Subgroups — C₅×#60584 #11983304

Order 1280.

2134 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3124	C₂	1	4	yes	maximal, complemented
4	C₅×#3119	C₂	1	4	yes	maximal, complemented
5	C₅×#3114	C₂	1	2	yes	maximal, complemented
6	C₅×#3112	C₂	1	2	yes	maximal, complemented
7	C₅×#3108	C₂	1	2	yes	maximal, complemented
8	C₅×#3100	C₂	1	2	yes	maximal, complemented
9	C₅×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3083	C₂	1	2	yes	maximal, complemented
12	C₅×#3045	C₂	1	2	yes	maximal, complemented
13	C₅×#3006	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3002	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2951	C₂	1	2	yes	maximal, complemented
16	C₅×#2946	C₂	1	2	yes	maximal, complemented
17	C₅×#2924	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
20	C₂×C₅×#135	C₂²	1	2	yes	—
21	C₅×#555	—	2	1	no	—
22	C₅×#553	—	2	1	no	—
23	C₅×#553	—	2	1	no	—
24	C₅×#551	—	2	2	no	—
25	C₅×#547	—	2	1	no	—
26	C₅×#546	—	2	2	no	—
27	C₅×#544	C₂²	1	1	yes	characteristic, complemented
28	C₅×#542	C₂²	1	2	yes	complemented
29	C₅×#540	C₂²	1	2	yes	complemented
30	C₅×#535	C₂²	1	1	yes	characteristic, complemented
31	C₅×#532	C₂²	1	2	yes	—
32	C₅×#529	C₂²	1	2	yes	—
33	C₅×#525	C₂²	1	1	yes	characteristic
34	C₂×C₅×#121	C₂²	1	1	yes	characteristic
35	C₅×#520	—	2	1	no	—
36	C₅×#520	—	2	1	no	—
37	C₅×#520	—	2	2	no	—
38	C₅×#520	C₂²	1	2	yes	—
39	C₅×#520	C₂²	1	2	yes	—
40	C₅×#520	C₂²	1	4	yes	complemented
41	C₅×#520	C₂²	1	1	yes	characteristic, complemented
42	C₅×#518	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
44	C₂×C₄×C₅×D₄	—	2	2	no	—
45	C₂×C₄×C₅×D₄	C₂²	1	2	yes	complemented
46	C₂×C₅×#117	—	2	1	no	—
47	C₂×C₅×#117	C₂²	1	1	yes	characteristic
48	C₂²×C₅×C₄⋊C₄	—	2	1	no	—
49	C₂²×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
50	C₅×#484	C₂²	1	2	yes	complemented
51	C₅×#483	C₂²	1	2	yes	complemented
52	C₅×#481	C₂²	1	2	yes	complemented
53	C₅×#480	C₂²	1	2	yes	—
54	C₅×#480	C₂²	1	2	yes	—
55	C₅×#480	C₂²	1	4	yes	complemented
56	C₅×#480	C₂²	1	2	yes	complemented
57	C₅×#479	C₂²	1	4	yes	complemented
58	C₅×#478	C₂²	1	4	yes	complemented
59	C₅×#477	C₂²	1	4	yes	complemented
60	C₅×#474	C₂²	1	4	yes	complemented
61	C₅×#464	C₂²	1	4	yes	complemented
62	C₅×#463	C₂²	1	4	yes	complemented
63	C₅×#460	C₂²	1	4	yes	complemented
64	C₅×#459	C₂²	1	4	yes	complemented
65	C₅×#452	C₂²	1	2	yes	complemented
66	C₅×#451	C₂²	1	1	yes	characteristic, complemented
67	C₅×#450	C₂²	1	1	yes	characteristic, complemented
68	C₅×#449	C₂²	1	4	yes	—
69	C₅×#449	C₂²	1	2	yes	complemented
70	C₅×#448	C₂²	1	2	yes	—
71	C₅×#448	C₂²	1	1	yes	characteristic, complemented
72	C₅×#447	C₂²	1	2	yes	—
73	C₅×#447	C₂²	1	1	yes	characteristic, complemented
74	C₅×#442	C₂²	1	4	yes	complemented
75	C₅×#440	C₂²	1	4	yes	complemented
76	C₅×#440	C₂²	1	4	yes	complemented
77	C₅×#440	C₂²	1	4	yes	complemented
78	C₄×C₅×Q₁₆	C₂²	1	4	yes	complemented
79	C₄×C₅×SD₁₆	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	C₂×C₅×#107	C₂²	1	2	yes	complemented
87	C₅×#424	C₂²	1	2	yes	complemented
88	C₅×#417	C₂²	1	2	yes	—
89	C₅×#417	C₂²	1	2	yes	complemented
90	C₅×#416	C₂²	1	2	yes	—
91	C₂×C₅×#102	C₂²	1	2	yes	complemented
92	C₅×#407	C₂²	1	1	yes	characteristic
93	C₂×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
94	C₅×#405	C₂²	1	2	yes	complemented
95	#60584	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₅×#41	—	2	8	no	—
97	C₂×C₅×#41	—	2	1	no	—
98	C₂×C₅×#41	—	2	1	no	—
99	C₂×C₅×#41	—	2	2	no	—
100	C₂×C₅×#41	C₂³	1	1	yes	characteristic
101	C₂×C₅×#41	C₂³	1	2	yes	—
102	C₂×C₅×#41	C₂³	1	2	yes	—
103	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₅×D₄	—	2	1	no	—
105	C₂²×C₅×D₄	—	2	1	no	—
106	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₅	—	2	1	no	—
109	C₂³×C₄×C₅	—	2	1	no	—
110	C₂³×C₄×C₅	—	2	2	no	—
111	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₅×AGL(1,ℤ/8)	—	2	8	no	—
113	C₅×#135	—	2	8	no	—
114	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
115	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
116	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
117	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
118	C₂×C₅×D₈	C₂³	1	2	yes	—
119	C₂×C₅×D₈	C₂³	1	4	yes	—
120	C₂×C₅×M₁₆	C₂³	1	2	yes	—
121	C₂²×C₅×C₈	C₂³	1	2	yes	—
122	C₅×C₄⋊Q₈	—	2	1	no	—
123	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
124	C₅×#127	C₂³	1	2	yes	—
125	C₅×#126	—	2	2	no	—
126	C₅×#126	—	2	2	no	—
127	C₅×#125	—	2	1	no	—
128	C₅×#125	C₂³	1	2	yes	—
129	C₅×#124	—	2	2	no	—
130	C₅×#124	—	2	2	no	—
131	C₅×#124	C₂³	1	2	yes	—
132	C₅×#123	—	2	1	no	—
133	C₅×#123	—	2	2	no	—
134	C₅×#123	—	2	2	no	—
135	C₅×#123	—	2	2	no	—
136	C₅×#123	—	2	2	no	—
137	C₅×C₂²⋊Q₈	—	2	2	no	—
138	C₅×C₂²⋊Q₈	—	2	2	no	—
139	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
140	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
141	C₅×#121	—	2	1	no	—
142	C₅×#121	—	2	1	no	—
143	C₅×#121	—	2	2	no	—
144	C₅×#121	—	2	1	no	—
145	C₅×#121	—	2	1	no	—
146	C₅×#121	—	2	2	no	—
147	C₅×#121	—	2	2	no	—
148	C₅×#121	C₂³	1	2	yes	—
149	C₅×#121	C₂³	1	1	yes	characteristic
150	C₅×#121	C₂³	1	2	yes	—
151	C₅×#121	C₂³	1	1	yes	characteristic
152	C₅×#120	—	2	1	no	—
153	C₅×#120	—	2	2	no	—
154	C₄×C₅×Q₈	—	2	2	no	—
155	C₄×C₅×Q₈	—	2	2	no	—
156	C₄×C₅×Q₈	C₂³	1	4	yes	—
157	C₄×C₅×Q₈	C₂³	1	2	yes	—
158	C₄×C₅×Q₈	C₂³	1	4	yes	—
159	C₄×C₅×D₄	—	2	1	no	—
160	C₄×C₅×D₄	—	2	1	no	—
161	C₄×C₅×D₄	—	2	2	no	—
162	C₄×C₅×D₄	—	2	1	no	—
163	C₄×C₅×D₄	—	2	1	no	—
164	C₄×C₅×D₄	—	2	4	no	—
165	C₄×C₅×D₄	—	2	4	no	—
166	C₄×C₅×D₄	—	2	4	no	—
167	C₄×C₅×D₄	—	2	4	no	—
168	C₄×C₅×D₄	—	2	2	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	C₂³	1	2	yes	—
173	C₄×C₅×D₄	C₂³	1	2	yes	—
174	C₄×C₅×D₄	C₂³	1	4	yes	—
175	C₄×C₅×D₄	C₂³	1	2	yes	—
176	C₄×C₅×D₄	C₂³	1	4	yes	—
177	C₅×#117	—	2	2	no	—
178	C₅×#117	—	2	2	no	—
179	C₅×#117	—	2	4	no	—
180	C₅×#117	—	2	1	no	—
181	C₅×#117	—	2	2	no	—
182	C₅×#117	D₄	1	2	yes	—
183	C₅×#117	D₄	1	1	yes	characteristic
184	C₅×#117	D₄	1	1	yes	characteristic
185	C₅×#117	C₂³	1	1	yes	characteristic
186	C₅×#117	C₂³	1	1	yes	characteristic
187	C₅×#117	C₂³	1	1	yes	characteristic
188	C₅×#117	C₂³	1	2	yes	—
189	C₂×C₅×C₄⋊C₄	—	2	1	no	—
190	C₂×C₅×C₄⋊C₄	—	2	2	no	—
191	C₂×C₅×C₄⋊C₄	—	2	1	no	—
192	C₂×C₅×C₄⋊C₄	—	2	1	no	—
193	C₂×C₅×C₄⋊C₄	—	2	2	no	—
194	C₂×C₅×C₄⋊C₄	—	2	2	no	—
195	C₂×C₅×C₄⋊C₄	—	2	4	no	—
196	C₂×C₅×C₄⋊C₄	—	2	1	no	—
197	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
198	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
199	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
200	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
201	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
202	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
204	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
205	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
206	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
207	C₂×C₄²×C₅	—	2	2	no	—
208	C₂×C₄²×C₅	C₂³	1	2	yes	—
209	C₅×#107	C₂³	1	4	yes	—
210	C₅×#107	C₂³	1	4	yes	—
211	C₅×#107	C₂³	1	4	yes	—
212	C₅×#106	C₂³	1	4	yes	—
213	C₅×C₄⋊C₈	C₂³	1	4	yes	—
214	C₅×C₄⋊C₈	C₂³	1	4	yes	—
215	C₅×#103	C₂³	1	2	yes	—
216	C₅×#103	C₂³	1	2	yes	—
217	C₅×#103	C₂³	1	4	yes	—
218	C₅×#103	C₂³	1	4	yes	—
219	C₅×#102	C₂³	1	4	yes	—
220	C₅×#102	C₂³	1	4	yes	—
221	C₅×#102	C₂³	1	2	yes	—
222	C₅×#102	C₂³	1	2	yes	—
223	C₅×#102	C₂³	1	4	yes	—
224	C₅×#102	C₂³	1	4	yes	—
225	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
226	C₅×C₂²⋊C₈	C₂³	1	1	yes	characteristic
227	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
228	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
229	C₅×C₂²⋊C₈	C₂³	1	2	yes	—
230	C₅×#97	C₂³	1	4	yes	—
231	C₄×C₅×C₈	C₂³	1	4	yes	—
232	#3494	C₂×C₅	1	1	yes	characteristic, complemented
233	C₂×#520	C₂×C₅	1	1	yes	characteristic, complemented
234	#3124	C₂×C₅	1	4	yes	complemented
235	#3119	C₂×C₅	1	4	yes	complemented
236	#3114	C₂×C₅	1	2	yes	complemented
237	#3112	C₂×C₅	1	2	yes	complemented
238	#3108	C₂×C₅	1	2	yes	complemented
239	#3100	C₂×C₅	1	2	yes	complemented
240	#3092	C₂×C₅	1	1	yes	characteristic, complemented
241	C₂×#480	C₂×C₅	1	1	yes	characteristic, complemented
242	#3083	C₂×C₅	1	2	yes	complemented
243	#3045	C₂×C₅	1	2	yes	complemented
244	#3006	C₂×C₅	1	1	yes	characteristic, complemented
245	#3002	C₂×C₅	1	1	yes	characteristic, complemented
246	#2951	C₂×C₅	1	2	yes	complemented
247	#2946	C₂×C₅	1	2	yes	complemented
248	#2924	C₂×C₅	1	1	yes	characteristic, complemented
249	C₂⁴×C₅	—	2	1	no	—
250	C₂⁴×C₅	—	2	1	no	—
251	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
252	C₅×#41	—	2	8	no	—
253	C₅×#41	—	2	8	no	—
254	C₅×#41	—	2	4	no	—
255	C₅×#41	—	2	4	no	—
256	C₅×#41	—	2	4	no	—
257	C₅×#41	—	2	4	no	—
258	C₅×#41	—	8	4	no	—
259	C₅×#41	#41	1	8	yes	complemented
260	C₂×C₅×Q₈	—	2	4	no	—
261	C₂×C₅×Q₈	—	2	1	no	—
262	C₂×C₅×Q₈	—	2	2	no	—
263	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
264	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
265	C₂×C₅×D₄	—	2	8	no	—
266	C₂×C₅×D₄	—	2	2	no	—
267	C₂×C₅×D₄	—	2	2	no	—
268	C₂×C₅×D₄	—	2	4	no	—
269	C₂×C₅×D₄	—	2	1	no	—
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	2	2	no	—
272	C₂×C₅×D₄	—	2	1	no	—
273	C₂×C₅×D₄	—	2	2	no	—
274	C₂×C₅×D₄	—	2	1	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	4	no	—
279	C₂×C₅×D₄	—	8	2	no	—
280	C₂×C₅×D₄	C₂⁴	1	2	yes	—
281	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
282	C₂×C₅×D₄	C₂⁴	1	2	yes	—
283	C₂²×C₄×C₅	—	2	8	no	—
284	C₂²×C₄×C₅	—	2	1	no	—
285	C₂²×C₄×C₅	—	2	2	no	—
286	C₂²×C₄×C₅	—	2	2	no	—
287	C₂²×C₄×C₅	—	2	4	no	—
288	C₂²×C₄×C₅	—	2	2	no	—
289	C₂²×C₄×C₅	—	2	1	no	—
290	C₂²×C₄×C₅	—	2	2	no	—
291	C₂²×C₄×C₅	—	2	2	no	—
292	C₂²×C₄×C₅	—	2	1	no	—
293	C₂²×C₄×C₅	—	2	2	no	—
294	C₂²×C₄×C₅	—	2	2	no	—
295	C₂²×C₄×C₅	—	2	4	no	—
296	C₂²×C₄×C₅	—	2	4	no	—
297	C₂²×C₄×C₅	—	2	2	no	—
298	C₂²×C₄×C₅	—	8	4	no	—
299	C₂²×C₄×C₅	—	8	2	no	—
300	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
301	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₅	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
305	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
308	C₅×Q₁₆	—	2	4	no	—
309	C₅×SD₁₆	—	2	4	no	—
310	C₅×SD₁₆	—	2	8	no	—
311	C₅×SD₁₆	—	2	4	no	—
312	C₅×D₈	—	2	4	no	—
313	C₅×D₈	—	2	8	no	—
314	C₅×M₁₆	—	2	4	no	—
315	C₂×C₅×C₈	—	2	4	no	—
316	C₂×C₅×C₈	C₂⁴	1	2	yes	—
317	C₂×C₅×C₈	C₂⁴	1	2	yes	—
318	C₂×C₅×C₈	C₂⁴	1	4	yes	—
319	C₅×C₄⋊C₄	—	2	2	no	—
320	C₅×C₄⋊C₄	—	2	2	no	—
321	C₅×C₄⋊C₄	—	2	4	no	—
322	C₅×C₄⋊C₄	—	2	4	no	—
323	C₅×C₄⋊C₄	—	2	2	no	—
324	C₅×C₄⋊C₄	—	2	1	no	—
325	C₅×C₄⋊C₄	—	2	2	no	—
326	C₅×C₄⋊C₄	—	2	1	no	—
327	C₅×C₄⋊C₄	—	2	2	no	—
328	C₅×C₄⋊C₄	—	2	2	no	—
329	C₅×C₄⋊C₄	—	2	2	no	—
330	C₅×C₄⋊C₄	—	2	1	no	—
331	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
332	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
333	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
334	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
335	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
336	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
337	C₅×C₄⋊C₄	C₂⁴	1	4	yes	—
338	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
339	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
340	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
341	C₅×C₂²⋊C₄	—	2	1	no	—
342	C₅×C₂²⋊C₄	—	2	1	no	—
343	C₅×C₂²⋊C₄	—	2	1	no	—
344	C₅×C₂²⋊C₄	—	2	4	no	—
345	C₅×C₂²⋊C₄	—	2	4	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	2	no	—
350	C₅×C₂²⋊C₄	—	2	2	no	—
351	C₅×C₂²⋊C₄	—	2	2	no	—
352	C₅×C₂²⋊C₄	—	2	1	no	—
353	C₅×C₂²⋊C₄	—	2	2	no	—
354	C₅×C₂²⋊C₄	—	2	1	no	—
355	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
356	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
357	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
358	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
359	C₄²×C₅	—	2	4	no	—
360	C₄²×C₅	—	2	4	no	—
361	C₄²×C₅	—	2	2	no	—
362	C₄²×C₅	—	2	1	no	—
363	C₄²×C₅	C₂×D₄	1	2	yes	—
364	C₄²×C₅	C₂×D₄	1	2	yes	—
365	C₄²×C₅	C₂⁴	1	2	yes	—
366	C₄²×C₅	C₂⁴	1	2	yes	—
367	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
368	C₂×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
369	C₂×#135	C₂²×C₅	1	2	yes	—
370	#555	—	2	1	no	—
371	#553	—	2	1	no	—
372	#553	—	2	1	no	—
373	#551	—	2	2	no	—
374	#547	—	2	1	no	—
375	#546	—	2	2	no	—
376	#544	C₂²×C₅	1	1	yes	characteristic, complemented
377	#542	C₂²×C₅	1	2	yes	complemented
378	#540	C₂²×C₅	1	2	yes	complemented
379	#535	C₂²×C₅	1	1	yes	characteristic, complemented
380	#532	C₂²×C₅	1	2	yes	—
381	#529	C₂²×C₅	1	2	yes	—
382	#525	C₂²×C₅	1	1	yes	characteristic
383	C₂×#121	C₂²×C₅	1	1	yes	characteristic
384	#520	—	2	1	no	—
385	#520	—	2	1	no	—
386	#520	—	2	2	no	—
387	#520	C₂²×C₅	1	2	yes	—
388	#520	C₂²×C₅	1	2	yes	—
389	#520	C₂²×C₅	1	4	yes	complemented
390	#520	C₂²×C₅	1	1	yes	characteristic, complemented
391	#518	C₂²×C₅	1	1	yes	characteristic, complemented
392	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
393	C₂×C₄×D₄	—	2	2	no	—
394	C₂×C₄×D₄	C₂²×C₅	1	2	yes	complemented
395	C₂×#117	—	2	1	no	—
396	C₂×#117	C₂²×C₅	1	1	yes	characteristic
397	C₂²×C₄⋊C₄	—	2	1	no	—
398	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
399	#484	C₂²×C₅	1	2	yes	complemented
400	#483	C₂²×C₅	1	2	yes	complemented
401	#481	C₂²×C₅	1	2	yes	complemented
402	#480	C₂²×C₅	1	2	yes	—
403	#480	C₂²×C₅	1	2	yes	—
404	#480	C₂²×C₅	1	4	yes	complemented
405	#480	C₂²×C₅	1	2	yes	complemented
406	#479	C₂²×C₅	1	4	yes	complemented
407	#478	C₂²×C₅	1	4	yes	complemented
408	#477	C₂²×C₅	1	4	yes	complemented
409	#474	C₂²×C₅	1	4	yes	complemented
410	#464	C₂²×C₅	1	4	yes	complemented
411	#463	C₂²×C₅	1	4	yes	complemented
412	#460	C₂²×C₅	1	4	yes	complemented
413	#459	C₂²×C₅	1	4	yes	complemented
414	#452	C₂²×C₅	1	2	yes	complemented
415	#451	C₂²×C₅	1	1	yes	characteristic, complemented
416	#450	C₂²×C₅	1	1	yes	characteristic, complemented
417	#449	C₂²×C₅	1	4	yes	—
418	#449	C₂²×C₅	1	2	yes	complemented
419	#448	C₂²×C₅	1	2	yes	—
420	#448	C₂²×C₅	1	1	yes	characteristic, complemented
421	#447	C₂²×C₅	1	2	yes	—
422	#447	C₂²×C₅	1	1	yes	characteristic, complemented
423	#442	C₂²×C₅	1	4	yes	complemented
424	#440	C₂²×C₅	1	4	yes	complemented
425	#440	C₂²×C₅	1	4	yes	complemented
426	#440	C₂²×C₅	1	4	yes	complemented
427	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
428	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
429	C₄×D₈	C₂²×C₅	1	4	yes	complemented
430	C₄×D₈	C₂²×C₅	1	4	yes	complemented
431	#433	C₂²×C₅	1	4	yes	complemented
432	#432	C₂²×C₅	1	2	yes	complemented
433	#431	C₂²×C₅	1	2	yes	complemented
434	#428	C₂²×C₅	1	2	yes	complemented
435	C₂×#107	C₂²×C₅	1	2	yes	complemented
436	#424	C₂²×C₅	1	2	yes	complemented
437	#417	C₂²×C₅	1	2	yes	—
438	#417	C₂²×C₅	1	2	yes	complemented
439	#416	C₂²×C₅	1	2	yes	—
440	C₂×#102	C₂²×C₅	1	2	yes	complemented
441	#407	C₂²×C₅	1	1	yes	characteristic
442	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
443	#405	C₂²×C₅	1	2	yes	complemented
444	C₂³×C₅	—	2	4	no	—
445	C₂³×C₅	—	2	2	no	—
446	C₂³×C₅	—	2	2	no	—
447	C₂³×C₅	—	2	2	no	—
448	C₂³×C₅	—	2	2	no	—
449	C₂³×C₅	—	2	1	no	—
450	C₂³×C₅	—	4	1	no	—
451	C₂³×C₅	—	4	2	no	—
452	C₂³×C₅	—	4	2	no	—
453	C₂³×C₅	—	4	2	no	—
454	C₂³×C₅	—	8	1	no	—
455	C₂³×C₅	—	8	1	no	—
456	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
457	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
459	C₅×Q₈	—	2	4	no	—
460	C₅×Q₈	—	2	2	no	—
461	C₅×Q₈	—	2	2	no	—
462	C₅×Q₈	—	8	2	no	—
463	C₅×Q₈	C₂×#41	1	4	yes	—
464	C₅×D₄	—	2	8	no	—
465	C₅×D₄	—	2	4	no	—
466	C₅×D₄	—	2	8	no	—
467	C₅×D₄	—	2	2	no	—
468	C₅×D₄	—	2	4	no	—
469	C₅×D₄	—	2	2	no	—
470	C₅×D₄	—	4	2	no	—
471	C₅×D₄	—	4	4	no	—
472	C₅×D₄	—	4	2	no	—
473	C₅×D₄	—	4	2	no	—
474	C₅×D₄	—	8	2	no	—
475	C₅×D₄	—	8	2	no	—
476	C₅×D₄	—	8	1	no	—
477	C₅×D₄	—	8	2	no	—
478	C₅×D₄	C₂×#41	1	4	yes	—
479	C₂×C₄×C₅	—	2	4	no	—
480	C₂×C₄×C₅	—	2	8	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	4	no	—
483	C₂×C₄×C₅	—	2	2	no	—
484	C₂×C₄×C₅	—	2	2	no	—
485	C₂×C₄×C₅	—	2	8	no	—
486	C₂×C₄×C₅	—	2	2	no	—
487	C₂×C₄×C₅	—	2	2	no	—
488	C₂×C₄×C₅	—	2	2	no	—
489	C₂×C₄×C₅	—	2	1	no	—
490	C₂×C₄×C₅	—	2	4	no	—
491	C₂×C₄×C₅	—	2	1	no	—
492	C₂×C₄×C₅	—	2	1	no	—
493	C₂×C₄×C₅	—	2	2	no	—
494	C₂×C₄×C₅	—	4	2	no	—
495	C₂×C₄×C₅	—	4	4	no	—
496	C₂×C₄×C₅	—	4	2	no	—
497	C₂×C₄×C₅	—	8	2	no	—
498	C₂×C₄×C₅	—	8	4	no	—
499	C₂×C₄×C₅	—	8	4	no	—
500	C₂×C₄×C₅	—	8	2	no	—
501	C₂×C₄×C₅	—	8	2	no	—
502	C₂×C₄×C₅	—	8	2	no	—
503	C₂×C₄×C₅	—	8	2	no	—
504	C₂×C₄×C₅	—	8	1	no	—
505	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
506	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
510	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₅	C₂×#41	1	4	yes	—
513	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
514	C₅×C₈	—	2	2	no	—
515	C₅×C₈	—	2	2	no	—
516	C₅×C₈	—	2	4	no	—
517	C₂×#41	—	2	8	no	—
518	C₂×#41	—	2	1	no	—
519	C₂×#41	—	2	1	no	—
520	C₂×#41	—	2	2	no	—
521	C₂×#41	C₂³×C₅	1	2	yes	—
522	C₂×#41	C₂³×C₅	1	1	yes	characteristic
523	C₂×#41	C₂³×C₅	1	2	yes	—
524	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
525	C₂²×D₄	—	2	1	no	—
526	C₂²×D₄	—	2	1	no	—
527	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
528	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
529	C₂³×C₄	—	2	1	no	—
530	C₂³×C₄	—	2	1	no	—
531	C₂³×C₄	—	2	2	no	—
532	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
533	AGL(1,ℤ/8)	—	2	8	no	—
534	#135	—	2	8	no	—
535	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
536	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
537	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
538	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
539	C₂×D₈	C₂³×C₅	1	2	yes	—
540	C₂×D₈	C₂³×C₅	1	4	yes	—
541	C₂×M₁₆	C₂³×C₅	1	2	yes	—
542	C₂²×C₈	C₂³×C₅	1	2	yes	—
543	C₄⋊Q₈	—	2	1	no	—
544	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
545	#127	C₂³×C₅	1	2	yes	—
546	#126	—	2	2	no	—
547	#126	—	2	2	no	—
548	#125	—	2	1	no	—
549	#125	C₂³×C₅	1	2	yes	—
550	#124	—	2	2	no	—
551	#124	—	2	2	no	—
552	#124	C₂³×C₅	1	2	yes	—
553	#123	—	2	1	no	—
554	#123	—	2	2	no	—
555	#123	—	2	2	no	—
556	#123	—	2	2	no	—
557	#123	—	2	2	no	—
558	C₂²⋊Q₈	—	2	2	no	—
559	C₂²⋊Q₈	—	2	2	no	—
560	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
561	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
562	#121	—	2	1	no	—
563	#121	—	2	1	no	—
564	#121	—	2	2	no	—
565	#121	—	2	1	no	—
566	#121	—	2	1	no	—
567	#121	—	2	2	no	—
568	#121	—	2	2	no	—
569	#121	C₂³×C₅	1	2	yes	—
570	#121	C₂³×C₅	1	2	yes	—
571	#121	C₂³×C₅	1	1	yes	characteristic
572	#121	C₂³×C₅	1	1	yes	characteristic
573	#120	—	2	1	no	—
574	#120	—	2	2	no	—
575	C₄×Q₈	—	2	2	no	—
576	C₄×Q₈	—	2	2	no	—
577	C₄×Q₈	C₂³×C₅	1	4	yes	—
578	C₄×Q₈	C₂³×C₅	1	4	yes	—
579	C₄×Q₈	C₂³×C₅	1	2	yes	—
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	1	no	—
585	C₄×D₄	—	2	4	no	—
586	C₄×D₄	—	2	4	no	—
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	4	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	C₂³×C₅	1	4	yes	—
594	C₄×D₄	C₂³×C₅	1	4	yes	—
595	C₄×D₄	C₂³×C₅	1	2	yes	—
596	C₄×D₄	C₂³×C₅	1	2	yes	—
597	C₄×D₄	C₂³×C₅	1	2	yes	—
598	#117	—	2	2	no	—
599	#117	—	2	2	no	—
600	#117	—	2	4	no	—
601	#117	—	2	1	no	—
602	#117	—	2	2	no	—
603	#117	C₅×D₄	1	2	yes	—
604	#117	C₅×D₄	1	1	yes	characteristic
605	#117	C₅×D₄	1	1	yes	characteristic
606	#117	C₂³×C₅	1	1	yes	characteristic
607	#117	C₂³×C₅	1	1	yes	characteristic
608	#117	C₂³×C₅	1	1	yes	characteristic
609	#117	C₂³×C₅	1	2	yes	—
610	C₂×C₄⋊C₄	—	2	1	no	—
611	C₂×C₄⋊C₄	—	2	2	no	—
612	C₂×C₄⋊C₄	—	2	1	no	—
613	C₂×C₄⋊C₄	—	2	1	no	—
614	C₂×C₄⋊C₄	—	2	2	no	—
615	C₂×C₄⋊C₄	—	2	2	no	—
616	C₂×C₄⋊C₄	—	2	4	no	—
617	C₂×C₄⋊C₄	—	2	1	no	—
618	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
619	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
620	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
621	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
622	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
623	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
624	C₂×C₂²⋊C₄	—	2	2	no	—
625	C₂×C₂²⋊C₄	—	2	1	no	—
626	C₂×C₂²⋊C₄	—	2	2	no	—
627	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
628	C₂×C₄²	—	2	2	no	—
629	C₂×C₄²	C₂³×C₅	1	2	yes	—
630	#107	C₂³×C₅	1	4	yes	—
631	#107	C₂³×C₅	1	4	yes	—
632	#107	C₂³×C₅	1	4	yes	—
633	#106	C₂³×C₅	1	4	yes	—
634	C₄⋊C₈	C₂³×C₅	1	4	yes	—
635	C₄⋊C₈	C₂³×C₅	1	4	yes	—
636	#103	C₂³×C₅	1	2	yes	—
637	#103	C₂³×C₅	1	2	yes	—
638	#103	C₂³×C₅	1	4	yes	—
639	#103	C₂³×C₅	1	4	yes	—
640	#102	C₂³×C₅	1	4	yes	—
641	#102	C₂³×C₅	1	4	yes	—
642	#102	C₂³×C₅	1	2	yes	—
643	#102	C₂³×C₅	1	2	yes	—
644	#102	C₂³×C₅	1	4	yes	—
645	#102	C₂³×C₅	1	4	yes	—
646	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
647	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
648	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
649	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
650	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
651	#97	C₂³×C₅	1	4	yes	—
652	C₄×C₈	C₂³×C₅	1	4	yes	—
653	C₂²×C₅	—	2	1	no	—
654	C₂²×C₅	—	2	1	no	—
655	C₂²×C₅	—	2	1	no	—
656	C₂²×C₅	—	2	1	no	—
657	C₂²×C₅	—	2	1	no	—
658	C₂²×C₅	—	2	1	no	—
659	C₂²×C₅	—	2	4	no	—
660	C₂²×C₅	—	2	1	no	—
661	C₂²×C₅	—	4	4	no	—
662	C₂²×C₅	—	4	8	no	—
663	C₂²×C₅	—	4	2	no	—
664	C₂²×C₅	—	4	2	no	—
665	C₂²×C₅	—	4	2	no	—
666	C₂²×C₅	—	4	1	no	—
667	C₂²×C₅	—	4	1	no	—
668	C₂²×C₅	—	4	2	no	—
669	C₂²×C₅	—	4	1	no	—
670	C₂²×C₅	—	4	2	no	—
671	C₂²×C₅	—	16	2	no	—
672	C₂²×C₅	#525	1	2	yes	—
673	C₂²×C₅	#576	1	2	yes	—
674	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
675	C₄×C₅	—	2	2	no	—
676	C₄×C₅	—	2	2	no	—
677	C₄×C₅	—	2	1	no	—
678	C₄×C₅	—	2	4	no	—
679	C₄×C₅	—	2	1	no	—
680	C₄×C₅	—	2	2	no	—
681	C₄×C₅	—	2	2	no	—
682	C₄×C₅	—	4	1	no	—
683	C₄×C₅	—	4	1	no	—
684	C₄×C₅	—	4	4	no	—
685	C₄×C₅	—	4	2	no	—
686	C₄×C₅	—	4	1	no	—
687	C₄×C₅	#525	1	2	yes	—
688	C₄×C₅	C₂²×#41	1	2	yes	—
689	C₂⁴	—	2	1	no	—
690	C₂⁴	—	2	1	no	—
691	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
692	#41	—	2	8	no	—
693	#41	—	2	8	no	—
694	#41	—	2	4	no	—
695	#41	—	2	4	no	—
696	#41	—	2	4	no	—
697	#41	—	2	4	no	—
698	#41	—	8	4	no	—
699	#41	C₅×#41	1	8	yes	complemented
700	C₂×Q₈	—	2	4	no	—
701	C₂×Q₈	—	2	1	no	—
702	C₂×Q₈	—	2	2	no	—
703	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
704	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
705	C₂×D₄	—	2	8	no	—
706	C₂×D₄	—	2	2	no	—
707	C₂×D₄	—	2	2	no	—
708	C₂×D₄	—	2	4	no	—
709	C₂×D₄	—	2	1	no	—
710	C₂×D₄	—	2	1	no	—
711	C₂×D₄	—	2	2	no	—
712	C₂×D₄	—	2	1	no	—
713	C₂×D₄	—	2	2	no	—
714	C₂×D₄	—	2	1	no	—
715	C₂×D₄	—	2	1	no	—
716	C₂×D₄	—	2	2	no	—
717	C₂×D₄	—	2	2	no	—
718	C₂×D₄	—	2	4	no	—
719	C₂×D₄	—	8	2	no	—
720	C₂×D₄	C₂⁴×C₅	1	2	yes	—
721	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
722	C₂×D₄	C₂⁴×C₅	1	2	yes	—
723	C₂²×C₄	—	2	8	no	—
724	C₂²×C₄	—	2	1	no	—
725	C₂²×C₄	—	2	2	no	—
726	C₂²×C₄	—	2	2	no	—
727	C₂²×C₄	—	2	4	no	—
728	C₂²×C₄	—	2	2	no	—
729	C₂²×C₄	—	2	1	no	—
730	C₂²×C₄	—	2	2	no	—
731	C₂²×C₄	—	2	2	no	—
732	C₂²×C₄	—	2	1	no	—
733	C₂²×C₄	—	2	2	no	—
734	C₂²×C₄	—	2	2	no	—
735	C₂²×C₄	—	2	4	no	—
736	C₂²×C₄	—	2	4	no	—
737	C₂²×C₄	—	2	2	no	—
738	C₂²×C₄	—	8	4	no	—
739	C₂²×C₄	—	8	2	no	—
740	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
741	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
742	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
743	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
744	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
745	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
746	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
747	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
748	Q₁₆	—	2	4	no	—
749	SD₁₆	—	2	4	no	—
750	SD₁₆	—	2	8	no	—
751	SD₁₆	—	2	4	no	—
752	D₈	—	2	4	no	—
753	D₈	—	2	8	no	—
754	M₁₆	—	2	4	no	—
755	C₂×C₈	—	2	4	no	—
756	C₂×C₈	C₂⁴×C₅	1	2	yes	—
757	C₂×C₈	C₂⁴×C₅	1	4	yes	—
758	C₂×C₈	C₂⁴×C₅	1	2	yes	—
759	C₄⋊C₄	—	2	2	no	—
760	C₄⋊C₄	—	2	2	no	—
761	C₄⋊C₄	—	2	4	no	—
762	C₄⋊C₄	—	2	4	no	—
763	C₄⋊C₄	—	2	2	no	—
764	C₄⋊C₄	—	2	1	no	—
765	C₄⋊C₄	—	2	2	no	—
766	C₄⋊C₄	—	2	1	no	—
767	C₄⋊C₄	—	2	2	no	—
768	C₄⋊C₄	—	2	2	no	—
769	C₄⋊C₄	—	2	2	no	—
770	C₄⋊C₄	—	2	1	no	—
771	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
772	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
773	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
774	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
775	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
776	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
777	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
778	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
779	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
780	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
781	C₂²⋊C₄	—	2	1	no	—
782	C₂²⋊C₄	—	2	1	no	—
783	C₂²⋊C₄	—	2	1	no	—
784	C₂²⋊C₄	—	2	4	no	—
785	C₂²⋊C₄	—	2	4	no	—
786	C₂²⋊C₄	—	2	2	no	—
787	C₂²⋊C₄	—	2	2	no	—
788	C₂²⋊C₄	—	2	2	no	—
789	C₂²⋊C₄	—	2	2	no	—
790	C₂²⋊C₄	—	2	2	no	—
791	C₂²⋊C₄	—	2	2	no	—
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	2	no	—
794	C₂²⋊C₄	—	2	1	no	—
795	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
796	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
797	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
798	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
799	C₄²	—	2	4	no	—
800	C₄²	—	2	4	no	—
801	C₄²	—	2	2	no	—
802	C₄²	—	2	1	no	—
803	C₄²	C₂×C₅×D₄	1	2	yes	—
804	C₄²	C₂×C₅×D₄	1	2	yes	—
805	C₄²	C₂⁴×C₅	1	2	yes	—
806	C₄²	C₂⁴×C₅	1	2	yes	—
807	C₂×C₅	—	2	2	no	—
808	C₂×C₅	—	2	2	no	—
809	C₂×C₅	—	4	1	no	—
810	C₂×C₅	—	4	4	no	—
811	C₂×C₅	—	8	1	no	—
812	C₂×C₅	—	8	2	no	—
813	C₂×C₅	C₂×#525	1	1	yes	characteristic
814	C₂×C₅	C₂×#576	1	1	yes	characteristic
815	C₂×C₅	#3586	1	1	yes	characteristic
816	C₂³	—	2	4	no	—
817	C₂³	—	2	2	no	—
818	C₂³	—	2	2	no	—
819	C₂³	—	2	2	no	—
820	C₂³	—	2	2	no	—
821	C₂³	—	2	1	no	—
822	C₂³	—	4	1	no	—
823	C₂³	—	4	2	no	—
824	C₂³	—	4	2	no	—
825	C₂³	—	4	2	no	—
826	C₂³	—	8	1	no	—
827	C₂³	—	8	1	no	—
828	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
829	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
830	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
831	Q₈	—	2	4	no	—
832	Q₈	—	2	2	no	—
833	Q₈	—	2	2	no	—
834	Q₈	—	8	2	no	—
835	Q₈	C₂×C₅×#41	1	4	yes	—
836	D₄	—	2	8	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	8	no	—
839	D₄	—	2	2	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	2	no	—
842	D₄	—	4	2	no	—
843	D₄	—	4	4	no	—
844	D₄	—	4	2	no	—
845	D₄	—	4	2	no	—
846	D₄	—	8	2	no	—
847	D₄	—	8	2	no	—
848	D₄	—	8	2	no	—
849	D₄	—	8	1	no	—
850	D₄	C₂×C₅×#41	1	4	yes	—
851	C₂×C₄	—	2	4	no	—
852	C₂×C₄	—	2	8	no	—
853	C₂×C₄	—	2	2	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	2	no	—
856	C₂×C₄	—	2	2	no	—
857	C₂×C₄	—	2	8	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	2	no	—
861	C₂×C₄	—	2	1	no	—
862	C₂×C₄	—	2	4	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	2	no	—
866	C₂×C₄	—	4	2	no	—
867	C₂×C₄	—	4	4	no	—
868	C₂×C₄	—	4	2	no	—
869	C₂×C₄	—	8	4	no	—
870	C₂×C₄	—	8	4	no	—
871	C₂×C₄	—	8	2	no	—
872	C₂×C₄	—	8	2	no	—
873	C₂×C₄	—	8	2	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	2	no	—
876	C₂×C₄	—	8	1	no	—
877	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
878	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
879	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
880	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
881	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
882	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
883	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
884	C₂×C₄	C₂×C₅×#41	1	4	yes	—
885	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
886	C₈	—	2	2	no	—
887	C₈	—	2	2	no	—
888	C₈	—	2	4	no	—
889	C₅	#60584	1	1	yes	characteristic, direct product factor, Sylow
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	1	no	—
893	C₂²	—	2	1	no	—
894	C₂²	—	2	1	no	—
895	C₂²	—	2	4	no	—
896	C₂²	—	2	1	no	—
897	C₂²	—	2	1	no	—
898	C₂²	—	4	4	no	—
899	C₂²	—	4	8	no	—
900	C₂²	—	4	2	no	—
901	C₂²	—	4	2	no	—
902	C₂²	—	4	1	no	—
903	C₂²	—	4	2	no	—
904	C₂²	—	4	1	no	—
905	C₂²	—	4	2	no	—
906	C₂²	—	4	2	no	—
907	C₂²	—	4	1	no	—
908	C₂²	—	16	2	no	—
909	C₂²	C₅×#525	1	2	yes	—
910	C₂²	C₅×#576	1	2	yes	—
911	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
912	C₄	—	2	1	no	—
913	C₄	—	2	4	no	—
914	C₄	—	2	1	no	—
915	C₄	—	2	2	no	—
916	C₄	—	2	2	no	—
917	C₄	—	2	2	no	—
918	C₄	—	2	2	no	—
919	C₄	—	4	1	no	—
920	C₄	—	4	4	no	—
921	C₄	—	4	2	no	—
922	C₄	—	4	1	no	—
923	C₄	—	4	1	no	—
924	C₄	C₅×#525	1	2	yes	—
925	C₄	C₂²×C₅×#41	1	2	yes	—
926	C₂	—	2	2	no	—
927	C₂	—	2	2	no	—
928	C₂	—	4	1	no	—
929	C₂	—	4	4	no	—
930	C₂	—	8	2	no	—
931	C₂	—	8	1	no	—
932	C₂	C₂×C₅×#525	1	1	yes	characteristic
933	C₂	C₂×C₅×#576	1	1	yes	characteristic
934	C₂	C₅×#3586	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 ◁ C₂×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₅×#3494	C₂	semidirect
2. C₂×C₅×#520	C₂	semidirect
3. C₅×#3124	C₂	semidirect
4. C₅×#3119	C₂	semidirect
5. C₅×#3114	C₂	semidirect
6. C₅×#3112	C₂	semidirect
7. C₅×#3108	C₂	semidirect
8. C₅×#3100	C₂	semidirect
9. C₅×#3092	C₂	semidirect
10. C₂×C₅×#480	C₂	semidirect
11. C₅×#3083	C₂	semidirect
12. C₅×#3045	C₂	semidirect
13. C₅×#3006	C₂	semidirect
14. C₅×#3002	C₂	semidirect
15. C₅×#2951	C₂	semidirect
16. C₅×#2946	C₂	semidirect
17. C₅×#2924	C₂	semidirect
27. C₅×#544	C₂²	semidirect
28. C₅×#542	C₂²	semidirect
29. C₅×#540	C₂²	semidirect
30. C₅×#535	C₂²	semidirect
40. C₅×#520	C₂²	semidirect
41. C₅×#520	C₂²	semidirect
42. C₅×#518	C₂²	semidirect
43. C₂×C₄×C₅×Q₈	C₂²	semidirect
45. C₂×C₄×C₅×D₄	C₂²	semidirect
50. C₅×#484	C₂²	semidirect
51. C₅×#483	C₂²	semidirect
52. C₅×#481	C₂²	semidirect
55. C₅×#480	C₂²	semidirect
56. C₅×#480	C₂²	semidirect
57. C₅×#479	C₂²	semidirect
58. C₅×#478	C₂²	semidirect
59. C₅×#477	C₂²	semidirect
60. C₅×#474	C₂²	semidirect
61. C₅×#464	C₂²	semidirect
62. C₅×#463	C₂²	semidirect
63. C₅×#460	C₂²	semidirect
64. C₅×#459	C₂²	semidirect
65. C₅×#452	C₂²	semidirect
66. C₅×#451	C₂²	semidirect
67. C₅×#450	C₂²	semidirect
69. C₅×#449	C₂²	semidirect
71. C₅×#448	C₂²	semidirect
73. C₅×#447	C₂²	semidirect
74. C₅×#442	C₂²	semidirect
75. C₅×#440	C₂²	semidirect
76. C₅×#440	C₂²	semidirect
77. C₅×#440	C₂²	semidirect
78. C₄×C₅×Q₁₆	C₂²	semidirect
79. C₄×C₅×SD₁₆	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. C₂×C₅×#107	C₂²	semidirect
87. C₅×#424	C₂²	semidirect
89. C₅×#417	C₂²	semidirect
91. C₂×C₅×#102	C₂²	semidirect
94. C₅×#405	C₂²	semidirect
95. #60584	C₅	direct (N × H)
232. #3494	C₂×C₅	semidirect
233. C₂×#520	C₂×C₅	semidirect
234. #3124	C₂×C₅	semidirect
235. #3119	C₂×C₅	semidirect
236. #3114	C₂×C₅	semidirect
237. #3112	C₂×C₅	semidirect
238. #3108	C₂×C₅	semidirect
239. #3100	C₂×C₅	semidirect
240. #3092	C₂×C₅	semidirect
241. C₂×#480	C₂×C₅	semidirect
242. #3083	C₂×C₅	semidirect
243. #3045	C₂×C₅	semidirect
244. #3006	C₂×C₅	semidirect
245. #3002	C₂×C₅	semidirect
246. #2951	C₂×C₅	semidirect
247. #2946	C₂×C₅	semidirect
248. #2924	C₂×C₅	semidirect
259. C₅×#41	#41	semidirect
376. #544	C₂²×C₅	semidirect
377. #542	C₂²×C₅	semidirect
378. #540	C₂²×C₅	semidirect
379. #535	C₂²×C₅	semidirect
389. #520	C₂²×C₅	semidirect
390. #520	C₂²×C₅	semidirect
391. #518	C₂²×C₅	semidirect
392. C₂×C₄×Q₈	C₂²×C₅	semidirect
394. C₂×C₄×D₄	C₂²×C₅	semidirect
399. #484	C₂²×C₅	semidirect
400. #483	C₂²×C₅	semidirect
401. #481	C₂²×C₅	semidirect
404. #480	C₂²×C₅	semidirect
405. #480	C₂²×C₅	semidirect
406. #479	C₂²×C₅	semidirect
407. #478	C₂²×C₅	semidirect
408. #477	C₂²×C₅	semidirect
409. #474	C₂²×C₅	semidirect
410. #464	C₂²×C₅	semidirect
411. #463	C₂²×C₅	semidirect
412. #460	C₂²×C₅	semidirect
413. #459	C₂²×C₅	semidirect
414. #452	C₂²×C₅	semidirect
415. #451	C₂²×C₅	semidirect
416. #450	C₂²×C₅	semidirect
418. #449	C₂²×C₅	semidirect
420. #448	C₂²×C₅	semidirect
422. #447	C₂²×C₅	semidirect
423. #442	C₂²×C₅	semidirect
424. #440	C₂²×C₅	semidirect
425. #440	C₂²×C₅	semidirect
426. #440	C₂²×C₅	semidirect
427. C₄×Q₁₆	C₂²×C₅	semidirect
428. C₄×SD₁₆	C₂²×C₅	semidirect
429. C₄×D₈	C₂²×C₅	semidirect
430. C₄×D₈	C₂²×C₅	semidirect
431. #433	C₂²×C₅	semidirect
432. #432	C₂²×C₅	semidirect
433. #431	C₂²×C₅	semidirect
434. #428	C₂²×C₅	semidirect
435. C₂×#107	C₂²×C₅	semidirect
436. #424	C₂²×C₅	semidirect
438. #417	C₂²×C₅	semidirect
440. C₂×#102	C₂²×C₅	semidirect
443. #405	C₂²×C₅	semidirect
699. #41	C₅×#41	semidirect
889. C₅	#60584	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×#3494	2
C₂×C₅×#520	2
C₅×#3124	2
C₅×#3119	2
C₅×#3114	2
C₅×#3112	2
C₅×#3108	2
C₅×#3100	2
C₅×#3092	2
C₂×C₅×#480	2
C₅×#3083	2
C₅×#3045	2
C₅×#3006	2
C₅×#3002	2
C₅×#2951	2
C₅×#2946	2
C₅×#2924	2
#60584	5

Subgroups — C5×#60584 #11983304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60584 #11983304