Subgroups — C₅×#85764 #14484129

Order 1920.

2264 conjugacy classes of subgroups.

The subgroup lattice has 920 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5806	C₂	1	2	yes	maximal, complemented
3	C₅×#5791	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#926	C₂	1	2	yes	maximal, complemented
5	C₅×#5565	C₂	1	2	yes	maximal, complemented
6	C₅×#5563	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#5557	C₂	1	2	yes	maximal, complemented
8	C₅×#5555	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×#5543	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#5542	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#5541	C₂	1	2	yes	maximal, complemented
12	C₅×#5538	C₂	1	4	yes	maximal, complemented
13	C₄×C₅×#237	C₂	1	2	yes	maximal, complemented
14	C₅×#5513	C₂	1	2	yes	maximal, complemented
15	C₅×#5495	C₂	1	4	yes	maximal, complemented
16	C₄×C₅×#235	C₂	1	1	yes	maximal, characteristic, complemented
17	C₅×#5470	C₂	1	1	yes	maximal, characteristic, complemented
18	C₅×#3475	—	3	1	no	maximal, Hall
19	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
20	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
21	C₂×C₅×#237	C₂²	1	2	yes	—
22	C₂×C₅×#235	C₂²	1	1	yes	characteristic
23	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
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	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₅×#953	C₂²	1	4	yes	—
33	C₂×C₅×#217	C₂²	1	4	yes	—
34	C₅×#939	C₂²	1	4	yes	—
35	C₅×#938	C₂²	1	2	yes	—
36	C₅×#936	C₂²	1	2	yes	—
37	C₅×#935	C₂²	1	4	yes	—
38	C₅×D₄×Dic₃	C₂²	1	2	yes	—
39	C₅×#930	C₂²	1	2	yes	complemented
40	C₅×#930	C₂²	1	2	yes	complemented
41	C₅×#929	C₂²	1	4	yes	—
42	C₄×C₅×#67	C₂²	1	2	yes	—
43	C₄×C₅×#67	C₂²	1	2	yes	—
44	C₄×C₅×#67	C₂²	1	4	yes	complemented
45	C₄×C₅×#67	C₂²	1	4	yes	complemented
46	C₅×#926	C₂²	1	2	yes	—
47	C₅×#926	C₂²	1	1	yes	characteristic
48	C₅×#926	C₂²	1	4	yes	—
49	C₅×#926	C₂²	1	4	yes	complemented
50	C₅×#926	C₂²	1	2	yes	complemented
51	C₅×#926	C₂²	1	2	yes	complemented
52	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
53	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
54	C₅×#924	C₂²	1	2	yes	—
55	C₅×#924	C₂²	1	2	yes	—
56	C₅×#924	C₂²	1	2	yes	complemented
57	C₅×#924	C₂²	1	2	yes	complemented
58	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
59	C₅×#898	C₂²	1	4	yes	complemented
60	C₅×#897	C₂²	1	2	yes	complemented
61	C₅×#892	C₂²	1	2	yes	complemented
62	C₅×#890	C₂²	1	2	yes	complemented
63	C₅×#889	C₂²	1	4	yes	complemented
64	C₅×#887	C₂²	1	2	yes	complemented
65	C₅×#886	C₂²	1	4	yes	complemented
66	C₅×#885	C₂²	1	4	yes	complemented
67	C₅×#883	C₂²	1	4	yes	complemented
68	C₅×#67⋊C₄	C₂²	1	4	yes	complemented
69	C₅×#879	C₂²	1	4	yes	complemented
70	C₅×#879	C₂²	1	4	yes	complemented
71	C₅×#878	C₂²	1	4	yes	complemented
72	C₅×#877	C₂²	1	4	yes	complemented
73	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic, complemented
75	C₅×#872	C₂²	1	2	yes	complemented
76	C₄²×C₅×D₃	C₂²	1	2	yes	complemented
77	C₅×#870	C₂²	1	2	yes	complemented
78	C₅×#869	C₂²	1	1	yes	characteristic, complemented
79	C₅×#869	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
81	C₄×C₅×Dic₆	C₂²	1	2	yes	complemented
82	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic, complemented
84	#85764	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
85	C₅×#556	—	3	1	no	—
86	C₅×#555	—	3	1	no	—
87	C₅×#554	—	3	1	no	—
88	C₅×#553	—	3	2	no	—
89	C₅×#552	—	3	2	no	—
90	C₅×#552	—	3	2	no	—
91	C₅×#551	—	3	4	no	—
92	C₅×#547	—	3	1	no	—
93	C₅×#546	—	3	2	no	—
94	C₅×#533	—	3	1	no	—
95	C₅×#529	—	3	4	no	—
96	C₅×#529	—	3	2	no	—
97	C₅×#525	—	3	2	no	—
98	C₄×C₅×#41	—	3	2	no	—
99	C₄×C₅×#41	—	3	1	no	—
100	C₂×C₄×C₅×D₄	D₃	1	1	yes	characteristic, complemented
101	C₂×C₅×#117	—	3	2	no	—
102	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
103	C₂×C₃×C₅×D₄	—	2	4	no	—
104	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
105	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
106	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
107	C₂²×C₃×C₄×C₅	—	2	8	no	—
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	2	yes	—
112	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
113	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
114	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
115	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
116	C₂×C₅×#67	C₂³	1	4	yes	—
117	C₂×C₅×#67	C₂³	1	2	yes	—
118	C₂×C₅×#67	C₂³	1	4	yes	—
119	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
120	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
121	C₅×#237	—	2	8	no	—
122	C₅×#235	—	2	4	no	—
123	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
124	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
125	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
126	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
127	C₂×C₅×Dic₆	C₂³	1	1	yes	characteristic
128	C₂×C₅×Dic₆	C₂³	1	2	yes	—
129	C₂×C₅×Dic₆	C₂³	1	2	yes	—
130	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
131	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
132	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
133	C₃×C₅×C₂²⋊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	C₅×#217	C₂³	1	4	yes	—
142	C₅×#217	C₂³	1	4	yes	—
143	C₅×#217	C₂³	1	4	yes	—
144	C₅×#217	C₂³	1	4	yes	—
145	C₅×#217	C₂³	1	4	yes	—
146	C₅×#217	C₂³	1	2	yes	—
147	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
148	C₅×(C₂×D₃)⋊C₄	C₂³	1	2	yes	—
149	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
150	C₅×(C₂×D₃)⋊C₄	C₂³	1	4	yes	—
151	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
152	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
153	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
154	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
155	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
156	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
157	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
158	C₅×C₄⋊Dic₃	C₂³	1	4	yes	—
159	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
160	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
161	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
162	C₅×Dic₃⋊C₄	C₂³	1	2	yes	—
163	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
164	C₅×Dic₃⋊C₄	C₂³	1	4	yes	—
165	C₄×C₅×Dic₃	C₂³	1	4	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	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic, complemented
172	#5806	C₂×C₅	1	2	yes	complemented
173	#5791	C₂×C₅	1	2	yes	complemented
174	C₂×#926	C₂×C₅	1	2	yes	complemented
175	#5565	C₂×C₅	1	2	yes	complemented
176	#5563	C₂×C₅	1	1	yes	characteristic, complemented
177	#5557	C₂×C₅	1	2	yes	complemented
178	#5555	C₂×C₅	1	1	yes	characteristic, complemented
179	#5543	C₂×C₅	1	1	yes	characteristic, complemented
180	#5542	C₂×C₅	1	1	yes	characteristic, complemented
181	#5541	C₂×C₅	1	2	yes	complemented
182	#5538	C₂×C₅	1	4	yes	complemented
183	C₄×#237	C₂×C₅	1	2	yes	complemented
184	#5513	C₂×C₅	1	2	yes	complemented
185	#5495	C₂×C₅	1	4	yes	complemented
186	C₄×#235	C₂×C₅	1	1	yes	characteristic, complemented
187	#5470	C₂×C₅	1	1	yes	characteristic, complemented
188	C₂×C₅×#41	—	3	2	no	—
189	C₂×C₅×#41	—	3	1	no	—
190	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
191	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
192	C₅×C₄⋊Q₈	—	3	1	no	—
193	C₅×C₄⋊Q₈	—	3	1	no	—
194	C₅×#126	—	3	4	no	—
195	C₅×#126	—	3	4	no	—
196	C₅×#126	—	3	4	no	—
197	C₅×#125	—	3	4	no	—
198	C₅×#125	—	3	2	no	—
199	C₅×#125	—	3	2	no	—
200	C₅×#124	—	3	2	no	—
201	C₅×#124	—	3	4	no	—
202	C₅×#123	—	3	4	no	—
203	C₅×#123	—	3	4	no	—
204	C₅×#123	—	3	4	no	—
205	C₅×#123	—	3	4	no	—
206	C₅×C₂²⋊Q₈	—	3	2	no	—
207	C₅×C₂²⋊Q₈	—	3	2	no	—
208	C₅×C₂²⋊Q₈	—	3	2	no	—
209	C₅×C₂²⋊Q₈	—	3	2	no	—
210	C₅×C₂²⋊Q₈	—	3	2	no	—
211	C₅×C₂²⋊Q₈	—	3	4	no	—
212	C₅×#121	—	3	2	no	—
213	C₅×#121	—	3	4	no	—
214	C₅×#121	—	3	2	no	—
215	C₅×#121	—	3	2	no	—
216	C₅×#120	—	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	1	no	—
221	C₄×C₅×Q₈	—	3	2	no	—
222	C₄×C₅×D₄	—	3	2	no	—
223	C₄×C₅×D₄	—	3	2	no	—
224	C₄×C₅×D₄	—	3	2	no	—
225	C₄×C₅×D₄	—	3	4	no	—
226	C₄×C₅×D₄	—	3	4	no	—
227	C₄×C₅×D₄	—	3	4	no	—
228	C₄×C₅×D₄	—	3	1	no	—
229	C₄×C₅×D₄	—	3	1	no	—
230	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
231	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
232	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
233	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
234	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
235	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
236	C₅×#117	—	3	1	no	—
237	C₅×#117	—	3	2	no	—
238	C₅×#117	—	3	4	no	—
239	C₅×#117	—	3	4	no	—
240	C₅×#117	—	3	2	no	—
241	C₅×#117	—	3	2	no	—
242	C₅×#117	—	3	2	no	—
243	C₅×#117	—	3	4	no	—
244	C₅×#117	—	3	2	no	—
245	C₂×C₅×C₄⋊C₄	—	3	2	no	—
246	C₂×C₅×C₄⋊C₄	—	3	2	no	—
247	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
248	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
249	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
250	C₂×C₄²×C₅	—	3	4	no	—
251	C₂×C₄²×C₅	—	3	2	no	—
252	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
253	#3475	—	3	1	no	Sylow
254	C₂³×C₃×C₅	—	2	4	no	—
255	C₂³×C₃×C₅	—	2	4	no	—
256	C₂³×C₃×C₅	—	4	2	no	—
257	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
258	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
259	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
260	C₂²×C₅×D₃	C₂⁴	1	2	yes	—
261	C₃×C₅×D₄	—	2	4	no	—
262	C₃×C₅×D₄	—	2	2	no	—
263	C₃×C₅×D₄	#41	1	4	yes	complemented
264	C₂×C₃×C₄×C₅	—	2	4	no	—
265	C₂×C₃×C₄×C₅	—	2	4	no	—
266	C₂×C₃×C₄×C₅	—	2	4	no	—
267	C₂×C₃×C₄×C₅	—	2	4	no	—
268	C₂×C₃×C₄×C₅	—	2	4	no	—
269	C₂×C₃×C₄×C₅	—	2	2	no	—
270	C₂×C₃×C₄×C₅	—	4	1	no	—
271	C₂×C₃×C₄×C₅	#41	1	4	yes	complemented
272	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
273	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
274	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
275	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
276	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
277	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
278	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
279	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
280	C₅×#67	—	2	4	no	—
281	C₅×#67	—	2	8	no	—
282	C₅×#67	—	4	4	no	—
283	C₂×C₅×Dic₃	—	2	8	no	—
284	C₂×C₅×Dic₃	—	4	4	no	—
285	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
286	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
287	C₂×C₅×Dic₃	C₂⁴	1	2	yes	—
288	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
289	C₂×C₅×Dic₃	C₂⁴	1	4	yes	—
290	C₅×D₁₂	—	2	2	no	—
291	C₄×C₅×D₃	—	2	4	no	—
292	C₄×C₅×D₃	—	2	4	no	—
293	C₄×C₅×D₃	—	4	2	no	—
294	C₅×Dic₆	—	2	2	no	—
295	C₅×Dic₆	—	2	4	no	—
296	C₅×Dic₆	—	4	2	no	—
297	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
298	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
299	C₂×#237	C₂²×C₅	1	2	yes	—
300	C₂×#235	C₂²×C₅	1	1	yes	characteristic
301	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
302	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
303	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
304	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
305	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
306	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
307	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
308	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
309	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
310	#953	C₂²×C₅	1	4	yes	—
311	C₂×#217	C₂²×C₅	1	4	yes	—
312	#939	C₂²×C₅	1	4	yes	—
313	#938	C₂²×C₅	1	2	yes	—
314	#936	C₂²×C₅	1	2	yes	—
315	#935	C₂²×C₅	1	4	yes	—
316	D₄×Dic₃	C₂²×C₅	1	2	yes	—
317	#930	C₂²×C₅	1	2	yes	complemented
318	#930	C₂²×C₅	1	2	yes	complemented
319	#929	C₂²×C₅	1	4	yes	—
320	C₄×#67	C₂²×C₅	1	2	yes	—
321	C₄×#67	C₂²×C₅	1	2	yes	—
322	C₄×#67	C₂²×C₅	1	4	yes	complemented
323	C₄×#67	C₂²×C₅	1	4	yes	complemented
324	#926	C₂²×C₅	1	2	yes	—
325	#926	C₂²×C₅	1	1	yes	characteristic
326	#926	C₂²×C₅	1	4	yes	—
327	#926	C₂²×C₅	1	4	yes	complemented
328	#926	C₂²×C₅	1	2	yes	complemented
329	#926	C₂²×C₅	1	2	yes	complemented
330	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
331	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
332	#924	C₂²×C₅	1	2	yes	—
333	#924	C₂²×C₅	1	2	yes	—
334	#924	C₂²×C₅	1	2	yes	complemented
335	#924	C₂²×C₅	1	2	yes	complemented
336	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
337	#898	C₂²×C₅	1	4	yes	complemented
338	#897	C₂²×C₅	1	2	yes	complemented
339	#892	C₂²×C₅	1	2	yes	complemented
340	#890	C₂²×C₅	1	2	yes	complemented
341	#889	C₂²×C₅	1	4	yes	complemented
342	#887	C₂²×C₅	1	2	yes	complemented
343	#886	C₂²×C₅	1	4	yes	complemented
344	#885	C₂²×C₅	1	4	yes	complemented
345	#883	C₂²×C₅	1	4	yes	complemented
346	#67⋊C₄	C₂²×C₅	1	4	yes	complemented
347	#879	C₂²×C₅	1	4	yes	complemented
348	#879	C₂²×C₅	1	4	yes	complemented
349	#878	C₂²×C₅	1	4	yes	complemented
350	#877	C₂²×C₅	1	4	yes	complemented
351	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
352	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic, complemented
353	#872	C₂²×C₅	1	2	yes	complemented
354	C₄²×D₃	C₂²×C₅	1	2	yes	complemented
355	#870	C₂²×C₅	1	2	yes	complemented
356	#869	C₂²×C₅	1	1	yes	characteristic, complemented
357	#869	C₂²×C₅	1	1	yes	characteristic, complemented
358	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
359	C₄×Dic₆	C₂²×C₅	1	2	yes	complemented
360	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
361	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic, complemented
362	C₂⁴×C₅	C₂²×D₃	1	2	yes	—
363	C₅×#41	—	6	8	no	—
364	C₅×#41	—	6	4	no	—
365	C₂×C₅×Q₈	—	3	1	no	—
366	C₂×C₅×Q₈	—	3	2	no	—
367	C₂×C₅×Q₈	—	3	2	no	—
368	C₂×C₅×D₄	—	2	4	no	—
369	C₂×C₅×D₄	—	3	2	no	—
370	C₂×C₅×D₄	—	3	4	no	—
371	C₂×C₅×D₄	—	3	4	no	—
372	C₂×C₅×D₄	—	3	1	no	—
373	C₂×C₅×D₄	C₂²×D₃	1	2	yes	—
374	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
375	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
376	C₂²×C₄×C₅	—	2	8	no	—
377	C₂²×C₄×C₅	—	3	4	no	—
378	C₂²×C₄×C₅	—	3	4	no	—
379	C₂²×C₄×C₅	—	3	2	no	—
380	C₂²×C₄×C₅	—	3	2	no	—
381	C₂²×C₄×C₅	—	3	2	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	2	yes	—
386	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
387	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
388	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
389	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
390	C₅×C₄⋊C₄	—	3	1	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	4	no	—
395	C₅×C₄⋊C₄	—	3	4	no	—
396	C₅×C₄⋊C₄	—	3	2	no	—
397	C₅×C₄⋊C₄	—	3	2	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	—	3	4	no	—
402	C₅×C₄⋊C₄	—	3	4	no	—
403	C₅×C₄⋊C₄	—	3	2	no	—
404	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
405	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
406	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
407	C₅×C₂²⋊C₄	—	3	2	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	—	3	2	no	—
414	C₅×C₂²⋊C₄	—	3	4	no	—
415	C₅×C₂²⋊C₄	—	3	2	no	—
416	C₅×C₂²⋊C₄	—	3	4	no	—
417	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
418	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
419	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
420	C₅×C₂²⋊C₄	C₂²×D₃	1	2	yes	—
421	C₄²×C₅	—	3	4	no	—
422	C₄²×C₅	—	3	4	no	—
423	C₄²×C₅	—	3	2	no	—
424	C₄²×C₅	—	3	2	no	—
425	C₄²×C₅	—	3	2	no	—
426	C₄²×C₅	—	3	4	no	—
427	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
428	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
429	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
430	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
431	#556	—	3	1	no	—
432	#555	—	3	1	no	—
433	#554	—	3	1	no	—
434	#553	—	3	2	no	—
435	#552	—	3	2	no	—
436	#552	—	3	2	no	—
437	#551	—	3	4	no	—
438	#547	—	3	1	no	—
439	#546	—	3	2	no	—
440	#533	—	3	1	no	—
441	#529	—	3	4	no	—
442	#529	—	3	2	no	—
443	#525	—	3	2	no	—
444	C₄×#41	—	3	2	no	—
445	C₄×#41	—	3	1	no	—
446	C₂×C₄×D₄	C₅×D₃	1	1	yes	characteristic, complemented
447	C₂×#117	—	3	2	no	—
448	C₂²×C₃×C₅	—	2	2	no	—
449	C₂²×C₃×C₅	—	2	1	no	—
450	C₂²×C₃×C₅	—	2	2	no	—
451	C₂²×C₃×C₅	—	2	1	no	—
452	C₂²×C₃×C₅	—	2	2	no	—
453	C₂²×C₃×C₅	—	2	2	no	—
454	C₂²×C₃×C₅	—	2	2	no	—
455	C₂²×C₃×C₅	—	4	8	no	—
456	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
457	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
458	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
459	C₂×C₅×D₃	—	2	2	no	—
460	C₂×C₅×D₃	—	2	2	no	—
461	C₂×C₅×D₃	—	2	2	no	—
462	C₃×C₄×C₅	—	2	2	no	—
463	C₃×C₄×C₅	—	2	2	no	—
464	C₃×C₄×C₅	—	2	1	no	—
465	C₃×C₄×C₅	—	2	1	no	—
466	C₃×C₄×C₅	—	2	1	no	—
467	C₃×C₄×C₅	C₂×#41	1	2	yes	—
468	C₃×C₄×C₅	C₂×#41	1	2	yes	—
469	C₃×C₄×C₅	C₂×#41	1	2	yes	—
470	C₅×Dic₃	—	2	2	no	—
471	C₅×Dic₃	—	2	4	no	—
472	C₅×Dic₃	—	2	2	no	—
473	C₅×Dic₃	—	2	4	no	—
474	C₅×Dic₃	—	2	2	no	—
475	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
476	C₂×C₃×D₄	—	2	4	no	—
477	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
478	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
479	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
480	C₂²×C₃×C₄	—	2	8	no	—
481	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
482	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
483	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
484	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
485	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
486	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
487	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
488	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
489	C₂×#67	C₂³×C₅	1	4	yes	—
490	C₂×#67	C₂³×C₅	1	2	yes	—
491	C₂×#67	C₂³×C₅	1	4	yes	—
492	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
493	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
494	#237	—	2	8	no	—
495	#235	—	2	4	no	—
496	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
497	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
498	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
499	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
500	C₂×Dic₆	C₂³×C₅	1	1	yes	characteristic
501	C₂×Dic₆	C₂³×C₅	1	2	yes	—
502	C₂×Dic₆	C₂³×C₅	1	2	yes	—
503	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
504	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
505	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
506	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
507	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
508	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
509	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
510	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
511	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
512	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
513	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
514	#217	C₂³×C₅	1	4	yes	—
515	#217	C₂³×C₅	1	4	yes	—
516	#217	C₂³×C₅	1	4	yes	—
517	#217	C₂³×C₅	1	4	yes	—
518	#217	C₂³×C₅	1	4	yes	—
519	#217	C₂³×C₅	1	2	yes	—
520	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
521	(C₂×D₃)⋊C₄	C₂³×C₅	1	2	yes	—
522	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
523	(C₂×D₃)⋊C₄	C₂³×C₅	1	4	yes	—
524	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
525	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
526	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
527	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
528	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
529	C₄⋊Dic₃	C₂³×C₅	1	2	yes	—
530	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
531	C₄⋊Dic₃	C₂³×C₅	1	4	yes	—
532	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
533	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
534	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
535	Dic₃⋊C₄	C₂³×C₅	1	2	yes	—
536	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
537	Dic₃⋊C₄	C₂³×C₅	1	4	yes	—
538	C₄×Dic₃	C₂³×C₅	1	4	yes	—
539	C₄×Dic₃	C₂³×C₅	1	2	yes	—
540	C₄×Dic₃	C₂³×C₅	1	2	yes	—
541	C₄×Dic₃	C₂³×C₅	1	2	yes	—
542	C₄×Dic₃	C₂³×C₅	1	4	yes	—
543	C₄×Dic₃	C₂³×C₅	1	4	yes	—
544	C₂³×C₅	—	2	4	no	—
545	C₂³×C₅	—	2	4	no	—
546	C₂³×C₅	—	3	2	no	—
547	C₂³×C₅	—	4	2	no	—
548	C₂³×C₅	C₂³×D₃	1	2	yes	—
549	C₂³×C₅	C₂³×D₃	1	2	yes	—
550	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
551	C₅×Q₈	—	6	4	no	—
552	C₅×Q₈	—	6	2	no	—
553	C₅×Q₈	—	12	2	no	—
554	C₅×D₄	—	2	4	no	—
555	C₅×D₄	—	2	2	no	—
556	C₅×D₄	—	6	8	no	—
557	C₅×D₄	—	6	4	no	—
558	C₅×D₄	—	6	2	no	—
559	C₅×D₄	—	12	4	no	—
560	C₅×D₄	#235	1	4	yes	complemented
561	C₂×C₄×C₅	—	2	4	no	—
562	C₂×C₄×C₅	—	2	2	no	—
563	C₂×C₄×C₅	—	2	4	no	—
564	C₂×C₄×C₅	—	2	4	no	—
565	C₂×C₄×C₅	—	2	4	no	—
566	C₂×C₄×C₅	—	2	4	no	—
567	C₂×C₄×C₅	—	3	2	no	—
568	C₂×C₄×C₅	—	3	2	no	—
569	C₂×C₄×C₅	—	3	4	no	—
570	C₂×C₄×C₅	—	3	2	no	—
571	C₂×C₄×C₅	—	3	4	no	—
572	C₂×C₄×C₅	—	4	1	no	—
573	C₂×C₄×C₅	—	6	8	no	—
574	C₂×C₄×C₅	—	6	4	no	—
575	C₂×C₄×C₅	—	6	4	no	—
576	C₂×C₄×C₅	—	12	2	no	—
577	C₂×C₄×C₅	—	12	4	no	—
578	C₂×C₄×C₅	#237	1	4	yes	complemented
579	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
580	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
581	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
582	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
583	C₂×C₄×C₅	C₂³×D₃	1	2	yes	—
584	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
585	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
586	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
587	C₂×#41	—	3	2	no	—
588	C₂×#41	—	3	1	no	—
589	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
590	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
591	C₄⋊Q₈	—	3	1	no	—
592	C₄⋊Q₈	—	3	1	no	—
593	#126	—	3	4	no	—
594	#126	—	3	4	no	—
595	#126	—	3	4	no	—
596	#125	—	3	4	no	—
597	#125	—	3	2	no	—
598	#125	—	3	2	no	—
599	#124	—	3	2	no	—
600	#124	—	3	4	no	—
601	#123	—	3	4	no	—
602	#123	—	3	4	no	—
603	#123	—	3	4	no	—
604	#123	—	3	4	no	—
605	C₂²⋊Q₈	—	3	2	no	—
606	C₂²⋊Q₈	—	3	2	no	—
607	C₂²⋊Q₈	—	3	2	no	—
608	C₂²⋊Q₈	—	3	2	no	—
609	C₂²⋊Q₈	—	3	2	no	—
610	C₂²⋊Q₈	—	3	4	no	—
611	#121	—	3	4	no	—
612	#121	—	3	2	no	—
613	#121	—	3	2	no	—
614	#121	—	3	2	no	—
615	#120	—	3	4	no	—
616	C₄×Q₈	—	3	2	no	—
617	C₄×Q₈	—	3	2	no	—
618	C₄×Q₈	—	3	1	no	—
619	C₄×Q₈	—	3	1	no	—
620	C₄×Q₈	—	3	2	no	—
621	C₄×D₄	—	3	2	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	1	no	—
628	C₄×D₄	—	3	1	no	—
629	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
630	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
631	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
632	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
633	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
634	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
635	#117	—	3	1	no	—
636	#117	—	3	2	no	—
637	#117	—	3	4	no	—
638	#117	—	3	4	no	—
639	#117	—	3	2	no	—
640	#117	—	3	2	no	—
641	#117	—	3	2	no	—
642	#117	—	3	4	no	—
643	#117	—	3	2	no	—
644	C₂×C₄⋊C₄	—	3	2	no	—
645	C₂×C₄⋊C₄	—	3	2	no	—
646	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
647	C₂×C₂²⋊C₄	—	3	4	no	—
648	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
649	C₂×C₄²	—	3	4	no	—
650	C₂×C₄²	—	3	2	no	—
651	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
652	C₂×C₃×C₅	—	2	2	no	—
653	C₂×C₃×C₅	—	2	4	no	—
654	C₂×C₃×C₅	—	4	2	no	—
655	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
656	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
657	C₂×C₃×C₅	#585	1	1	yes	characteristic
658	C₅×D₃	—	4	2	no	—
659	C₂³×C₃	—	2	4	no	—
660	C₂³×C₃	—	2	4	no	—
661	C₂³×C₃	—	4	2	no	—
662	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
663	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
664	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
665	C₂²×D₃	C₂⁴×C₅	1	2	yes	—
666	C₃×D₄	—	2	4	no	—
667	C₃×D₄	—	2	2	no	—
668	C₃×D₄	C₅×#41	1	4	yes	complemented
669	C₂×C₃×C₄	—	2	4	no	—
670	C₂×C₃×C₄	—	2	4	no	—
671	C₂×C₃×C₄	—	2	4	no	—
672	C₂×C₃×C₄	—	2	4	no	—
673	C₂×C₃×C₄	—	2	4	no	—
674	C₂×C₃×C₄	—	2	2	no	—
675	C₂×C₃×C₄	—	4	1	no	—
676	C₂×C₃×C₄	C₅×#41	1	4	yes	complemented
677	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
678	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
679	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
680	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
681	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
682	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
683	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
684	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
685	#67	—	2	4	no	—
686	#67	—	2	8	no	—
687	#67	—	4	4	no	—
688	C₂×Dic₃	—	2	8	no	—
689	C₂×Dic₃	—	4	4	no	—
690	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
691	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
692	C₂×Dic₃	C₂⁴×C₅	1	2	yes	—
693	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
694	C₂×Dic₃	C₂⁴×C₅	1	4	yes	—
695	D₁₂	—	2	2	no	—
696	C₄×D₃	—	2	4	no	—
697	C₄×D₃	—	2	4	no	—
698	C₄×D₃	—	4	2	no	—
699	Dic₆	—	2	2	no	—
700	Dic₆	—	2	4	no	—
701	Dic₆	—	4	2	no	—
702	C₂²×C₅	—	2	1	no	—
703	C₂²×C₅	—	2	2	no	—
704	C₂²×C₅	—	2	1	no	—
705	C₂²×C₅	—	2	2	no	—
706	C₂²×C₅	—	2	2	no	—
707	C₂²×C₅	—	2	2	no	—
708	C₂²×C₅	—	2	2	no	—
709	C₂²×C₅	—	4	8	no	—
710	C₂²×C₅	—	6	2	no	—
711	C₂²×C₅	—	6	2	no	—
712	C₂²×C₅	—	6	2	no	—
713	C₂²×C₅	C₂×#235	1	4	yes	—
714	C₂²×C₅	C₂×#237	1	2	yes	—
715	C₂²×C₅	C₂⁴×D₃	1	1	yes	characteristic
716	C₄×C₅	—	2	1	no	—
717	C₄×C₅	—	2	2	no	—
718	C₄×C₅	—	2	2	no	—
719	C₄×C₅	—	2	1	no	—
720	C₄×C₅	—	2	1	no	—
721	C₄×C₅	—	6	2	no	—
722	C₄×C₅	—	6	4	no	—
723	C₄×C₅	—	6	2	no	—
724	C₄×C₅	—	6	2	no	—
725	C₄×C₅	—	6	4	no	—
726	C₄×C₅	C₂×#235	1	2	yes	—
727	C₄×C₅	C₂×#237	1	2	yes	—
728	C₄×C₅	C₂×#237	1	2	yes	—
729	C₂⁴	C₂²×C₅×D₃	1	2	yes	—
730	#41	—	6	8	no	—
731	#41	—	6	4	no	—
732	C₂×Q₈	—	3	1	no	—
733	C₂×Q₈	—	3	2	no	—
734	C₂×Q₈	—	3	2	no	—
735	C₂×D₄	—	2	4	no	—
736	C₂×D₄	—	3	2	no	—
737	C₂×D₄	—	3	4	no	—
738	C₂×D₄	—	3	4	no	—
739	C₂×D₄	—	3	1	no	—
740	C₂×D₄	C₂²×C₅×D₃	1	2	yes	—
741	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
742	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
743	C₂²×C₄	—	2	8	no	—
744	C₂²×C₄	—	3	4	no	—
745	C₂²×C₄	—	3	4	no	—
746	C₂²×C₄	—	3	2	no	—
747	C₂²×C₄	—	3	2	no	—
748	C₂²×C₄	—	3	2	no	—
749	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
750	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
751	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
752	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
753	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
754	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
755	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
756	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
757	C₄⋊C₄	—	3	1	no	—
758	C₄⋊C₄	—	3	1	no	—
759	C₄⋊C₄	—	3	2	no	—
760	C₄⋊C₄	—	3	2	no	—
761	C₄⋊C₄	—	3	4	no	—
762	C₄⋊C₄	—	3	4	no	—
763	C₄⋊C₄	—	3	2	no	—
764	C₄⋊C₄	—	3	2	no	—
765	C₄⋊C₄	—	3	4	no	—
766	C₄⋊C₄	—	3	4	no	—
767	C₄⋊C₄	—	3	2	no	—
768	C₄⋊C₄	—	3	4	no	—
769	C₄⋊C₄	—	3	4	no	—
770	C₄⋊C₄	—	3	2	no	—
771	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
774	C₂²⋊C₄	—	3	2	no	—
775	C₂²⋊C₄	—	3	4	no	—
776	C₂²⋊C₄	—	3	4	no	—
777	C₂²⋊C₄	—	3	4	no	—
778	C₂²⋊C₄	—	3	4	no	—
779	C₂²⋊C₄	—	3	4	no	—
780	C₂²⋊C₄	—	3	2	no	—
781	C₂²⋊C₄	—	3	4	no	—
782	C₂²⋊C₄	—	3	2	no	—
783	C₂²⋊C₄	—	3	4	no	—
784	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
785	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
786	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
787	C₂²⋊C₄	C₂²×C₅×D₃	1	2	yes	—
788	C₄²	—	3	2	no	—
789	C₄²	—	3	4	no	—
790	C₄²	—	3	4	no	—
791	C₄²	—	3	4	no	—
792	C₄²	—	3	2	no	—
793	C₄²	—	3	2	no	—
794	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
795	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
796	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
797	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
798	C₃×C₅	#3475	1	1	yes	characteristic, complemented, Hall
799	C₂²×C₃	—	2	2	no	—
800	C₂²×C₃	—	2	1	no	—
801	C₂²×C₃	—	2	2	no	—
802	C₂²×C₃	—	2	1	no	—
803	C₂²×C₃	—	2	2	no	—
804	C₂²×C₃	—	2	2	no	—
805	C₂²×C₃	—	2	2	no	—
806	C₂²×C₃	—	4	8	no	—
807	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
808	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
809	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
810	C₂×D₃	—	2	2	no	—
811	C₂×D₃	—	2	2	no	—
812	C₂×D₃	—	2	2	no	—
813	C₃×C₄	—	2	2	no	—
814	C₃×C₄	—	2	2	no	—
815	C₃×C₄	—	2	1	no	—
816	C₃×C₄	—	2	1	no	—
817	C₃×C₄	—	2	1	no	—
818	C₃×C₄	C₂×C₅×#41	1	2	yes	—
819	C₃×C₄	C₂×C₅×#41	1	2	yes	—
820	C₃×C₄	C₂×C₅×#41	1	2	yes	—
821	Dic₃	—	2	2	no	—
822	Dic₃	—	2	4	no	—
823	Dic₃	—	2	2	no	—
824	Dic₃	—	2	4	no	—
825	Dic₃	—	2	2	no	—
826	C₂×C₅	—	2	2	no	—
827	C₂×C₅	—	2	4	no	—
828	C₂×C₅	—	4	2	no	—
829	C₂×C₅	—	12	2	no	—
830	C₂×C₅	C₂²×#235	1	1	yes	characteristic
831	C₂×C₅	C₂²×#237	1	1	yes	characteristic
832	C₂×C₅	#5964	1	1	yes	characteristic
833	C₂³	—	2	4	no	—
834	C₂³	—	2	4	no	—
835	C₂³	—	3	2	no	—
836	C₂³	—	4	2	no	—
837	C₂³	C₂³×C₅×D₃	1	2	yes	—
838	C₂³	C₂³×C₅×D₃	1	2	yes	—
839	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
840	Q₈	—	6	4	no	—
841	Q₈	—	6	2	no	—
842	Q₈	—	12	2	no	—
843	D₄	—	2	4	no	—
844	D₄	—	2	2	no	—
845	D₄	—	6	8	no	—
846	D₄	—	6	4	no	—
847	D₄	—	6	2	no	—
848	D₄	—	12	4	no	—
849	D₄	C₅×#235	1	4	yes	complemented
850	C₂×C₄	—	2	4	no	—
851	C₂×C₄	—	2	2	no	—
852	C₂×C₄	—	2	4	no	—
853	C₂×C₄	—	2	4	no	—
854	C₂×C₄	—	2	4	no	—
855	C₂×C₄	—	2	4	no	—
856	C₂×C₄	—	3	2	no	—
857	C₂×C₄	—	3	2	no	—
858	C₂×C₄	—	3	4	no	—
859	C₂×C₄	—	3	2	no	—
860	C₂×C₄	—	3	4	no	—
861	C₂×C₄	—	4	1	no	—
862	C₂×C₄	—	6	8	no	—
863	C₂×C₄	—	6	4	no	—
864	C₂×C₄	—	6	4	no	—
865	C₂×C₄	—	12	2	no	—
866	C₂×C₄	—	12	4	no	—
867	C₂×C₄	C₅×#237	1	4	yes	complemented
868	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
869	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
870	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
871	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
872	C₂×C₄	C₂³×C₅×D₃	1	2	yes	—
873	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
874	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
875	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
876	C₂×C₃	—	2	2	no	—
877	C₂×C₃	—	2	4	no	—
878	C₂×C₃	—	4	2	no	—
879	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
880	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
881	C₂×C₃	C₅×#585	1	1	yes	characteristic
882	D₃	—	4	2	no	—
883	C₅	#85764	1	1	yes	characteristic, direct product factor, Sylow
884	C₂²	—	2	1	no	—
885	C₂²	—	2	2	no	—
886	C₂²	—	2	1	no	—
887	C₂²	—	2	2	no	—
888	C₂²	—	2	2	no	—
889	C₂²	—	2	2	no	—
890	C₂²	—	2	2	no	—
891	C₂²	—	4	8	no	—
892	C₂²	—	6	2	no	—
893	C₂²	—	6	2	no	—
894	C₂²	—	6	2	no	—
895	C₂²	C₂×C₅×#235	1	4	yes	—
896	C₂²	C₂×C₅×#237	1	2	yes	—
897	C₂²	C₂⁴×C₅×D₃	1	1	yes	characteristic
898	C₄	—	2	1	no	—
899	C₄	—	2	2	no	—
900	C₄	—	2	2	no	—
901	C₄	—	2	1	no	—
902	C₄	—	2	1	no	—
903	C₄	—	6	2	no	—
904	C₄	—	6	4	no	—
905	C₄	—	6	2	no	—
906	C₄	—	6	2	no	—
907	C₄	—	6	4	no	—
908	C₄	C₂×C₅×#235	1	2	yes	—
909	C₄	C₂×C₅×#237	1	2	yes	—
910	C₄	C₂×C₅×#237	1	2	yes	—
911	C₃	C₅×#3475	1	1	yes	characteristic, complemented, Sylow
912	C₂	—	2	2	no	—
913	C₂	—	2	4	no	—
914	C₂	—	4	2	no	—
915	C₂	—	12	2	no	—
916	C₂	C₂²×C₅×#235	1	1	yes	characteristic
917	C₂	C₂²×C₅×#237	1	1	yes	characteristic
918	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	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₂×C₄×C₅×D₄	D₃
hypocenter	C₃	C₅×#3475
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₂×C₄×C₅×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₅×#5806	C₂	semidirect
3. C₅×#5791	C₂	semidirect
4. C₂×C₅×#926	C₂	semidirect
5. C₅×#5565	C₂	semidirect
6. C₅×#5563	C₂	semidirect
7. C₅×#5557	C₂	semidirect
8. C₅×#5555	C₂	semidirect
9. C₅×#5543	C₂	semidirect
10. C₅×#5542	C₂	semidirect
11. C₅×#5541	C₂	semidirect
12. C₅×#5538	C₂	semidirect
13. C₄×C₅×#237	C₂	semidirect
14. C₅×#5513	C₂	semidirect
15. C₅×#5495	C₂	semidirect
16. C₄×C₅×#235	C₂	semidirect
17. C₅×#5470	C₂	semidirect
39. C₅×#930	C₂²	semidirect
40. C₅×#930	C₂²	semidirect
44. C₄×C₅×#67	C₂²	semidirect
45. C₄×C₅×#67	C₂²	semidirect
49. C₅×#926	C₂²	semidirect
50. C₅×#926	C₂²	semidirect
51. C₅×#926	C₂²	semidirect
52. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
53. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
56. C₅×#924	C₂²	semidirect
57. C₅×#924	C₂²	semidirect
58. C₂×C₄×C₅×Dic₃	C₂²	semidirect
59. C₅×#898	C₂²	semidirect
60. C₅×#897	C₂²	semidirect
61. C₅×#892	C₂²	semidirect
62. C₅×#890	C₂²	semidirect
63. C₅×#889	C₂²	semidirect
64. C₅×#887	C₂²	semidirect
65. C₅×#886	C₂²	semidirect
66. C₅×#885	C₂²	semidirect
67. C₅×#883	C₂²	semidirect
68. C₅×#67⋊C₄	C₂²	semidirect
69. C₅×#879	C₂²	semidirect
70. C₅×#879	C₂²	semidirect
71. C₅×#878	C₂²	semidirect
72. C₅×#877	C₂²	semidirect
73. C₄×C₅×D₁₂	C₂²	semidirect
74. C₄×C₅×D₁₂	C₂²	semidirect
75. C₅×#872	C₂²	semidirect
76. C₄²×C₅×D₃	C₂²	semidirect
77. C₅×#870	C₂²	semidirect
78. C₅×#869	C₂²	semidirect
79. C₅×#869	C₂²	semidirect
80. C₄×C₅×Dic₆	C₂²	semidirect
81. C₄×C₅×Dic₆	C₂²	semidirect
82. C₄×C₅×Dic₆	C₂²	semidirect
83. C₄×C₅×Dic₆	C₂²	semidirect
84. #85764	C₅	direct (N × H)
100. C₂×C₄×C₅×D₄	D₃	semidirect
171. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
172. #5806	C₂×C₅	semidirect
173. #5791	C₂×C₅	semidirect
174. C₂×#926	C₂×C₅	semidirect
175. #5565	C₂×C₅	semidirect
176. #5563	C₂×C₅	semidirect
177. #5557	C₂×C₅	semidirect
178. #5555	C₂×C₅	semidirect
179. #5543	C₂×C₅	semidirect
180. #5542	C₂×C₅	semidirect
181. #5541	C₂×C₅	semidirect
182. #5538	C₂×C₅	semidirect
183. C₄×#237	C₂×C₅	semidirect
184. #5513	C₂×C₅	semidirect
185. #5495	C₂×C₅	semidirect
186. C₄×#235	C₂×C₅	semidirect
187. #5470	C₂×C₅	semidirect
263. C₃×C₅×D₄	#41	semidirect
271. C₂×C₃×C₄×C₅	#41	semidirect
317. #930	C₂²×C₅	semidirect
318. #930	C₂²×C₅	semidirect
322. C₄×#67	C₂²×C₅	semidirect
323. C₄×#67	C₂²×C₅	semidirect
327. #926	C₂²×C₅	semidirect
328. #926	C₂²×C₅	semidirect
329. #926	C₂²×C₅	semidirect
330. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
331. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
334. #924	C₂²×C₅	semidirect
335. #924	C₂²×C₅	semidirect
336. C₂×C₄×Dic₃	C₂²×C₅	semidirect
337. #898	C₂²×C₅	semidirect
338. #897	C₂²×C₅	semidirect
339. #892	C₂²×C₅	semidirect
340. #890	C₂²×C₅	semidirect
341. #889	C₂²×C₅	semidirect
342. #887	C₂²×C₅	semidirect
343. #886	C₂²×C₅	semidirect
344. #885	C₂²×C₅	semidirect
345. #883	C₂²×C₅	semidirect
346. #67⋊C₄	C₂²×C₅	semidirect
347. #879	C₂²×C₅	semidirect
348. #879	C₂²×C₅	semidirect
349. #878	C₂²×C₅	semidirect
350. #877	C₂²×C₅	semidirect
351. C₄×D₁₂	C₂²×C₅	semidirect
352. C₄×D₁₂	C₂²×C₅	semidirect
353. #872	C₂²×C₅	semidirect
354. C₄²×D₃	C₂²×C₅	semidirect
355. #870	C₂²×C₅	semidirect
356. #869	C₂²×C₅	semidirect
357. #869	C₂²×C₅	semidirect
358. C₄×Dic₆	C₂²×C₅	semidirect
359. C₄×Dic₆	C₂²×C₅	semidirect
360. C₄×Dic₆	C₂²×C₅	semidirect
361. C₄×Dic₆	C₂²×C₅	semidirect
446. C₂×C₄×D₄	C₅×D₃	semidirect
560. C₅×D₄	#235	semidirect
578. C₂×C₄×C₅	#237	semidirect
668. C₃×D₄	C₅×#41	semidirect
676. C₂×C₃×C₄	C₅×#41	semidirect
798. C₃×C₅	#3475	semidirect
849. D₄	C₅×#235	semidirect
867. C₂×C₄	C₅×#237	semidirect
883. C₅	#85764	direct (N × H)
911. C₃	C₅×#3475	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₅×#5806	2
C₅×#5791	2
C₂×C₅×#926	2
C₅×#5565	2
C₅×#5563	2
C₅×#5557	2
C₅×#5555	2
C₅×#5543	2
C₅×#5542	2
C₅×#5541	2
C₅×#5538	2
C₄×C₅×#237	2
C₅×#5513	2
C₅×#5495	2
C₄×C₅×#235	2
C₅×#5470	2
C₅×#3475	3
#85764	5

Subgroups — C5×#85764 #14484129

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#85764 #14484129