Subgroups — C₃×C₅×#3118 #14276152

Order 1920.

812 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#542	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic
11	C₃×C₅×#442	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#440	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3118	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×#126	—	2	1	no	—
24	C₃×C₅×#124	—	2	1	no	—
25	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×#123	—	2	1	no	—
27	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×#121	C₂²	1	1	yes	characteristic
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₃×C₄×C₅×D₄	—	2	1	no	—
32	C₃×C₄×C₅×D₄	—	2	1	no	—
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
38	C₃×C₅×#117	C₂²	1	1	yes	characteristic
39	C₃×C₅×#117	C₂²	1	1	yes	characteristic
40	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
41	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
42	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic, complemented
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
47	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic, complemented
50	C₃×C₅×#102	C₂²	1	1	yes	characteristic
51	C₃×C₅×#102	C₂²	1	1	yes	characteristic
52	C₃×C₅×#102	C₂²	1	1	yes	characteristic
53	C₃×C₅×#102	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic, complemented
56	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
60	C₃×#3118	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#518	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#482	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#447	C₂×C₃	1	1	yes	characteristic
71	C₅×#442	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#440	C₂×C₃	1	1	yes	characteristic, complemented
73	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
74	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
75	C₅×#433	C₂×C₃	1	1	yes	characteristic, complemented
76	C₂⁴×C₃×C₅	—	2	1	no	—
77	C₂×C₃×C₅×Q₈	—	2	1	no	—
78	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	2	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂²×C₃×C₄×C₅	—	2	1	no	—
87	C₂²×C₃×C₄×C₅	—	2	1	no	—
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	1	no	—
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
92	C₃×C₅×SD₁₆	—	2	2	no	—
93	C₃×C₅×SD₁₆	—	2	2	no	—
94	C₃×C₅×D₈	—	2	2	no	—
95	C₃×C₅×D₈	—	2	2	no	—
96	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
98	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₃×C₅×C₄⋊C₄	—	2	1	no	—
101	C₃×C₅×C₄⋊C₄	—	2	1	no	—
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
104	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
105	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
106	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
107	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
109	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
111	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
112	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
113	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
114	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
115	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
116	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
120	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
121	C₃×C₄²×C₅	—	2	1	no	—
122	C₃×C₄²×C₅	—	2	1	no	—
123	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
124	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
125	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
126	C₃×#518	C₂×C₅	1	1	yes	characteristic, complemented
127	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
128	C₃×#482	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
130	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#447	C₂×C₅	1	1	yes	characteristic
135	C₃×#442	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#440	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
140	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
143	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
144	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
145	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
146	C₅×#126	—	2	1	no	—
147	C₅×#124	—	2	1	no	—
148	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₅×#123	—	2	1	no	—
150	C₅×C₂²⋊Q₈	—	2	1	no	—
151	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
152	C₅×#121	C₂²×C₃	1	1	yes	characteristic
153	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
154	C₄×C₅×D₄	—	2	1	no	—
155	C₄×C₅×D₄	—	2	1	no	—
156	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
157	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
158	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
159	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
160	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
161	C₅×#117	C₂²×C₃	1	1	yes	characteristic
162	C₅×#117	C₂²×C₃	1	1	yes	characteristic
163	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
164	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
165	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
167	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
168	C₅×#106	C₂²×C₃	1	1	yes	characteristic, complemented
169	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
170	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
171	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
172	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₅×#102	C₂²×C₃	1	1	yes	characteristic
174	C₅×#102	C₂²×C₃	1	1	yes	characteristic
175	C₅×#102	C₂²×C₃	1	1	yes	characteristic
176	C₅×#102	C₂²×C₃	1	1	yes	characteristic
177	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
180	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
181	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
182	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
183	#3118	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
184	C₂³×C₃×C₅	—	2	4	no	—
185	C₂³×C₃×C₅	—	2	1	no	—
186	C₂³×C₃×C₅	—	2	1	no	—
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	—	8	1	no	—
189	C₂³×C₃×C₅	—	8	1	no	—
190	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	—	8	1	no	—
194	C₃×C₅×D₄	—	2	4	no	—
195	C₃×C₅×D₄	—	2	1	no	—
196	C₃×C₅×D₄	—	2	1	no	—
197	C₃×C₅×D₄	—	2	1	no	—
198	C₃×C₅×D₄	—	2	1	no	—
199	C₃×C₅×D₄	—	8	1	no	—
200	C₃×C₅×D₄	#41	1	2	yes	—
201	C₃×C₅×D₄	#41	1	2	yes	—
202	C₂×C₃×C₄×C₅	—	2	1	no	—
203	C₂×C₃×C₄×C₅	—	2	1	no	—
204	C₂×C₃×C₄×C₅	—	2	1	no	—
205	C₂×C₃×C₄×C₅	—	2	1	no	—
206	C₂×C₃×C₄×C₅	—	2	1	no	—
207	C₂×C₃×C₄×C₅	—	2	1	no	—
208	C₂×C₃×C₄×C₅	—	2	1	no	—
209	C₂×C₃×C₄×C₅	—	8	1	no	—
210	C₂×C₃×C₄×C₅	—	8	1	no	—
211	C₂×C₃×C₄×C₅	—	8	1	no	—
212	C₂×C₃×C₄×C₅	—	8	1	no	—
213	C₂×C₃×C₄×C₅	—	8	1	no	—
214	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
215	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
216	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
217	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
218	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
219	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
220	C₃×C₅×C₈	—	2	1	no	—
221	C₃×C₅×C₈	—	2	1	no	—
222	C₃×C₅×C₈	—	2	1	no	—
223	C₃×C₅×C₈	—	2	1	no	—
224	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
225	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
226	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
229	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
230	C₃×#126	—	2	1	no	—
231	C₃×#124	—	2	1	no	—
232	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
233	C₃×#123	—	2	1	no	—
234	C₃×C₂²⋊Q₈	—	2	1	no	—
235	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
236	C₃×#121	C₂²×C₅	1	1	yes	characteristic
237	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
238	C₃×C₄×D₄	—	2	1	no	—
239	C₃×C₄×D₄	—	2	1	no	—
240	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
242	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
243	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
244	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
245	C₃×#117	C₂²×C₅	1	1	yes	characteristic
246	C₃×#117	C₂²×C₅	1	1	yes	characteristic
247	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
249	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
250	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
251	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
252	C₃×#106	C₂²×C₅	1	1	yes	characteristic, complemented
253	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
255	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
256	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
257	C₃×#102	C₂²×C₅	1	1	yes	characteristic
258	C₃×#102	C₂²×C₅	1	1	yes	characteristic
259	C₃×#102	C₂²×C₅	1	1	yes	characteristic
260	C₃×#102	C₂²×C₅	1	1	yes	characteristic
261	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
262	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
264	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
265	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₂⁴×C₅	—	2	1	no	—
268	C₂×C₅×Q₈	—	2	1	no	—
269	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
270	C₂×C₅×D₄	—	2	2	no	—
271	C₂×C₅×D₄	—	2	2	no	—
272	C₂×C₅×D₄	—	2	1	no	—
273	C₂×C₅×D₄	—	2	1	no	—
274	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
277	C₂²×C₄×C₅	—	2	1	no	—
278	C₂²×C₄×C₅	—	2	1	no	—
279	C₂²×C₄×C₅	—	2	1	no	—
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	2	1	no	—
282	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
283	C₅×SD₁₆	—	2	2	no	—
284	C₅×SD₁₆	—	2	2	no	—
285	C₅×D₈	—	2	2	no	—
286	C₅×D₈	—	2	2	no	—
287	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
288	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
289	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
290	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
291	C₅×C₄⋊C₄	—	2	1	no	—
292	C₅×C₄⋊C₄	—	2	1	no	—
293	C₅×C₄⋊C₄	—	2	1	no	—
294	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
295	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
296	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
297	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
298	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
299	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
300	C₅×C₂²⋊C₄	—	2	1	no	—
301	C₅×C₂²⋊C₄	—	2	1	no	—
302	C₅×C₂²⋊C₄	—	2	1	no	—
303	C₅×C₂²⋊C₄	—	2	1	no	—
304	C₅×C₂²⋊C₄	—	2	1	no	—
305	C₅×C₂²⋊C₄	—	2	1	no	—
306	C₅×C₂²⋊C₄	—	2	1	no	—
307	C₅×C₂²⋊C₄	—	2	1	no	—
308	C₅×C₂²⋊C₄	—	2	1	no	—
309	C₅×C₂²⋊C₄	—	2	1	no	—
310	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
311	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
312	C₄²×C₅	—	2	1	no	—
313	C₄²×C₅	—	2	1	no	—
314	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
315	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
316	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
317	#518	C₂×C₃×C₅	1	1	yes	characteristic, complemented
318	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
319	#482	C₂×C₃×C₅	1	1	yes	characteristic, complemented
320	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
322	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#447	C₂×C₃×C₅	1	1	yes	characteristic
326	#442	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#440	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	C₂²×C₃×C₅	—	2	1	no	—
332	C₂²×C₃×C₅	—	2	2	no	—
333	C₂²×C₃×C₅	—	2	2	no	—
334	C₂²×C₃×C₅	—	2	1	no	—
335	C₂²×C₃×C₅	—	2	1	no	—
336	C₂²×C₃×C₅	—	4	1	no	—
337	C₂²×C₃×C₅	—	4	1	no	—
338	C₂²×C₃×C₅	—	4	1	no	—
339	C₂²×C₃×C₅	—	4	1	no	—
340	C₂²×C₃×C₅	—	4	1	no	—
341	C₂²×C₃×C₅	—	4	1	no	—
342	C₂²×C₃×C₅	—	4	1	no	—
343	C₂²×C₃×C₅	—	8	4	no	—
344	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
345	C₃×C₄×C₅	—	2	1	no	—
346	C₃×C₄×C₅	—	2	1	no	—
347	C₃×C₄×C₅	—	2	1	no	—
348	C₃×C₄×C₅	—	2	1	no	—
349	C₃×C₄×C₅	—	2	1	no	—
350	C₃×C₄×C₅	—	4	1	no	—
351	C₃×C₄×C₅	—	4	1	no	—
352	C₃×C₄×C₅	—	4	1	no	—
353	C₃×C₄×C₅	—	4	1	no	—
354	C₃×C₄×C₅	—	4	1	no	—
355	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
356	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₂⁴×C₃	—	2	1	no	—
358	C₂×C₃×Q₈	—	2	1	no	—
359	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
360	C₂×C₃×D₄	—	2	2	no	—
361	C₂×C₃×D₄	—	2	2	no	—
362	C₂×C₃×D₄	—	2	1	no	—
363	C₂×C₃×D₄	—	2	1	no	—
364	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
367	C₂²×C₃×C₄	—	2	1	no	—
368	C₂²×C₃×C₄	—	2	1	no	—
369	C₂²×C₃×C₄	—	2	1	no	—
370	C₂²×C₃×C₄	—	2	1	no	—
371	C₂²×C₃×C₄	—	2	1	no	—
372	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
373	C₃×SD₁₆	—	2	2	no	—
374	C₃×SD₁₆	—	2	2	no	—
375	C₃×D₈	—	2	2	no	—
376	C₃×D₈	—	2	2	no	—
377	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
378	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
379	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
380	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₃×C₄⋊C₄	—	2	1	no	—
382	C₃×C₄⋊C₄	—	2	1	no	—
383	C₃×C₄⋊C₄	—	2	1	no	—
384	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
385	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
386	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
387	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
388	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
389	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
390	C₃×C₂²⋊C₄	—	2	1	no	—
391	C₃×C₂²⋊C₄	—	2	1	no	—
392	C₃×C₂²⋊C₄	—	2	1	no	—
393	C₃×C₂²⋊C₄	—	2	1	no	—
394	C₃×C₂²⋊C₄	—	2	1	no	—
395	C₃×C₂²⋊C₄	—	2	1	no	—
396	C₃×C₂²⋊C₄	—	2	1	no	—
397	C₃×C₂²⋊C₄	—	2	1	no	—
398	C₃×C₂²⋊C₄	—	2	1	no	—
399	C₃×C₂²⋊C₄	—	2	1	no	—
400	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
401	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
402	C₃×C₄²	—	2	1	no	—
403	C₃×C₄²	—	2	1	no	—
404	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
405	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
406	C₂³×C₅	—	2	4	no	—
407	C₂³×C₅	—	2	1	no	—
408	C₂³×C₅	—	2	1	no	—
409	C₂³×C₅	—	2	1	no	—
410	C₂³×C₅	—	8	1	no	—
411	C₂³×C₅	—	8	1	no	—
412	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
413	C₅×Q₈	—	2	1	no	—
414	C₅×Q₈	—	2	1	no	—
415	C₅×Q₈	—	8	1	no	—
416	C₅×D₄	—	2	4	no	—
417	C₅×D₄	—	2	1	no	—
418	C₅×D₄	—	2	1	no	—
419	C₅×D₄	—	2	1	no	—
420	C₅×D₄	—	2	1	no	—
421	C₅×D₄	—	8	1	no	—
422	C₅×D₄	C₃×#41	1	2	yes	—
423	C₅×D₄	C₃×#41	1	2	yes	—
424	C₂×C₄×C₅	—	2	1	no	—
425	C₂×C₄×C₅	—	2	1	no	—
426	C₂×C₄×C₅	—	2	1	no	—
427	C₂×C₄×C₅	—	2	1	no	—
428	C₂×C₄×C₅	—	2	1	no	—
429	C₂×C₄×C₅	—	2	1	no	—
430	C₂×C₄×C₅	—	2	1	no	—
431	C₂×C₄×C₅	—	8	1	no	—
432	C₂×C₄×C₅	—	8	1	no	—
433	C₂×C₄×C₅	—	8	1	no	—
434	C₂×C₄×C₅	—	8	1	no	—
435	C₂×C₄×C₅	—	8	1	no	—
436	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
437	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
438	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
439	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
440	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
441	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
442	C₅×C₈	—	2	1	no	—
443	C₅×C₈	—	2	1	no	—
444	C₅×C₈	—	2	1	no	—
445	C₅×C₈	—	2	1	no	—
446	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
447	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
448	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
451	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
452	#126	—	2	1	no	—
453	#124	—	2	1	no	—
454	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
455	#123	—	2	1	no	—
456	C₂²⋊Q₈	—	2	1	no	—
457	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
458	#121	C₂²×C₃×C₅	1	1	yes	characteristic
459	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
460	C₄×D₄	—	2	1	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
465	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
466	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
467	#117	C₂²×C₃×C₅	1	1	yes	characteristic
468	#117	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₂×C₂²⋊C₄	—	2	1	no	—
470	C₂×C₂²⋊C₄	—	2	1	no	—
471	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
472	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
473	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
474	#106	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
475	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
476	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
477	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
478	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
479	#102	C₂²×C₃×C₅	1	1	yes	characteristic
480	#102	C₂²×C₃×C₅	1	1	yes	characteristic
481	#102	C₂²×C₃×C₅	1	1	yes	characteristic
482	#102	C₂²×C₃×C₅	1	1	yes	characteristic
483	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
484	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
485	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
487	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	C₂×C₃×C₅	—	4	1	no	—
490	C₂×C₃×C₅	—	4	2	no	—
491	C₂×C₃×C₅	—	4	2	no	—
492	C₂×C₃×C₅	—	8	1	no	—
493	C₂×C₃×C₅	#525	1	1	yes	characteristic
494	C₂×C₃×C₅	#576	1	1	yes	characteristic
495	C₂×C₃×C₅	#577	1	1	yes	characteristic
496	C₂³×C₃	—	2	4	no	—
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	—	2	1	no	—
499	C₂³×C₃	—	2	1	no	—
500	C₂³×C₃	—	8	1	no	—
501	C₂³×C₃	—	8	1	no	—
502	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
503	C₃×Q₈	—	2	1	no	—
504	C₃×Q₈	—	2	1	no	—
505	C₃×Q₈	—	8	1	no	—
506	C₃×D₄	—	2	4	no	—
507	C₃×D₄	—	2	1	no	—
508	C₃×D₄	—	2	1	no	—
509	C₃×D₄	—	2	1	no	—
510	C₃×D₄	—	2	1	no	—
511	C₃×D₄	—	8	1	no	—
512	C₃×D₄	C₅×#41	1	2	yes	—
513	C₃×D₄	C₅×#41	1	2	yes	—
514	C₂×C₃×C₄	—	2	1	no	—
515	C₂×C₃×C₄	—	2	1	no	—
516	C₂×C₃×C₄	—	2	1	no	—
517	C₂×C₃×C₄	—	2	1	no	—
518	C₂×C₃×C₄	—	2	1	no	—
519	C₂×C₃×C₄	—	2	1	no	—
520	C₂×C₃×C₄	—	2	1	no	—
521	C₂×C₃×C₄	—	8	1	no	—
522	C₂×C₃×C₄	—	8	1	no	—
523	C₂×C₃×C₄	—	8	1	no	—
524	C₂×C₃×C₄	—	8	1	no	—
525	C₂×C₃×C₄	—	8	1	no	—
526	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
527	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
528	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
529	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
530	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
531	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
532	C₃×C₈	—	2	1	no	—
533	C₃×C₈	—	2	1	no	—
534	C₃×C₈	—	2	1	no	—
535	C₃×C₈	—	2	1	no	—
536	C₂²×C₅	—	2	1	no	—
537	C₂²×C₅	—	2	1	no	—
538	C₂²×C₅	—	2	1	no	—
539	C₂²×C₅	—	2	2	no	—
540	C₂²×C₅	—	2	2	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	—	4	1	no	—
544	C₂²×C₅	—	4	1	no	—
545	C₂²×C₅	—	4	1	no	—
546	C₂²×C₅	—	4	1	no	—
547	C₂²×C₅	—	4	1	no	—
548	C₂²×C₅	—	8	4	no	—
549	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
550	C₄×C₅	—	2	1	no	—
551	C₄×C₅	—	2	1	no	—
552	C₄×C₅	—	2	1	no	—
553	C₄×C₅	—	2	1	no	—
554	C₄×C₅	—	2	1	no	—
555	C₄×C₅	—	4	1	no	—
556	C₄×C₅	—	4	1	no	—
557	C₄×C₅	—	4	1	no	—
558	C₄×C₅	—	4	1	no	—
559	C₄×C₅	—	4	1	no	—
560	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
561	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
562	C₂⁴	—	2	1	no	—
563	C₂×Q₈	—	2	1	no	—
564	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
565	C₂×D₄	—	2	2	no	—
566	C₂×D₄	—	2	2	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	—	2	1	no	—
569	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
570	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
571	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	—	2	1	no	—
574	C₂²×C₄	—	2	1	no	—
575	C₂²×C₄	—	2	1	no	—
576	C₂²×C₄	—	2	1	no	—
577	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
578	SD₁₆	—	2	2	no	—
579	SD₁₆	—	2	2	no	—
580	D₈	—	2	2	no	—
581	D₈	—	2	2	no	—
582	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
583	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
584	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
585	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
590	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
591	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
592	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
593	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
594	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
595	C₂²⋊C₄	—	2	1	no	—
596	C₂²⋊C₄	—	2	1	no	—
597	C₂²⋊C₄	—	2	1	no	—
598	C₂²⋊C₄	—	2	1	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
606	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
610	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
611	C₃×C₅	#3118	1	1	yes	characteristic, direct product factor, Hall
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	2	no	—
614	C₂²×C₃	—	2	2	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	2	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	—	4	1	no	—
620	C₂²×C₃	—	4	1	no	—
621	C₂²×C₃	—	4	1	no	—
622	C₂²×C₃	—	4	1	no	—
623	C₂²×C₃	—	4	1	no	—
624	C₂²×C₃	—	8	4	no	—
625	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
626	C₃×C₄	—	2	1	no	—
627	C₃×C₄	—	2	1	no	—
628	C₃×C₄	—	2	1	no	—
629	C₃×C₄	—	2	1	no	—
630	C₃×C₄	—	2	1	no	—
631	C₃×C₄	—	4	1	no	—
632	C₃×C₄	—	4	1	no	—
633	C₃×C₄	—	4	1	no	—
634	C₃×C₄	—	4	1	no	—
635	C₃×C₄	—	4	1	no	—
636	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
637	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
638	C₂×C₅	—	4	1	no	—
639	C₂×C₅	—	4	2	no	—
640	C₂×C₅	—	4	2	no	—
641	C₂×C₅	—	8	1	no	—
642	C₂×C₅	C₃×#525	1	1	yes	characteristic
643	C₂×C₅	C₃×#576	1	1	yes	characteristic
644	C₂×C₅	C₃×#577	1	1	yes	characteristic
645	C₂³	—	2	4	no	—
646	C₂³	—	2	1	no	—
647	C₂³	—	2	1	no	—
648	C₂³	—	2	1	no	—
649	C₂³	—	8	1	no	—
650	C₂³	—	8	1	no	—
651	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
652	Q₈	—	2	1	no	—
653	Q₈	—	2	1	no	—
654	Q₈	—	8	1	no	—
655	D₄	—	2	4	no	—
656	D₄	—	2	1	no	—
657	D₄	—	2	1	no	—
658	D₄	—	2	1	no	—
659	D₄	—	2	1	no	—
660	D₄	—	8	1	no	—
661	D₄	C₃×C₅×#41	1	2	yes	—
662	D₄	C₃×C₅×#41	1	2	yes	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	8	1	no	—
671	C₂×C₄	—	8	1	no	—
672	C₂×C₄	—	8	1	no	—
673	C₂×C₄	—	8	1	no	—
674	C₂×C₄	—	8	1	no	—
675	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
676	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
677	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
678	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
679	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
680	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
681	C₈	—	2	1	no	—
682	C₈	—	2	1	no	—
683	C₈	—	2	1	no	—
684	C₈	—	2	1	no	—
685	C₂×C₃	—	4	1	no	—
686	C₂×C₃	—	4	2	no	—
687	C₂×C₃	—	4	2	no	—
688	C₂×C₃	—	8	1	no	—
689	C₂×C₃	C₅×#525	1	1	yes	characteristic
690	C₂×C₃	C₅×#576	1	1	yes	characteristic
691	C₂×C₃	C₅×#577	1	1	yes	characteristic
692	C₅	C₃×#3118	1	1	yes	characteristic, direct product factor, Sylow
693	C₂²	—	2	1	no	—
694	C₂²	—	2	2	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	4	1	no	—
699	C₂²	—	4	1	no	—
700	C₂²	—	4	1	no	—
701	C₂²	—	4	1	no	—
702	C₂²	—	4	1	no	—
703	C₂²	—	4	1	no	—
704	C₂²	—	4	1	no	—
705	C₂²	—	8	4	no	—
706	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
707	C₄	—	2	1	no	—
708	C₄	—	2	1	no	—
709	C₄	—	2	1	no	—
710	C₄	—	2	1	no	—
711	C₄	—	2	1	no	—
712	C₄	—	4	1	no	—
713	C₄	—	4	1	no	—
714	C₄	—	4	1	no	—
715	C₄	—	4	1	no	—
716	C₄	—	4	1	no	—
717	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
718	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
719	C₃	C₅×#3118	1	1	yes	characteristic, direct product factor, Sylow
720	C₂	—	4	1	no	—
721	C₂	—	4	2	no	—
722	C₂	—	4	2	no	—
723	C₂	—	8	1	no	—
724	C₂	C₃×C₅×#525	1	1	yes	characteristic
725	C₂	C₃×C₅×#576	1	1	yes	characteristic
726	C₂	C₃×C₅×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#447	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#542	C₂	semidirect
2. C₃×C₅×#518	C₂	semidirect
3. C₃×C₅×#485	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#474	C₂	semidirect
7. C₃×C₅×#463	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#450	C₂	semidirect
11. C₃×C₅×#442	C₂	semidirect
12. C₃×C₅×#440	C₂	semidirect
13. C₃×C₄×C₅×SD₁₆	C₂	semidirect
14. C₃×C₄×C₅×D₈	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3118	C₃	direct (N × H)
22. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
30. C₃×C₄×C₅×Q₈	C₂²	semidirect
37. C₃×C₄×C₅×D₄	C₂²	semidirect
42. C₃×C₅×#107	C₂²	semidirect
43. C₃×C₅×#107	C₂²	semidirect
44. C₃×C₅×#106	C₂²	semidirect
45. C₃×C₅×#106	C₂²	semidirect
46. C₃×C₅×C₄⋊C₈	C₂²	semidirect
47. C₃×C₅×C₄⋊C₈	C₂²	semidirect
48. C₃×C₅×#103	C₂²	semidirect
49. C₃×C₅×#103	C₂²	semidirect
54. C₃×C₅×#102	C₂²	semidirect
55. C₃×C₅×#102	C₂²	semidirect
58. C₃×C₅×#97	C₂²	semidirect
59. C₃×C₄×C₅×C₈	C₂²	semidirect
60. C₃×#3118	C₅	direct (N × H)
61. C₅×#542	C₂×C₃	semidirect
62. C₅×#518	C₂×C₃	semidirect
63. C₅×#485	C₂×C₃	semidirect
64. C₅×#482	C₂×C₃	semidirect
65. C₅×#476	C₂×C₃	semidirect
66. C₅×#474	C₂×C₃	semidirect
67. C₅×#463	C₂×C₃	semidirect
68. C₅×#463	C₂×C₃	semidirect
69. C₅×#450	C₂×C₃	semidirect
71. C₅×#442	C₂×C₃	semidirect
72. C₅×#440	C₂×C₃	semidirect
73. C₄×C₅×SD₁₆	C₂×C₃	semidirect
74. C₄×C₅×D₈	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
125. C₃×#542	C₂×C₅	semidirect
126. C₃×#518	C₂×C₅	semidirect
127. C₃×#485	C₂×C₅	semidirect
128. C₃×#482	C₂×C₅	semidirect
129. C₃×#476	C₂×C₅	semidirect
130. C₃×#474	C₂×C₅	semidirect
131. C₃×#463	C₂×C₅	semidirect
132. C₃×#463	C₂×C₅	semidirect
133. C₃×#450	C₂×C₅	semidirect
135. C₃×#442	C₂×C₅	semidirect
136. C₃×#440	C₂×C₅	semidirect
137. C₃×C₄×SD₁₆	C₂×C₅	semidirect
138. C₃×C₄×D₈	C₂×C₅	semidirect
139. C₃×#433	C₂×C₅	semidirect
145. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
148. C₅×#124	C₂²×C₃	semidirect
153. C₄×C₅×Q₈	C₂²×C₃	semidirect
160. C₄×C₅×D₄	C₂²×C₃	semidirect
165. C₅×#107	C₂²×C₃	semidirect
166. C₅×#107	C₂²×C₃	semidirect
167. C₅×#106	C₂²×C₃	semidirect
168. C₅×#106	C₂²×C₃	semidirect
169. C₅×C₄⋊C₈	C₂²×C₃	semidirect
170. C₅×C₄⋊C₈	C₂²×C₃	semidirect
171. C₅×#103	C₂²×C₃	semidirect
172. C₅×#103	C₂²×C₃	semidirect
177. C₅×#102	C₂²×C₃	semidirect
178. C₅×#102	C₂²×C₃	semidirect
181. C₅×#97	C₂²×C₃	semidirect
182. C₄×C₅×C₈	C₂²×C₃	semidirect
183. #3118	C₃×C₅	direct (N × H)
229. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
232. C₃×#124	C₂²×C₅	semidirect
237. C₃×C₄×Q₈	C₂²×C₅	semidirect
244. C₃×C₄×D₄	C₂²×C₅	semidirect
249. C₃×#107	C₂²×C₅	semidirect
250. C₃×#107	C₂²×C₅	semidirect
251. C₃×#106	C₂²×C₅	semidirect
252. C₃×#106	C₂²×C₅	semidirect
253. C₃×C₄⋊C₈	C₂²×C₅	semidirect
254. C₃×C₄⋊C₈	C₂²×C₅	semidirect
255. C₃×#103	C₂²×C₅	semidirect
256. C₃×#103	C₂²×C₅	semidirect
261. C₃×#102	C₂²×C₅	semidirect
262. C₃×#102	C₂²×C₅	semidirect
265. C₃×#97	C₂²×C₅	semidirect
266. C₃×C₄×C₈	C₂²×C₅	semidirect
316. #542	C₂×C₃×C₅	semidirect
317. #518	C₂×C₃×C₅	semidirect
318. #485	C₂×C₃×C₅	semidirect
319. #482	C₂×C₃×C₅	semidirect
320. #476	C₂×C₃×C₅	semidirect
321. #474	C₂×C₃×C₅	semidirect
322. #463	C₂×C₃×C₅	semidirect
323. #463	C₂×C₃×C₅	semidirect
324. #450	C₂×C₃×C₅	semidirect
326. #442	C₂×C₃×C₅	semidirect
327. #440	C₂×C₃×C₅	semidirect
328. C₄×SD₁₆	C₂×C₃×C₅	semidirect
329. C₄×D₈	C₂×C₃×C₅	semidirect
330. #433	C₂×C₃×C₅	semidirect
451. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
454. #124	C₂²×C₃×C₅	semidirect
459. C₄×Q₈	C₂²×C₃×C₅	semidirect
466. C₄×D₄	C₂²×C₃×C₅	semidirect
471. #107	C₂²×C₃×C₅	semidirect
472. #107	C₂²×C₃×C₅	semidirect
473. #106	C₂²×C₃×C₅	semidirect
474. #106	C₂²×C₃×C₅	semidirect
475. C₄⋊C₈	C₂²×C₃×C₅	semidirect
476. C₄⋊C₈	C₂²×C₃×C₅	semidirect
477. #103	C₂²×C₃×C₅	semidirect
478. #103	C₂²×C₃×C₅	semidirect
483. #102	C₂²×C₃×C₅	semidirect
484. #102	C₂²×C₃×C₅	semidirect
487. #97	C₂²×C₃×C₅	semidirect
488. C₄×C₈	C₂²×C₃×C₅	semidirect
611. C₃×C₅	#3118	direct (N × H)
692. C₅	C₃×#3118	direct (N × H)
719. C₃	C₅×#3118	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₅×#542	2
C₃×C₅×#518	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#476	2
C₃×C₅×#474	2
C₃×C₅×#463	2
C₃×C₅×#450	2
C₃×C₅×#447	2
C₃×C₅×#442	2
C₃×C₅×#440	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₄×C₅×D₈	2
C₃×C₅×#433	2
C₅×#3118	3
C₃×#3118	5

Subgroups — C3×C5×#3118 #14276152

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3118 #14276152