Subgroups — C₅×#85837 #14481502

Order 1920.

2080 conjugacy classes of subgroups.

The subgroup lattice has 812 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	1	yes	maximal, characteristic, complemented
3	C₅×#5828	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5583	C₂	1	2	yes	maximal, complemented
5	C₅×#5582	C₂	1	2	yes	maximal, complemented
6	C₅×#5564	C₂	1	4	yes	maximal, complemented
7	C₅×#5562	C₂	1	2	yes	maximal, complemented
8	C₅×#5561	C₂	1	2	yes	maximal, complemented
9	C₅×#5560	C₂	1	4	yes	maximal, complemented
10	C₅×#5528	C₂	1	4	yes	maximal, complemented
11	C₅×#5524	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#5517	C₂	1	1	yes	maximal, characteristic, complemented
13	C₅×#5479	C₂	1	4	yes	maximal, complemented
14	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3455	—	3	1	no	maximal, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂×C₅×#235	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
21	C₃×C₄×C₅×D₄	C₂²	1	4	yes	—
22	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
23	C₃×C₅×#117	C₂²	1	1	yes	characteristic
24	C₃×C₅×#117	C₂²	1	2	yes	complemented
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
27	C₅×#947	C₂²	1	1	yes	characteristic, complemented
28	C₅×#946	C₂²	1	2	yes	—
29	C₅×#944	C₂²	1	1	yes	characteristic, complemented
30	C₅×#940	C₂²	1	1	yes	characteristic, complemented
31	C₅×#939	C₂²	1	4	yes	—
32	C₅×#938	C₂²	1	2	yes	—
33	C₅×#937	C₂²	1	2	yes	—
34	C₅×#936	C₂²	1	1	yes	characteristic, complemented
35	C₅×#935	C₂²	1	2	yes	—
36	C₅×#930	C₂²	1	4	yes	—
37	C₅×#929	C₂²	1	4	yes	—
38	C₅×#929	C₂²	1	4	yes	complemented
39	C₄×C₅×#67	C₂²	1	4	yes	—
40	C₄×C₅×#67	C₂²	1	4	yes	—
41	C₄×C₅×#67	C₂²	1	4	yes	complemented
42	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
43	C₅×#926	C₂²	1	1	yes	characteristic
44	C₅×#924	C₂²	1	4	yes	complemented
45	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
46	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
47	C₅×#898	C₂²	1	4	yes	—
48	C₅×#897	C₂²	1	2	yes	—
49	C₅×#896	C₂²	1	4	yes	complemented
50	C₅×#895	C₂²	1	2	yes	—
51	C₅×#894	C₂²	1	4	yes	—
52	C₅×#890	C₂²	1	2	yes	complemented
53	C₅×#889	C₂²	1	4	yes	complemented
54	C₅×#888	C₂²	1	2	yes	complemented
55	C₅×#886	C₂²	1	2	yes	—
56	C₅×#885	C₂²	1	4	yes	—
57	C₅×#884	C₂²	1	4	yes	—
58	C₅×#883	C₂²	1	4	yes	complemented
59	C₅×#882	C₂²	1	2	yes	—
60	C₅×#879	C₂²	1	4	yes	complemented
61	C₅×#878	C₂²	1	4	yes	—
62	C₅×#876	C₂²	1	4	yes	—
63	C₅×#876	C₂²	1	4	yes	complemented
64	C₅×#875	C₂²	1	4	yes	—
65	C₄×C₅×D₁₂	C₂²	1	4	yes	—
66	C₄×C₅×D₁₂	C₂²	1	2	yes	complemented
67	C₅×#872	C₂²	1	2	yes	—
68	C₅×#872	C₂²	1	2	yes	—
69	C₅×#872	C₂²	1	2	yes	—
70	C₅×#872	C₂²	1	2	yes	—
71	C₅×#872	C₂²	1	2	yes	complemented
72	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
73	C₅×#870	C₂²	1	4	yes	complemented
74	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
75	C₄×C₅×Dic₆	C₂²	1	4	yes	complemented
76	#85837	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
77	C₅×#542	—	3	2	no	—
78	C₅×#542	—	3	2	no	—
79	C₅×#541	—	3	2	no	—
80	C₅×#540	—	3	2	no	—
81	C₅×#539	—	3	4	no	—
82	C₅×#538	—	3	4	no	—
83	C₅×#533	—	3	1	no	—
84	C₅×#532	—	3	1	no	—
85	C₅×#529	—	3	4	no	—
86	C₅×#529	—	3	4	no	—
87	C₅×#525	—	3	1	no	—
88	C₅×#525	—	3	1	no	—
89	C₄×C₅×#41	—	3	1	no	—
90	C₄×C₅×#41	D₃	1	1	yes	characteristic, complemented
91	C₂×C₅×#117	—	3	1	no	—
92	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
93	C₃×C₅×#41	—	2	4	no	—
94	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
96	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
97	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
98	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
99	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
100	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
101	C₂×C₅×#67	C₂³	1	2	yes	—
102	C₂×C₅×#67	C₂³	1	4	yes	—
103	C₂×C₅×#67	C₂³	1	4	yes	—
104	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
105	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
106	C₅×#235	—	2	4	no	—
107	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
108	C₂×C₅×D₁₂	C₂³	1	4	yes	—
109	C₂×C₄×C₅×D₃	—	2	4	no	—
110	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
111	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
112	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
113	C₂×C₄×C₅×D₃	C₂³	1	4	yes	—
114	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
115	C₂×C₅×Dic₆	C₂³	1	4	yes	—
116	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
117	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
118	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
119	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₃×C₄²×C₅	C₂³	1	2	yes	—
121	C₃×C₄²×C₅	C₂³	1	2	yes	—
122	C₃×C₄²×C₅	C₂³	1	4	yes	—
123	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₅×#217	C₂³	1	2	yes	—
126	C₅×#217	C₂³	1	4	yes	—
127	C₅×#217	C₂³	1	4	yes	—
128	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
129	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
130	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
131	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
132	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
133	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
134	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
135	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
136	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
137	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
138	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
139	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
140	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
141	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
142	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
143	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
144	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
145	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
146	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
147	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
148	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
149	C₄×C₅×Dic₃	C₂³	1	2	yes	—
150	C₄×C₅×Dic₃	C₂³	1	2	yes	—
151	C₄×C₅×Dic₃	C₂³	1	4	yes	—
152	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
153	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
154	C₃×C₄×#41	C₂×C₅	1	1	yes	characteristic, complemented
155	#5832	C₂×C₅	1	1	yes	characteristic, complemented
156	#5828	C₂×C₅	1	1	yes	characteristic, complemented
157	#5583	C₂×C₅	1	2	yes	complemented
158	#5582	C₂×C₅	1	2	yes	complemented
159	#5564	C₂×C₅	1	4	yes	complemented
160	#5562	C₂×C₅	1	2	yes	complemented
161	#5561	C₂×C₅	1	2	yes	complemented
162	#5560	C₂×C₅	1	4	yes	complemented
163	#5528	C₂×C₅	1	4	yes	complemented
164	#5524	C₂×C₅	1	1	yes	characteristic, complemented
165	#5517	C₂×C₅	1	1	yes	characteristic, complemented
166	#5479	C₂×C₅	1	4	yes	complemented
167	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
168	C₂×#872	C₂×C₅	1	1	yes	characteristic, complemented
169	C₂×C₅×#41	—	3	1	no	—
170	C₂×C₅×#41	C₂×D₃	1	1	yes	characteristic
171	C₂³×C₄×C₅	—	3	1	no	—
172	C₅×C₄⋊Q₈	—	3	1	no	—
173	C₅×C₄⋊Q₈	—	3	2	no	—
174	C₅×#127	—	3	1	no	—
175	C₅×#126	—	3	4	no	—
176	C₅×#126	—	3	4	no	—
177	C₅×#126	—	3	4	no	—
178	C₅×#126	—	3	4	no	—
179	C₅×#125	—	3	4	no	—
180	C₅×#125	—	3	2	no	—
181	C₅×#125	—	3	4	no	—
182	C₅×#124	—	3	1	no	—
183	C₅×#124	—	3	1	no	—
184	C₅×#124	—	3	4	no	—
185	C₅×#124	—	3	4	no	—
186	C₅×#123	—	3	2	no	—
187	C₅×#123	—	3	4	no	—
188	C₅×#123	—	3	4	no	—
189	C₅×#123	—	3	4	no	—
190	C₅×#123	—	3	4	no	—
191	C₅×#123	—	3	2	no	—
192	C₅×C₂²⋊Q₈	—	3	2	no	—
193	C₅×C₂²⋊Q₈	—	3	4	no	—
194	C₅×C₂²⋊Q₈	—	3	4	no	—
195	C₅×C₂²⋊Q₈	—	3	2	no	—
196	C₅×C₂²⋊Q₈	—	3	4	no	—
197	C₅×#121	—	3	2	no	—
198	C₅×#121	—	3	4	no	—
199	C₅×#121	—	3	4	no	—
200	C₅×#121	—	3	2	no	—
201	C₅×#121	—	3	4	no	—
202	C₅×#120	—	3	2	no	—
203	C₅×#120	—	3	2	no	—
204	C₄×C₅×Q₈	—	3	2	no	—
205	C₄×C₅×Q₈	—	3	4	no	—
206	C₄×C₅×Q₈	C₂×D₃	1	2	yes	complemented
207	C₄×C₅×D₄	—	3	4	no	—
208	C₄×C₅×D₄	—	3	4	no	—
209	C₄×C₅×D₄	—	3	4	no	—
210	C₄×C₅×D₄	—	3	4	no	—
211	C₄×C₅×D₄	—	3	2	no	—
212	C₄×C₅×D₄	C₂×D₃	1	4	yes	—
213	C₄×C₅×D₄	C₂×D₃	1	2	yes	complemented
214	C₅×#117	—	3	1	no	—
215	C₅×#117	—	3	2	no	—
216	C₅×#117	—	3	2	no	—
217	C₅×#117	—	3	2	no	—
218	C₅×#117	—	3	2	no	—
219	C₅×#117	—	3	2	no	—
220	C₅×#117	C₂×D₃	1	1	yes	characteristic
221	C₅×#117	C₂×D₃	1	2	yes	complemented
222	C₂×C₅×C₄⋊C₄	—	3	2	no	—
223	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
224	C₂×C₄²×C₅	—	3	1	no	—
225	C₂×C₄²×C₅	—	3	2	no	—
226	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
227	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
228	#3455	—	3	1	no	Sylow
229	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
230	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
231	C₂²×C₅×D₃	—	2	2	no	—
232	C₂²×C₅×D₃	—	4	2	no	—
233	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
234	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
235	C₃×C₅×Q₈	—	2	2	no	—
236	C₃×C₅×D₄	—	2	4	no	—
237	C₃×C₅×D₄	—	2	2	no	—
238	C₂×C₃×C₄×C₅	—	2	4	no	—
239	C₂×C₃×C₄×C₅	—	4	4	no	—
240	C₂×C₃×C₄×C₅	—	4	2	no	—
241	C₂×C₃×C₄×C₅	#41	1	4	yes	—
242	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
243	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
244	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
245	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
246	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
247	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
248	C₅×#67	—	2	4	no	—
249	C₅×#67	—	4	4	no	—
250	C₅×#67	—	4	4	no	—
251	C₂×C₅×Dic₃	—	2	2	no	—
252	C₂×C₅×Dic₃	—	4	2	no	—
253	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
254	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
255	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
256	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
257	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
258	C₅×D₁₂	—	2	2	no	—
259	C₅×D₁₂	—	4	4	no	—
260	C₄×C₅×D₃	—	2	4	no	—
261	C₄×C₅×D₃	—	2	4	no	—
262	C₄×C₅×D₃	—	2	4	no	—
263	C₄×C₅×D₃	—	4	4	no	—
264	C₅×Dic₆	—	2	2	no	—
265	C₅×Dic₆	—	4	4	no	—
266	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
267	C₂×#235	C₂²×C₅	1	1	yes	characteristic
268	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
269	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	complemented
270	C₃×C₄×D₄	C₂²×C₅	1	4	yes	—
271	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
272	C₃×#117	C₂²×C₅	1	1	yes	characteristic
273	C₃×#117	C₂²×C₅	1	2	yes	complemented
274	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
275	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
276	#947	C₂²×C₅	1	1	yes	characteristic, complemented
277	#946	C₂²×C₅	1	2	yes	—
278	#944	C₂²×C₅	1	1	yes	characteristic, complemented
279	#940	C₂²×C₅	1	1	yes	characteristic, complemented
280	#939	C₂²×C₅	1	4	yes	—
281	#938	C₂²×C₅	1	2	yes	—
282	#937	C₂²×C₅	1	2	yes	—
283	#936	C₂²×C₅	1	1	yes	characteristic, complemented
284	#935	C₂²×C₅	1	2	yes	—
285	#930	C₂²×C₅	1	4	yes	—
286	#929	C₂²×C₅	1	4	yes	—
287	#929	C₂²×C₅	1	4	yes	complemented
288	C₄×#67	C₂²×C₅	1	4	yes	—
289	C₄×#67	C₂²×C₅	1	4	yes	—
290	C₄×#67	C₂²×C₅	1	4	yes	complemented
291	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
292	#926	C₂²×C₅	1	1	yes	characteristic
293	#924	C₂²×C₅	1	4	yes	complemented
294	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
295	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
296	#898	C₂²×C₅	1	4	yes	—
297	#897	C₂²×C₅	1	2	yes	—
298	#896	C₂²×C₅	1	4	yes	complemented
299	#895	C₂²×C₅	1	2	yes	—
300	#894	C₂²×C₅	1	4	yes	—
301	#890	C₂²×C₅	1	2	yes	complemented
302	#889	C₂²×C₅	1	4	yes	complemented
303	#888	C₂²×C₅	1	2	yes	complemented
304	#886	C₂²×C₅	1	2	yes	—
305	#885	C₂²×C₅	1	4	yes	—
306	#884	C₂²×C₅	1	4	yes	—
307	#883	C₂²×C₅	1	4	yes	complemented
308	#882	C₂²×C₅	1	2	yes	—
309	#879	C₂²×C₅	1	4	yes	complemented
310	#878	C₂²×C₅	1	4	yes	—
311	#876	C₂²×C₅	1	4	yes	—
312	#876	C₂²×C₅	1	4	yes	complemented
313	#875	C₂²×C₅	1	4	yes	—
314	C₄×D₁₂	C₂²×C₅	1	4	yes	—
315	C₄×D₁₂	C₂²×C₅	1	2	yes	complemented
316	#872	C₂²×C₅	1	2	yes	—
317	#872	C₂²×C₅	1	2	yes	—
318	#872	C₂²×C₅	1	2	yes	—
319	#872	C₂²×C₅	1	2	yes	—
320	#872	C₂²×C₅	1	2	yes	complemented
321	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
322	#870	C₂²×C₅	1	4	yes	complemented
323	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
324	C₄×Dic₆	C₂²×C₅	1	4	yes	complemented
325	C₂⁴×C₅	—	3	1	no	—
326	C₅×#41	—	2	4	no	—
327	C₅×#41	—	6	4	no	—
328	C₂×C₅×Q₈	—	3	1	no	—
329	C₂×C₅×Q₈	—	3	4	no	—
330	C₂×C₅×Q₈	C₂²×D₃	1	1	yes	characteristic
331	C₂×C₅×D₄	—	3	2	no	—
332	C₂×C₅×D₄	—	3	4	no	—
333	C₂×C₅×D₄	—	3	4	no	—
334	C₂×C₅×D₄	—	3	1	no	—
335	C₂×C₅×D₄	—	3	4	no	—
336	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
337	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
338	C₂²×C₄×C₅	—	3	1	no	—
339	C₂²×C₄×C₅	—	3	2	no	—
340	C₂²×C₄×C₅	—	3	2	no	—
341	C₂²×C₄×C₅	—	3	2	no	—
342	C₂²×C₄×C₅	—	3	2	no	—
343	C₂²×C₄×C₅	—	3	4	no	—
344	C₂²×C₄×C₅	—	6	4	no	—
345	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
346	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
347	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
348	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
349	C₅×C₄⋊C₄	—	3	2	no	—
350	C₅×C₄⋊C₄	—	3	2	no	—
351	C₅×C₄⋊C₄	—	3	2	no	—
352	C₅×C₄⋊C₄	—	3	2	no	—
353	C₅×C₄⋊C₄	—	3	2	no	—
354	C₅×C₄⋊C₄	—	3	4	no	—
355	C₅×C₄⋊C₄	—	3	4	no	—
356	C₅×C₄⋊C₄	—	3	4	no	—
357	C₅×C₄⋊C₄	—	3	4	no	—
358	C₅×C₄⋊C₄	—	3	4	no	—
359	C₅×C₄⋊C₄	—	3	4	no	—
360	C₅×C₄⋊C₄	—	3	4	no	—
361	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
362	C₅×C₄⋊C₄	C₂²×D₃	1	4	yes	—
363	C₅×C₂²⋊C₄	—	3	2	no	—
364	C₅×C₂²⋊C₄	—	3	4	no	—
365	C₅×C₂²⋊C₄	—	3	4	no	—
366	C₅×C₂²⋊C₄	—	3	2	no	—
367	C₅×C₂²⋊C₄	—	3	2	no	—
368	C₅×C₂²⋊C₄	—	3	2	no	—
369	C₅×C₂²⋊C₄	—	3	2	no	—
370	C₅×C₂²⋊C₄	—	3	4	no	—
371	C₅×C₂²⋊C₄	—	3	4	no	—
372	C₅×C₂²⋊C₄	—	3	4	no	—
373	C₅×C₂²⋊C₄	—	3	4	no	—
374	C₅×C₂²⋊C₄	—	3	4	no	—
375	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
376	C₅×C₂²⋊C₄	C₂²×D₃	1	4	yes	—
377	C₄²×C₅	—	3	1	no	—
378	C₄²×C₅	—	3	1	no	—
379	C₄²×C₅	—	3	4	no	—
380	C₄²×C₅	—	3	2	no	—
381	C₄²×C₅	—	3	2	no	—
382	C₄²×C₅	C₂²×D₃	1	2	yes	—
383	C₄²×C₅	C₂²×D₃	1	4	yes	—
384	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
385	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
386	C₄²×C₅	C₂²×D₃	1	2	yes	—
387	#542	—	3	2	no	—
388	#542	—	3	2	no	—
389	#541	—	3	2	no	—
390	#540	—	3	2	no	—
391	#539	—	3	4	no	—
392	#538	—	3	4	no	—
393	#533	—	3	1	no	—
394	#532	—	3	1	no	—
395	#529	—	3	4	no	—
396	#529	—	3	4	no	—
397	#525	—	3	1	no	—
398	#525	—	3	1	no	—
399	C₄×#41	—	3	1	no	—
400	C₄×#41	C₅×D₃	1	1	yes	characteristic, complemented
401	C₂×#117	—	3	1	no	—
402	C₂²×C₃×C₅	—	2	2	no	—
403	C₂²×C₃×C₅	—	2	2	no	—
404	C₂²×C₃×C₅	—	2	4	no	—
405	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
406	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
407	C₂×C₅×D₃	—	2	2	no	—
408	C₂×C₅×D₃	—	2	2	no	—
409	C₂×C₅×D₃	—	2	4	no	—
410	C₂×C₅×D₃	—	2	2	no	—
411	C₂×C₅×D₃	—	2	2	no	—
412	C₂×C₅×D₃	—	4	4	no	—
413	C₃×C₄×C₅	—	2	2	no	—
414	C₃×C₄×C₅	—	2	4	no	—
415	C₃×C₄×C₅	—	2	2	no	—
416	C₃×C₄×C₅	—	2	2	no	—
417	C₃×C₄×C₅	C₂×#41	1	2	yes	—
418	C₃×C₄×C₅	C₂×#41	1	2	yes	—
419	C₅×Dic₃	—	2	2	no	—
420	C₅×Dic₃	—	2	2	no	—
421	C₅×Dic₃	—	2	2	no	—
422	C₅×Dic₃	—	2	4	no	—
423	C₅×Dic₃	—	2	2	no	—
424	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
425	C₃×#41	—	2	4	no	—
426	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
427	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
428	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
429	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
430	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
431	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
432	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
433	C₂×#67	C₂³×C₅	1	2	yes	—
434	C₂×#67	C₂³×C₅	1	4	yes	—
435	C₂×#67	C₂³×C₅	1	4	yes	—
436	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
437	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
438	#235	—	2	4	no	—
439	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
440	C₂×D₁₂	C₂³×C₅	1	4	yes	—
441	C₂×C₄×D₃	—	2	4	no	—
442	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
443	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
444	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
445	C₂×C₄×D₃	C₂³×C₅	1	4	yes	—
446	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
447	C₂×Dic₆	C₂³×C₅	1	4	yes	—
448	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
449	C₃×C₄⋊C₄	C₂³×C₅	1	4	yes	—
450	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
451	C₃×C₂²⋊C₄	C₂³×C₅	1	4	yes	—
452	C₃×C₄²	C₂³×C₅	1	2	yes	—
453	C₃×C₄²	C₂³×C₅	1	2	yes	—
454	C₃×C₄²	C₂³×C₅	1	4	yes	—
455	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
456	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
457	#217	C₂³×C₅	1	2	yes	—
458	#217	C₂³×C₅	1	4	yes	—
459	#217	C₂³×C₅	1	4	yes	—
460	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
461	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
462	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
463	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
464	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
465	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
466	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
467	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
468	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
469	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
470	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
471	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
472	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
473	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
474	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
475	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
476	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
477	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
478	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
479	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
480	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
481	C₄×Dic₃	C₂³×C₅	1	2	yes	—
482	C₄×Dic₃	C₂³×C₅	1	2	yes	—
483	C₄×Dic₃	C₂³×C₅	1	4	yes	—
484	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
485	C₄×Dic₃	C₂³×C₅	1	1	yes	characteristic
486	C₂³×C₅	—	3	2	no	—
487	C₂³×C₅	—	3	2	no	—
488	C₂³×C₅	—	6	2	no	—
489	C₂³×C₅	—	12	2	no	—
490	C₂³×C₅	C₂³×D₃	1	2	yes	—
491	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
492	C₅×Q₈	—	2	2	no	—
493	C₅×Q₈	—	6	2	no	—
494	C₅×Q₈	—	12	4	no	—
495	C₅×D₄	—	2	4	no	—
496	C₅×D₄	—	2	2	no	—
497	C₅×D₄	—	6	4	no	—
498	C₅×D₄	—	6	2	no	—
499	C₅×D₄	—	12	4	no	—
500	C₅×D₄	—	12	4	no	—
501	C₅×D₄	—	12	4	no	—
502	C₂×C₄×C₅	—	2	4	no	—
503	C₂×C₄×C₅	—	3	2	no	—
504	C₂×C₄×C₅	—	3	2	no	—
505	C₂×C₄×C₅	—	3	4	no	—
506	C₂×C₄×C₅	—	3	2	no	—
507	C₂×C₄×C₅	—	3	2	no	—
508	C₂×C₄×C₅	—	4	2	no	—
509	C₂×C₄×C₅	—	4	4	no	—
510	C₂×C₄×C₅	—	6	2	no	—
511	C₂×C₄×C₅	—	6	4	no	—
512	C₂×C₄×C₅	—	6	4	no	—
513	C₂×C₄×C₅	—	6	4	no	—
514	C₂×C₄×C₅	—	12	4	no	—
515	C₂×C₄×C₅	—	12	2	no	—
516	C₂×C₄×C₅	#235	1	4	yes	—
517	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
518	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
519	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
520	C₂×C₄×C₅	C₂³×D₃	1	4	yes	—
521	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
522	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
523	C₂×#41	—	3	1	no	—
524	C₂×#41	C₂×C₅×D₃	1	1	yes	characteristic
525	C₂³×C₄	—	3	1	no	—
526	C₄⋊Q₈	—	3	1	no	—
527	C₄⋊Q₈	—	3	2	no	—
528	#127	—	3	1	no	—
529	#126	—	3	4	no	—
530	#126	—	3	4	no	—
531	#126	—	3	4	no	—
532	#126	—	3	4	no	—
533	#125	—	3	4	no	—
534	#125	—	3	2	no	—
535	#125	—	3	4	no	—
536	#124	—	3	1	no	—
537	#124	—	3	1	no	—
538	#124	—	3	4	no	—
539	#124	—	3	4	no	—
540	#123	—	3	2	no	—
541	#123	—	3	4	no	—
542	#123	—	3	4	no	—
543	#123	—	3	4	no	—
544	#123	—	3	2	no	—
545	#123	—	3	4	no	—
546	C₂²⋊Q₈	—	3	2	no	—
547	C₂²⋊Q₈	—	3	4	no	—
548	C₂²⋊Q₈	—	3	2	no	—
549	C₂²⋊Q₈	—	3	4	no	—
550	C₂²⋊Q₈	—	3	4	no	—
551	#121	—	3	2	no	—
552	#121	—	3	4	no	—
553	#121	—	3	4	no	—
554	#121	—	3	2	no	—
555	#121	—	3	4	no	—
556	#120	—	3	2	no	—
557	#120	—	3	2	no	—
558	C₄×Q₈	—	3	2	no	—
559	C₄×Q₈	—	3	4	no	—
560	C₄×Q₈	C₂×C₅×D₃	1	2	yes	complemented
561	C₄×D₄	—	3	4	no	—
562	C₄×D₄	—	3	4	no	—
563	C₄×D₄	—	3	4	no	—
564	C₄×D₄	—	3	2	no	—
565	C₄×D₄	—	3	4	no	—
566	C₄×D₄	C₂×C₅×D₃	1	4	yes	—
567	C₄×D₄	C₂×C₅×D₃	1	2	yes	complemented
568	#117	—	3	1	no	—
569	#117	—	3	2	no	—
570	#117	—	3	2	no	—
571	#117	—	3	2	no	—
572	#117	—	3	2	no	—
573	#117	—	3	2	no	—
574	#117	C₂×C₅×D₃	1	1	yes	characteristic
575	#117	C₂×C₅×D₃	1	2	yes	complemented
576	C₂×C₄⋊C₄	—	3	2	no	—
577	C₂×C₂²⋊C₄	—	3	2	no	—
578	C₂×C₄²	—	3	1	no	—
579	C₂×C₄²	—	3	2	no	—
580	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
581	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
582	C₂×C₃×C₅	—	2	2	no	—
583	C₂×C₃×C₅	—	4	2	no	—
584	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
585	C₂×C₃×C₅	#585	1	2	yes	—
586	C₅×D₃	—	4	2	no	—
587	C₅×D₃	—	4	2	no	—
588	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
589	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
590	C₂²×D₃	—	2	2	no	—
591	C₂²×D₃	—	4	2	no	—
592	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
593	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
594	C₃×Q₈	—	2	2	no	—
595	C₃×D₄	—	2	4	no	—
596	C₃×D₄	—	2	2	no	—
597	C₂×C₃×C₄	—	2	4	no	—
598	C₂×C₃×C₄	—	4	4	no	—
599	C₂×C₃×C₄	—	4	2	no	—
600	C₂×C₃×C₄	C₅×#41	1	4	yes	—
601	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
602	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
603	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
604	C₂×C₃×C₄	C₂⁴×C₅	1	4	yes	—
605	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
606	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
607	#67	—	2	4	no	—
608	#67	—	4	4	no	—
609	#67	—	4	4	no	—
610	C₂×Dic₃	—	2	2	no	—
611	C₂×Dic₃	—	4	2	no	—
612	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
613	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
614	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
615	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
616	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
617	D₁₂	—	2	2	no	—
618	D₁₂	—	4	4	no	—
619	C₄×D₃	—	2	4	no	—
620	C₄×D₃	—	2	4	no	—
621	C₄×D₃	—	2	4	no	—
622	C₄×D₃	—	4	4	no	—
623	Dic₆	—	2	2	no	—
624	Dic₆	—	4	4	no	—
625	C₂²×C₅	—	2	2	no	—
626	C₂²×C₅	—	2	2	no	—
627	C₂²×C₅	—	2	4	no	—
628	C₂²×C₅	—	6	2	no	—
629	C₂²×C₅	—	6	2	no	—
630	C₂²×C₅	—	6	4	no	—
631	C₂²×C₅	—	6	2	no	—
632	C₂²×C₅	—	6	2	no	—
633	C₂²×C₅	—	12	4	no	—
634	C₂²×C₅	C₂×#235	1	2	yes	—
635	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
636	C₄×C₅	—	2	2	no	—
637	C₄×C₅	—	2	2	no	—
638	C₄×C₅	—	2	2	no	—
639	C₄×C₅	—	2	4	no	—
640	C₄×C₅	—	6	2	no	—
641	C₄×C₅	—	6	2	no	—
642	C₄×C₅	—	6	2	no	—
643	C₄×C₅	—	6	4	no	—
644	C₄×C₅	—	6	2	no	—
645	C₄×C₅	C₂×#235	1	2	yes	—
646	C₄×C₅	C₂×#235	1	2	yes	—
647	C₂⁴	—	3	1	no	—
648	#41	—	2	4	no	—
649	#41	—	6	4	no	—
650	C₂×Q₈	—	3	1	no	—
651	C₂×Q₈	—	3	4	no	—
652	C₂×Q₈	C₂²×C₅×D₃	1	1	yes	characteristic
653	C₂×D₄	—	3	2	no	—
654	C₂×D₄	—	3	4	no	—
655	C₂×D₄	—	3	4	no	—
656	C₂×D₄	—	3	1	no	—
657	C₂×D₄	—	3	4	no	—
658	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
659	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
660	C₂²×C₄	—	3	1	no	—
661	C₂²×C₄	—	3	2	no	—
662	C₂²×C₄	—	3	2	no	—
663	C₂²×C₄	—	3	2	no	—
664	C₂²×C₄	—	3	2	no	—
665	C₂²×C₄	—	3	4	no	—
666	C₂²×C₄	—	6	4	no	—
667	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
668	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
669	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
670	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
671	C₄⋊C₄	—	3	2	no	—
672	C₄⋊C₄	—	3	2	no	—
673	C₄⋊C₄	—	3	2	no	—
674	C₄⋊C₄	—	3	2	no	—
675	C₄⋊C₄	—	3	2	no	—
676	C₄⋊C₄	—	3	4	no	—
677	C₄⋊C₄	—	3	4	no	—
678	C₄⋊C₄	—	3	4	no	—
679	C₄⋊C₄	—	3	4	no	—
680	C₄⋊C₄	—	3	4	no	—
681	C₄⋊C₄	—	3	4	no	—
682	C₄⋊C₄	—	3	4	no	—
683	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
684	C₄⋊C₄	C₂²×C₅×D₃	1	4	yes	—
685	C₂²⋊C₄	—	3	2	no	—
686	C₂²⋊C₄	—	3	4	no	—
687	C₂²⋊C₄	—	3	4	no	—
688	C₂²⋊C₄	—	3	2	no	—
689	C₂²⋊C₄	—	3	2	no	—
690	C₂²⋊C₄	—	3	2	no	—
691	C₂²⋊C₄	—	3	2	no	—
692	C₂²⋊C₄	—	3	4	no	—
693	C₂²⋊C₄	—	3	4	no	—
694	C₂²⋊C₄	—	3	4	no	—
695	C₂²⋊C₄	—	3	4	no	—
696	C₂²⋊C₄	—	3	4	no	—
697	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
698	C₂²⋊C₄	C₂²×C₅×D₃	1	4	yes	—
699	C₄²	—	3	2	no	—
700	C₄²	—	3	2	no	—
701	C₄²	—	3	1	no	—
702	C₄²	—	3	1	no	—
703	C₄²	—	3	4	no	—
704	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
705	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
706	C₄²	C₂²×C₅×D₃	1	2	yes	—
707	C₄²	C₂²×C₅×D₃	1	2	yes	—
708	C₄²	C₂²×C₅×D₃	1	4	yes	—
709	C₃×C₅	#3455	1	1	yes	characteristic, complemented, Hall
710	C₂²×C₃	—	2	2	no	—
711	C₂²×C₃	—	2	2	no	—
712	C₂²×C₃	—	2	4	no	—
713	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
714	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
715	C₂×D₃	—	2	2	no	—
716	C₂×D₃	—	2	2	no	—
717	C₂×D₃	—	2	4	no	—
718	C₂×D₃	—	2	2	no	—
719	C₂×D₃	—	2	2	no	—
720	C₂×D₃	—	4	4	no	—
721	C₃×C₄	—	2	2	no	—
722	C₃×C₄	—	2	4	no	—
723	C₃×C₄	—	2	2	no	—
724	C₃×C₄	—	2	2	no	—
725	C₃×C₄	C₂×C₅×#41	1	2	yes	—
726	C₃×C₄	C₂×C₅×#41	1	2	yes	—
727	Dic₃	—	2	2	no	—
728	Dic₃	—	2	2	no	—
729	Dic₃	—	2	2	no	—
730	Dic₃	—	2	4	no	—
731	Dic₃	—	2	2	no	—
732	C₂×C₅	—	2	2	no	—
733	C₂×C₅	—	4	2	no	—
734	C₂×C₅	—	12	2	no	—
735	C₂×C₅	—	12	2	no	—
736	C₂×C₅	C₂²×#235	1	1	yes	characteristic
737	C₂×C₅	#5964	1	2	yes	—
738	C₂³	—	3	2	no	—
739	C₂³	—	3	2	no	—
740	C₂³	—	6	2	no	—
741	C₂³	—	12	2	no	—
742	C₂³	C₂³×C₅×D₃	1	2	yes	—
743	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
744	Q₈	—	2	2	no	—
745	Q₈	—	6	2	no	—
746	Q₈	—	12	4	no	—
747	D₄	—	2	4	no	—
748	D₄	—	2	2	no	—
749	D₄	—	6	4	no	—
750	D₄	—	6	2	no	—
751	D₄	—	12	4	no	—
752	D₄	—	12	4	no	—
753	D₄	—	12	4	no	—
754	C₂×C₄	—	2	4	no	—
755	C₂×C₄	—	3	2	no	—
756	C₂×C₄	—	3	2	no	—
757	C₂×C₄	—	3	4	no	—
758	C₂×C₄	—	3	2	no	—
759	C₂×C₄	—	3	2	no	—
760	C₂×C₄	—	4	2	no	—
761	C₂×C₄	—	4	4	no	—
762	C₂×C₄	—	6	2	no	—
763	C₂×C₄	—	6	4	no	—
764	C₂×C₄	—	6	4	no	—
765	C₂×C₄	—	6	4	no	—
766	C₂×C₄	—	12	4	no	—
767	C₂×C₄	—	12	2	no	—
768	C₂×C₄	C₅×#235	1	4	yes	—
769	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
770	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
771	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
772	C₂×C₄	C₂³×C₅×D₃	1	4	yes	—
773	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
774	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
775	C₂×C₃	—	2	2	no	—
776	C₂×C₃	—	4	2	no	—
777	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
778	C₂×C₃	C₅×#585	1	2	yes	—
779	D₃	—	4	2	no	—
780	D₃	—	4	2	no	—
781	C₅	#85837	1	1	yes	characteristic, direct product factor, Sylow
782	C₂²	—	2	2	no	—
783	C₂²	—	2	2	no	—
784	C₂²	—	2	4	no	—
785	C₂²	—	6	2	no	—
786	C₂²	—	6	2	no	—
787	C₂²	—	6	4	no	—
788	C₂²	—	6	2	no	—
789	C₂²	—	6	2	no	—
790	C₂²	—	12	4	no	—
791	C₂²	C₂×C₅×#235	1	2	yes	—
792	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
793	C₄	—	2	2	no	—
794	C₄	—	2	2	no	—
795	C₄	—	2	2	no	—
796	C₄	—	2	4	no	—
797	C₄	—	6	2	no	—
798	C₄	—	6	2	no	—
799	C₄	—	6	2	no	—
800	C₄	—	6	4	no	—
801	C₄	—	6	2	no	—
802	C₄	C₂×C₅×#235	1	2	yes	—
803	C₄	C₂×C₅×#235	1	2	yes	—
804	C₃	C₅×#3455	1	1	yes	characteristic, complemented, Sylow
805	C₂	—	2	2	no	—
806	C₂	—	4	2	no	—
807	C₂	—	12	2	no	—
808	C₂	—	12	2	no	—
809	C₂	C₂²×C₅×#235	1	1	yes	characteristic
810	C₂	C₅×#5964	1	2	yes	—

	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×#3455
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×#5828	C₂	semidirect
4. C₅×#5583	C₂	semidirect
5. C₅×#5582	C₂	semidirect
6. C₅×#5564	C₂	semidirect
7. C₅×#5562	C₂	semidirect
8. C₅×#5561	C₂	semidirect
9. C₅×#5560	C₂	semidirect
10. C₅×#5528	C₂	semidirect
11. C₅×#5524	C₂	semidirect
12. C₅×#5517	C₂	semidirect
13. C₅×#5479	C₂	semidirect
14. C₄×C₅×#235	C₂	semidirect
15. C₂×C₅×#872	C₂	semidirect
20. C₃×C₄×C₅×Q₈	C₂²	semidirect
22. C₃×C₄×C₅×D₄	C₂²	semidirect
24. C₃×C₅×#117	C₂²	semidirect
26. C₂×C₃×C₄²×C₅	C₂²	semidirect
27. C₅×#947	C₂²	semidirect
29. C₅×#944	C₂²	semidirect
30. C₅×#940	C₂²	semidirect
34. C₅×#936	C₂²	semidirect
38. C₅×#929	C₂²	semidirect
41. C₄×C₅×#67	C₂²	semidirect
44. C₅×#924	C₂²	semidirect
49. C₅×#896	C₂²	semidirect
52. C₅×#890	C₂²	semidirect
53. C₅×#889	C₂²	semidirect
54. C₅×#888	C₂²	semidirect
58. C₅×#883	C₂²	semidirect
60. C₅×#879	C₂²	semidirect
63. C₅×#876	C₂²	semidirect
66. C₄×C₅×D₁₂	C₂²	semidirect
71. C₅×#872	C₂²	semidirect
72. C₄²×C₅×D₃	C₂²	semidirect
73. C₅×#870	C₂²	semidirect
74. C₄×C₅×Dic₆	C₂²	semidirect
75. C₄×C₅×Dic₆	C₂²	semidirect
76. #85837	C₅	direct (N × H)
90. C₄×C₅×#41	D₃	semidirect
154. C₃×C₄×#41	C₂×C₅	semidirect
155. #5832	C₂×C₅	semidirect
156. #5828	C₂×C₅	semidirect
157. #5583	C₂×C₅	semidirect
158. #5582	C₂×C₅	semidirect
159. #5564	C₂×C₅	semidirect
160. #5562	C₂×C₅	semidirect
161. #5561	C₂×C₅	semidirect
162. #5560	C₂×C₅	semidirect
163. #5528	C₂×C₅	semidirect
164. #5524	C₂×C₅	semidirect
165. #5517	C₂×C₅	semidirect
166. #5479	C₂×C₅	semidirect
167. C₄×#235	C₂×C₅	semidirect
168. C₂×#872	C₂×C₅	semidirect
206. C₄×C₅×Q₈	C₂×D₃	semidirect
213. C₄×C₅×D₄	C₂×D₃	semidirect
221. C₅×#117	C₂×D₃	semidirect
227. C₂×C₄²×C₅	C₂×D₃	semidirect
269. C₃×C₄×Q₈	C₂²×C₅	semidirect
271. C₃×C₄×D₄	C₂²×C₅	semidirect
273. C₃×#117	C₂²×C₅	semidirect
275. C₂×C₃×C₄²	C₂²×C₅	semidirect
276. #947	C₂²×C₅	semidirect
278. #944	C₂²×C₅	semidirect
279. #940	C₂²×C₅	semidirect
283. #936	C₂²×C₅	semidirect
287. #929	C₂²×C₅	semidirect
290. C₄×#67	C₂²×C₅	semidirect
293. #924	C₂²×C₅	semidirect
298. #896	C₂²×C₅	semidirect
301. #890	C₂²×C₅	semidirect
302. #889	C₂²×C₅	semidirect
303. #888	C₂²×C₅	semidirect
307. #883	C₂²×C₅	semidirect
309. #879	C₂²×C₅	semidirect
312. #876	C₂²×C₅	semidirect
315. C₄×D₁₂	C₂²×C₅	semidirect
320. #872	C₂²×C₅	semidirect
321. C₄²×D₃	C₂²×C₅	semidirect
322. #870	C₂²×C₅	semidirect
323. C₄×Dic₆	C₂²×C₅	semidirect
324. C₄×Dic₆	C₂²×C₅	semidirect
400. C₄×#41	C₅×D₃	semidirect
560. C₄×Q₈	C₂×C₅×D₃	semidirect
567. C₄×D₄	C₂×C₅×D₃	semidirect
575. #117	C₂×C₅×D₃	semidirect
581. C₂×C₄²	C₂×C₅×D₃	semidirect
709. C₃×C₅	#3455	semidirect
781. C₅	#85837	direct (N × H)
804. C₃	C₅×#3455	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×#5828	2
C₅×#5583	2
C₅×#5582	2
C₅×#5564	2
C₅×#5562	2
C₅×#5561	2
C₅×#5560	2
C₅×#5528	2
C₅×#5524	2
C₅×#5517	2
C₅×#5479	2
C₄×C₅×#235	2
C₂×C₅×#872	2
C₅×#3455	3
#85837	5

Subgroups — C5×#85837 #14481502

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#85837 #14481502