Subgroups — C₅×#60585 #11983305

Order 1280.

2074 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#3495	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3125	C₂	1	4	yes	maximal, complemented
4	C₅×#3120	C₂	1	4	yes	maximal, complemented
5	C₅×#3114	C₂	1	2	yes	maximal, complemented
6	C₅×#3113	C₂	1	2	yes	maximal, complemented
7	C₅×#3108	C₂	1	2	yes	maximal, complemented
8	C₅×#3101	C₂	1	2	yes	maximal, complemented
9	C₅×#3092	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₅×#483	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3084	C₂	1	2	yes	maximal, complemented
12	C₅×#3046	C₂	1	2	yes	maximal, complemented
13	C₅×#3007	C₂	1	1	yes	maximal, characteristic, complemented
14	C₅×#3002	C₂	1	1	yes	maximal, characteristic
15	C₅×#2952	C₂	1	2	yes	maximal, complemented
16	C₅×#2947	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×#137	C₂²	1	2	yes	—
20	C₂×C₅×#135	C₂²	1	2	yes	—
21	C₅×#556	—	2	1	no	—
22	C₅×#554	—	2	1	no	—
23	C₅×#552	—	2	2	no	—
24	C₅×#552	—	2	1	no	—
25	C₅×#552	—	2	1	no	—
26	C₅×#551	—	2	2	no	—
27	C₅×#544	C₂²	1	1	yes	characteristic, complemented
28	C₅×#542	C₂²	1	2	yes	complemented
29	C₅×#541	C₂²	1	2	yes	complemented
30	C₅×#536	C₂²	1	1	yes	characteristic, complemented
31	C₅×#533	C₂²	1	2	yes	—
32	C₅×#529	C₂²	1	2	yes	—
33	C₅×#525	C₂²	1	1	yes	characteristic
34	C₂×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₅×#520	—	2	2	no	—
36	C₅×#520	—	2	1	no	—
37	C₅×#520	—	2	1	no	—
38	C₅×#520	C₂²	1	2	yes	—
39	C₅×#520	C₂²	1	4	yes	—
40	C₅×#520	C₂²	1	2	yes	—
41	C₅×#520	C₂²	1	1	yes	characteristic, complemented
42	C₅×#519	C₂²	1	1	yes	characteristic, complemented
43	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
44	C₂×C₄×C₅×D₄	—	2	2	no	—
45	C₂×C₄×C₅×D₄	C₂²	1	2	yes	—
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	—
52	C₅×#483	C₂²	1	2	yes	—
53	C₅×#483	C₂²	1	2	yes	—
54	C₅×#483	C₂²	1	4	yes	complemented
55	C₅×#481	C₂²	1	2	yes	complemented
56	C₅×#480	C₂²	1	2	yes	—
57	C₅×#479	C₂²	1	4	yes	complemented
58	C₅×#478	C₂²	1	4	yes	complemented
59	C₅×#476	C₂²	1	4	yes	complemented
60	C₅×#475	C₂²	1	4	yes	complemented
61	C₅×#464	C₂²	1	4	yes	complemented
62	C₅×#463	C₂²	1	4	yes	complemented
63	C₅×#462	C₂²	1	4	yes	complemented
64	C₅×#461	C₂²	1	4	yes	complemented
65	C₅×#452	C₂²	1	2	yes	—
66	C₅×#452	C₂²	1	4	yes	—
67	C₅×#451	C₂²	1	1	yes	characteristic
68	C₅×#451	C₂²	1	2	yes	—
69	C₅×#450	C₂²	1	1	yes	characteristic
70	C₅×#450	C₂²	1	2	yes	—
71	C₅×#449	C₂²	1	2	yes	—
72	C₅×#448	C₂²	1	1	yes	characteristic
73	C₅×#447	C₂²	1	1	yes	characteristic
74	C₅×#442	C₂²	1	4	yes	complemented
75	C₅×#441	C₂²	1	4	yes	complemented
76	C₅×#441	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×SD₁₆	C₂²	1	4	yes	complemented
81	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
82	C₅×#433	C₂²	1	4	yes	complemented
83	C₅×#432	C₂²	1	2	yes	—
84	C₅×#431	C₂²	1	2	yes	—
85	C₅×#428	C₂²	1	2	yes	complemented
86	C₂×C₅×#106	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×#103	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	#60585	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	C₂³	1	1	yes	characteristic
100	C₂×C₅×#41	C₂³	1	2	yes	—
101	C₂×C₅×#41	C₂³	1	2	yes	—
102	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
103	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂²×C₅×D₄	—	2	1	no	—
105	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₅	—	2	1	no	—
107	C₂³×C₄×C₅	—	2	1	no	—
108	C₂³×C₄×C₅	—	2	2	no	—
109	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₅×#137	—	2	8	no	—
111	C₅×#135	—	2	8	no	—
112	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
113	C₂×C₅×Q₁₆	C₂³	1	2	yes	—
114	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
115	C₂×C₅×SD₁₆	C₂³	1	2	yes	—
116	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
117	C₂×C₅×D₈	C₂³	1	2	yes	—
118	C₂×C₅×M₁₆	C₂³	1	2	yes	—
119	C₂²×C₅×C₈	C₂³	1	2	yes	—
120	C₅×C₄⋊Q₈	—	2	1	no	—
121	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
122	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
123	C₅×#126	—	2	2	no	—
124	C₅×#126	—	2	2	no	—
125	C₅×#126	—	2	2	no	—
126	C₅×#126	—	2	2	no	—
127	C₅×#125	—	2	2	no	—
128	C₅×#125	—	2	2	no	—
129	C₅×#125	—	2	1	no	—
130	C₅×#125	—	2	2	no	—
131	C₅×#125	C₂³	1	2	yes	—
132	C₅×#124	—	2	2	no	—
133	C₅×#124	C₂³	1	2	yes	—
134	C₅×#123	—	2	1	no	—
135	C₅×#123	—	2	2	no	—
136	C₅×#123	—	2	2	no	—
137	C₅×#123	—	2	2	no	—
138	C₅×C₂²⋊Q₈	—	2	1	no	—
139	C₅×C₂²⋊Q₈	—	2	1	no	—
140	C₅×C₂²⋊Q₈	—	2	2	no	—
141	C₅×C₂²⋊Q₈	—	2	1	no	—
142	C₅×C₂²⋊Q₈	—	2	1	no	—
143	C₅×C₂²⋊Q₈	—	2	2	no	—
144	C₅×C₂²⋊Q₈	—	2	2	no	—
145	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
146	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
147	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
148	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
149	C₅×#121	C₂³	1	1	yes	characteristic
150	C₅×#121	C₂³	1	1	yes	characteristic
151	C₅×#120	—	2	1	no	—
152	C₄×C₅×Q₈	—	2	1	no	—
153	C₄×C₅×Q₈	—	2	1	no	—
154	C₄×C₅×Q₈	—	2	2	no	—
155	C₄×C₅×Q₈	—	2	2	no	—
156	C₄×C₅×Q₈	—	2	2	no	—
157	C₄×C₅×Q₈	C₂³	1	2	yes	—
158	C₄×C₅×Q₈	C₂³	1	2	yes	—
159	C₄×C₅×Q₈	C₂³	1	4	yes	—
160	C₄×C₅×Q₈	C₂³	1	2	yes	—
161	C₄×C₅×Q₈	C₂³	1	4	yes	—
162	C₄×C₅×D₄	—	2	1	no	—
163	C₄×C₅×D₄	—	2	1	no	—
164	C₄×C₅×D₄	—	2	2	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	4	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	4	yes	—
173	C₄×C₅×D₄	C₂³	1	2	yes	—
174	C₄×C₅×D₄	C₂³	1	4	yes	—
175	C₅×#117	—	2	2	no	—
176	C₅×#117	—	2	2	no	—
177	C₅×#117	—	2	4	no	—
178	C₅×#117	—	2	2	no	—
179	C₅×#117	—	2	1	no	—
180	C₅×#117	—	2	2	no	—
181	C₅×#117	—	2	2	no	—
182	C₅×#117	D₄	1	1	yes	characteristic
183	C₅×#117	D₄	1	2	yes	—
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	1	no	—
194	C₂×C₅×C₄⋊C₄	—	2	2	no	—
195	C₂×C₅×C₄⋊C₄	—	2	2	no	—
196	C₂×C₅×C₄⋊C₄	—	2	4	no	—
197	C₂×C₅×C₄⋊C₄	—	2	1	no	—
198	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
199	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
200	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
201	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
202	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
203	C₂×C₅×C₄⋊C₄	C₂³	1	2	yes	—
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×#106	C₂³	1	4	yes	—
211	C₅×#106	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	4	yes	—
216	C₅×#103	C₂³	1	4	yes	—
217	C₅×#103	C₂³	1	2	yes	—
218	C₅×#103	C₂³	1	2	yes	—
219	C₅×#103	C₂³	1	4	yes	—
220	C₅×#103	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	#3495	C₂×C₅	1	1	yes	characteristic, complemented
233	C₂×#520	C₂×C₅	1	1	yes	characteristic, complemented
234	#3125	C₂×C₅	1	4	yes	complemented
235	#3120	C₂×C₅	1	4	yes	complemented
236	#3114	C₂×C₅	1	2	yes	complemented
237	#3113	C₂×C₅	1	2	yes	complemented
238	#3108	C₂×C₅	1	2	yes	complemented
239	#3101	C₂×C₅	1	2	yes	complemented
240	#3092	C₂×C₅	1	1	yes	characteristic, complemented
241	C₂×#483	C₂×C₅	1	1	yes	characteristic, complemented
242	#3084	C₂×C₅	1	2	yes	complemented
243	#3046	C₂×C₅	1	2	yes	complemented
244	#3007	C₂×C₅	1	1	yes	characteristic, complemented
245	#3002	C₂×C₅	1	1	yes	characteristic
246	#2952	C₂×C₅	1	2	yes	complemented
247	#2947	C₂×C₅	1	2	yes	complemented
248	#2924	C₂×C₅	1	1	yes	characteristic, complemented
249	C₂⁴×C₅	—	2	1	no	—
250	C₂⁴×C₅	C₂×D₄	1	1	yes	characteristic
251	C₅×#41	—	2	8	no	—
252	C₅×#41	—	2	8	no	—
253	C₅×#41	—	2	4	no	—
254	C₅×#41	—	2	4	no	—
255	C₅×#41	—	2	4	no	—
256	C₅×#41	—	2	4	no	—
257	C₅×#41	#41	1	8	yes	—
258	C₂×C₅×Q₈	—	2	4	no	—
259	C₂×C₅×Q₈	—	2	1	no	—
260	C₂×C₅×Q₈	—	2	1	no	—
261	C₂×C₅×Q₈	—	2	2	no	—
262	C₂×C₅×Q₈	—	2	4	no	—
263	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
264	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
266	C₂×C₅×D₄	—	2	8	no	—
267	C₂×C₅×D₄	—	2	2	no	—
268	C₂×C₅×D₄	—	2	2	no	—
269	C₂×C₅×D₄	—	2	4	no	—
270	C₂×C₅×D₄	—	2	1	no	—
271	C₂×C₅×D₄	—	2	1	no	—
272	C₂×C₅×D₄	—	2	1	no	—
273	C₂×C₅×D₄	—	2	1	no	—
274	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
275	C₂×C₅×D₄	C₂⁴	1	2	yes	—
276	C₂²×C₄×C₅	—	2	8	no	—
277	C₂²×C₄×C₅	—	2	1	no	—
278	C₂²×C₄×C₅	—	2	2	no	—
279	C₂²×C₄×C₅	—	2	2	no	—
280	C₂²×C₄×C₅	—	2	4	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	1	no	—
283	C₂²×C₄×C₅	—	2	1	no	—
284	C₂²×C₄×C₅	—	2	2	no	—
285	C₂²×C₄×C₅	—	2	2	no	—
286	C₂²×C₄×C₅	—	2	1	no	—
287	C₂²×C₄×C₅	—	2	4	no	—
288	C₂²×C₄×C₅	—	2	4	no	—
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	—	8	4	no	—
291	C₂²×C₄×C₅	—	8	2	no	—
292	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
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	C₂×D₄	1	2	yes	—
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
299	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
300	C₅×Q₁₆	—	2	4	no	—
301	C₅×Q₁₆	—	2	8	no	—
302	C₅×SD₁₆	—	2	4	no	—
303	C₅×SD₁₆	—	2	4	no	—
304	C₅×SD₁₆	—	2	8	no	—
305	C₅×D₈	—	2	4	no	—
306	C₅×M₁₆	—	2	4	no	—
307	C₂×C₅×C₈	—	2	4	no	—
308	C₂×C₅×C₈	C₂⁴	1	2	yes	—
309	C₂×C₅×C₈	C₂⁴	1	2	yes	—
310	C₂×C₅×C₈	C₂⁴	1	4	yes	—
311	C₅×C₄⋊C₄	—	2	2	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	2	4	no	—
314	C₅×C₄⋊C₄	—	2	4	no	—
315	C₅×C₄⋊C₄	—	2	2	no	—
316	C₅×C₄⋊C₄	—	2	1	no	—
317	C₅×C₄⋊C₄	—	2	2	no	—
318	C₅×C₄⋊C₄	—	2	2	no	—
319	C₅×C₄⋊C₄	—	2	2	no	—
320	C₅×C₄⋊C₄	—	2	2	no	—
321	C₅×C₄⋊C₄	—	2	2	no	—
322	C₅×C₄⋊C₄	—	2	2	no	—
323	C₅×C₄⋊C₄	—	2	2	no	—
324	C₅×C₄⋊C₄	—	2	2	no	—
325	C₅×C₄⋊C₄	—	2	1	no	—
326	C₅×C₄⋊C₄	—	2	2	no	—
327	C₅×C₄⋊C₄	—	2	1	no	—
328	C₅×C₄⋊C₄	—	2	2	no	—
329	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
330	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
331	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
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	C₂⁴	1	4	yes	—
336	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
337	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
338	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
339	C₅×C₂²⋊C₄	—	2	2	no	—
340	C₅×C₂²⋊C₄	—	2	2	no	—
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	1	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	2	no	—
351	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
352	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
353	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
354	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
355	C₄²×C₅	—	2	4	no	—
356	C₄²×C₅	—	2	4	no	—
357	C₄²×C₅	—	2	2	no	—
358	C₄²×C₅	—	2	2	no	—
359	C₄²×C₅	—	2	2	no	—
360	C₄²×C₅	—	2	1	no	—
361	C₄²×C₅	C₂×D₄	1	2	yes	—
362	C₄²×C₅	C₂×D₄	1	2	yes	—
363	C₄²×C₅	C₂⁴	1	2	yes	—
364	C₄²×C₅	C₂⁴	1	2	yes	—
365	C₂²×#41	C₂²×C₅	1	1	yes	characteristic
366	C₂×#137	C₂²×C₅	1	2	yes	—
367	C₂×#135	C₂²×C₅	1	2	yes	—
368	#556	—	2	1	no	—
369	#554	—	2	1	no	—
370	#552	—	2	2	no	—
371	#552	—	2	1	no	—
372	#552	—	2	1	no	—
373	#551	—	2	2	no	—
374	#544	C₂²×C₅	1	1	yes	characteristic, complemented
375	#542	C₂²×C₅	1	2	yes	complemented
376	#541	C₂²×C₅	1	2	yes	complemented
377	#536	C₂²×C₅	1	1	yes	characteristic, complemented
378	#533	C₂²×C₅	1	2	yes	—
379	#529	C₂²×C₅	1	2	yes	—
380	#525	C₂²×C₅	1	1	yes	characteristic
381	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
382	#520	—	2	2	no	—
383	#520	—	2	1	no	—
384	#520	—	2	1	no	—
385	#520	C₂²×C₅	1	2	yes	—
386	#520	C₂²×C₅	1	4	yes	—
387	#520	C₂²×C₅	1	2	yes	—
388	#520	C₂²×C₅	1	1	yes	characteristic, complemented
389	#519	C₂²×C₅	1	1	yes	characteristic, complemented
390	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
391	C₂×C₄×D₄	—	2	2	no	—
392	C₂×C₄×D₄	C₂²×C₅	1	2	yes	—
393	C₂×#117	—	2	1	no	—
394	C₂×#117	C₂²×C₅	1	1	yes	characteristic
395	C₂²×C₄⋊C₄	—	2	1	no	—
396	C₂²×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
397	#484	C₂²×C₅	1	2	yes	complemented
398	#483	C₂²×C₅	1	2	yes	—
399	#483	C₂²×C₅	1	2	yes	—
400	#483	C₂²×C₅	1	2	yes	—
401	#483	C₂²×C₅	1	4	yes	complemented
402	#481	C₂²×C₅	1	2	yes	complemented
403	#480	C₂²×C₅	1	2	yes	—
404	#479	C₂²×C₅	1	4	yes	complemented
405	#478	C₂²×C₅	1	4	yes	complemented
406	#476	C₂²×C₅	1	4	yes	complemented
407	#475	C₂²×C₅	1	4	yes	complemented
408	#464	C₂²×C₅	1	4	yes	complemented
409	#463	C₂²×C₅	1	4	yes	complemented
410	#462	C₂²×C₅	1	4	yes	complemented
411	#461	C₂²×C₅	1	4	yes	complemented
412	#452	C₂²×C₅	1	2	yes	—
413	#452	C₂²×C₅	1	4	yes	—
414	#451	C₂²×C₅	1	2	yes	—
415	#451	C₂²×C₅	1	1	yes	characteristic
416	#450	C₂²×C₅	1	1	yes	characteristic
417	#450	C₂²×C₅	1	2	yes	—
418	#449	C₂²×C₅	1	2	yes	—
419	#448	C₂²×C₅	1	1	yes	characteristic
420	#447	C₂²×C₅	1	1	yes	characteristic
421	#442	C₂²×C₅	1	4	yes	complemented
422	#441	C₂²×C₅	1	4	yes	complemented
423	#441	C₂²×C₅	1	4	yes	complemented
424	#440	C₂²×C₅	1	4	yes	complemented
425	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
426	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
427	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
428	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
429	#433	C₂²×C₅	1	4	yes	complemented
430	#432	C₂²×C₅	1	2	yes	—
431	#431	C₂²×C₅	1	2	yes	—
432	#428	C₂²×C₅	1	2	yes	complemented
433	C₂×#106	C₂²×C₅	1	2	yes	complemented
434	#424	C₂²×C₅	1	2	yes	complemented
435	#417	C₂²×C₅	1	2	yes	—
436	#417	C₂²×C₅	1	2	yes	complemented
437	#416	C₂²×C₅	1	2	yes	—
438	C₂×#103	C₂²×C₅	1	2	yes	complemented
439	#407	C₂²×C₅	1	1	yes	characteristic
440	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
441	#405	C₂²×C₅	1	2	yes	complemented
442	C₂³×C₅	—	2	4	no	—
443	C₂³×C₅	—	2	2	no	—
444	C₂³×C₅	—	2	2	no	—
445	C₂³×C₅	—	2	2	no	—
446	C₂³×C₅	—	2	1	no	—
447	C₂³×C₅	—	4	1	no	—
448	C₂³×C₅	—	4	2	no	—
449	C₂³×C₅	—	4	2	no	—
450	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
451	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
452	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
453	C₅×Q₈	—	2	4	no	—
454	C₅×Q₈	—	2	2	no	—
455	C₅×Q₈	—	2	4	no	—
456	C₅×Q₈	—	2	2	no	—
457	C₅×Q₈	—	4	2	no	—
458	C₅×Q₈	—	8	2	no	—
459	C₅×Q₈	C₂×#41	1	4	yes	—
460	C₅×D₄	—	2	8	no	—
461	C₅×D₄	—	2	4	no	—
462	C₅×D₄	—	2	8	no	—
463	C₅×D₄	—	2	2	no	—
464	C₅×D₄	—	2	2	no	—
465	C₅×D₄	—	4	2	no	—
466	C₅×D₄	—	4	2	no	—
467	C₅×D₄	—	8	1	no	—
468	C₅×D₄	C₂×#41	1	4	yes	—
469	C₂×C₄×C₅	—	2	4	no	—
470	C₂×C₄×C₅	—	2	8	no	—
471	C₂×C₄×C₅	—	2	2	no	—
472	C₂×C₄×C₅	—	2	4	no	—
473	C₂×C₄×C₅	—	2	2	no	—
474	C₂×C₄×C₅	—	2	2	no	—
475	C₂×C₄×C₅	—	2	8	no	—
476	C₂×C₄×C₅	—	2	2	no	—
477	C₂×C₄×C₅	—	2	2	no	—
478	C₂×C₄×C₅	—	2	2	no	—
479	C₂×C₄×C₅	—	2	1	no	—
480	C₂×C₄×C₅	—	2	1	no	—
481	C₂×C₄×C₅	—	2	2	no	—
482	C₂×C₄×C₅	—	2	1	no	—
483	C₂×C₄×C₅	—	2	4	no	—
484	C₂×C₄×C₅	—	2	2	no	—
485	C₂×C₄×C₅	—	4	2	no	—
486	C₂×C₄×C₅	—	4	2	no	—
487	C₂×C₄×C₅	—	4	4	no	—
488	C₂×C₄×C₅	—	4	2	no	—
489	C₂×C₄×C₅	—	8	2	no	—
490	C₂×C₄×C₅	—	8	4	no	—
491	C₂×C₄×C₅	—	8	4	no	—
492	C₂×C₄×C₅	—	8	1	no	—
493	C₂×C₄×C₅	—	8	2	no	—
494	C₂×C₄×C₅	—	8	2	no	—
495	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
498	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
502	C₂×C₄×C₅	C₂×#41	1	4	yes	—
503	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
504	C₅×C₈	—	2	2	no	—
505	C₅×C₈	—	2	2	no	—
506	C₅×C₈	—	2	4	no	—
507	C₂×#41	—	2	8	no	—
508	C₂×#41	—	2	1	no	—
509	C₂×#41	—	2	1	no	—
510	C₂×#41	C₂³×C₅	1	2	yes	—
511	C₂×#41	C₂³×C₅	1	1	yes	characteristic
512	C₂×#41	C₂³×C₅	1	2	yes	—
513	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
514	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
515	C₂²×D₄	—	2	1	no	—
516	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
517	C₂³×C₄	—	2	1	no	—
518	C₂³×C₄	—	2	1	no	—
519	C₂³×C₄	—	2	2	no	—
520	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
521	#137	—	2	8	no	—
522	#135	—	2	8	no	—
523	C₂×Q₁₆	C₂³×C₅	1	2	yes	—
524	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
525	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
526	C₂×SD₁₆	C₂³×C₅	1	2	yes	—
527	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
528	C₂×D₈	C₂³×C₅	1	2	yes	—
529	C₂×M₁₆	C₂³×C₅	1	2	yes	—
530	C₂²×C₈	C₂³×C₅	1	2	yes	—
531	C₄⋊Q₈	—	2	1	no	—
532	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
533	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
534	#126	—	2	2	no	—
535	#126	—	2	2	no	—
536	#126	—	2	2	no	—
537	#126	—	2	2	no	—
538	#125	—	2	2	no	—
539	#125	—	2	2	no	—
540	#125	—	2	1	no	—
541	#125	—	2	2	no	—
542	#125	C₂³×C₅	1	2	yes	—
543	#124	—	2	2	no	—
544	#124	C₂³×C₅	1	2	yes	—
545	#123	—	2	1	no	—
546	#123	—	2	2	no	—
547	#123	—	2	2	no	—
548	#123	—	2	2	no	—
549	C₂²⋊Q₈	—	2	1	no	—
550	C₂²⋊Q₈	—	2	1	no	—
551	C₂²⋊Q₈	—	2	2	no	—
552	C₂²⋊Q₈	—	2	1	no	—
553	C₂²⋊Q₈	—	2	1	no	—
554	C₂²⋊Q₈	—	2	2	no	—
555	C₂²⋊Q₈	—	2	2	no	—
556	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
557	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
558	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
559	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
560	#121	C₂³×C₅	1	1	yes	characteristic
561	#121	C₂³×C₅	1	1	yes	characteristic
562	#120	—	2	1	no	—
563	C₄×Q₈	—	2	1	no	—
564	C₄×Q₈	—	2	1	no	—
565	C₄×Q₈	—	2	2	no	—
566	C₄×Q₈	—	2	2	no	—
567	C₄×Q₈	—	2	2	no	—
568	C₄×Q₈	C₂³×C₅	1	4	yes	—
569	C₄×Q₈	C₂³×C₅	1	4	yes	—
570	C₄×Q₈	C₂³×C₅	1	2	yes	—
571	C₄×Q₈	C₂³×C₅	1	2	yes	—
572	C₄×Q₈	C₂³×C₅	1	2	yes	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	4	no	—
577	C₄×D₄	—	2	4	no	—
578	C₄×D₄	—	2	4	no	—
579	C₄×D₄	—	2	4	no	—
580	C₄×D₄	—	2	2	no	—
581	C₄×D₄	—	2	2	no	—
582	C₄×D₄	—	2	2	no	—
583	C₄×D₄	C₂³×C₅	1	4	yes	—
584	C₄×D₄	C₂³×C₅	1	4	yes	—
585	C₄×D₄	C₂³×C₅	1	2	yes	—
586	#117	—	2	2	no	—
587	#117	—	2	2	no	—
588	#117	—	2	4	no	—
589	#117	—	2	2	no	—
590	#117	—	2	1	no	—
591	#117	—	2	2	no	—
592	#117	—	2	2	no	—
593	#117	C₅×D₄	1	1	yes	characteristic
594	#117	C₅×D₄	1	2	yes	—
595	#117	C₅×D₄	1	1	yes	characteristic
596	#117	C₂³×C₅	1	1	yes	characteristic
597	#117	C₂³×C₅	1	1	yes	characteristic
598	#117	C₂³×C₅	1	1	yes	characteristic
599	#117	C₂³×C₅	1	2	yes	—
600	C₂×C₄⋊C₄	—	2	1	no	—
601	C₂×C₄⋊C₄	—	2	2	no	—
602	C₂×C₄⋊C₄	—	2	1	no	—
603	C₂×C₄⋊C₄	—	2	1	no	—
604	C₂×C₄⋊C₄	—	2	1	no	—
605	C₂×C₄⋊C₄	—	2	2	no	—
606	C₂×C₄⋊C₄	—	2	2	no	—
607	C₂×C₄⋊C₄	—	2	4	no	—
608	C₂×C₄⋊C₄	—	2	1	no	—
609	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
610	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
611	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
612	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
613	C₂×C₄⋊C₄	C₂³×C₅	1	2	yes	—
614	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
615	C₂×C₂²⋊C₄	—	2	1	no	—
616	C₂×C₂²⋊C₄	—	2	2	no	—
617	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
618	C₂×C₄²	—	2	2	no	—
619	C₂×C₄²	C₂³×C₅	1	2	yes	—
620	#107	C₂³×C₅	1	4	yes	—
621	#106	C₂³×C₅	1	4	yes	—
622	#106	C₂³×C₅	1	4	yes	—
623	#106	C₂³×C₅	1	4	yes	—
624	C₄⋊C₈	C₂³×C₅	1	4	yes	—
625	C₄⋊C₈	C₂³×C₅	1	4	yes	—
626	#103	C₂³×C₅	1	4	yes	—
627	#103	C₂³×C₅	1	4	yes	—
628	#103	C₂³×C₅	1	2	yes	—
629	#103	C₂³×C₅	1	2	yes	—
630	#103	C₂³×C₅	1	4	yes	—
631	#103	C₂³×C₅	1	4	yes	—
632	#102	C₂³×C₅	1	2	yes	—
633	#102	C₂³×C₅	1	2	yes	—
634	#102	C₂³×C₅	1	4	yes	—
635	#102	C₂³×C₅	1	4	yes	—
636	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
637	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
638	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
639	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
640	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
641	#97	C₂³×C₅	1	4	yes	—
642	C₄×C₈	C₂³×C₅	1	4	yes	—
643	C₂²×C₅	—	2	1	no	—
644	C₂²×C₅	—	2	1	no	—
645	C₂²×C₅	—	2	1	no	—
646	C₂²×C₅	—	2	1	no	—
647	C₂²×C₅	—	2	1	no	—
648	C₂²×C₅	—	2	1	no	—
649	C₂²×C₅	—	2	4	no	—
650	C₂²×C₅	—	2	1	no	—
651	C₂²×C₅	—	4	4	no	—
652	C₂²×C₅	—	4	8	no	—
653	C₂²×C₅	—	4	2	no	—
654	C₂²×C₅	—	4	2	no	—
655	C₂²×C₅	—	4	1	no	—
656	C₂²×C₅	—	4	1	no	—
657	C₂²×C₅	—	4	1	no	—
658	C₂²×C₅	#525	1	2	yes	—
659	C₂²×C₅	#577	1	2	yes	—
660	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
661	C₄×C₅	—	2	2	no	—
662	C₄×C₅	—	2	2	no	—
663	C₄×C₅	—	2	1	no	—
664	C₄×C₅	—	2	4	no	—
665	C₄×C₅	—	2	1	no	—
666	C₄×C₅	—	2	2	no	—
667	C₄×C₅	—	2	2	no	—
668	C₄×C₅	—	4	2	no	—
669	C₄×C₅	—	4	1	no	—
670	C₄×C₅	—	4	1	no	—
671	C₄×C₅	—	4	2	no	—
672	C₄×C₅	—	4	4	no	—
673	C₄×C₅	—	4	1	no	—
674	C₄×C₅	#525	1	2	yes	—
675	C₄×C₅	C₂²×#41	1	2	yes	—
676	C₂⁴	—	2	1	no	—
677	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
678	#41	—	2	8	no	—
679	#41	—	2	8	no	—
680	#41	—	2	4	no	—
681	#41	—	2	4	no	—
682	#41	—	2	4	no	—
683	#41	—	2	4	no	—
684	#41	C₅×#41	1	8	yes	—
685	C₂×Q₈	—	2	4	no	—
686	C₂×Q₈	—	2	1	no	—
687	C₂×Q₈	—	2	1	no	—
688	C₂×Q₈	—	2	2	no	—
689	C₂×Q₈	—	2	4	no	—
690	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
691	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
692	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
693	C₂×D₄	—	2	8	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	2	1	no	—
698	C₂×D₄	—	2	1	no	—
699	C₂×D₄	—	2	1	no	—
700	C₂×D₄	—	2	1	no	—
701	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
702	C₂×D₄	C₂⁴×C₅	1	2	yes	—
703	C₂²×C₄	—	2	8	no	—
704	C₂²×C₄	—	2	1	no	—
705	C₂²×C₄	—	2	2	no	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	2	4	no	—
708	C₂²×C₄	—	2	2	no	—
709	C₂²×C₄	—	2	1	no	—
710	C₂²×C₄	—	2	1	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	—	2	2	no	—
713	C₂²×C₄	—	2	1	no	—
714	C₂²×C₄	—	2	4	no	—
715	C₂²×C₄	—	2	4	no	—
716	C₂²×C₄	—	2	2	no	—
717	C₂²×C₄	—	8	4	no	—
718	C₂²×C₄	—	8	2	no	—
719	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
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	2	yes	—
724	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
725	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
726	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
727	Q₁₆	—	2	4	no	—
728	Q₁₆	—	2	8	no	—
729	SD₁₆	—	2	4	no	—
730	SD₁₆	—	2	4	no	—
731	SD₁₆	—	2	8	no	—
732	D₈	—	2	4	no	—
733	M₁₆	—	2	4	no	—
734	C₂×C₈	—	2	4	no	—
735	C₂×C₈	C₂⁴×C₅	1	2	yes	—
736	C₂×C₈	C₂⁴×C₅	1	4	yes	—
737	C₂×C₈	C₂⁴×C₅	1	2	yes	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	4	no	—
741	C₄⋊C₄	—	2	4	no	—
742	C₄⋊C₄	—	2	2	no	—
743	C₄⋊C₄	—	2	1	no	—
744	C₄⋊C₄	—	2	2	no	—
745	C₄⋊C₄	—	2	2	no	—
746	C₄⋊C₄	—	2	2	no	—
747	C₄⋊C₄	—	2	2	no	—
748	C₄⋊C₄	—	2	2	no	—
749	C₄⋊C₄	—	2	2	no	—
750	C₄⋊C₄	—	2	2	no	—
751	C₄⋊C₄	—	2	2	no	—
752	C₄⋊C₄	—	2	1	no	—
753	C₄⋊C₄	—	2	2	no	—
754	C₄⋊C₄	—	2	1	no	—
755	C₄⋊C₄	—	2	2	no	—
756	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
757	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
758	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
759	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
760	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
761	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
762	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
763	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
764	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
765	C₄⋊C₄	C₂⁴×C₅	1	4	yes	—
766	C₂²⋊C₄	—	2	2	no	—
767	C₂²⋊C₄	—	2	2	no	—
768	C₂²⋊C₄	—	2	1	no	—
769	C₂²⋊C₄	—	2	1	no	—
770	C₂²⋊C₄	—	2	1	no	—
771	C₂²⋊C₄	—	2	4	no	—
772	C₂²⋊C₄	—	2	4	no	—
773	C₂²⋊C₄	—	2	1	no	—
774	C₂²⋊C₄	—	2	2	no	—
775	C₂²⋊C₄	—	2	2	no	—
776	C₂²⋊C₄	—	2	1	no	—
777	C₂²⋊C₄	—	2	2	no	—
778	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
779	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
780	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
781	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
782	C₄²	—	2	4	no	—
783	C₄²	—	2	4	no	—
784	C₄²	—	2	2	no	—
785	C₄²	—	2	2	no	—
786	C₄²	—	2	2	no	—
787	C₄²	—	2	1	no	—
788	C₄²	C₂×C₅×D₄	1	2	yes	—
789	C₄²	C₂×C₅×D₄	1	2	yes	—
790	C₄²	C₂⁴×C₅	1	2	yes	—
791	C₄²	C₂⁴×C₅	1	2	yes	—
792	C₂×C₅	—	2	2	no	—
793	C₂×C₅	—	2	2	no	—
794	C₂×C₅	—	4	1	no	—
795	C₂×C₅	—	4	4	no	—
796	C₂×C₅	—	8	1	no	—
797	C₂×C₅	C₂×#525	1	1	yes	characteristic
798	C₂×C₅	C₂×#577	1	1	yes	characteristic
799	C₂×C₅	#3586	1	1	yes	characteristic
800	C₂³	—	2	4	no	—
801	C₂³	—	2	2	no	—
802	C₂³	—	2	2	no	—
803	C₂³	—	2	2	no	—
804	C₂³	—	2	1	no	—
805	C₂³	—	4	1	no	—
806	C₂³	—	4	2	no	—
807	C₂³	—	4	2	no	—
808	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
809	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
810	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
811	Q₈	—	2	4	no	—
812	Q₈	—	2	2	no	—
813	Q₈	—	2	4	no	—
814	Q₈	—	2	2	no	—
815	Q₈	—	4	2	no	—
816	Q₈	—	8	2	no	—
817	Q₈	C₂×C₅×#41	1	4	yes	—
818	D₄	—	2	8	no	—
819	D₄	—	2	4	no	—
820	D₄	—	2	8	no	—
821	D₄	—	2	2	no	—
822	D₄	—	2	2	no	—
823	D₄	—	4	2	no	—
824	D₄	—	4	2	no	—
825	D₄	—	8	1	no	—
826	D₄	C₂×C₅×#41	1	4	yes	—
827	C₂×C₄	—	2	4	no	—
828	C₂×C₄	—	2	8	no	—
829	C₂×C₄	—	2	2	no	—
830	C₂×C₄	—	2	4	no	—
831	C₂×C₄	—	2	2	no	—
832	C₂×C₄	—	2	2	no	—
833	C₂×C₄	—	2	8	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	2	2	no	—
836	C₂×C₄	—	2	2	no	—
837	C₂×C₄	—	2	1	no	—
838	C₂×C₄	—	2	1	no	—
839	C₂×C₄	—	2	2	no	—
840	C₂×C₄	—	2	1	no	—
841	C₂×C₄	—	2	4	no	—
842	C₂×C₄	—	2	2	no	—
843	C₂×C₄	—	4	2	no	—
844	C₂×C₄	—	4	2	no	—
845	C₂×C₄	—	4	4	no	—
846	C₂×C₄	—	4	2	no	—
847	C₂×C₄	—	8	4	no	—
848	C₂×C₄	—	8	4	no	—
849	C₂×C₄	—	8	2	no	—
850	C₂×C₄	—	8	2	no	—
851	C₂×C₄	—	8	2	no	—
852	C₂×C₄	—	8	1	no	—
853	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
854	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
855	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
856	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
857	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
858	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
859	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
860	C₂×C₄	C₂×C₅×#41	1	4	yes	—
861	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
862	C₈	—	2	2	no	—
863	C₈	—	2	2	no	—
864	C₈	—	2	4	no	—
865	C₅	#60585	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	1	no	—
879	C₂²	—	4	1	no	—
880	C₂²	—	4	1	no	—
881	C₂²	C₅×#525	1	2	yes	—
882	C₂²	C₅×#577	1	2	yes	—
883	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
884	C₄	—	2	1	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	1	no	—
887	C₄	—	2	2	no	—
888	C₄	—	2	2	no	—
889	C₄	—	2	2	no	—
890	C₄	—	2	2	no	—
891	C₄	—	4	1	no	—
892	C₄	—	4	2	no	—
893	C₄	—	4	4	no	—
894	C₄	—	4	1	no	—
895	C₄	—	4	2	no	—
896	C₄	—	4	1	no	—
897	C₄	C₅×#525	1	2	yes	—
898	C₄	C₂²×C₅×#41	1	2	yes	—
899	C₂	—	2	2	no	—
900	C₂	—	2	2	no	—
901	C₂	—	4	1	no	—
902	C₂	—	4	4	no	—
903	C₂	—	8	1	no	—
904	C₂	C₂×C₅×#525	1	1	yes	characteristic
905	C₂	C₂×C₅×#577	1	1	yes	characteristic
906	C₂	C₅×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₅	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₅
prime radical	C₅×#3002	C₂
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×#3495	C₂	semidirect
2. C₂×C₅×#520	C₂	semidirect
3. C₅×#3125	C₂	semidirect
4. C₅×#3120	C₂	semidirect
5. C₅×#3114	C₂	semidirect
6. C₅×#3113	C₂	semidirect
7. C₅×#3108	C₂	semidirect
8. C₅×#3101	C₂	semidirect
9. C₅×#3092	C₂	semidirect
10. C₂×C₅×#483	C₂	semidirect
11. C₅×#3084	C₂	semidirect
12. C₅×#3046	C₂	semidirect
13. C₅×#3007	C₂	semidirect
15. C₅×#2952	C₂	semidirect
16. C₅×#2947	C₂	semidirect
17. C₅×#2924	C₂	semidirect
27. C₅×#544	C₂²	semidirect
28. C₅×#542	C₂²	semidirect
29. C₅×#541	C₂²	semidirect
30. C₅×#536	C₂²	semidirect
41. C₅×#520	C₂²	semidirect
42. C₅×#519	C₂²	semidirect
50. C₅×#484	C₂²	semidirect
54. C₅×#483	C₂²	semidirect
55. C₅×#481	C₂²	semidirect
57. C₅×#479	C₂²	semidirect
58. C₅×#478	C₂²	semidirect
59. C₅×#476	C₂²	semidirect
60. C₅×#475	C₂²	semidirect
61. C₅×#464	C₂²	semidirect
62. C₅×#463	C₂²	semidirect
63. C₅×#462	C₂²	semidirect
64. C₅×#461	C₂²	semidirect
74. C₅×#442	C₂²	semidirect
75. C₅×#441	C₂²	semidirect
76. C₅×#441	C₂²	semidirect
77. C₅×#440	C₂²	semidirect
78. C₄×C₅×Q₁₆	C₂²	semidirect
79. C₄×C₅×SD₁₆	C₂²	semidirect
80. C₄×C₅×SD₁₆	C₂²	semidirect
81. C₄×C₅×SD₁₆	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
85. C₅×#428	C₂²	semidirect
86. C₂×C₅×#106	C₂²	semidirect
87. C₅×#424	C₂²	semidirect
89. C₅×#417	C₂²	semidirect
91. C₂×C₅×#103	C₂²	semidirect
94. C₅×#405	C₂²	semidirect
95. #60585	C₅	direct (N × H)
232. #3495	C₂×C₅	semidirect
233. C₂×#520	C₂×C₅	semidirect
234. #3125	C₂×C₅	semidirect
235. #3120	C₂×C₅	semidirect
236. #3114	C₂×C₅	semidirect
237. #3113	C₂×C₅	semidirect
238. #3108	C₂×C₅	semidirect
239. #3101	C₂×C₅	semidirect
240. #3092	C₂×C₅	semidirect
241. C₂×#483	C₂×C₅	semidirect
242. #3084	C₂×C₅	semidirect
243. #3046	C₂×C₅	semidirect
244. #3007	C₂×C₅	semidirect
246. #2952	C₂×C₅	semidirect
247. #2947	C₂×C₅	semidirect
248. #2924	C₂×C₅	semidirect
374. #544	C₂²×C₅	semidirect
375. #542	C₂²×C₅	semidirect
376. #541	C₂²×C₅	semidirect
377. #536	C₂²×C₅	semidirect
388. #520	C₂²×C₅	semidirect
389. #519	C₂²×C₅	semidirect
397. #484	C₂²×C₅	semidirect
401. #483	C₂²×C₅	semidirect
402. #481	C₂²×C₅	semidirect
404. #479	C₂²×C₅	semidirect
405. #478	C₂²×C₅	semidirect
406. #476	C₂²×C₅	semidirect
407. #475	C₂²×C₅	semidirect
408. #464	C₂²×C₅	semidirect
409. #463	C₂²×C₅	semidirect
410. #462	C₂²×C₅	semidirect
411. #461	C₂²×C₅	semidirect
421. #442	C₂²×C₅	semidirect
422. #441	C₂²×C₅	semidirect
423. #441	C₂²×C₅	semidirect
424. #440	C₂²×C₅	semidirect
425. C₄×Q₁₆	C₂²×C₅	semidirect
426. C₄×SD₁₆	C₂²×C₅	semidirect
427. C₄×SD₁₆	C₂²×C₅	semidirect
428. C₄×SD₁₆	C₂²×C₅	semidirect
429. #433	C₂²×C₅	semidirect
432. #428	C₂²×C₅	semidirect
433. C₂×#106	C₂²×C₅	semidirect
434. #424	C₂²×C₅	semidirect
436. #417	C₂²×C₅	semidirect
438. C₂×#103	C₂²×C₅	semidirect
441. #405	C₂²×C₅	semidirect
865. C₅	#60585	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×#3495	2
C₂×C₅×#520	2
C₅×#3125	2
C₅×#3120	2
C₅×#3114	2
C₅×#3113	2
C₅×#3108	2
C₅×#3101	2
C₅×#3092	2
C₂×C₅×#483	2
C₅×#3084	2
C₅×#3046	2
C₅×#3007	2
C₅×#3002	2
C₅×#2952	2
C₅×#2947	2
C₅×#2924	2
#60585	5

Subgroups — C5×#60585 #11983305

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60585 #11983305