Subgroups — C₅×#60583 #11983303

Order 1280.

1998 conjugacy classes of subgroups.

The subgroup lattice has 870 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
2	C₂×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3127	C₂	1	4	yes	maximal, complemented
4	C₅×#3121	C₂	1	4	yes	maximal, complemented
5	C₅×#3117	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×#3104	C₂	1	2	yes	maximal, complemented
9	C₅×#3095	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3091	C₂	1	1	yes	maximal, characteristic
11	C₅×#3082	C₂	1	2	yes	maximal, complemented
12	C₅×#3044	C₂	1	2	yes	maximal, complemented
13	C₅×#3004	C₂	1	1	yes	maximal, characteristic
14	C₂×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2950	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	C₂³×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₅×#137	C₂²	1	2	yes	—
20	C₂²×C₅×Q₁₆	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
28	C₅×#542	C₂²	1	2	yes	—
29	C₅×#541	C₂²	1	2	yes	—
30	C₅×#536	C₂²	1	1	yes	characteristic
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	C₂²	1	1	yes	characteristic
36	C₅×#519	—	2	2	no	—
37	C₅×#519	—	2	1	no	—
38	C₅×#519	—	2	1	no	—
39	C₅×#519	C₂²	1	2	yes	—
40	C₅×#519	C₂²	1	4	yes	—
41	C₅×#519	C₂²	1	2	yes	—
42	C₅×#519	C₂²	1	1	yes	characteristic
43	C₂×C₄×C₅×Q₈	—	2	1	no	—
44	C₂×C₄×C₅×Q₈	—	2	1	no	—
45	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
46	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	—
47	C₂×C₅×#117	—	2	2	no	—
48	C₂×C₅×#117	C₂²	1	1	yes	characteristic
49	C₂×C₅×#117	C₂²	1	1	yes	characteristic
50	C₅×#485	C₂²	1	2	yes	—
51	C₅×#485	C₂²	1	4	yes	—
52	C₅×#484	C₂²	1	1	yes	characteristic
53	C₅×#484	C₂²	1	2	yes	—
54	C₅×#483	C₂²	1	1	yes	characteristic
55	C₅×#483	C₂²	1	2	yes	—
56	C₅×#482	C₂²	1	2	yes	—
57	C₅×#481	C₂²	1	1	yes	characteristic
58	C₅×#480	C₂²	1	1	yes	characteristic
59	C₅×#479	C₂²	1	4	yes	complemented
60	C₅×#479	C₂²	1	4	yes	complemented
61	C₅×#477	C₂²	1	4	yes	complemented
62	C₅×#475	C₂²	1	4	yes	complemented
63	C₅×#464	C₂²	1	4	yes	complemented
64	C₅×#464	C₂²	1	4	yes	complemented
65	C₅×#462	C₂²	1	4	yes	complemented
66	C₅×#462	C₂²	1	4	yes	complemented
67	C₅×#451	C₂²	1	2	yes	—
68	C₅×#451	C₂²	1	2	yes	—
69	C₅×#451	C₂²	1	4	yes	—
70	C₅×#451	C₂²	1	2	yes	—
71	C₅×#451	C₂²	1	2	yes	—
72	C₅×#448	C₂²	1	2	yes	—
73	C₅×#448	C₂²	1	2	yes	—
74	C₅×#441	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×Q₁₆	C₂²	1	4	yes	complemented
80	C₄×C₅×Q₁₆	C₂²	1	4	yes	complemented
81	C₄×C₅×SD₁₆	C₂²	1	4	yes	complemented
82	C₅×#433	C₂²	1	4	yes	—
83	C₅×#432	C₂²	1	2	yes	—
84	C₅×#431	C₂²	1	2	yes	—
85	C₅×#428	C₂²	1	2	yes	—
86	C₅×#427	C₂²	1	2	yes	—
87	C₅×#424	C₂²	1	2	yes	—
88	C₅×#419	C₂²	1	2	yes	—
89	C₅×#419	C₂²	1	2	yes	—
90	C₅×#416	C₂²	1	2	yes	—
91	C₂×C₅×#103	C₂²	1	2	yes	—
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	—
95	#60583	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₅×#41	C₂³	1	1	yes	characteristic
97	C₂²×C₅×Q₈	—	2	8	no	—
98	C₂²×C₅×Q₈	—	2	1	no	—
99	C₂²×C₅×Q₈	—	2	1	no	—
100	C₂²×C₅×Q₈	—	2	1	no	—
101	C₂²×C₅×Q₈	C₂³	1	1	yes	characteristic
102	C₂²×C₅×Q₈	C₂³	1	2	yes	—
103	C₂²×C₅×Q₈	C₂³	1	2	yes	—
104	C₂²×C₅×Q₈	C₂³	1	2	yes	—
105	C₂³×C₄×C₅	—	2	1	no	—
106	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
107	C₅×#137	—	2	8	no	—
108	C₂×C₅×Q₁₆	—	2	8	no	—
109	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
110	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
112	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₅×M₁₆	C₂³	1	2	yes	—
114	C₂²×C₅×C₈	C₂³	1	2	yes	—
115	C₅×C₄⋊Q₈	—	2	1	no	—
116	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
117	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
118	C₅×#126	—	2	2	no	—
119	C₅×#126	—	2	2	no	—
120	C₅×#126	—	2	2	no	—
121	C₅×#126	—	2	2	no	—
122	C₅×#125	—	2	2	no	—
123	C₅×#125	—	2	2	no	—
124	C₅×#125	—	2	1	no	—
125	C₅×#125	—	2	2	no	—
126	C₅×#125	C₂³	1	2	yes	—
127	C₅×#124	—	2	2	no	—
128	C₅×#124	C₂³	1	2	yes	—
129	C₅×#123	—	2	1	no	—
130	C₅×#123	—	2	2	no	—
131	C₅×#123	—	2	2	no	—
132	C₅×#123	—	2	2	no	—
133	C₅×C₂²⋊Q₈	—	2	1	no	—
134	C₅×C₂²⋊Q₈	—	2	1	no	—
135	C₅×C₂²⋊Q₈	—	2	2	no	—
136	C₅×C₂²⋊Q₈	—	2	1	no	—
137	C₅×C₂²⋊Q₈	—	2	1	no	—
138	C₅×C₂²⋊Q₈	—	2	2	no	—
139	C₅×C₂²⋊Q₈	—	2	2	no	—
140	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
141	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
142	C₅×C₂²⋊Q₈	C₂³	1	2	yes	—
143	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
144	C₅×#121	C₂³	1	1	yes	characteristic
145	C₅×#121	C₂³	1	1	yes	characteristic
146	C₅×#120	—	2	1	no	—
147	C₄×C₅×Q₈	—	2	2	no	—
148	C₄×C₅×Q₈	—	2	2	no	—
149	C₄×C₅×Q₈	—	2	2	no	—
150	C₄×C₅×Q₈	—	2	4	no	—
151	C₄×C₅×Q₈	—	2	2	no	—
152	C₄×C₅×Q₈	—	2	4	no	—
153	C₄×C₅×Q₈	—	2	1	no	—
154	C₄×C₅×Q₈	—	2	1	no	—
155	C₄×C₅×Q₈	—	2	2	no	—
156	C₄×C₅×Q₈	—	2	2	no	—
157	C₄×C₅×Q₈	—	2	2	no	—
158	C₄×C₅×Q₈	—	2	2	no	—
159	C₄×C₅×Q₈	—	2	2	no	—
160	C₄×C₅×Q₈	C₂³	1	4	yes	—
161	C₄×C₅×Q₈	C₂³	1	4	yes	—
162	C₄×C₅×Q₈	C₂³	1	2	yes	—
163	C₄×C₅×Q₈	C₂³	1	2	yes	—
164	C₄×C₅×Q₈	C₂³	1	2	yes	—
165	C₄×C₅×Q₈	C₂³	1	4	yes	—
166	C₄×C₅×Q₈	C₂³	1	4	yes	—
167	C₄×C₅×D₄	—	2	1	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	C₂³	1	2	yes	—
172	C₅×#117	—	2	1	no	—
173	C₅×#117	—	2	1	no	—
174	C₅×#117	—	2	2	no	—
175	C₅×#117	—	2	1	no	—
176	C₅×#117	—	2	4	no	—
177	C₅×#117	—	2	4	no	—
178	C₅×#117	—	2	4	no	—
179	C₅×#117	—	2	4	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	2	yes	—
186	C₅×#117	C₂³	1	1	yes	characteristic
187	C₅×#117	C₂³	1	2	yes	—
188	C₅×#117	C₂³	1	1	yes	characteristic
189	C₅×#117	C₂³	1	1	yes	characteristic
190	C₅×#117	C₂³	1	2	yes	—
191	C₂×C₅×C₄⋊C₄	—	2	2	no	—
192	C₂×C₅×C₄⋊C₄	—	2	2	no	—
193	C₂×C₅×C₄⋊C₄	—	2	1	no	—
194	C₂×C₅×C₄⋊C₄	—	2	1	no	—
195	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
197	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
200	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
202	C₂×C₅×C₂²⋊C₄	D₄	1	2	yes	—
203	C₂×C₄²×C₅	—	2	2	no	—
204	C₂×C₄²×C₅	—	2	2	no	—
205	C₂×C₄²×C₅	—	2	1	no	—
206	C₂×C₄²×C₅	C₂³	1	2	yes	—
207	C₅×#107	C₂³	1	2	yes	—
208	C₅×#107	C₂³	1	2	yes	—
209	C₅×#107	C₂³	1	4	yes	—
210	C₅×#106	C₂³	1	2	yes	—
211	C₅×#106	C₂³	1	2	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×#103	C₂³	1	4	yes	—
222	C₅×#103	C₂³	1	4	yes	—
223	C₅×#102	C₂³	1	2	yes	—
224	C₅×#102	C₂³	1	2	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
233	C₂×#519	C₂×C₅	1	1	yes	characteristic, complemented
234	#3127	C₂×C₅	1	4	yes	complemented
235	#3121	C₂×C₅	1	4	yes	complemented
236	#3117	C₂×C₅	1	2	yes	complemented
237	#3113	C₂×C₅	1	2	yes	complemented
238	#3108	C₂×C₅	1	2	yes	complemented
239	#3104	C₂×C₅	1	2	yes	complemented
240	#3095	C₂×C₅	1	1	yes	characteristic, complemented
241	#3091	C₂×C₅	1	1	yes	characteristic
242	#3082	C₂×C₅	1	2	yes	complemented
243	#3044	C₂×C₅	1	2	yes	complemented
244	#3004	C₂×C₅	1	1	yes	characteristic
245	C₂×#451	C₂×C₅	1	1	yes	characteristic, complemented
246	#2950	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	C₂×D₄	1	1	yes	characteristic
250	C₅×#41	—	2	4	no	—
251	C₂×C₅×Q₈	—	2	8	no	—
252	C₂×C₅×Q₈	—	2	8	no	—
253	C₂×C₅×Q₈	—	2	8	no	—
254	C₂×C₅×Q₈	—	2	8	no	—
255	C₂×C₅×Q₈	—	2	8	no	—
256	C₂×C₅×Q₈	—	2	2	no	—
257	C₂×C₅×Q₈	—	2	2	no	—
258	C₂×C₅×Q₈	—	2	2	no	—
259	C₂×C₅×Q₈	—	2	1	no	—
260	C₂×C₅×Q₈	—	2	2	no	—
261	C₂×C₅×Q₈	—	2	4	no	—
262	C₂×C₅×Q₈	—	2	4	no	—
263	C₂×C₅×Q₈	#41	1	8	yes	—
264	C₂×C₅×Q₈	C₂⁴	1	2	yes	—
265	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
266	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
267	C₂×C₅×D₄	—	2	1	no	—
268	C₂×C₅×D₄	—	2	1	no	—
269	C₂×C₅×D₄	—	2	1	no	—
270	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
271	C₂²×C₄×C₅	—	2	8	no	—
272	C₂²×C₄×C₅	—	2	2	no	—
273	C₂²×C₄×C₅	—	2	2	no	—
274	C₂²×C₄×C₅	—	2	2	no	—
275	C₂²×C₄×C₅	—	2	4	no	—
276	C₂²×C₄×C₅	—	2	1	no	—
277	C₂²×C₄×C₅	—	2	1	no	—
278	C₂²×C₄×C₅	—	2	1	no	—
279	C₂²×C₄×C₅	—	2	1	no	—
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
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	2	yes	—
287	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
288	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
290	C₅×Q₁₆	—	2	8	no	—
291	C₅×Q₁₆	—	2	8	no	—
292	C₅×Q₁₆	—	2	8	no	—
293	C₅×SD₁₆	—	2	8	no	—
294	C₅×M₁₆	—	2	4	no	—
295	C₂×C₅×C₈	—	2	4	no	—
296	C₂×C₅×C₈	C₂⁴	1	2	yes	—
297	C₂×C₅×C₈	C₂⁴	1	2	yes	—
298	C₂×C₅×C₈	C₂⁴	1	4	yes	—
299	C₅×C₄⋊C₄	—	2	1	no	—
300	C₅×C₄⋊C₄	—	2	4	no	—
301	C₅×C₄⋊C₄	—	2	4	no	—
302	C₅×C₄⋊C₄	—	2	4	no	—
303	C₅×C₄⋊C₄	—	2	4	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	1	no	—
308	C₅×C₄⋊C₄	—	2	1	no	—
309	C₅×C₄⋊C₄	—	2	2	no	—
310	C₅×C₄⋊C₄	—	2	2	no	—
311	C₅×C₄⋊C₄	—	2	2	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	2	2	no	—
314	C₅×C₄⋊C₄	—	2	1	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	C₂×D₄	1	1	yes	characteristic
319	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
320	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
321	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
322	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
323	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
324	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
325	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
326	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
328	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
329	C₅×C₂²⋊C₄	—	2	2	no	—
330	C₅×C₂²⋊C₄	—	2	2	no	—
331	C₅×C₂²⋊C₄	—	2	2	no	—
332	C₅×C₂²⋊C₄	—	2	2	no	—
333	C₅×C₂²⋊C₄	—	2	1	no	—
334	C₅×C₂²⋊C₄	—	2	1	no	—
335	C₅×C₂²⋊C₄	—	2	1	no	—
336	C₅×C₂²⋊C₄	—	2	1	no	—
337	C₅×C₂²⋊C₄	—	2	2	no	—
338	C₅×C₂²⋊C₄	—	2	2	no	—
339	C₅×C₂²⋊C₄	—	2	1	no	—
340	C₅×C₂²⋊C₄	—	2	2	no	—
341	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
342	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
343	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
344	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
345	C₄²×C₅	—	2	4	no	—
346	C₄²×C₅	—	2	4	no	—
347	C₄²×C₅	—	2	4	no	—
348	C₄²×C₅	—	2	4	no	—
349	C₄²×C₅	—	2	2	no	—
350	C₄²×C₅	—	2	2	no	—
351	C₄²×C₅	—	2	2	no	—
352	C₄²×C₅	—	2	2	no	—
353	C₄²×C₅	—	2	2	no	—
354	C₄²×C₅	—	2	1	no	—
355	C₄²×C₅	C₂×D₄	1	2	yes	—
356	C₄²×C₅	C₂×D₄	1	2	yes	—
357	C₄²×C₅	C₂⁴	1	2	yes	—
358	C₄²×C₅	C₂⁴	1	2	yes	—
359	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
360	C₂×#137	C₂²×C₅	1	2	yes	—
361	C₂²×Q₁₆	C₂²×C₅	1	2	yes	—
362	#556	—	2	1	no	—
363	#554	—	2	1	no	—
364	#552	—	2	2	no	—
365	#552	—	2	1	no	—
366	#552	—	2	1	no	—
367	#551	—	2	2	no	—
368	#544	C₂²×C₅	1	1	yes	characteristic
369	#542	C₂²×C₅	1	2	yes	—
370	#541	C₂²×C₅	1	2	yes	—
371	#536	C₂²×C₅	1	1	yes	characteristic
372	#533	C₂²×C₅	1	2	yes	—
373	#529	C₂²×C₅	1	2	yes	—
374	#525	C₂²×C₅	1	1	yes	characteristic
375	C₂×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
376	#520	C₂²×C₅	1	1	yes	characteristic
377	#519	—	2	2	no	—
378	#519	—	2	1	no	—
379	#519	—	2	1	no	—
380	#519	C₂²×C₅	1	2	yes	—
381	#519	C₂²×C₅	1	4	yes	—
382	#519	C₂²×C₅	1	2	yes	—
383	#519	C₂²×C₅	1	1	yes	characteristic
384	C₂×C₄×Q₈	—	2	1	no	—
385	C₂×C₄×Q₈	—	2	1	no	—
386	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
387	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	—
388	C₂×#117	—	2	2	no	—
389	C₂×#117	C₂²×C₅	1	1	yes	characteristic
390	C₂×#117	C₂²×C₅	1	1	yes	characteristic
391	#485	C₂²×C₅	1	2	yes	—
392	#485	C₂²×C₅	1	4	yes	—
393	#484	C₂²×C₅	1	1	yes	characteristic
394	#484	C₂²×C₅	1	2	yes	—
395	#483	C₂²×C₅	1	1	yes	characteristic
396	#483	C₂²×C₅	1	2	yes	—
397	#482	C₂²×C₅	1	2	yes	—
398	#481	C₂²×C₅	1	1	yes	characteristic
399	#480	C₂²×C₅	1	1	yes	characteristic
400	#479	C₂²×C₅	1	4	yes	complemented
401	#479	C₂²×C₅	1	4	yes	complemented
402	#477	C₂²×C₅	1	4	yes	complemented
403	#475	C₂²×C₅	1	4	yes	complemented
404	#464	C₂²×C₅	1	4	yes	complemented
405	#464	C₂²×C₅	1	4	yes	complemented
406	#462	C₂²×C₅	1	4	yes	complemented
407	#462	C₂²×C₅	1	4	yes	complemented
408	#451	C₂²×C₅	1	2	yes	—
409	#451	C₂²×C₅	1	2	yes	—
410	#451	C₂²×C₅	1	2	yes	—
411	#451	C₂²×C₅	1	4	yes	—
412	#451	C₂²×C₅	1	2	yes	—
413	#448	C₂²×C₅	1	2	yes	—
414	#448	C₂²×C₅	1	2	yes	—
415	#441	C₂²×C₅	1	4	yes	complemented
416	#441	C₂²×C₅	1	4	yes	complemented
417	#441	C₂²×C₅	1	4	yes	complemented
418	#440	C₂²×C₅	1	4	yes	complemented
419	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
420	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
421	C₄×Q₁₆	C₂²×C₅	1	4	yes	complemented
422	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
423	#433	C₂²×C₅	1	4	yes	—
424	#432	C₂²×C₅	1	2	yes	—
425	#431	C₂²×C₅	1	2	yes	—
426	#428	C₂²×C₅	1	2	yes	—
427	#427	C₂²×C₅	1	2	yes	—
428	#424	C₂²×C₅	1	2	yes	—
429	#419	C₂²×C₅	1	2	yes	—
430	#419	C₂²×C₅	1	2	yes	—
431	#416	C₂²×C₅	1	2	yes	—
432	C₂×#103	C₂²×C₅	1	2	yes	—
433	#407	C₂²×C₅	1	1	yes	characteristic
434	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
435	#405	C₂²×C₅	1	2	yes	—
436	C₂³×C₅	—	2	2	no	—
437	C₂³×C₅	—	2	2	no	—
438	C₂³×C₅	—	2	1	no	—
439	C₂³×C₅	—	4	1	no	—
440	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
441	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
442	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
443	C₅×Q₈	—	2	8	no	—
444	C₅×Q₈	—	2	8	no	—
445	C₅×Q₈	—	2	8	no	—
446	C₅×Q₈	—	2	4	no	—
447	C₅×Q₈	—	2	4	no	—
448	C₅×Q₈	—	2	2	no	—
449	C₅×Q₈	—	4	2	no	—
450	C₅×Q₈	—	8	2	no	—
451	C₅×Q₈	C₂×#41	1	8	yes	—
452	C₅×D₄	—	2	2	no	—
453	C₅×D₄	—	4	2	no	—
454	C₅×D₄	—	4	2	no	—
455	C₅×D₄	—	8	1	no	—
456	C₂×C₄×C₅	—	2	8	no	—
457	C₂×C₄×C₅	—	2	8	no	—
458	C₂×C₄×C₅	—	2	8	no	—
459	C₂×C₄×C₅	—	2	2	no	—
460	C₂×C₄×C₅	—	2	4	no	—
461	C₂×C₄×C₅	—	2	4	no	—
462	C₂×C₄×C₅	—	2	2	no	—
463	C₂×C₄×C₅	—	2	2	no	—
464	C₂×C₄×C₅	—	2	2	no	—
465	C₂×C₄×C₅	—	2	2	no	—
466	C₂×C₄×C₅	—	2	2	no	—
467	C₂×C₄×C₅	—	2	2	no	—
468	C₂×C₄×C₅	—	2	1	no	—
469	C₂×C₄×C₅	—	2	1	no	—
470	C₂×C₄×C₅	—	2	2	no	—
471	C₂×C₄×C₅	—	2	1	no	—
472	C₂×C₄×C₅	—	2	2	no	—
473	C₂×C₄×C₅	—	4	2	no	—
474	C₂×C₄×C₅	—	4	2	no	—
475	C₂×C₄×C₅	—	4	2	no	—
476	C₂×C₄×C₅	—	4	2	no	—
477	C₂×C₄×C₅	—	4	2	no	—
478	C₂×C₄×C₅	—	8	2	no	—
479	C₂×C₄×C₅	—	8	1	no	—
480	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
481	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
482	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
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	2	no	—
490	C₅×C₈	—	2	2	no	—
491	C₅×C₈	—	2	4	no	—
492	C₂×#41	C₂³×C₅	1	1	yes	characteristic
493	C₂²×Q₈	—	2	8	no	—
494	C₂²×Q₈	—	2	1	no	—
495	C₂²×Q₈	—	2	1	no	—
496	C₂²×Q₈	—	2	1	no	—
497	C₂²×Q₈	C₂³×C₅	1	2	yes	—
498	C₂²×Q₈	C₂³×C₅	1	2	yes	—
499	C₂²×Q₈	C₂³×C₅	1	1	yes	characteristic
500	C₂²×Q₈	C₂³×C₅	1	2	yes	—
501	C₂³×C₄	—	2	1	no	—
502	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
503	#137	—	2	8	no	—
504	C₂×Q₁₆	—	2	8	no	—
505	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
506	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
507	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
508	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
509	C₂×M₁₆	C₂³×C₅	1	2	yes	—
510	C₂²×C₈	C₂³×C₅	1	2	yes	—
511	C₄⋊Q₈	—	2	1	no	—
512	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
513	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
514	#126	—	2	2	no	—
515	#126	—	2	2	no	—
516	#126	—	2	2	no	—
517	#126	—	2	2	no	—
518	#125	—	2	2	no	—
519	#125	—	2	2	no	—
520	#125	—	2	1	no	—
521	#125	—	2	2	no	—
522	#125	C₂³×C₅	1	2	yes	—
523	#124	—	2	2	no	—
524	#124	C₂³×C₅	1	2	yes	—
525	#123	—	2	1	no	—
526	#123	—	2	2	no	—
527	#123	—	2	2	no	—
528	#123	—	2	2	no	—
529	C₂²⋊Q₈	—	2	1	no	—
530	C₂²⋊Q₈	—	2	1	no	—
531	C₂²⋊Q₈	—	2	2	no	—
532	C₂²⋊Q₈	—	2	1	no	—
533	C₂²⋊Q₈	—	2	1	no	—
534	C₂²⋊Q₈	—	2	2	no	—
535	C₂²⋊Q₈	—	2	2	no	—
536	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
537	C₂²⋊Q₈	C₂³×C₅	1	2	yes	—
538	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
539	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
540	#121	C₂³×C₅	1	1	yes	characteristic
541	#121	C₂³×C₅	1	1	yes	characteristic
542	#120	—	2	1	no	—
543	C₄×Q₈	—	2	2	no	—
544	C₄×Q₈	—	2	2	no	—
545	C₄×Q₈	—	2	2	no	—
546	C₄×Q₈	—	2	4	no	—
547	C₄×Q₈	—	2	2	no	—
548	C₄×Q₈	—	2	4	no	—
549	C₄×Q₈	—	2	1	no	—
550	C₄×Q₈	—	2	1	no	—
551	C₄×Q₈	—	2	2	no	—
552	C₄×Q₈	—	2	2	no	—
553	C₄×Q₈	—	2	2	no	—
554	C₄×Q₈	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	C₂³×C₅	1	4	yes	—
557	C₄×Q₈	C₂³×C₅	1	4	yes	—
558	C₄×Q₈	C₂³×C₅	1	4	yes	—
559	C₄×Q₈	C₂³×C₅	1	4	yes	—
560	C₄×Q₈	C₂³×C₅	1	2	yes	—
561	C₄×Q₈	C₂³×C₅	1	2	yes	—
562	C₄×Q₈	C₂³×C₅	1	2	yes	—
563	C₄×D₄	—	2	1	no	—
564	C₄×D₄	—	2	1	no	—
565	C₄×D₄	—	2	2	no	—
566	C₄×D₄	—	2	2	no	—
567	C₄×D₄	C₂³×C₅	1	2	yes	—
568	#117	—	2	1	no	—
569	#117	—	2	1	no	—
570	#117	—	2	2	no	—
571	#117	—	2	1	no	—
572	#117	—	2	4	no	—
573	#117	—	2	4	no	—
574	#117	—	2	4	no	—
575	#117	—	2	4	no	—
576	#117	—	2	2	no	—
577	#117	—	2	2	no	—
578	#117	C₅×D₄	1	1	yes	characteristic
579	#117	C₅×D₄	1	2	yes	—
580	#117	C₅×D₄	1	1	yes	characteristic
581	#117	C₂³×C₅	1	2	yes	—
582	#117	C₂³×C₅	1	2	yes	—
583	#117	C₂³×C₅	1	1	yes	characteristic
584	#117	C₂³×C₅	1	1	yes	characteristic
585	#117	C₂³×C₅	1	1	yes	characteristic
586	#117	C₂³×C₅	1	2	yes	—
587	C₂×C₄⋊C₄	—	2	2	no	—
588	C₂×C₄⋊C₄	—	2	2	no	—
589	C₂×C₄⋊C₄	—	2	1	no	—
590	C₂×C₄⋊C₄	—	2	1	no	—
591	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
592	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
593	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
594	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
595	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
596	C₂×C₂²⋊C₄	—	2	1	no	—
597	C₂×C₂²⋊C₄	—	2	1	no	—
598	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
599	C₂×C₄²	—	2	2	no	—
600	C₂×C₄²	—	2	2	no	—
601	C₂×C₄²	—	2	1	no	—
602	C₂×C₄²	C₂³×C₅	1	2	yes	—
603	#107	C₂³×C₅	1	2	yes	—
604	#107	C₂³×C₅	1	2	yes	—
605	#107	C₂³×C₅	1	4	yes	—
606	#106	C₂³×C₅	1	2	yes	—
607	#106	C₂³×C₅	1	2	yes	—
608	#106	C₂³×C₅	1	4	yes	—
609	C₄⋊C₈	C₂³×C₅	1	4	yes	—
610	C₄⋊C₈	C₂³×C₅	1	4	yes	—
611	#103	C₂³×C₅	1	4	yes	—
612	#103	C₂³×C₅	1	4	yes	—
613	#103	C₂³×C₅	1	2	yes	—
614	#103	C₂³×C₅	1	2	yes	—
615	#103	C₂³×C₅	1	4	yes	—
616	#103	C₂³×C₅	1	4	yes	—
617	#103	C₂³×C₅	1	4	yes	—
618	#103	C₂³×C₅	1	4	yes	—
619	#102	C₂³×C₅	1	2	yes	—
620	#102	C₂³×C₅	1	2	yes	—
621	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
622	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
623	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
624	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
626	#97	C₂³×C₅	1	4	yes	—
627	C₄×C₈	C₂³×C₅	1	4	yes	—
628	C₂²×C₅	—	2	1	no	—
629	C₂²×C₅	—	2	1	no	—
630	C₂²×C₅	—	2	1	no	—
631	C₂²×C₅	—	2	1	no	—
632	C₂²×C₅	—	2	1	no	—
633	C₂²×C₅	—	2	1	no	—
634	C₂²×C₅	—	2	1	no	—
635	C₂²×C₅	—	4	4	no	—
636	C₂²×C₅	—	4	1	no	—
637	C₂²×C₅	—	4	1	no	—
638	C₂²×C₅	—	4	1	no	—
639	C₂²×C₅	#525	1	2	yes	—
640	C₂²×C₅	#578	1	2	yes	—
641	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
642	C₄×C₅	—	2	2	no	—
643	C₄×C₅	—	2	2	no	—
644	C₄×C₅	—	2	8	no	—
645	C₄×C₅	—	2	1	no	—
646	C₄×C₅	—	2	1	no	—
647	C₄×C₅	—	2	2	no	—
648	C₄×C₅	—	2	2	no	—
649	C₄×C₅	—	4	2	no	—
650	C₄×C₅	—	4	2	no	—
651	C₄×C₅	—	4	1	no	—
652	C₄×C₅	—	4	1	no	—
653	C₄×C₅	—	4	2	no	—
654	C₄×C₅	—	4	2	no	—
655	C₄×C₅	—	4	1	no	—
656	C₄×C₅	#525	1	2	yes	—
657	C₄×C₅	C₂²×#41	1	2	yes	—
658	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
659	#41	—	2	4	no	—
660	C₂×Q₈	—	2	8	no	—
661	C₂×Q₈	—	2	8	no	—
662	C₂×Q₈	—	2	8	no	—
663	C₂×Q₈	—	2	8	no	—
664	C₂×Q₈	—	2	8	no	—
665	C₂×Q₈	—	2	2	no	—
666	C₂×Q₈	—	2	2	no	—
667	C₂×Q₈	—	2	2	no	—
668	C₂×Q₈	—	2	1	no	—
669	C₂×Q₈	—	2	2	no	—
670	C₂×Q₈	—	2	4	no	—
671	C₂×Q₈	—	2	4	no	—
672	C₂×Q₈	C₅×#41	1	8	yes	—
673	C₂×Q₈	C₂⁴×C₅	1	2	yes	—
674	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
675	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
676	C₂×D₄	—	2	1	no	—
677	C₂×D₄	—	2	1	no	—
678	C₂×D₄	—	2	1	no	—
679	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
680	C₂²×C₄	—	2	8	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	4	no	—
685	C₂²×C₄	—	2	1	no	—
686	C₂²×C₄	—	2	1	no	—
687	C₂²×C₄	—	2	1	no	—
688	C₂²×C₄	—	2	1	no	—
689	C₂²×C₄	—	2	1	no	—
690	C₂²×C₄	—	2	2	no	—
691	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
692	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
693	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
694	C₂²×C₄	C₂×C₅×D₄	1	1	yes	characteristic
695	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
697	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
698	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
699	Q₁₆	—	2	8	no	—
700	Q₁₆	—	2	8	no	—
701	Q₁₆	—	2	8	no	—
702	SD₁₆	—	2	8	no	—
703	M₁₆	—	2	4	no	—
704	C₂×C₈	—	2	4	no	—
705	C₂×C₈	C₂⁴×C₅	1	2	yes	—
706	C₂×C₈	C₂⁴×C₅	1	4	yes	—
707	C₂×C₈	C₂⁴×C₅	1	2	yes	—
708	C₄⋊C₄	—	2	1	no	—
709	C₄⋊C₄	—	2	4	no	—
710	C₄⋊C₄	—	2	4	no	—
711	C₄⋊C₄	—	2	4	no	—
712	C₄⋊C₄	—	2	4	no	—
713	C₄⋊C₄	—	2	2	no	—
714	C₄⋊C₄	—	2	2	no	—
715	C₄⋊C₄	—	2	2	no	—
716	C₄⋊C₄	—	2	1	no	—
717	C₄⋊C₄	—	2	1	no	—
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	2	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	1	no	—
724	C₄⋊C₄	—	2	2	no	—
725	C₄⋊C₄	—	2	1	no	—
726	C₄⋊C₄	—	2	2	no	—
727	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
728	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
729	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
730	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
731	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
732	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
733	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
734	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
735	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
736	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
737	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
738	C₂²⋊C₄	—	2	2	no	—
739	C₂²⋊C₄	—	2	2	no	—
740	C₂²⋊C₄	—	2	2	no	—
741	C₂²⋊C₄	—	2	2	no	—
742	C₂²⋊C₄	—	2	1	no	—
743	C₂²⋊C₄	—	2	1	no	—
744	C₂²⋊C₄	—	2	1	no	—
745	C₂²⋊C₄	—	2	1	no	—
746	C₂²⋊C₄	—	2	2	no	—
747	C₂²⋊C₄	—	2	2	no	—
748	C₂²⋊C₄	—	2	1	no	—
749	C₂²⋊C₄	—	2	2	no	—
750	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
751	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
752	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
753	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
754	C₄²	—	2	4	no	—
755	C₄²	—	2	4	no	—
756	C₄²	—	2	4	no	—
757	C₄²	—	2	4	no	—
758	C₄²	—	2	2	no	—
759	C₄²	—	2	2	no	—
760	C₄²	—	2	2	no	—
761	C₄²	—	2	2	no	—
762	C₄²	—	2	2	no	—
763	C₄²	—	2	1	no	—
764	C₄²	C₂×C₅×D₄	1	2	yes	—
765	C₄²	C₂×C₅×D₄	1	2	yes	—
766	C₄²	C₂⁴×C₅	1	2	yes	—
767	C₄²	C₂⁴×C₅	1	2	yes	—
768	C₂×C₅	—	2	2	no	—
769	C₂×C₅	—	2	2	no	—
770	C₂×C₅	—	4	1	no	—
771	C₂×C₅	—	8	1	no	—
772	C₂×C₅	C₂×#525	1	1	yes	characteristic
773	C₂×C₅	C₂×#578	1	1	yes	characteristic
774	C₂×C₅	#3586	1	1	yes	characteristic
775	C₂³	—	2	2	no	—
776	C₂³	—	2	2	no	—
777	C₂³	—	2	1	no	—
778	C₂³	—	4	1	no	—
779	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
780	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
781	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
782	Q₈	—	2	8	no	—
783	Q₈	—	2	8	no	—
784	Q₈	—	2	8	no	—
785	Q₈	—	2	4	no	—
786	Q₈	—	2	4	no	—
787	Q₈	—	2	2	no	—
788	Q₈	—	4	2	no	—
789	Q₈	—	8	2	no	—
790	Q₈	C₂×C₅×#41	1	8	yes	—
791	D₄	—	2	2	no	—
792	D₄	—	4	2	no	—
793	D₄	—	4	2	no	—
794	D₄	—	8	1	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	4	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	1	no	—
808	C₂×C₄	—	2	1	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	1	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	4	2	no	—
813	C₂×C₄	—	4	2	no	—
814	C₂×C₄	—	4	2	no	—
815	C₂×C₄	—	4	2	no	—
816	C₂×C₄	—	4	2	no	—
817	C₂×C₄	—	8	2	no	—
818	C₂×C₄	—	8	1	no	—
819	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
820	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
821	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
822	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
823	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
824	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
825	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
826	C₂×C₄	C₂×C₅×#41	1	4	yes	—
827	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
828	C₈	—	2	2	no	—
829	C₈	—	2	2	no	—
830	C₈	—	2	4	no	—
831	C₅	#60583	1	1	yes	characteristic, direct product factor, Sylow
832	C₂²	—	2	1	no	—
833	C₂²	—	2	1	no	—
834	C₂²	—	2	1	no	—
835	C₂²	—	2	1	no	—
836	C₂²	—	2	1	no	—
837	C₂²	—	2	1	no	—
838	C₂²	—	2	1	no	—
839	C₂²	—	4	4	no	—
840	C₂²	—	4	1	no	—
841	C₂²	—	4	1	no	—
842	C₂²	—	4	1	no	—
843	C₂²	C₅×#525	1	2	yes	—
844	C₂²	C₅×#578	1	2	yes	—
845	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
846	C₄	—	2	8	no	—
847	C₄	—	2	1	no	—
848	C₄	—	2	1	no	—
849	C₄	—	2	2	no	—
850	C₄	—	2	2	no	—
851	C₄	—	2	2	no	—
852	C₄	—	2	2	no	—
853	C₄	—	4	1	no	—
854	C₄	—	4	2	no	—
855	C₄	—	4	2	no	—
856	C₄	—	4	1	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	no	—
859	C₄	—	4	1	no	—
860	C₄	C₅×#525	1	2	yes	—
861	C₄	C₂²×C₅×#41	1	2	yes	—
862	C₂	—	2	2	no	—
863	C₂	—	2	2	no	—
864	C₂	—	4	1	no	—
865	C₂	—	8	1	no	—
866	C₂	C₂×C₅×#525	1	1	yes	characteristic
867	C₂	C₂×C₅×#578	1	1	yes	characteristic
868	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×#525	C₂²
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
2. C₂×C₅×#519	C₂	semidirect
3. C₅×#3127	C₂	semidirect
4. C₅×#3121	C₂	semidirect
5. C₅×#3117	C₂	semidirect
6. C₅×#3113	C₂	semidirect
7. C₅×#3108	C₂	semidirect
8. C₅×#3104	C₂	semidirect
9. C₅×#3095	C₂	semidirect
11. C₅×#3082	C₂	semidirect
12. C₅×#3044	C₂	semidirect
14. C₂×C₅×#451	C₂	semidirect
15. C₅×#2950	C₂	semidirect
16. C₅×#2947	C₂	semidirect
17. C₅×#2924	C₂	semidirect
59. C₅×#479	C₂²	semidirect
60. C₅×#479	C₂²	semidirect
61. C₅×#477	C₂²	semidirect
62. C₅×#475	C₂²	semidirect
63. C₅×#464	C₂²	semidirect
64. C₅×#464	C₂²	semidirect
65. C₅×#462	C₂²	semidirect
66. C₅×#462	C₂²	semidirect
74. C₅×#441	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×Q₁₆	C₂²	semidirect
80. C₄×C₅×Q₁₆	C₂²	semidirect
81. C₄×C₅×SD₁₆	C₂²	semidirect
95. #60583	C₅	direct (N × H)
233. C₂×#519	C₂×C₅	semidirect
234. #3127	C₂×C₅	semidirect
235. #3121	C₂×C₅	semidirect
236. #3117	C₂×C₅	semidirect
237. #3113	C₂×C₅	semidirect
238. #3108	C₂×C₅	semidirect
239. #3104	C₂×C₅	semidirect
240. #3095	C₂×C₅	semidirect
242. #3082	C₂×C₅	semidirect
243. #3044	C₂×C₅	semidirect
245. C₂×#451	C₂×C₅	semidirect
246. #2950	C₂×C₅	semidirect
247. #2947	C₂×C₅	semidirect
248. #2924	C₂×C₅	semidirect
400. #479	C₂²×C₅	semidirect
401. #479	C₂²×C₅	semidirect
402. #477	C₂²×C₅	semidirect
403. #475	C₂²×C₅	semidirect
404. #464	C₂²×C₅	semidirect
405. #464	C₂²×C₅	semidirect
406. #462	C₂²×C₅	semidirect
407. #462	C₂²×C₅	semidirect
415. #441	C₂²×C₅	semidirect
416. #441	C₂²×C₅	semidirect
417. #441	C₂²×C₅	semidirect
418. #440	C₂²×C₅	semidirect
419. C₄×Q₁₆	C₂²×C₅	semidirect
420. C₄×Q₁₆	C₂²×C₅	semidirect
421. C₄×Q₁₆	C₂²×C₅	semidirect
422. C₄×SD₁₆	C₂²×C₅	semidirect
831. C₅	#60583	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×#519	2
C₅×#3127	2
C₅×#3121	2
C₅×#3117	2
C₅×#3113	2
C₅×#3108	2
C₅×#3104	2
C₅×#3095	2
C₅×#3091	2
C₅×#3082	2
C₅×#3044	2
C₅×#3004	2
C₂×C₅×#451	2
C₅×#2950	2
C₅×#2947	2
C₅×#2924	2
#60583	5

Subgroups — C5×#60583 #11983303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60583 #11983303