Subgroups — C₅×#85825 #14484777

Order 1920.

2224 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₅×#41	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5832	C₂	1	2	yes	maximal, complemented
3	C₅×#5585	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5568	C₂	1	2	yes	maximal, complemented
5	C₅×#5567	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#5565	C₂	1	2	yes	maximal, complemented
7	C₅×#5559	C₂	1	2	yes	maximal, complemented
8	C₅×#5553	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5552	C₂	1	2	yes	maximal, complemented
10	C₅×#5542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5540	C₂	1	4	yes	maximal, complemented
12	C₅×#5528	C₂	1	4	yes	maximal, complemented
13	C₅×#5522	C₂	1	2	yes	maximal, complemented
14	C₅×#5479	C₂	1	2	yes	maximal, complemented
15	C₅×#5477	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₅×#235	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×C₅×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3480	—	3	1	no	maximal, Hall
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂×C₅×#235	C₂²	1	2	yes	—
21	C₂×C₅×#235	C₂²	1	2	yes	—
22	C₂²×C₅×Dic₆	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
26	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×#117	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
33	C₅×#947	C₂²	1	2	yes	—
34	C₅×#944	C₂²	1	2	yes	—
35	C₅×#940	C₂²	1	2	yes	—
36	C₅×#939	C₂²	1	4	yes	—
37	C₅×#939	C₂²	1	4	yes	—
38	C₅×#936	C₂²	1	2	yes	—
39	C₅×#930	C₂²	1	2	yes	—
40	C₅×#930	C₂²	1	2	yes	—
41	C₅×#930	C₂²	1	2	yes	—
42	C₅×#929	C₂²	1	4	yes	—
43	C₄×C₅×#67	C₂²	1	4	yes	—
44	C₄×C₅×#67	C₂²	1	4	yes	—
45	C₄×C₅×#67	C₂²	1	4	yes	—
46	C₅×#926	C₂²	1	2	yes	—
47	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
48	C₅×#924	C₂²	1	2	yes	—
49	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
50	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
51	C₅×#898	C₂²	1	4	yes	—
52	C₅×#896	C₂²	1	4	yes	—
53	C₅×#894	C₂²	1	4	yes	—
54	C₅×#893	C₂²	1	2	yes	—
55	C₅×#893	C₂²	1	2	yes	—
56	C₅×#889	C₂²	1	4	yes	—
57	C₅×#887	C₂²	1	2	yes	—
58	C₅×#887	C₂²	1	2	yes	—
59	C₅×#885	C₂²	1	4	yes	—
60	C₅×#884	C₂²	1	4	yes	—
61	C₅×#883	C₂²	1	4	yes	—
62	C₅×#67⋊C₄	C₂²	1	4	yes	—
63	C₅×#67⋊C₄	C₂²	1	4	yes	—
64	C₅×#879	C₂²	1	4	yes	—
65	C₅×#876	C₂²	1	4	yes	—
66	C₅×#875	C₂²	1	2	yes	—
67	C₅×#875	C₂²	1	2	yes	—
68	C₅×#874	C₂²	1	1	yes	characteristic
69	C₄×C₅×D₁₂	C₂²	1	2	yes	—
70	C₄×C₅×D₁₂	C₂²	1	2	yes	—
71	C₄×C₅×D₁₂	C₂²	1	2	yes	—
72	C₅×#872	C₂²	1	4	yes	—
73	C₅×#872	C₂²	1	4	yes	—
74	C₄²×C₅×D₃	C₂²	1	4	yes	—
75	C₅×#870	C₂²	1	2	yes	—
76	C₅×#869	C₂²	1	1	yes	characteristic
77	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
78	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
79	C₄×C₅×Dic₆	C₂²	1	2	yes	—
80	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
81	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
82	C₄×C₅×Dic₆	C₂²	1	2	yes	—
83	C₄×C₅×Dic₆	C₂²	1	2	yes	—
84	#85825	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#559	—	3	1	no	—
86	C₅×#559	—	3	2	no	—
87	C₅×#557	—	3	1	no	—
88	C₅×#556	—	3	2	no	—
89	C₅×#556	—	3	1	no	—
90	C₅×#553	—	3	4	no	—
91	C₅×#553	—	3	2	no	—
92	C₅×#550	—	3	1	no	—
93	C₅×#548	—	3	2	no	—
94	C₅×#532	—	3	2	no	—
95	C₅×#532	—	3	1	no	—
96	C₅×#529	—	3	4	no	—
97	C₅×#529	—	3	2	no	—
98	C₄×C₅×#41	—	3	2	no	—
99	C₄×C₅×#41	—	3	2	no	—
100	C₄×C₅×#41	D₃	1	1	yes	characteristic, complemented
101	C₂×C₄×C₅×Q₈	—	3	1	no	—
102	C₃×C₅×#41	—	2	4	no	—
103	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
106	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
107	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
108	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
109	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
110	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
111	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
112	C₂×C₅×#67	C₂³	1	4	yes	—
113	C₂×C₅×#67	C₂³	1	4	yes	—
114	C₂×C₅×#67	C₂³	1	4	yes	—
115	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
116	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
117	C₅×#235	—	2	8	no	—
118	C₅×#235	—	2	8	no	—
119	C₂×C₅×D₁₂	C₂³	1	2	yes	—
120	C₂×C₅×D₁₂	C₂³	1	2	yes	—
121	C₂×C₅×D₁₂	C₂³	1	2	yes	—
122	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
123	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
124	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
125	C₂×C₅×Dic₆	—	2	4	no	—
126	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
127	C₂×C₅×Dic₆	C₂³	1	2	yes	—
128	C₂×C₅×Dic₆	C₂³	1	2	yes	—
129	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
130	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
132	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
133	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
134	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
135	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
136	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
137	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
138	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
139	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
140	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
141	C₃×C₄²×C₅	C₂³	1	2	yes	—
142	C₃×C₄²×C₅	C₂³	1	2	yes	—
143	C₃×C₄²×C₅	C₂³	1	2	yes	—
144	C₅×#217	C₂³	1	4	yes	—
145	C₅×#217	C₂³	1	4	yes	—
146	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
149	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
150	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
151	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
152	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
153	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
155	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
156	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
157	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
158	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
159	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
160	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
161	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
162	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
163	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
164	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
165	C₄×C₅×Dic₃	C₂³	1	2	yes	—
166	C₄×C₅×Dic₃	C₂³	1	2	yes	—
167	C₄×C₅×Dic₃	C₂³	1	2	yes	—
168	C₄×C₅×Dic₃	C₂³	1	2	yes	—
169	C₄×C₅×Dic₃	C₂³	1	4	yes	—
170	C₄×C₅×Dic₃	C₂³	1	4	yes	—
171	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
172	#5832	C₂×C₅	1	2	yes	complemented
173	#5585	C₂×C₅	1	1	yes	characteristic, complemented
174	#5568	C₂×C₅	1	2	yes	complemented
175	#5567	C₂×C₅	1	1	yes	characteristic, complemented
176	#5565	C₂×C₅	1	2	yes	complemented
177	#5559	C₂×C₅	1	2	yes	complemented
178	#5553	C₂×C₅	1	1	yes	characteristic, complemented
179	#5552	C₂×C₅	1	2	yes	complemented
180	#5542	C₂×C₅	1	1	yes	characteristic, complemented
181	#5540	C₂×C₅	1	4	yes	complemented
182	#5528	C₂×C₅	1	4	yes	complemented
183	#5522	C₂×C₅	1	2	yes	complemented
184	#5479	C₂×C₅	1	2	yes	complemented
185	#5477	C₂×C₅	1	1	yes	characteristic, complemented
186	C₄×#235	C₂×C₅	1	2	yes	complemented
187	C₂×C₄×Dic₆	C₂×C₅	1	1	yes	characteristic, complemented
188	C₂×C₅×#41	—	3	2	no	—
189	C₂×C₅×#41	—	3	2	no	—
190	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
191	C₂²×C₅×Q₈	—	3	1	no	—
192	C₅×C₄⋊Q₈	—	3	2	no	—
193	C₅×C₄⋊Q₈	—	3	1	no	—
194	C₅×#127	—	3	2	no	—
195	C₅×#127	—	3	1	no	—
196	C₅×#126	—	3	4	no	—
197	C₅×#126	—	3	4	no	—
198	C₅×#126	—	3	4	no	—
199	C₅×#125	—	3	4	no	—
200	C₅×#125	—	3	2	no	—
201	C₅×#124	—	3	2	no	—
202	C₅×#124	—	3	2	no	—
203	C₅×#124	—	3	4	no	—
204	C₅×#124	—	3	2	no	—
205	C₅×#124	—	3	2	no	—
206	C₅×#123	—	3	4	no	—
207	C₅×#123	—	3	4	no	—
208	C₅×#123	—	3	4	no	—
209	C₅×C₂²⋊Q₈	—	3	2	no	—
210	C₅×C₂²⋊Q₈	—	3	4	no	—
211	C₅×#121	—	3	4	no	—
212	C₅×#121	—	3	4	no	—
213	C₅×#121	—	3	2	no	—
214	C₅×#121	—	3	2	no	—
215	C₅×#121	—	3	2	no	—
216	C₅×#121	—	3	4	no	—
217	C₄×C₅×Q₈	—	3	2	no	—
218	C₄×C₅×Q₈	—	3	2	no	—
219	C₄×C₅×Q₈	—	3	1	no	—
220	C₄×C₅×Q₈	—	3	2	no	—
221	C₄×C₅×Q₈	—	3	1	no	—
222	C₄×C₅×Q₈	—	3	1	no	—
223	C₄×C₅×Q₈	—	3	1	no	—
224	C₄×C₅×Q₈	—	3	2	no	—
225	C₄×C₅×Q₈	—	3	2	no	—
226	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
227	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
228	C₄×C₅×D₄	—	3	4	no	—
229	C₄×C₅×D₄	—	3	4	no	—
230	C₄×C₅×D₄	—	3	4	no	—
231	C₄×C₅×D₄	—	3	2	no	—
232	C₄×C₅×D₄	—	3	2	no	—
233	C₄×C₅×D₄	—	3	4	no	—
234	C₄×C₅×D₄	—	3	4	no	—
235	C₄×C₅×D₄	—	3	2	no	—
236	C₄×C₅×D₄	—	3	2	no	—
237	C₄×C₅×D₄	—	3	2	no	—
238	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
239	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
240	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
241	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
242	C₅×#117	—	3	2	no	—
243	C₅×#117	—	3	4	no	—
244	C₅×#117	—	3	4	no	—
245	C₅×#117	C₂×D₃	1	1	yes	characteristic
246	C₅×#117	C₂×D₃	1	2	yes	—
247	C₂×C₅×C₄⋊C₄	—	3	2	no	—
248	C₂×C₅×C₄⋊C₄	—	3	1	no	—
249	C₂×C₄²×C₅	—	3	2	no	—
250	C₂×C₄²×C₅	—	3	4	no	—
251	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
252	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
253	#3480	—	3	1	no	Sylow
254	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
255	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
256	C₂²×C₅×D₃	C₂⁴	1	4	yes	—
257	C₃×C₅×Q₈	—	2	2	no	—
258	C₃×C₅×D₄	—	2	4	no	—
259	C₃×C₅×D₄	—	2	2	no	—
260	C₂×C₃×C₄×C₅	—	2	2	no	—
261	C₂×C₃×C₄×C₅	—	2	4	no	—
262	C₂×C₃×C₄×C₅	—	2	4	no	—
263	C₂×C₃×C₄×C₅	—	4	2	no	—
264	C₂×C₃×C₄×C₅	—	4	1	no	—
265	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
266	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
267	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
268	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
269	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
270	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
271	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
272	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
273	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₅×#67	—	2	8	no	—
276	C₅×#67	—	2	8	no	—
277	C₅×#67	—	4	4	no	—
278	C₂×C₅×Dic₃	—	2	4	no	—
279	C₂×C₅×Dic₃	—	4	2	no	—
280	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
281	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
282	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
283	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
284	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
285	C₅×D₁₂	—	2	4	no	—
286	C₅×D₁₂	—	2	4	no	—
287	C₅×D₁₂	—	4	2	no	—
288	C₄×C₅×D₃	—	2	8	no	—
289	C₄×C₅×D₃	—	2	8	no	—
290	C₄×C₅×D₃	—	4	4	no	—
291	C₅×Dic₆	—	2	2	no	—
292	C₅×Dic₆	—	2	4	no	—
293	C₅×Dic₆	—	2	4	no	—
294	C₅×Dic₆	#41	1	4	yes	complemented
295	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
296	C₂×#235	C₂²×C₅	1	2	yes	—
297	C₂×#235	C₂²×C₅	1	2	yes	—
298	C₂²×Dic₆	C₂²×C₅	1	1	yes	characteristic
299	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
300	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
301	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
302	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
303	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
304	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
305	C₃×#117	C₂²×C₅	1	1	yes	characteristic
306	C₃×#117	C₂²×C₅	1	2	yes	—
307	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
309	#947	C₂²×C₅	1	2	yes	—
310	#944	C₂²×C₅	1	2	yes	—
311	#940	C₂²×C₅	1	2	yes	—
312	#939	C₂²×C₅	1	4	yes	—
313	#939	C₂²×C₅	1	4	yes	—
314	#936	C₂²×C₅	1	2	yes	—
315	#930	C₂²×C₅	1	2	yes	—
316	#930	C₂²×C₅	1	2	yes	—
317	#930	C₂²×C₅	1	2	yes	—
318	#929	C₂²×C₅	1	4	yes	—
319	C₄×#67	C₂²×C₅	1	4	yes	—
320	C₄×#67	C₂²×C₅	1	4	yes	—
321	C₄×#67	C₂²×C₅	1	4	yes	—
322	#926	C₂²×C₅	1	2	yes	—
323	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
324	#924	C₂²×C₅	1	2	yes	—
325	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
326	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
327	#898	C₂²×C₅	1	4	yes	—
328	#896	C₂²×C₅	1	4	yes	—
329	#894	C₂²×C₅	1	4	yes	—
330	#893	C₂²×C₅	1	2	yes	—
331	#893	C₂²×C₅	1	2	yes	—
332	#889	C₂²×C₅	1	4	yes	—
333	#887	C₂²×C₅	1	2	yes	—
334	#887	C₂²×C₅	1	2	yes	—
335	#885	C₂²×C₅	1	4	yes	—
336	#884	C₂²×C₅	1	4	yes	—
337	#883	C₂²×C₅	1	4	yes	—
338	#67⋊C₄	C₂²×C₅	1	4	yes	—
339	#67⋊C₄	C₂²×C₅	1	4	yes	—
340	#879	C₂²×C₅	1	4	yes	—
341	#876	C₂²×C₅	1	4	yes	—
342	#875	C₂²×C₅	1	2	yes	—
343	#875	C₂²×C₅	1	2	yes	—
344	#874	C₂²×C₅	1	1	yes	characteristic
345	C₄×D₁₂	C₂²×C₅	1	2	yes	—
346	C₄×D₁₂	C₂²×C₅	1	2	yes	—
347	C₄×D₁₂	C₂²×C₅	1	2	yes	—
348	#872	C₂²×C₅	1	4	yes	—
349	#872	C₂²×C₅	1	4	yes	—
350	C₄²×D₃	C₂²×C₅	1	4	yes	—
351	#870	C₂²×C₅	1	2	yes	—
352	#869	C₂²×C₅	1	1	yes	characteristic
353	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
354	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
355	C₄×Dic₆	C₂²×C₅	1	2	yes	—
356	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
357	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
358	C₄×Dic₆	C₂²×C₅	1	2	yes	—
359	C₄×Dic₆	C₂²×C₅	1	2	yes	—
360	C₅×#41	—	2	4	no	—
361	C₅×#41	—	6	8	no	—
362	C₅×#41	—	6	8	no	—
363	C₂×C₅×Q₈	—	3	1	no	—
364	C₂×C₅×Q₈	—	3	2	no	—
365	C₂×C₅×Q₈	—	3	1	no	—
366	C₂×C₅×Q₈	—	3	2	no	—
367	C₂×C₅×Q₈	—	6	4	no	—
368	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
369	C₂×C₅×D₄	—	3	4	no	—
370	C₂×C₅×D₄	—	3	4	no	—
371	C₂×C₅×D₄	—	3	4	no	—
372	C₂×C₅×D₄	—	3	2	no	—
373	C₂×C₅×D₄	—	3	2	no	—
374	C₂×C₅×D₄	—	3	2	no	—
375	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
376	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
377	C₂²×C₄×C₅	—	3	2	no	—
378	C₂²×C₄×C₅	—	3	2	no	—
379	C₂²×C₄×C₅	—	3	4	no	—
380	C₂²×C₄×C₅	—	3	4	no	—
381	C₂²×C₄×C₅	—	3	4	no	—
382	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
383	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
384	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
385	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
386	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
387	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
388	C₅×C₄⋊C₄	—	3	2	no	—
389	C₅×C₄⋊C₄	—	3	1	no	—
390	C₅×C₄⋊C₄	—	3	2	no	—
391	C₅×C₄⋊C₄	—	3	1	no	—
392	C₅×C₄⋊C₄	—	3	2	no	—
393	C₅×C₄⋊C₄	—	3	2	no	—
394	C₅×C₄⋊C₄	—	3	2	no	—
395	C₅×C₄⋊C₄	—	3	4	no	—
396	C₅×C₄⋊C₄	—	3	2	no	—
397	C₅×C₄⋊C₄	—	3	4	no	—
398	C₅×C₄⋊C₄	—	3	4	no	—
399	C₅×C₄⋊C₄	—	3	4	no	—
400	C₅×C₄⋊C₄	—	3	2	no	—
401	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
402	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
403	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
404	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
405	C₅×C₂²⋊C₄	—	3	4	no	—
406	C₅×C₂²⋊C₄	—	3	4	no	—
407	C₅×C₂²⋊C₄	—	3	4	no	—
408	C₅×C₂²⋊C₄	—	3	4	no	—
409	C₅×C₂²⋊C₄	—	3	4	no	—
410	C₅×C₂²⋊C₄	—	3	4	no	—
411	C₅×C₂²⋊C₄	—	3	4	no	—
412	C₅×C₂²⋊C₄	—	3	4	no	—
413	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
414	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
415	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
416	C₄²×C₅	—	3	4	no	—
417	C₄²×C₅	—	3	4	no	—
418	C₄²×C₅	—	3	2	no	—
419	C₄²×C₅	—	3	2	no	—
420	C₄²×C₅	—	3	2	no	—
421	C₄²×C₅	—	3	2	no	—
422	C₄²×C₅	C₂²×D₃	1	2	yes	—
423	C₄²×C₅	C₂²×D₃	1	2	yes	—
424	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
425	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
426	C₄²×C₅	C₂²×D₃	1	2	yes	—
427	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
428	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
429	#559	—	3	1	no	—
430	#559	—	3	2	no	—
431	#557	—	3	1	no	—
432	#556	—	3	2	no	—
433	#556	—	3	1	no	—
434	#553	—	3	4	no	—
435	#553	—	3	2	no	—
436	#550	—	3	1	no	—
437	#548	—	3	2	no	—
438	#532	—	3	2	no	—
439	#532	—	3	1	no	—
440	#529	—	3	4	no	—
441	#529	—	3	2	no	—
442	C₄×#41	—	3	2	no	—
443	C₄×#41	—	3	2	no	—
444	C₄×#41	C₅×D₃	1	1	yes	characteristic, complemented
445	C₂×C₄×Q₈	—	3	1	no	—
446	C₂²×C₃×C₅	—	2	1	no	—
447	C₂²×C₃×C₅	—	2	1	no	—
448	C₂²×C₃×C₅	—	2	2	no	—
449	C₂²×C₃×C₅	—	2	2	no	—
450	C₂²×C₃×C₅	—	2	2	no	—
451	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
452	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
453	C₂×C₅×D₃	—	2	4	no	—
454	C₂×C₅×D₃	—	2	4	no	—
455	C₂×C₅×D₃	—	2	4	no	—
456	C₃×C₄×C₅	—	2	1	no	—
457	C₃×C₄×C₅	—	2	2	no	—
458	C₃×C₄×C₅	—	2	2	no	—
459	C₃×C₄×C₅	—	2	2	no	—
460	C₃×C₄×C₅	—	2	1	no	—
461	C₃×C₄×C₅	—	2	1	no	—
462	C₃×C₄×C₅	C₂×#41	1	2	yes	—
463	C₃×C₄×C₅	C₂×#41	1	2	yes	—
464	C₃×C₄×C₅	C₂×#41	1	2	yes	—
465	C₅×Dic₃	—	2	2	no	—
466	C₅×Dic₃	—	2	4	no	—
467	C₅×Dic₃	—	2	2	no	—
468	C₅×Dic₃	—	2	2	no	—
469	C₅×Dic₃	C₂×#41	1	4	yes	—
470	C₃×#41	—	2	4	no	—
471	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
472	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
473	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
474	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
475	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
476	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
477	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
478	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
479	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
480	C₂×#67	C₂³×C₅	1	4	yes	—
481	C₂×#67	C₂³×C₅	1	4	yes	—
482	C₂×#67	C₂³×C₅	1	4	yes	—
483	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
484	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
485	#235	—	2	8	no	—
486	#235	—	2	8	no	—
487	C₂×D₁₂	C₂³×C₅	1	2	yes	—
488	C₂×D₁₂	C₂³×C₅	1	2	yes	—
489	C₂×D₁₂	C₂³×C₅	1	2	yes	—
490	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
491	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
492	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
493	C₂×Dic₆	—	2	4	no	—
494	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
495	C₂×Dic₆	C₂³×C₅	1	2	yes	—
496	C₂×Dic₆	C₂³×C₅	1	2	yes	—
497	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
498	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
499	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
500	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
501	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
502	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
503	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
504	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
505	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
506	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
507	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
508	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
509	C₃×C₄²	C₂³×C₅	1	2	yes	—
510	C₃×C₄²	C₂³×C₅	1	2	yes	—
511	C₃×C₄²	C₂³×C₅	1	2	yes	—
512	#217	C₂³×C₅	1	4	yes	—
513	#217	C₂³×C₅	1	4	yes	—
514	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
515	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
516	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
517	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
518	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
519	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
520	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
521	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
522	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
523	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
524	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
525	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
526	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
527	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
528	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
529	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
530	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
531	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
532	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
533	C₄×Dic₃	C₂³×C₅	1	2	yes	—
534	C₄×Dic₃	C₂³×C₅	1	2	yes	—
535	C₄×Dic₃	C₂³×C₅	1	2	yes	—
536	C₄×Dic₃	C₂³×C₅	1	2	yes	—
537	C₄×Dic₃	C₂³×C₅	1	4	yes	—
538	C₄×Dic₃	C₂³×C₅	1	4	yes	—
539	C₂³×C₅	—	3	4	no	—
540	C₂³×C₅	C₂³×D₃	1	2	yes	—
541	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
542	C₅×Q₈	—	2	2	no	—
543	C₅×Q₈	—	3	4	no	—
544	C₅×Q₈	—	6	4	no	—
545	C₅×Q₈	—	6	4	no	—
546	C₅×Q₈	—	6	2	no	—
547	C₅×D₄	—	2	4	no	—
548	C₅×D₄	—	2	2	no	—
549	C₅×D₄	—	6	8	no	—
550	C₅×D₄	—	6	8	no	—
551	C₅×D₄	—	6	4	no	—
552	C₅×D₄	—	6	4	no	—
553	C₅×D₄	—	12	2	no	—
554	C₅×D₄	—	12	4	no	—
555	C₂×C₄×C₅	—	2	4	no	—
556	C₂×C₄×C₅	—	2	2	no	—
557	C₂×C₄×C₅	—	2	4	no	—
558	C₂×C₄×C₅	—	3	2	no	—
559	C₂×C₄×C₅	—	3	2	no	—
560	C₂×C₄×C₅	—	3	2	no	—
561	C₂×C₄×C₅	—	3	4	no	—
562	C₂×C₄×C₅	—	3	2	no	—
563	C₂×C₄×C₅	—	4	2	no	—
564	C₂×C₄×C₅	—	4	1	no	—
565	C₂×C₄×C₅	—	6	8	no	—
566	C₂×C₄×C₅	—	6	4	no	—
567	C₂×C₄×C₅	—	6	8	no	—
568	C₂×C₄×C₅	—	12	4	no	—
569	C₂×C₄×C₅	—	12	2	no	—
570	C₂×C₄×C₅	#235	1	4	yes	complemented
571	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
572	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
573	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
574	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
575	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
576	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
577	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
578	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
579	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
580	C₂×#41	—	3	2	no	—
581	C₂×#41	—	3	2	no	—
582	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
583	C₂²×Q₈	—	3	1	no	—
584	C₄⋊Q₈	—	3	2	no	—
585	C₄⋊Q₈	—	3	1	no	—
586	#127	—	3	2	no	—
587	#127	—	3	1	no	—
588	#126	—	3	4	no	—
589	#126	—	3	4	no	—
590	#126	—	3	4	no	—
591	#125	—	3	4	no	—
592	#125	—	3	2	no	—
593	#124	—	3	2	no	—
594	#124	—	3	2	no	—
595	#124	—	3	4	no	—
596	#124	—	3	2	no	—
597	#124	—	3	2	no	—
598	#123	—	3	4	no	—
599	#123	—	3	4	no	—
600	#123	—	3	4	no	—
601	C₂²⋊Q₈	—	3	2	no	—
602	C₂²⋊Q₈	—	3	4	no	—
603	#121	—	3	4	no	—
604	#121	—	3	4	no	—
605	#121	—	3	2	no	—
606	#121	—	3	2	no	—
607	#121	—	3	2	no	—
608	#121	—	3	4	no	—
609	C₄×Q₈	—	3	2	no	—
610	C₄×Q₈	—	3	2	no	—
611	C₄×Q₈	—	3	1	no	—
612	C₄×Q₈	—	3	2	no	—
613	C₄×Q₈	—	3	1	no	—
614	C₄×Q₈	—	3	1	no	—
615	C₄×Q₈	—	3	1	no	—
616	C₄×Q₈	—	3	2	no	—
617	C₄×Q₈	—	3	2	no	—
618	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
619	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
620	C₄×D₄	—	3	4	no	—
621	C₄×D₄	—	3	4	no	—
622	C₄×D₄	—	3	4	no	—
623	C₄×D₄	—	3	2	no	—
624	C₄×D₄	—	3	2	no	—
625	C₄×D₄	—	3	4	no	—
626	C₄×D₄	—	3	4	no	—
627	C₄×D₄	—	3	2	no	—
628	C₄×D₄	—	3	2	no	—
629	C₄×D₄	—	3	2	no	—
630	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
631	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
632	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
633	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
634	#117	—	3	2	no	—
635	#117	—	3	4	no	—
636	#117	—	3	4	no	—
637	#117	C₂×C₅×D₃	1	1	yes	characteristic
638	#117	C₂×C₅×D₃	1	2	yes	—
639	C₂×C₄⋊C₄	—	3	2	no	—
640	C₂×C₄⋊C₄	—	3	1	no	—
641	C₂×C₄²	—	3	2	no	—
642	C₂×C₄²	—	3	4	no	—
643	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
644	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
645	C₂×C₃×C₅	—	2	2	no	—
646	C₂×C₃×C₅	—	4	2	no	—
647	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
648	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
649	C₂×C₃×C₅	#585	1	1	yes	characteristic
650	C₅×D₃	—	4	4	no	—
651	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
652	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
653	C₂²×D₃	C₂⁴×C₅	1	4	yes	—
654	C₃×Q₈	—	2	2	no	—
655	C₃×D₄	—	2	4	no	—
656	C₃×D₄	—	2	2	no	—
657	C₂×C₃×C₄	—	2	2	no	—
658	C₂×C₃×C₄	—	2	4	no	—
659	C₂×C₃×C₄	—	2	4	no	—
660	C₂×C₃×C₄	—	4	2	no	—
661	C₂×C₃×C₄	—	4	1	no	—
662	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
663	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
664	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
665	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
666	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
667	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
668	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
669	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
670	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
671	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
672	#67	—	2	8	no	—
673	#67	—	2	8	no	—
674	#67	—	4	4	no	—
675	C₂×Dic₃	—	2	4	no	—
676	C₂×Dic₃	—	4	2	no	—
677	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
678	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
679	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
680	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
681	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
682	D₁₂	—	2	4	no	—
683	D₁₂	—	2	4	no	—
684	D₁₂	—	4	2	no	—
685	C₄×D₃	—	2	8	no	—
686	C₄×D₃	—	2	8	no	—
687	C₄×D₃	—	4	4	no	—
688	Dic₆	—	2	2	no	—
689	Dic₆	—	2	4	no	—
690	Dic₆	—	2	4	no	—
691	Dic₆	C₅×#41	1	4	yes	complemented
692	C₂²×C₅	—	2	1	no	—
693	C₂²×C₅	—	2	1	no	—
694	C₂²×C₅	—	2	2	no	—
695	C₂²×C₅	—	2	2	no	—
696	C₂²×C₅	—	2	2	no	—
697	C₂²×C₅	—	6	4	no	—
698	C₂²×C₅	—	6	4	no	—
699	C₂²×C₅	—	6	4	no	—
700	C₂²×C₅	C₂×#235	1	2	yes	—
701	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
702	C₄×C₅	—	2	2	no	—
703	C₄×C₅	—	2	2	no	—
704	C₄×C₅	—	2	1	no	—
705	C₄×C₅	—	2	1	no	—
706	C₄×C₅	—	2	2	no	—
707	C₄×C₅	—	2	1	no	—
708	C₄×C₅	—	3	4	no	—
709	C₄×C₅	—	6	4	no	—
710	C₄×C₅	—	6	2	no	—
711	C₄×C₅	—	6	2	no	—
712	C₄×C₅	—	6	2	no	—
713	C₄×C₅	C₂×#235	1	2	yes	—
714	C₄×C₅	C₂×#235	1	2	yes	—
715	C₄×C₅	D₃×#41	1	2	yes	—
716	#41	—	2	4	no	—
717	#41	—	6	8	no	—
718	#41	—	6	8	no	—
719	C₂×Q₈	—	3	1	no	—
720	C₂×Q₈	—	3	2	no	—
721	C₂×Q₈	—	3	1	no	—
722	C₂×Q₈	—	3	2	no	—
723	C₂×Q₈	—	6	4	no	—
724	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
725	C₂×D₄	—	3	4	no	—
726	C₂×D₄	—	3	4	no	—
727	C₂×D₄	—	3	4	no	—
728	C₂×D₄	—	3	2	no	—
729	C₂×D₄	—	3	2	no	—
730	C₂×D₄	—	3	2	no	—
731	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
732	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
733	C₂²×C₄	—	3	2	no	—
734	C₂²×C₄	—	3	2	no	—
735	C₂²×C₄	—	3	4	no	—
736	C₂²×C₄	—	3	4	no	—
737	C₂²×C₄	—	3	4	no	—
738	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
739	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
740	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
741	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
742	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
743	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
744	C₄⋊C₄	—	3	2	no	—
745	C₄⋊C₄	—	3	1	no	—
746	C₄⋊C₄	—	3	2	no	—
747	C₄⋊C₄	—	3	1	no	—
748	C₄⋊C₄	—	3	2	no	—
749	C₄⋊C₄	—	3	2	no	—
750	C₄⋊C₄	—	3	2	no	—
751	C₄⋊C₄	—	3	4	no	—
752	C₄⋊C₄	—	3	2	no	—
753	C₄⋊C₄	—	3	4	no	—
754	C₄⋊C₄	—	3	4	no	—
755	C₄⋊C₄	—	3	4	no	—
756	C₄⋊C₄	—	3	2	no	—
757	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
758	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
759	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
760	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
761	C₂²⋊C₄	—	3	4	no	—
762	C₂²⋊C₄	—	3	4	no	—
763	C₂²⋊C₄	—	3	4	no	—
764	C₂²⋊C₄	—	3	4	no	—
765	C₂²⋊C₄	—	3	4	no	—
766	C₂²⋊C₄	—	3	4	no	—
767	C₂²⋊C₄	—	3	4	no	—
768	C₂²⋊C₄	—	3	4	no	—
769	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
770	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
771	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
772	C₄²	—	3	2	no	—
773	C₄²	—	3	2	no	—
774	C₄²	—	3	4	no	—
775	C₄²	—	3	4	no	—
776	C₄²	—	3	2	no	—
777	C₄²	—	3	2	no	—
778	C₄²	C₂²×C₅×D₃	1	2	yes	—
779	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
780	C₄²	C₂²×C₅×D₃	1	2	yes	—
781	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
782	C₄²	C₂²×C₅×D₃	1	2	yes	—
783	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
784	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
785	C₃×C₅	#3480	1	1	yes	characteristic, complemented, Hall
786	C₂²×C₃	—	2	1	no	—
787	C₂²×C₃	—	2	1	no	—
788	C₂²×C₃	—	2	2	no	—
789	C₂²×C₃	—	2	2	no	—
790	C₂²×C₃	—	2	2	no	—
791	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
792	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
793	C₂×D₃	—	2	4	no	—
794	C₂×D₃	—	2	4	no	—
795	C₂×D₃	—	2	4	no	—
796	C₃×C₄	—	2	1	no	—
797	C₃×C₄	—	2	2	no	—
798	C₃×C₄	—	2	2	no	—
799	C₃×C₄	—	2	2	no	—
800	C₃×C₄	—	2	1	no	—
801	C₃×C₄	—	2	1	no	—
802	C₃×C₄	C₂×C₅×#41	1	2	yes	—
803	C₃×C₄	C₂×C₅×#41	1	2	yes	—
804	C₃×C₄	C₂×C₅×#41	1	2	yes	—
805	Dic₃	—	2	2	no	—
806	Dic₃	—	2	4	no	—
807	Dic₃	—	2	2	no	—
808	Dic₃	—	2	2	no	—
809	Dic₃	C₂×C₅×#41	1	4	yes	—
810	C₂×C₅	—	2	2	no	—
811	C₂×C₅	—	4	2	no	—
812	C₂×C₅	—	12	4	no	—
813	C₂×C₅	C₂²×#235	1	1	yes	characteristic
814	C₂×C₅	C₂×D₃×#41	1	1	yes	characteristic
815	C₂×C₅	#5964	1	1	yes	characteristic
816	C₂³	—	3	4	no	—
817	C₂³	C₂³×C₅×D₃	1	2	yes	—
818	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
819	Q₈	—	2	2	no	—
820	Q₈	—	3	4	no	—
821	Q₈	—	6	4	no	—
822	Q₈	—	6	4	no	—
823	Q₈	—	6	2	no	—
824	D₄	—	2	4	no	—
825	D₄	—	2	2	no	—
826	D₄	—	6	8	no	—
827	D₄	—	6	8	no	—
828	D₄	—	6	4	no	—
829	D₄	—	6	4	no	—
830	D₄	—	12	2	no	—
831	D₄	—	12	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	2	4	no	—
835	C₂×C₄	—	3	2	no	—
836	C₂×C₄	—	3	2	no	—
837	C₂×C₄	—	3	2	no	—
838	C₂×C₄	—	3	4	no	—
839	C₂×C₄	—	3	2	no	—
840	C₂×C₄	—	4	2	no	—
841	C₂×C₄	—	4	1	no	—
842	C₂×C₄	—	6	8	no	—
843	C₂×C₄	—	6	4	no	—
844	C₂×C₄	—	6	8	no	—
845	C₂×C₄	—	12	4	no	—
846	C₂×C₄	—	12	2	no	—
847	C₂×C₄	C₅×#235	1	4	yes	complemented
848	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
849	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
850	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
851	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
852	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
853	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
854	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
855	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
856	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
857	C₂×C₃	—	2	2	no	—
858	C₂×C₃	—	4	2	no	—
859	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
860	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
861	C₂×C₃	C₅×#585	1	1	yes	characteristic
862	D₃	—	4	4	no	—
863	C₅	#85825	1	1	yes	characteristic, direct product factor, Sylow
864	C₂²	—	2	1	no	—
865	C₂²	—	2	1	no	—
866	C₂²	—	2	2	no	—
867	C₂²	—	2	2	no	—
868	C₂²	—	2	2	no	—
869	C₂²	—	6	4	no	—
870	C₂²	—	6	4	no	—
871	C₂²	—	6	4	no	—
872	C₂²	C₂×C₅×#235	1	2	yes	—
873	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
874	C₄	—	2	2	no	—
875	C₄	—	2	2	no	—
876	C₄	—	2	1	no	—
877	C₄	—	2	1	no	—
878	C₄	—	2	2	no	—
879	C₄	—	2	1	no	—
880	C₄	—	3	4	no	—
881	C₄	—	6	4	no	—
882	C₄	—	6	2	no	—
883	C₄	—	6	2	no	—
884	C₄	—	6	2	no	—
885	C₄	C₂×C₅×#235	1	2	yes	—
886	C₄	C₂×C₅×#235	1	2	yes	—
887	C₄	C₅×D₃×#41	1	2	yes	—
888	C₃	C₅×#3480	1	1	yes	characteristic, complemented, Sylow
889	C₂	—	2	2	no	—
890	C₂	—	4	2	no	—
891	C₂	—	12	4	no	—
892	C₂	C₂²×C₅×#235	1	1	yes	characteristic
893	C₂	C₂×C₅×D₃×#41	1	1	yes	characteristic
894	C₂	C₅×#5964	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator, cosocle	C₂²×C₃	C₂⁵×C₅
Frattini	C₂²	C₂⁴×C₅×D₃
Fitting	C₃×C₄×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₄×C₅×#41	D₃
hypocenter	C₃	C₅×#3480
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₄×C₅×#41

Complements

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

N	H ≅ G/N	type
1. C₃×C₄×C₅×#41	C₂	semidirect
2. C₅×#5832	C₂	semidirect
3. C₅×#5585	C₂	semidirect
4. C₅×#5568	C₂	semidirect
5. C₅×#5567	C₂	semidirect
6. C₅×#5565	C₂	semidirect
7. C₅×#5559	C₂	semidirect
8. C₅×#5553	C₂	semidirect
9. C₅×#5552	C₂	semidirect
10. C₅×#5542	C₂	semidirect
11. C₅×#5540	C₂	semidirect
12. C₅×#5528	C₂	semidirect
13. C₅×#5522	C₂	semidirect
14. C₅×#5479	C₂	semidirect
15. C₅×#5477	C₂	semidirect
16. C₄×C₅×#235	C₂	semidirect
17. C₂×C₄×C₅×Dic₆	C₂	semidirect
84. #85825	C₅	direct (N × H)
100. C₄×C₅×#41	D₃	semidirect
171. C₃×C₄×#41	C₂×C₅	semidirect
172. #5832	C₂×C₅	semidirect
173. #5585	C₂×C₅	semidirect
174. #5568	C₂×C₅	semidirect
175. #5567	C₂×C₅	semidirect
176. #5565	C₂×C₅	semidirect
177. #5559	C₂×C₅	semidirect
178. #5553	C₂×C₅	semidirect
179. #5552	C₂×C₅	semidirect
180. #5542	C₂×C₅	semidirect
181. #5540	C₂×C₅	semidirect
182. #5528	C₂×C₅	semidirect
183. #5522	C₂×C₅	semidirect
184. #5479	C₂×C₅	semidirect
185. #5477	C₂×C₅	semidirect
186. C₄×#235	C₂×C₅	semidirect
187. C₂×C₄×Dic₆	C₂×C₅	semidirect
265. C₂×C₃×C₄×C₅	#41	semidirect
294. C₅×Dic₆	#41	semidirect
444. C₄×#41	C₅×D₃	semidirect
570. C₂×C₄×C₅	#235	semidirect
662. C₂×C₃×C₄	C₅×#41	semidirect
691. Dic₆	C₅×#41	semidirect
785. C₃×C₅	#3480	semidirect
847. C₂×C₄	C₅×#235	semidirect
863. C₅	#85825	direct (N × H)
888. C₃	C₅×#3480	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₅×#41	2
C₅×#5832	2
C₅×#5585	2
C₅×#5568	2
C₅×#5567	2
C₅×#5565	2
C₅×#5559	2
C₅×#5553	2
C₅×#5552	2
C₅×#5542	2
C₅×#5540	2
C₅×#5528	2
C₅×#5522	2
C₅×#5479	2
C₅×#5477	2
C₄×C₅×#235	2
C₂×C₄×C₅×Dic₆	2
C₅×#3480	3
#85825	5

Subgroups — C5×#85825 #14484777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#85825 #14484777