Subgroups — C₅×#60582 #11983302

Order 1280.

2058 conjugacy classes of subgroups.

The subgroup lattice has 898 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
2	C₂×C₅×#519	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#3126	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×#3112	C₂	1	2	yes	maximal, complemented
7	C₅×#3108	C₂	1	2	yes	maximal, complemented
8	C₅×#3103	C₂	1	2	yes	maximal, complemented
9	C₅×#3094	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#3091	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#3082	C₂	1	2	yes	maximal, complemented
12	C₅×#3043	C₂	1	2	yes	maximal, complemented
13	C₅×#3004	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₅×#448	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅×#2949	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×SD₁₆	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
28	C₅×#542	C₂²	1	2	yes	—
29	C₅×#540	C₂²	1	2	yes	—
30	C₅×#535	C₂²	1	1	yes	characteristic
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	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	2	yes	—
41	C₅×#519	C₂²	1	4	yes	complemented
42	C₅×#518	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	complemented
46	C₂×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
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	complemented
51	C₅×#484	C₂²	1	1	yes	characteristic, complemented
52	C₅×#483	C₂²	1	1	yes	characteristic, complemented
53	C₅×#482	C₂²	1	4	yes	—
54	C₅×#482	C₂²	1	2	yes	complemented
55	C₅×#481	C₂²	1	2	yes	—
56	C₅×#481	C₂²	1	1	yes	characteristic, complemented
57	C₅×#480	C₂²	1	2	yes	—
58	C₅×#480	C₂²	1	1	yes	characteristic, complemented
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×#460	C₂²	1	4	yes	complemented
66	C₅×#460	C₂²	1	4	yes	complemented
67	C₅×#451	C₂²	1	2	yes	complemented
68	C₅×#451	C₂²	1	2	yes	complemented
69	C₅×#448	C₂²	1	2	yes	—
70	C₅×#448	C₂²	1	2	yes	—
71	C₅×#448	C₂²	1	4	yes	—
72	C₅×#448	C₂²	1	2	yes	complemented
73	C₅×#448	C₂²	1	2	yes	complemented
74	C₅×#441	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×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	complemented
84	C₅×#431	C₂²	1	2	yes	complemented
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×#418	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	#60582	C₅	1	1	yes	maximal, characteristic, direct product factor, Sylow
96	C₂×C₅×#41	—	2	2	no	—
97	C₂×C₅×#41	C₂³	1	1	yes	characteristic
98	C₂²×C₅×Q₈	—	2	8	no	—
99	C₂²×C₅×Q₈	—	2	1	no	—
100	C₂²×C₅×Q₈	—	2	1	no	—
101	C₂²×C₅×Q₈	—	2	1	no	—
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	C₂²×C₅×D₄	—	2	1	no	—
106	C₂²×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₅	—	2	1	no	—
108	C₂³×C₄×C₅	C₂³	1	1	yes	characteristic
109	C₅×#137	—	2	8	no	—
110	C₂×C₅×Q₁₆	C₂³	1	4	yes	—
111	C₂×C₅×SD₁₆	—	2	8	no	—
112	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
113	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
114	C₂×C₅×SD₁₆	C₂³	1	4	yes	—
115	C₂×C₅×M₁₆	C₂³	1	2	yes	—
116	C₂²×C₅×C₈	C₂³	1	2	yes	—
117	C₅×C₄⋊Q₈	—	2	1	no	—
118	C₅×C₄⋊Q₈	C₂³	1	2	yes	—
119	C₅×#127	C₂³	1	2	yes	—
120	C₅×#126	—	2	2	no	—
121	C₅×#126	—	2	2	no	—
122	C₅×#125	—	2	1	no	—
123	C₅×#125	C₂³	1	2	yes	—
124	C₅×#124	—	2	2	no	—
125	C₅×#124	—	2	2	no	—
126	C₅×#124	C₂³	1	2	yes	—
127	C₅×#123	—	2	1	no	—
128	C₅×#123	—	2	2	no	—
129	C₅×#123	—	2	2	no	—
130	C₅×#123	—	2	2	no	—
131	C₅×#123	—	2	2	no	—
132	C₅×C₂²⋊Q₈	—	2	2	no	—
133	C₅×C₂²⋊Q₈	—	2	2	no	—
134	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
135	C₅×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
136	C₅×#121	—	2	1	no	—
137	C₅×#121	—	2	1	no	—
138	C₅×#121	—	2	2	no	—
139	C₅×#121	—	2	1	no	—
140	C₅×#121	—	2	1	no	—
141	C₅×#121	—	2	2	no	—
142	C₅×#121	—	2	2	no	—
143	C₅×#121	C₂³	1	2	yes	—
144	C₅×#121	C₂³	1	2	yes	—
145	C₅×#121	C₂³	1	1	yes	characteristic
146	C₅×#121	C₂³	1	1	yes	characteristic
147	C₅×#120	—	2	1	no	—
148	C₅×#120	—	2	2	no	—
149	C₄×C₅×Q₈	—	2	2	no	—
150	C₄×C₅×Q₈	—	2	2	no	—
151	C₄×C₅×Q₈	—	2	2	no	—
152	C₄×C₅×Q₈	—	2	2	no	—
153	C₄×C₅×Q₈	—	2	4	no	—
154	C₄×C₅×Q₈	—	2	4	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	C₂³	1	4	yes	—
160	C₄×C₅×Q₈	C₂³	1	4	yes	—
161	C₄×C₅×Q₈	C₂³	1	2	yes	—
162	C₄×C₅×Q₈	C₂³	1	4	yes	—
163	C₄×C₅×Q₈	C₂³	1	4	yes	—
164	C₄×C₅×D₄	—	2	1	no	—
165	C₄×C₅×D₄	—	2	1	no	—
166	C₄×C₅×D₄	—	2	2	no	—
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	C₄×C₅×D₄	C₂³	1	2	yes	—
173	C₄×C₅×D₄	C₂³	1	2	yes	—
174	C₅×#117	—	2	1	no	—
175	C₅×#117	—	2	1	no	—
176	C₅×#117	—	2	1	no	—
177	C₅×#117	—	2	4	no	—
178	C₅×#117	—	2	4	no	—
179	C₅×#117	—	2	4	no	—
180	C₅×#117	—	2	4	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	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	D₄	1	1	yes	characteristic
195	C₂×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
196	C₂×C₅×C₄⋊C₄	C₂³	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×C₂²⋊C₄	—	2	1	no	—
200	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
201	C₂×C₅×C₂²⋊C₄	—	2	2	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×#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
233	C₂×#519	C₂×C₅	1	1	yes	characteristic, complemented
234	#3126	C₂×C₅	1	4	yes	complemented
235	#3121	C₂×C₅	1	4	yes	complemented
236	#3117	C₂×C₅	1	2	yes	complemented
237	#3112	C₂×C₅	1	2	yes	complemented
238	#3108	C₂×C₅	1	2	yes	complemented
239	#3103	C₂×C₅	1	2	yes	complemented
240	#3094	C₂×C₅	1	1	yes	characteristic, complemented
241	#3091	C₂×C₅	1	1	yes	characteristic, complemented
242	#3082	C₂×C₅	1	2	yes	complemented
243	#3043	C₂×C₅	1	2	yes	complemented
244	#3004	C₂×C₅	1	1	yes	characteristic, complemented
245	C₂×#448	C₂×C₅	1	1	yes	characteristic, complemented
246	#2949	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	4	no	—
252	C₅×#41	—	8	4	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	8	no	—
257	C₂×C₅×Q₈	—	2	8	no	—
258	C₂×C₅×Q₈	—	2	2	no	—
259	C₂×C₅×Q₈	—	2	2	no	—
260	C₂×C₅×Q₈	—	2	2	no	—
261	C₂×C₅×Q₈	—	2	2	no	—
262	C₂×C₅×Q₈	—	2	4	no	—
263	C₂×C₅×Q₈	#41	1	8	yes	complemented
264	C₂×C₅×Q₈	C₂⁴	1	1	yes	characteristic
265	C₂×C₅×Q₈	C₂⁴	1	4	yes	—
266	C₂×C₅×D₄	—	2	1	no	—
267	C₂×C₅×D₄	—	2	1	no	—
268	C₂×C₅×D₄	—	2	2	no	—
269	C₂×C₅×D₄	—	2	1	no	—
270	C₂×C₅×D₄	—	2	2	no	—
271	C₂×C₅×D₄	—	2	1	no	—
272	C₂×C₅×D₄	—	2	2	no	—
273	C₂×C₅×D₄	—	2	2	no	—
274	C₂×C₅×D₄	—	2	4	no	—
275	C₂×C₅×D₄	—	8	2	no	—
276	C₂×C₅×D₄	C₂⁴	1	2	yes	—
277	C₂×C₅×D₄	C₂⁴	1	1	yes	characteristic
278	C₂²×C₄×C₅	—	2	8	no	—
279	C₂²×C₄×C₅	—	2	2	no	—
280	C₂²×C₄×C₅	—	2	2	no	—
281	C₂²×C₄×C₅	—	2	2	no	—
282	C₂²×C₄×C₅	—	2	4	no	—
283	C₂²×C₄×C₅	—	2	1	no	—
284	C₂²×C₄×C₅	—	2	1	no	—
285	C₂²×C₄×C₅	—	2	1	no	—
286	C₂²×C₄×C₅	—	2	1	no	—
287	C₂²×C₄×C₅	—	2	2	no	—
288	C₂²×C₄×C₅	—	2	2	no	—
289	C₂²×C₄×C₅	—	2	2	no	—
290	C₂²×C₄×C₅	C₂×D₄	1	2	yes	—
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	2	yes	—
295	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
296	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄×C₅	C₂⁴	1	1	yes	characteristic
298	C₅×Q₁₆	—	2	8	no	—
299	C₅×SD₁₆	—	2	8	no	—
300	C₅×SD₁₆	—	2	8	no	—
301	C₅×SD₁₆	—	2	8	no	—
302	C₅×M₁₆	—	2	4	no	—
303	C₂×C₅×C₈	—	2	4	no	—
304	C₂×C₅×C₈	C₂⁴	1	2	yes	—
305	C₂×C₅×C₈	C₂⁴	1	2	yes	—
306	C₂×C₅×C₈	C₂⁴	1	4	yes	—
307	C₅×C₄⋊C₄	—	2	1	no	—
308	C₅×C₄⋊C₄	—	2	4	no	—
309	C₅×C₄⋊C₄	—	2	4	no	—
310	C₅×C₄⋊C₄	—	2	4	no	—
311	C₅×C₄⋊C₄	—	2	4	no	—
312	C₅×C₄⋊C₄	—	2	2	no	—
313	C₅×C₄⋊C₄	—	2	1	no	—
314	C₅×C₄⋊C₄	—	2	1	no	—
315	C₅×C₄⋊C₄	—	2	1	no	—
316	C₅×C₄⋊C₄	—	2	2	no	—
317	C₅×C₄⋊C₄	—	2	2	no	—
318	C₅×C₄⋊C₄	—	2	2	no	—
319	C₅×C₄⋊C₄	—	2	1	no	—
320	C₅×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
324	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
325	C₅×C₄⋊C₄	C₂×D₄	1	2	yes	—
326	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
327	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
328	C₅×C₄⋊C₄	C₂⁴	1	2	yes	—
329	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
330	C₅×C₄⋊C₄	C₂⁴	1	1	yes	characteristic
331	C₅×C₂²⋊C₄	—	2	1	no	—
332	C₅×C₂²⋊C₄	—	2	2	no	—
333	C₅×C₂²⋊C₄	—	2	2	no	—
334	C₅×C₂²⋊C₄	—	2	1	no	—
335	C₅×C₂²⋊C₄	—	2	1	no	—
336	C₅×C₂²⋊C₄	—	2	2	no	—
337	C₅×C₂²⋊C₄	—	2	2	no	—
338	C₅×C₂²⋊C₄	—	2	2	no	—
339	C₅×C₂²⋊C₄	—	2	2	no	—
340	C₅×C₂²⋊C₄	—	2	2	no	—
341	C₅×C₂²⋊C₄	—	2	2	no	—
342	C₅×C₂²⋊C₄	—	2	1	no	—
343	C₅×C₂²⋊C₄	—	2	2	no	—
344	C₅×C₂²⋊C₄	—	2	1	no	—
345	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
346	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
347	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
348	C₅×C₂²⋊C₄	C₂×D₄	1	2	yes	—
349	C₄²×C₅	—	2	4	no	—
350	C₄²×C₅	—	2	4	no	—
351	C₄²×C₅	—	2	4	no	—
352	C₄²×C₅	—	2	4	no	—
353	C₄²×C₅	—	2	2	no	—
354	C₄²×C₅	—	2	2	no	—
355	C₄²×C₅	—	2	2	no	—
356	C₄²×C₅	—	2	1	no	—
357	C₄²×C₅	C₂×D₄	1	2	yes	—
358	C₄²×C₅	C₂×D₄	1	2	yes	—
359	C₄²×C₅	C₂⁴	1	2	yes	—
360	C₄²×C₅	C₂⁴	1	2	yes	—
361	C₂³×Q₈	C₂²×C₅	1	1	yes	characteristic
362	C₂×#137	C₂²×C₅	1	2	yes	—
363	C₂²×SD₁₆	C₂²×C₅	1	2	yes	—
364	#555	—	2	1	no	—
365	#553	—	2	1	no	—
366	#553	—	2	1	no	—
367	#551	—	2	2	no	—
368	#547	—	2	1	no	—
369	#546	—	2	2	no	—
370	#544	C₂²×C₅	1	1	yes	characteristic
371	#542	C₂²×C₅	1	2	yes	—
372	#540	C₂²×C₅	1	2	yes	—
373	#535	C₂²×C₅	1	1	yes	characteristic
374	#532	C₂²×C₅	1	2	yes	—
375	#529	C₂²×C₅	1	2	yes	—
376	#525	C₂²×C₅	1	1	yes	characteristic
377	C₂×#121	C₂²×C₅	1	1	yes	characteristic
378	#520	C₂²×C₅	1	1	yes	characteristic
379	#519	—	2	2	no	—
380	#519	—	2	1	no	—
381	#519	—	2	1	no	—
382	#519	C₂²×C₅	1	2	yes	—
383	#519	C₂²×C₅	1	2	yes	—
384	#519	C₂²×C₅	1	4	yes	complemented
385	#518	C₂²×C₅	1	1	yes	characteristic
386	C₂×C₄×Q₈	—	2	1	no	—
387	C₂×C₄×Q₈	—	2	1	no	—
388	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
389	C₂×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
390	C₂×#117	—	2	2	no	—
391	C₂×#117	C₂²×C₅	1	1	yes	characteristic
392	C₂×#117	C₂²×C₅	1	1	yes	characteristic
393	#485	C₂²×C₅	1	2	yes	complemented
394	#484	C₂²×C₅	1	1	yes	characteristic, complemented
395	#483	C₂²×C₅	1	1	yes	characteristic, complemented
396	#482	C₂²×C₅	1	4	yes	—
397	#482	C₂²×C₅	1	2	yes	complemented
398	#481	C₂²×C₅	1	2	yes	—
399	#481	C₂²×C₅	1	1	yes	characteristic, complemented
400	#480	C₂²×C₅	1	2	yes	—
401	#480	C₂²×C₅	1	1	yes	characteristic, complemented
402	#479	C₂²×C₅	1	4	yes	complemented
403	#479	C₂²×C₅	1	4	yes	complemented
404	#477	C₂²×C₅	1	4	yes	complemented
405	#475	C₂²×C₅	1	4	yes	complemented
406	#464	C₂²×C₅	1	4	yes	complemented
407	#464	C₂²×C₅	1	4	yes	complemented
408	#460	C₂²×C₅	1	4	yes	complemented
409	#460	C₂²×C₅	1	4	yes	complemented
410	#451	C₂²×C₅	1	2	yes	complemented
411	#451	C₂²×C₅	1	2	yes	complemented
412	#448	C₂²×C₅	1	2	yes	—
413	#448	C₂²×C₅	1	2	yes	—
414	#448	C₂²×C₅	1	4	yes	—
415	#448	C₂²×C₅	1	2	yes	complemented
416	#448	C₂²×C₅	1	2	yes	complemented
417	#441	C₂²×C₅	1	4	yes	complemented
418	#440	C₂²×C₅	1	4	yes	complemented
419	#440	C₂²×C₅	1	4	yes	complemented
420	#440	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	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
424	C₄×SD₁₆	C₂²×C₅	1	4	yes	complemented
425	#433	C₂²×C₅	1	4	yes	complemented
426	#432	C₂²×C₅	1	2	yes	complemented
427	#431	C₂²×C₅	1	2	yes	complemented
428	#428	C₂²×C₅	1	2	yes	—
429	#427	C₂²×C₅	1	2	yes	—
430	#424	C₂²×C₅	1	2	yes	—
431	#419	C₂²×C₅	1	2	yes	—
432	#418	C₂²×C₅	1	2	yes	—
433	#416	C₂²×C₅	1	2	yes	—
434	C₂×#103	C₂²×C₅	1	2	yes	—
435	#407	C₂²×C₅	1	1	yes	characteristic
436	C₂×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
437	#405	C₂²×C₅	1	2	yes	—
438	C₂³×C₅	—	2	2	no	—
439	C₂³×C₅	—	2	2	no	—
440	C₂³×C₅	—	2	2	no	—
441	C₂³×C₅	—	2	1	no	—
442	C₂³×C₅	—	4	1	no	—
443	C₂³×C₅	—	4	2	no	—
444	C₂³×C₅	—	8	1	no	—
445	C₂³×C₅	—	8	1	no	—
446	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
447	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
448	C₂³×C₅	C₂²×D₄	1	1	yes	characteristic
449	C₅×Q₈	—	2	8	no	—
450	C₅×Q₈	—	2	8	no	—
451	C₅×Q₈	—	2	8	no	—
452	C₅×Q₈	—	2	4	no	—
453	C₅×Q₈	—	2	2	no	—
454	C₅×Q₈	—	8	2	no	—
455	C₅×Q₈	C₂×#41	1	8	yes	—
456	C₅×D₄	—	2	4	no	—
457	C₅×D₄	—	2	2	no	—
458	C₅×D₄	—	4	2	no	—
459	C₅×D₄	—	4	4	no	—
460	C₅×D₄	—	4	2	no	—
461	C₅×D₄	—	4	2	no	—
462	C₅×D₄	—	8	2	no	—
463	C₅×D₄	—	8	2	no	—
464	C₅×D₄	—	8	1	no	—
465	C₅×D₄	—	8	2	no	—
466	C₂×C₄×C₅	—	2	8	no	—
467	C₂×C₄×C₅	—	2	8	no	—
468	C₂×C₄×C₅	—	2	8	no	—
469	C₂×C₄×C₅	—	2	2	no	—
470	C₂×C₄×C₅	—	2	4	no	—
471	C₂×C₄×C₅	—	2	4	no	—
472	C₂×C₄×C₅	—	2	2	no	—
473	C₂×C₄×C₅	—	2	2	no	—
474	C₂×C₄×C₅	—	2	2	no	—
475	C₂×C₄×C₅	—	2	2	no	—
476	C₂×C₄×C₅	—	2	2	no	—
477	C₂×C₄×C₅	—	2	2	no	—
478	C₂×C₄×C₅	—	2	1	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	—	4	2	no	—
483	C₂×C₄×C₅	—	4	2	no	—
484	C₂×C₄×C₅	—	4	2	no	—
485	C₂×C₄×C₅	—	4	2	no	—
486	C₂×C₄×C₅	—	8	2	no	—
487	C₂×C₄×C₅	—	8	2	no	—
488	C₂×C₄×C₅	—	8	2	no	—
489	C₂×C₄×C₅	—	8	1	no	—
490	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₅	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₅	C₂×#41	1	4	yes	—
498	C₂×C₄×C₅	C₂⁵	1	1	yes	characteristic
499	C₅×C₈	—	2	2	no	—
500	C₅×C₈	—	2	2	no	—
501	C₅×C₈	—	2	4	no	—
502	C₂×#41	—	2	2	no	—
503	C₂×#41	C₂³×C₅	1	1	yes	characteristic
504	C₂²×Q₈	—	2	8	no	—
505	C₂²×Q₈	—	2	1	no	—
506	C₂²×Q₈	—	2	1	no	—
507	C₂²×Q₈	—	2	1	no	—
508	C₂²×Q₈	C₂³×C₅	1	2	yes	—
509	C₂²×Q₈	C₂³×C₅	1	2	yes	—
510	C₂²×Q₈	C₂³×C₅	1	2	yes	—
511	C₂²×D₄	—	2	1	no	—
512	C₂²×D₄	C₂³×C₅	1	1	yes	characteristic
513	C₂³×C₄	—	2	1	no	—
514	C₂³×C₄	C₂³×C₅	1	1	yes	characteristic
515	#137	—	2	8	no	—
516	C₂×Q₁₆	C₂³×C₅	1	4	yes	—
517	C₂×SD₁₆	—	2	8	no	—
518	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
519	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
520	C₂×SD₁₆	C₂³×C₅	1	4	yes	—
521	C₂×M₁₆	C₂³×C₅	1	2	yes	—
522	C₂²×C₈	C₂³×C₅	1	2	yes	—
523	C₄⋊Q₈	—	2	1	no	—
524	C₄⋊Q₈	C₂³×C₅	1	2	yes	—
525	#127	C₂³×C₅	1	2	yes	—
526	#126	—	2	2	no	—
527	#126	—	2	2	no	—
528	#125	—	2	1	no	—
529	#125	C₂³×C₅	1	2	yes	—
530	#124	—	2	2	no	—
531	#124	—	2	2	no	—
532	#124	C₂³×C₅	1	2	yes	—
533	#123	—	2	1	no	—
534	#123	—	2	2	no	—
535	#123	—	2	2	no	—
536	#123	—	2	2	no	—
537	#123	—	2	2	no	—
538	C₂²⋊Q₈	—	2	2	no	—
539	C₂²⋊Q₈	—	2	2	no	—
540	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
541	C₂²⋊Q₈	C₂³×C₅	1	1	yes	characteristic
542	#121	—	2	1	no	—
543	#121	—	2	1	no	—
544	#121	—	2	2	no	—
545	#121	—	2	1	no	—
546	#121	—	2	1	no	—
547	#121	—	2	2	no	—
548	#121	—	2	2	no	—
549	#121	C₂³×C₅	1	2	yes	—
550	#121	C₂³×C₅	1	2	yes	—
551	#121	C₂³×C₅	1	1	yes	characteristic
552	#121	C₂³×C₅	1	1	yes	characteristic
553	#120	—	2	1	no	—
554	#120	—	2	2	no	—
555	C₄×Q₈	—	2	2	no	—
556	C₄×Q₈	—	2	2	no	—
557	C₄×Q₈	—	2	2	no	—
558	C₄×Q₈	—	2	2	no	—
559	C₄×Q₈	—	2	4	no	—
560	C₄×Q₈	—	2	4	no	—
561	C₄×Q₈	—	2	2	no	—
562	C₄×Q₈	—	2	2	no	—
563	C₄×Q₈	—	2	2	no	—
564	C₄×Q₈	—	2	2	no	—
565	C₄×Q₈	C₂³×C₅	1	4	yes	—
566	C₄×Q₈	C₂³×C₅	1	4	yes	—
567	C₄×Q₈	C₂³×C₅	1	4	yes	—
568	C₄×Q₈	C₂³×C₅	1	4	yes	—
569	C₄×Q₈	C₂³×C₅	1	2	yes	—
570	C₄×D₄	—	2	1	no	—
571	C₄×D₄	—	2	1	no	—
572	C₄×D₄	—	2	2	no	—
573	C₄×D₄	—	2	1	no	—
574	C₄×D₄	—	2	1	no	—
575	C₄×D₄	—	2	2	no	—
576	C₄×D₄	—	2	2	no	—
577	C₄×D₄	C₂³×C₅	1	2	yes	—
578	C₄×D₄	C₂³×C₅	1	2	yes	—
579	C₄×D₄	C₂³×C₅	1	2	yes	—
580	#117	—	2	1	no	—
581	#117	—	2	1	no	—
582	#117	—	2	1	no	—
583	#117	—	2	4	no	—
584	#117	—	2	4	no	—
585	#117	—	2	4	no	—
586	#117	—	2	4	no	—
587	#117	—	2	2	no	—
588	#117	C₅×D₄	1	2	yes	—
589	#117	C₅×D₄	1	1	yes	characteristic
590	#117	C₅×D₄	1	1	yes	characteristic
591	#117	C₂³×C₅	1	2	yes	—
592	#117	C₂³×C₅	1	2	yes	—
593	#117	C₂³×C₅	1	1	yes	characteristic
594	#117	C₂³×C₅	1	1	yes	characteristic
595	#117	C₂³×C₅	1	1	yes	characteristic
596	#117	C₂³×C₅	1	2	yes	—
597	C₂×C₄⋊C₄	—	2	2	no	—
598	C₂×C₄⋊C₄	—	2	2	no	—
599	C₂×C₄⋊C₄	—	2	1	no	—
600	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
601	C₂×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
602	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
603	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
604	C₂×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
605	C₂×C₂²⋊C₄	—	2	1	no	—
606	C₂×C₂²⋊C₄	—	2	1	no	—
607	C₂×C₂²⋊C₄	—	2	2	no	—
608	C₂×C₂²⋊C₄	C₅×D₄	1	2	yes	—
609	C₂×C₄²	—	2	2	no	—
610	C₂×C₄²	—	2	2	no	—
611	C₂×C₄²	—	2	1	no	—
612	C₂×C₄²	C₂³×C₅	1	2	yes	—
613	#107	C₂³×C₅	1	2	yes	—
614	#107	C₂³×C₅	1	2	yes	—
615	#107	C₂³×C₅	1	4	yes	—
616	#106	C₂³×C₅	1	2	yes	—
617	#106	C₂³×C₅	1	2	yes	—
618	#106	C₂³×C₅	1	4	yes	—
619	C₄⋊C₈	C₂³×C₅	1	4	yes	—
620	C₄⋊C₈	C₂³×C₅	1	4	yes	—
621	#103	C₂³×C₅	1	4	yes	—
622	#103	C₂³×C₅	1	4	yes	—
623	#103	C₂³×C₅	1	2	yes	—
624	#103	C₂³×C₅	1	2	yes	—
625	#103	C₂³×C₅	1	4	yes	—
626	#103	C₂³×C₅	1	4	yes	—
627	#102	C₂³×C₅	1	2	yes	—
628	#102	C₂³×C₅	1	2	yes	—
629	#102	C₂³×C₅	1	4	yes	—
630	#102	C₂³×C₅	1	4	yes	—
631	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
632	C₂²⋊C₈	C₂³×C₅	1	1	yes	characteristic
633	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
634	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
635	C₂²⋊C₈	C₂³×C₅	1	2	yes	—
636	#97	C₂³×C₅	1	4	yes	—
637	C₄×C₈	C₂³×C₅	1	4	yes	—
638	C₂²×C₅	—	2	1	no	—
639	C₂²×C₅	—	2	1	no	—
640	C₂²×C₅	—	2	1	no	—
641	C₂²×C₅	—	2	1	no	—
642	C₂²×C₅	—	2	1	no	—
643	C₂²×C₅	—	2	1	no	—
644	C₂²×C₅	—	2	1	no	—
645	C₂²×C₅	—	4	4	no	—
646	C₂²×C₅	—	4	2	no	—
647	C₂²×C₅	—	4	1	no	—
648	C₂²×C₅	—	4	1	no	—
649	C₂²×C₅	—	4	2	no	—
650	C₂²×C₅	—	4	1	no	—
651	C₂²×C₅	—	4	2	no	—
652	C₂²×C₅	—	16	2	no	—
653	C₂²×C₅	#525	1	2	yes	—
654	C₂²×C₅	#577	1	2	yes	—
655	C₂²×C₅	C₂³×D₄	1	1	yes	characteristic
656	C₄×C₅	—	2	2	no	—
657	C₄×C₅	—	2	2	no	—
658	C₄×C₅	—	2	8	no	—
659	C₄×C₅	—	2	1	no	—
660	C₄×C₅	—	2	1	no	—
661	C₄×C₅	—	2	2	no	—
662	C₄×C₅	—	2	2	no	—
663	C₄×C₅	—	4	2	no	—
664	C₄×C₅	—	4	1	no	—
665	C₄×C₅	—	4	1	no	—
666	C₄×C₅	—	4	2	no	—
667	C₄×C₅	—	4	2	no	—
668	C₄×C₅	—	4	1	no	—
669	C₄×C₅	#525	1	2	yes	—
670	C₄×C₅	C₂²×#41	1	2	yes	—
671	C₂⁴	—	2	1	no	—
672	C₂⁴	C₂×C₅×D₄	1	1	yes	characteristic
673	#41	—	2	4	no	—
674	#41	—	8	4	no	—
675	C₂×Q₈	—	2	8	no	—
676	C₂×Q₈	—	2	8	no	—
677	C₂×Q₈	—	2	8	no	—
678	C₂×Q₈	—	2	8	no	—
679	C₂×Q₈	—	2	8	no	—
680	C₂×Q₈	—	2	2	no	—
681	C₂×Q₈	—	2	2	no	—
682	C₂×Q₈	—	2	2	no	—
683	C₂×Q₈	—	2	2	no	—
684	C₂×Q₈	—	2	4	no	—
685	C₂×Q₈	C₅×#41	1	8	yes	complemented
686	C₂×Q₈	C₂⁴×C₅	1	1	yes	characteristic
687	C₂×Q₈	C₂⁴×C₅	1	4	yes	—
688	C₂×D₄	—	2	1	no	—
689	C₂×D₄	—	2	1	no	—
690	C₂×D₄	—	2	2	no	—
691	C₂×D₄	—	2	1	no	—
692	C₂×D₄	—	2	2	no	—
693	C₂×D₄	—	2	1	no	—
694	C₂×D₄	—	2	2	no	—
695	C₂×D₄	—	2	2	no	—
696	C₂×D₄	—	2	4	no	—
697	C₂×D₄	—	8	2	no	—
698	C₂×D₄	C₂⁴×C₅	1	2	yes	—
699	C₂×D₄	C₂⁴×C₅	1	1	yes	characteristic
700	C₂²×C₄	—	2	8	no	—
701	C₂²×C₄	—	2	2	no	—
702	C₂²×C₄	—	2	2	no	—
703	C₂²×C₄	—	2	2	no	—
704	C₂²×C₄	—	2	4	no	—
705	C₂²×C₄	—	2	1	no	—
706	C₂²×C₄	—	2	1	no	—
707	C₂²×C₄	—	2	1	no	—
708	C₂²×C₄	—	2	1	no	—
709	C₂²×C₄	—	2	2	no	—
710	C₂²×C₄	—	2	2	no	—
711	C₂²×C₄	—	2	2	no	—
712	C₂²×C₄	C₂×C₅×D₄	1	2	yes	—
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	2	yes	—
717	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
718	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
719	C₂²×C₄	C₂⁴×C₅	1	1	yes	characteristic
720	Q₁₆	—	2	8	no	—
721	SD₁₆	—	2	8	no	—
722	SD₁₆	—	2	8	no	—
723	SD₁₆	—	2	8	no	—
724	M₁₆	—	2	4	no	—
725	C₂×C₈	—	2	4	no	—
726	C₂×C₈	C₂⁴×C₅	1	2	yes	—
727	C₂×C₈	C₂⁴×C₅	1	4	yes	—
728	C₂×C₈	C₂⁴×C₅	1	2	yes	—
729	C₄⋊C₄	—	2	1	no	—
730	C₄⋊C₄	—	2	4	no	—
731	C₄⋊C₄	—	2	4	no	—
732	C₄⋊C₄	—	2	4	no	—
733	C₄⋊C₄	—	2	4	no	—
734	C₄⋊C₄	—	2	2	no	—
735	C₄⋊C₄	—	2	1	no	—
736	C₄⋊C₄	—	2	1	no	—
737	C₄⋊C₄	—	2	1	no	—
738	C₄⋊C₄	—	2	2	no	—
739	C₄⋊C₄	—	2	2	no	—
740	C₄⋊C₄	—	2	2	no	—
741	C₄⋊C₄	—	2	1	no	—
742	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
743	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
744	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
745	C₄⋊C₄	C₂×C₅×D₄	1	1	yes	characteristic
746	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
747	C₄⋊C₄	C₂×C₅×D₄	1	2	yes	—
748	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
749	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
750	C₄⋊C₄	C₂⁴×C₅	1	2	yes	—
751	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
752	C₄⋊C₄	C₂⁴×C₅	1	1	yes	characteristic
753	C₂²⋊C₄	—	2	1	no	—
754	C₂²⋊C₄	—	2	2	no	—
755	C₂²⋊C₄	—	2	2	no	—
756	C₂²⋊C₄	—	2	1	no	—
757	C₂²⋊C₄	—	2	1	no	—
758	C₂²⋊C₄	—	2	2	no	—
759	C₂²⋊C₄	—	2	2	no	—
760	C₂²⋊C₄	—	2	2	no	—
761	C₂²⋊C₄	—	2	2	no	—
762	C₂²⋊C₄	—	2	2	no	—
763	C₂²⋊C₄	—	2	2	no	—
764	C₂²⋊C₄	—	2	1	no	—
765	C₂²⋊C₄	—	2	2	no	—
766	C₂²⋊C₄	—	2	1	no	—
767	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
768	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
769	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
770	C₂²⋊C₄	C₂×C₅×D₄	1	2	yes	—
771	C₄²	—	2	4	no	—
772	C₄²	—	2	4	no	—
773	C₄²	—	2	4	no	—
774	C₄²	—	2	4	no	—
775	C₄²	—	2	2	no	—
776	C₄²	—	2	2	no	—
777	C₄²	—	2	2	no	—
778	C₄²	—	2	1	no	—
779	C₄²	C₂×C₅×D₄	1	2	yes	—
780	C₄²	C₂×C₅×D₄	1	2	yes	—
781	C₄²	C₂⁴×C₅	1	2	yes	—
782	C₄²	C₂⁴×C₅	1	2	yes	—
783	C₂×C₅	—	2	2	no	—
784	C₂×C₅	—	2	2	no	—
785	C₂×C₅	—	4	1	no	—
786	C₂×C₅	—	8	1	no	—
787	C₂×C₅	—	8	2	no	—
788	C₂×C₅	C₂×#525	1	1	yes	characteristic
789	C₂×C₅	C₂×#577	1	1	yes	characteristic
790	C₂×C₅	#3586	1	1	yes	characteristic
791	C₂³	—	2	2	no	—
792	C₂³	—	2	2	no	—
793	C₂³	—	2	2	no	—
794	C₂³	—	2	1	no	—
795	C₂³	—	4	1	no	—
796	C₂³	—	4	2	no	—
797	C₂³	—	8	1	no	—
798	C₂³	—	8	1	no	—
799	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
800	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
801	C₂³	C₂²×C₅×D₄	1	1	yes	characteristic
802	Q₈	—	2	8	no	—
803	Q₈	—	2	8	no	—
804	Q₈	—	2	8	no	—
805	Q₈	—	2	4	no	—
806	Q₈	—	2	2	no	—
807	Q₈	—	8	2	no	—
808	Q₈	C₂×C₅×#41	1	8	yes	—
809	D₄	—	2	4	no	—
810	D₄	—	2	2	no	—
811	D₄	—	4	2	no	—
812	D₄	—	4	4	no	—
813	D₄	—	4	2	no	—
814	D₄	—	4	2	no	—
815	D₄	—	8	2	no	—
816	D₄	—	8	2	no	—
817	D₄	—	8	2	no	—
818	D₄	—	8	1	no	—
819	C₂×C₄	—	2	8	no	—
820	C₂×C₄	—	2	8	no	—
821	C₂×C₄	—	2	8	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	4	no	—
824	C₂×C₄	—	2	4	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	1	no	—
832	C₂×C₄	—	2	1	no	—
833	C₂×C₄	—	2	1	no	—
834	C₂×C₄	—	2	2	no	—
835	C₂×C₄	—	4	2	no	—
836	C₂×C₄	—	4	2	no	—
837	C₂×C₄	—	4	2	no	—
838	C₂×C₄	—	4	2	no	—
839	C₂×C₄	—	8	2	no	—
840	C₂×C₄	—	8	2	no	—
841	C₂×C₄	—	8	2	no	—
842	C₂×C₄	—	8	1	no	—
843	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
844	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
845	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
846	C₂×C₄	C₂²×C₅×D₄	1	2	yes	—
847	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
848	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
849	C₂×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
850	C₂×C₄	C₂×C₅×#41	1	4	yes	—
851	C₂×C₄	C₂⁵×C₅	1	1	yes	characteristic
852	C₈	—	2	2	no	—
853	C₈	—	2	2	no	—
854	C₈	—	2	4	no	—
855	C₅	#60582	1	1	yes	characteristic, direct product factor, Sylow
856	C₂²	—	2	1	no	—
857	C₂²	—	2	1	no	—
858	C₂²	—	2	1	no	—
859	C₂²	—	2	1	no	—
860	C₂²	—	2	1	no	—
861	C₂²	—	2	1	no	—
862	C₂²	—	2	1	no	—
863	C₂²	—	4	4	no	—
864	C₂²	—	4	1	no	—
865	C₂²	—	4	2	no	—
866	C₂²	—	4	1	no	—
867	C₂²	—	4	2	no	—
868	C₂²	—	4	2	no	—
869	C₂²	—	4	1	no	—
870	C₂²	—	16	2	no	—
871	C₂²	C₅×#525	1	2	yes	—
872	C₂²	C₅×#577	1	2	yes	—
873	C₂²	C₂³×C₅×D₄	1	1	yes	characteristic
874	C₄	—	2	8	no	—
875	C₄	—	2	1	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	2	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	2	no	—
880	C₄	—	2	2	no	—
881	C₄	—	4	1	no	—
882	C₄	—	4	2	no	—
883	C₄	—	4	2	no	—
884	C₄	—	4	1	no	—
885	C₄	—	4	2	no	—
886	C₄	—	4	1	no	—
887	C₄	C₅×#525	1	2	yes	—
888	C₄	C₂²×C₅×#41	1	2	yes	—
889	C₂	—	2	2	no	—
890	C₂	—	2	2	no	—
891	C₂	—	4	1	no	—
892	C₂	—	8	2	no	—
893	C₂	—	8	1	no	—
894	C₂	C₂×C₅×#525	1	1	yes	characteristic
895	C₂	C₂×C₅×#577	1	1	yes	characteristic
896	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×#3494	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
2. C₂×C₅×#519	C₂	semidirect
3. C₅×#3126	C₂	semidirect
4. C₅×#3121	C₂	semidirect
5. C₅×#3117	C₂	semidirect
6. C₅×#3112	C₂	semidirect
7. C₅×#3108	C₂	semidirect
8. C₅×#3103	C₂	semidirect
9. C₅×#3094	C₂	semidirect
10. C₅×#3091	C₂	semidirect
11. C₅×#3082	C₂	semidirect
12. C₅×#3043	C₂	semidirect
13. C₅×#3004	C₂	semidirect
14. C₂×C₅×#448	C₂	semidirect
15. C₅×#2949	C₂	semidirect
16. C₅×#2947	C₂	semidirect
17. C₅×#2924	C₂	semidirect
41. C₅×#519	C₂²	semidirect
45. C₂×C₄×C₅×Q₈	C₂²	semidirect
46. C₂×C₄×C₅×Q₈	C₂²	semidirect
50. C₅×#485	C₂²	semidirect
51. C₅×#484	C₂²	semidirect
52. C₅×#483	C₂²	semidirect
54. C₅×#482	C₂²	semidirect
56. C₅×#481	C₂²	semidirect
58. C₅×#480	C₂²	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×#460	C₂²	semidirect
66. C₅×#460	C₂²	semidirect
67. C₅×#451	C₂²	semidirect
68. C₅×#451	C₂²	semidirect
72. C₅×#448	C₂²	semidirect
73. C₅×#448	C₂²	semidirect
74. C₅×#441	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×SD₁₆	C₂²	semidirect
81. C₄×C₅×SD₁₆	C₂²	semidirect
82. C₅×#433	C₂²	semidirect
83. C₅×#432	C₂²	semidirect
84. C₅×#431	C₂²	semidirect
95. #60582	C₅	direct (N × H)
233. C₂×#519	C₂×C₅	semidirect
234. #3126	C₂×C₅	semidirect
235. #3121	C₂×C₅	semidirect
236. #3117	C₂×C₅	semidirect
237. #3112	C₂×C₅	semidirect
238. #3108	C₂×C₅	semidirect
239. #3103	C₂×C₅	semidirect
240. #3094	C₂×C₅	semidirect
241. #3091	C₂×C₅	semidirect
242. #3082	C₂×C₅	semidirect
243. #3043	C₂×C₅	semidirect
244. #3004	C₂×C₅	semidirect
245. C₂×#448	C₂×C₅	semidirect
246. #2949	C₂×C₅	semidirect
247. #2947	C₂×C₅	semidirect
248. #2924	C₂×C₅	semidirect
263. C₂×C₅×Q₈	#41	semidirect
384. #519	C₂²×C₅	semidirect
388. C₂×C₄×Q₈	C₂²×C₅	semidirect
389. C₂×C₄×Q₈	C₂²×C₅	semidirect
393. #485	C₂²×C₅	semidirect
394. #484	C₂²×C₅	semidirect
395. #483	C₂²×C₅	semidirect
397. #482	C₂²×C₅	semidirect
399. #481	C₂²×C₅	semidirect
401. #480	C₂²×C₅	semidirect
402. #479	C₂²×C₅	semidirect
403. #479	C₂²×C₅	semidirect
404. #477	C₂²×C₅	semidirect
405. #475	C₂²×C₅	semidirect
406. #464	C₂²×C₅	semidirect
407. #464	C₂²×C₅	semidirect
408. #460	C₂²×C₅	semidirect
409. #460	C₂²×C₅	semidirect
410. #451	C₂²×C₅	semidirect
411. #451	C₂²×C₅	semidirect
415. #448	C₂²×C₅	semidirect
416. #448	C₂²×C₅	semidirect
417. #441	C₂²×C₅	semidirect
418. #440	C₂²×C₅	semidirect
419. #440	C₂²×C₅	semidirect
420. #440	C₂²×C₅	semidirect
421. C₄×Q₁₆	C₂²×C₅	semidirect
422. C₄×SD₁₆	C₂²×C₅	semidirect
423. C₄×SD₁₆	C₂²×C₅	semidirect
424. C₄×SD₁₆	C₂²×C₅	semidirect
425. #433	C₂²×C₅	semidirect
426. #432	C₂²×C₅	semidirect
427. #431	C₂²×C₅	semidirect
685. C₂×Q₈	C₅×#41	semidirect
855. C₅	#60582	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×#519	2
C₅×#3126	2
C₅×#3121	2
C₅×#3117	2
C₅×#3112	2
C₅×#3108	2
C₅×#3103	2
C₅×#3094	2
C₅×#3091	2
C₅×#3082	2
C₅×#3043	2
C₅×#3004	2
C₂×C₅×#448	2
C₅×#2949	2
C₅×#2947	2
C₅×#2924	2
#60582	5

Subgroups — C5×#60582 #11983302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#60582 #11983302