2	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	4	no	—
838	C₂×C₄	—	4	1	no	—
839	C₂×C₄	—	4	1	no	—
840	C₂×C₄	—	4	1	no	—
841	C₂×C₄	—	4	8	no	—
842	C₂×C₄	—	4	4	no	—
843	C₂×C₄	—	4	4	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	2	no	—
846	C₂×C₄	—	4	8	no	—
847	C₂×C₄	—	4	4	no	—
848	C₂×C₄	—	4	4	no	—
849	C₂×C₄	—	4	4	no	—
850	C₂×C₄	C₅×AGL(1,ℤ/8)	1	4	yes	complemented
851	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
852	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
853	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
854	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
855	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
856	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
857	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
858	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
859	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
860	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
861	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
862	C₂×C₄	C₂×C₅×#41	1	4	yes	—
863	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
864	C₈	—	2	8	no	—
865	C₅	#60561	1	1	yes	characteristic, direct product factor, Sylow
866	C₂²	—	2	1	no	—
867	C₂²	—	2	1	no	—
868	C₂²	—	2	1	no	—
869	C₂²	—	2	1	no	—
870	C₂²	—	2	1	no	—
871	C₂²	—	2	4	no	—
872	C₂²	—	2	1	no	—
873	C₂²	—	2	1	no	—
874	C₂²	—	4	4	no	—
875	C₂²	—	4	8	no	—
876	C₂²	—	4	2	no	—
877	C₂²	—	4	2	no	—
878	C₂²	—	4	4	no	—
879	C₂²	—	4	4	no	—
880	C₂²	—	4	4	no	—
881	C₂²	—	8	8	no	—
882	C₂²	C₅×#525	1	2	yes	—
883	C₂²	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
884	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
885	C₄	—	2	1	no	—
886	C₄	—	2	4	no	—
887	C₄	—	2	1	no	—
888	C₄	—	2	1	no	—
889	C₄	—	2	1	no	—
890	C₄	—	2	1	no	—
891	C₄	—	2	1	no	—
892	C₄	—	2	1	no	—
893	C₄	—	4	4	no	—
894	C₄	—	4	2	no	—
895	C₄	—	4	2	no	—
896	C₄	C₅×#525	1	2	yes	—
897	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
898	C₄	C₂×C₅×AGL(1,ℤ/8)	1	2	yes	—
899	C₄	C₅×#575	1	2	yes	—
900	C₄	C₂²×C₅×#41	1	2	yes	—
901	C₂	—	2	2	no	—
902	C₂	—	2	2	no	—
903	C₂	—	4	1	no	—
904	C₂	—	4	4	no	—
905	C₂	—	8	4	no	—
906	C₂	C₂×C₅×#525	1	1	yes	characteristic
907	C₂	C₂²×C₅×AGL(1,ℤ/8)	1	1	yes	characteristic
908	C₂	C₂×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
socle	C₂²×C₅	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂²×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₅×#532	C₂	semidirect
2. C₂×C₄×C₅×#41	C₂	semidirect
3. C₅×#3115	C₂	semidirect
4. C₅×#3112	C₂	semidirect
5. C₅×#3109	C₂	semidirect
6. C₅×#3106	C₂	semidirect
7. C₅×#3103	C₂	semidirect
8. C₅×#3100	C₂	semidirect
9. C₅×#3094	C₂	semidirect
10. C₅×#3079	C₂	semidirect
11. C₅×#3038	C₂	semidirect
12. C₅×#3006	C₂	semidirect
13. C₄×C₅×AGL(1,ℤ/8)	C₂	semidirect
14. C₅×#2920	C₂	semidirect
24. C₅×#532	C₂²	semidirect
25. C₅×#532	C₂²	semidirect
26. C₂×C₅×C₄⋊Q₈	C₂²	semidirect
27. C₂×C₅×#127	C₂²	semidirect
37. C₄×C₅×#41	C₂²	semidirect
38. C₄×C₅×#41	C₂²	semidirect
39. C₂×C₄×C₅×Q₈	C₂²	semidirect
40. C₂×C₄×C₅×Q₈	C₂²	semidirect
44. C₂×C₄×C₅×D₄	C₂²	semidirect
45. C₂×C₄×C₅×D₄	C₂²	semidirect
46. C₂×C₄×C₅×D₄	C₂²	semidirect
51. C₅×#482	C₂²	semidirect
52. C₅×#481	C₂²	semidirect
53. C₅×#480	C₂²	semidirect
54. C₅×#477	C₂²	semidirect
55. C₅×#476	C₂²	semidirect
56. C₅×#475	C₂²	semidirect
57. C₅×#474	C₂²	semidirect
58. C₅×#460	C₂²	semidirect
59. C₅×#460	C₂²	semidirect
60. C₅×#459	C₂²	semidirect
61. C₅×#459	C₂²	semidirect
62. C₅×#449	C₂²	semidirect
63. C₅×#448	C₂²	semidirect
64. C₅×#447	C₂²	semidirect
65. C₅×#442	C₂²	semidirect
66. C₅×#440	C₂²	semidirect
67. C₄×C₅×SD₁₆	C₂²	semidirect
68. C₄×C₅×D₈	C₂²	semidirect
69. C₅×#432	C₂²	semidirect
70. C₅×#432	C₂²	semidirect
71. C₅×#431	C₂²	semidirect
72. C₅×#431	C₂²	semidirect
73. C₅×#428	C₂²	semidirect
74. C₅×#423	C₂²	semidirect
75. C₅×#418	C₂²	semidirect
78. C₄×C₅×M₁₆	C₂²	semidirect
79. #60561	C₅	direct (N × H)
211. C₂×#532	C₂×C₅	semidirect
212. C₂×C₄×#41	C₂×C₅	semidirect
213. #3115	C₂×C₅	semidirect
214. #3112	C₂×C₅	semidirect
215. #3109	C₂×C₅	semidirect
216. #3106	C₂×C₅	semidirect
217. #3103	C₂×C₅	semidirect
218. #3100	C₂×C₅	semidirect
219. #3094	C₂×C₅	semidirect
220. #3079	C₂×C₅	semidirect
221. #3038	C₂×C₅	semidirect
222. #3006	C₂×C₅	semidirect
223. C₄×AGL(1,ℤ/8)	C₂×C₅	semidirect
224. #2920	C₂×C₅	semidirect
237. C₅×#41	#41	semidirect
356. #532	C₂²×C₅	semidirect
357. #532	C₂²×C₅	semidirect
358. C₂×C₄⋊Q₈	C₂²×C₅	semidirect
359. C₂×#127	C₂²×C₅	semidirect
369. C₄×#41	C₂²×C₅	semidirect
370. C₄×#41	C₂²×C₅	semidirect
371. C₂×C₄×Q₈	C₂²×C₅	semidirect
372. C₂×C₄×Q₈	C₂²×C₅	semidirect
376. C₂×C₄×D₄	C₂²×C₅	semidirect
377. C₂×C₄×D₄	C₂²×C₅	semidirect
378. C₂×C₄×D₄	C₂²×C₅	semidirect
383. #482	C₂²×C₅	semidirect
384. #481	C₂²×C₅	semidirect
385. #480	C₂²×C₅	semidirect
386. #477	C₂²×C₅	semidirect
387. #476	C₂²×C₅	semidirect
388. #475	C₂²×C₅	semidirect
389. #474	C₂²×C₅	semidirect
390. #460	C₂²×C₅	semidirect
391. #460	C₂²×C₅	semidirect
392. #459	C₂²×C₅	semidirect
393. #459	C₂²×C₅	semidirect
394. #449	C₂²×C₅	semidirect
395. #448	C₂²×C₅	semidirect
396. #447	C₂²×C₅	semidirect
397. #442	C₂²×C₅	semidirect
398. #440	C₂²×C₅	semidirect
399. C₄×SD₁₆	C₂²×C₅	semidirect
400. C₄×D₈	C₂²×C₅	semidirect
401. #432	C₂²×C₅	semidirect
402. #432	C₂²×C₅	semidirect
403. #431	C₂²×C₅	semidirect
404. #431	C₂²×C₅	semidirect
405. #428	C₂²×C₅	semidirect
406. #423	C₂²×C₅	semidirect
407. #418	C₂²×C₅	semidirect
410. C₄×M₁₆	C₂²×C₅	semidirect
429. C₅×Q₈	C₂×#41	semidirect
442. C₅×D₄	C₂×#41	semidirect
475. C₂×C₄×C₅	AGL(1,ℤ/8)	semidirect
668. #41	C₅×#41	semidirect
804. Q₈	C₂×C₅×#41	semidirect
817. D₄	C₂×C₅×#41	semidirect
850. C₂×C₄	C₅×AGL(1,ℤ/8)	semidirect
865. C₅	#60561	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₅×#532	2
C₂×C₄×C₅×#41	2
C₅×#3115	2
C₅×#3112	2
C₅×#3109	2
C₅×#3106	2
C₅×#3103	2
C₅×#3100	2
C₅×#3094	2
C₅×#3079	2
C₅×#3038	2
C₅×#3006	2
C₄×C₅×AGL(1,ℤ/8)	2
C₅×#2920	2
#60561	5

Subgroups — C5×#60561 #11983281

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60561 #11983281