Subgroups — C₃×C₅×#3224 #14276258

Order 1920.

816 conjugacy classes of subgroups.

The subgroup lattice has 788 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×#535	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#489	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#463	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#459	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₅×#450	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×#449	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#447	C₂	1	1	yes	maximal, characteristic, complemented
15	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3224	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
27	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₅×#127	C₂²	1	1	yes	characteristic
29	C₃×C₅×#127	C₂²	1	1	yes	characteristic
30	C₃×C₅×#126	—	2	1	no	—
31	C₃×C₅×#124	—	2	1	no	—
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#124	C₂²	1	1	yes	characteristic
34	C₃×C₅×#124	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×#123	—	2	1	no	—
36	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
37	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×#121	—	2	1	no	—
39	C₃×C₅×#121	—	2	1	no	—
40	C₃×C₅×#121	C₂²	1	1	yes	characteristic
41	C₃×C₅×#120	—	2	1	no	—
42	C₃×C₅×#120	—	2	1	no	—
43	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic, complemented
44	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic, complemented
45	C₃×C₅×#117	C₂²	1	1	yes	characteristic
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×#3224	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#542	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
63	C₅×#496	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#489	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#463	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#459	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
72	C₅×#450	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×#449	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#447	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	C₃×C₅×#41	—	4	1	no	—
78	C₃×C₅×#41	—	4	1	no	—
79	C₂×C₃×C₅×Q₈	—	2	1	no	—
80	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×D₄	—	2	1	no	—
83	C₂×C₃×C₅×D₄	—	2	1	no	—
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	—	2	1	no	—
87	C₂×C₃×C₅×D₄	—	2	1	no	—
88	C₂×C₃×C₅×D₄	—	2	1	no	—
89	C₂×C₃×C₅×D₄	—	4	1	no	—
90	C₂×C₃×C₅×D₄	—	4	1	no	—
91	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
92	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
95	C₂²×C₃×C₄×C₅	—	2	1	no	—
96	C₂²×C₃×C₄×C₅	—	2	1	no	—
97	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
98	C₃×C₅×Q₁₆	—	4	1	no	—
99	C₃×C₅×SD₁₆	—	4	1	no	—
100	C₃×C₅×SD₁₆	—	4	1	no	—
101	C₃×C₅×SD₁₆	—	4	1	no	—
102	C₃×C₅×SD₁₆	—	4	1	no	—
103	C₃×C₅×D₈	—	4	1	no	—
104	C₃×C₅×D₈	—	4	1	no	—
105	C₃×C₅×D₈	—	4	1	no	—
106	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
107	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
108	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
109	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
110	C₃×C₅×C₄⋊C₄	—	2	1	no	—
111	C₃×C₅×C₄⋊C₄	—	2	1	no	—
112	C₃×C₅×C₄⋊C₄	—	2	1	no	—
113	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
115	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
118	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
119	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
123	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
124	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
125	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
126	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
127	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
128	C₃×C₄²×C₅	—	2	1	no	—
129	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
130	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
131	C₃×#542	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#496	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#489	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#463	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×#459	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
142	C₃×#450	C₂×C₅	1	1	yes	characteristic, complemented
143	C₃×#449	C₂×C₅	1	1	yes	characteristic, complemented
144	C₃×#447	C₂×C₅	1	1	yes	characteristic, complemented
145	C₃×#433	C₂×C₅	1	1	yes	characteristic, complemented
146	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
147	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
148	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
149	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
150	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
151	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
152	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
153	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
154	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
155	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
156	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
157	C₅×#127	C₂²×C₃	1	1	yes	characteristic
158	C₅×#127	C₂²×C₃	1	1	yes	characteristic
159	C₅×#126	—	2	1	no	—
160	C₅×#124	—	2	1	no	—
161	C₅×#124	C₂²×C₃	1	1	yes	characteristic
162	C₅×#124	C₂²×C₃	1	1	yes	characteristic
163	C₅×#124	C₂²×C₃	1	1	yes	characteristic, complemented
164	C₅×#123	—	2	1	no	—
165	C₅×C₂²⋊Q₈	—	2	1	no	—
166	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
167	C₅×#121	—	2	1	no	—
168	C₅×#121	—	2	1	no	—
169	C₅×#121	C₂²×C₃	1	1	yes	characteristic
170	C₅×#120	—	2	1	no	—
171	C₅×#120	—	2	1	no	—
172	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
173	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
174	C₅×#117	C₂²×C₃	1	1	yes	characteristic
175	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
176	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
177	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
178	C₅×#103	C₂²×C₃	1	1	yes	characteristic, complemented
179	C₅×#102	C₂²×C₃	1	1	yes	characteristic
180	C₅×#102	C₂²×C₃	1	1	yes	characteristic
181	C₅×#102	C₂²×C₃	1	1	yes	characteristic
182	C₅×#102	C₂²×C₃	1	1	yes	characteristic
183	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
184	C₅×#102	C₂²×C₃	1	1	yes	characteristic, complemented
185	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
186	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
187	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
188	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
189	#3224	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
190	C₂³×C₃×C₅	—	2	1	no	—
191	C₂³×C₃×C₅	—	2	1	no	—
192	C₂³×C₃×C₅	—	2	1	no	—
193	C₂³×C₃×C₅	—	2	1	no	—
194	C₂³×C₃×C₅	—	4	2	no	—
195	C₂³×C₃×C₅	—	8	1	no	—
196	C₂³×C₃×C₅	—	8	1	no	—
197	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
198	C₃×C₅×Q₈	—	2	1	no	—
199	C₃×C₅×Q₈	—	2	1	no	—
200	C₃×C₅×Q₈	—	2	1	no	—
201	C₃×C₅×Q₈	—	2	1	no	—
202	C₃×C₅×Q₈	—	8	1	no	—
203	C₃×C₅×D₄	—	2	1	no	—
204	C₃×C₅×D₄	—	2	1	no	—
205	C₃×C₅×D₄	—	2	1	no	—
206	C₃×C₅×D₄	—	2	1	no	—
207	C₃×C₅×D₄	—	2	1	no	—
208	C₃×C₅×D₄	—	2	1	no	—
209	C₃×C₅×D₄	—	2	1	no	—
210	C₃×C₅×D₄	—	2	1	no	—
211	C₃×C₅×D₄	—	4	2	no	—
212	C₃×C₅×D₄	—	4	2	no	—
213	C₃×C₅×D₄	—	8	1	no	—
214	C₃×C₅×D₄	—	8	1	no	—
215	C₃×C₅×D₄	—	8	1	no	—
216	C₃×C₅×D₄	—	8	1	no	—
217	C₃×C₅×D₄	—	8	1	no	—
218	C₂×C₃×C₄×C₅	—	2	1	no	—
219	C₂×C₃×C₄×C₅	—	2	1	no	—
220	C₂×C₃×C₄×C₅	—	2	1	no	—
221	C₂×C₃×C₄×C₅	—	2	1	no	—
222	C₂×C₃×C₄×C₅	—	2	1	no	—
223	C₂×C₃×C₄×C₅	—	2	1	no	—
224	C₂×C₃×C₄×C₅	—	4	2	no	—
225	C₂×C₃×C₄×C₅	—	8	1	no	—
226	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
227	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
229	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
230	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
231	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
232	C₃×C₅×C₈	—	2	1	no	—
233	C₃×C₅×C₈	—	2	1	no	—
234	C₃×C₅×C₈	—	2	1	no	—
235	C₃×C₅×C₈	—	2	1	no	—
236	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
237	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
238	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
239	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
240	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
241	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
242	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
243	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
244	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
245	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
246	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
247	C₃×#127	C₂²×C₅	1	1	yes	characteristic
248	C₃×#127	C₂²×C₅	1	1	yes	characteristic
249	C₃×#126	—	2	1	no	—
250	C₃×#124	—	2	1	no	—
251	C₃×#124	C₂²×C₅	1	1	yes	characteristic
252	C₃×#124	C₂²×C₅	1	1	yes	characteristic
253	C₃×#124	C₂²×C₅	1	1	yes	characteristic, complemented
254	C₃×#123	—	2	1	no	—
255	C₃×C₂²⋊Q₈	—	2	1	no	—
256	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
257	C₃×#121	—	2	1	no	—
258	C₃×#121	—	2	1	no	—
259	C₃×#121	C₂²×C₅	1	1	yes	characteristic
260	C₃×#120	—	2	1	no	—
261	C₃×#120	—	2	1	no	—
262	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
263	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic, complemented
264	C₃×#117	C₂²×C₅	1	1	yes	characteristic
265	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
266	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
267	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
268	C₃×#103	C₂²×C₅	1	1	yes	characteristic, complemented
269	C₃×#102	C₂²×C₅	1	1	yes	characteristic
270	C₃×#102	C₂²×C₅	1	1	yes	characteristic
271	C₃×#102	C₂²×C₅	1	1	yes	characteristic
272	C₃×#102	C₂²×C₅	1	1	yes	characteristic
273	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
274	C₃×#102	C₂²×C₅	1	1	yes	characteristic, complemented
275	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
277	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
278	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
279	C₂⁴×C₅	—	2	1	no	—
280	C₅×#41	—	4	1	no	—
281	C₅×#41	—	4	1	no	—
282	C₂×C₅×Q₈	—	2	1	no	—
283	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
284	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
285	C₂×C₅×D₄	—	2	1	no	—
286	C₂×C₅×D₄	—	2	1	no	—
287	C₂×C₅×D₄	—	2	1	no	—
288	C₂×C₅×D₄	—	2	1	no	—
289	C₂×C₅×D₄	—	2	1	no	—
290	C₂×C₅×D₄	—	2	1	no	—
291	C₂×C₅×D₄	—	2	1	no	—
292	C₂×C₅×D₄	—	4	1	no	—
293	C₂×C₅×D₄	—	4	1	no	—
294	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
295	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
296	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
297	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
298	C₂²×C₄×C₅	—	2	1	no	—
299	C₂²×C₄×C₅	—	2	1	no	—
300	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
301	C₅×Q₁₆	—	4	1	no	—
302	C₅×SD₁₆	—	4	1	no	—
303	C₅×SD₁₆	—	4	1	no	—
304	C₅×SD₁₆	—	4	1	no	—
305	C₅×SD₁₆	—	4	1	no	—
306	C₅×D₈	—	4	1	no	—
307	C₅×D₈	—	4	1	no	—
308	C₅×D₈	—	4	1	no	—
309	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
311	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
312	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
313	C₅×C₄⋊C₄	—	2	1	no	—
314	C₅×C₄⋊C₄	—	2	1	no	—
315	C₅×C₄⋊C₄	—	2	1	no	—
316	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
317	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
318	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
319	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
320	C₅×C₂²⋊C₄	—	2	1	no	—
321	C₅×C₂²⋊C₄	—	2	1	no	—
322	C₅×C₂²⋊C₄	—	2	1	no	—
323	C₅×C₂²⋊C₄	—	2	1	no	—
324	C₅×C₂²⋊C₄	—	2	1	no	—
325	C₅×C₂²⋊C₄	—	2	1	no	—
326	C₅×C₂²⋊C₄	—	2	1	no	—
327	C₅×C₂²⋊C₄	—	2	1	no	—
328	C₅×C₂²⋊C₄	—	2	1	no	—
329	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
330	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
331	C₄²×C₅	—	2	1	no	—
332	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
333	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
334	#542	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
336	#496	C₂×C₃×C₅	1	1	yes	characteristic, complemented
337	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
338	#489	C₂×C₃×C₅	1	1	yes	characteristic, complemented
339	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
340	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
341	#463	C₂×C₃×C₅	1	1	yes	characteristic, complemented
342	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
343	#459	C₂×C₃×C₅	1	1	yes	characteristic, complemented
344	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
345	#450	C₂×C₃×C₅	1	1	yes	characteristic, complemented
346	#449	C₂×C₃×C₅	1	1	yes	characteristic, complemented
347	#447	C₂×C₃×C₅	1	1	yes	characteristic, complemented
348	#433	C₂×C₃×C₅	1	1	yes	characteristic, complemented
349	C₂²×C₃×C₅	—	2	1	no	—
350	C₂²×C₃×C₅	—	2	1	no	—
351	C₂²×C₃×C₅	—	2	1	no	—
352	C₂²×C₃×C₅	—	4	1	no	—
353	C₂²×C₃×C₅	—	4	1	no	—
354	C₂²×C₃×C₅	—	4	1	no	—
355	C₂²×C₃×C₅	—	4	1	no	—
356	C₂²×C₃×C₅	—	4	1	no	—
357	C₂²×C₃×C₅	—	4	1	no	—
358	C₂²×C₃×C₅	—	4	1	no	—
359	C₂²×C₃×C₅	—	4	1	no	—
360	C₂²×C₃×C₅	—	4	1	no	—
361	C₂²×C₃×C₅	—	4	1	no	—
362	C₂²×C₃×C₅	—	4	1	no	—
363	C₂²×C₃×C₅	—	4	1	no	—
364	C₂²×C₃×C₅	—	8	4	no	—
365	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
366	C₃×C₄×C₅	—	2	1	no	—
367	C₃×C₄×C₅	—	2	1	no	—
368	C₃×C₄×C₅	—	2	1	no	—
369	C₃×C₄×C₅	—	2	1	no	—
370	C₃×C₄×C₅	—	2	1	no	—
371	C₃×C₄×C₅	—	4	1	no	—
372	C₃×C₄×C₅	—	4	1	no	—
373	C₃×C₄×C₅	—	4	1	no	—
374	C₃×C₄×C₅	—	4	1	no	—
375	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
376	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
377	C₂⁴×C₃	—	2	1	no	—
378	C₃×#41	—	4	1	no	—
379	C₃×#41	—	4	1	no	—
380	C₂×C₃×Q₈	—	2	1	no	—
381	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₃×D₄	—	2	1	no	—
384	C₂×C₃×D₄	—	2	1	no	—
385	C₂×C₃×D₄	—	2	1	no	—
386	C₂×C₃×D₄	—	2	1	no	—
387	C₂×C₃×D₄	—	2	1	no	—
388	C₂×C₃×D₄	—	2	1	no	—
389	C₂×C₃×D₄	—	2	1	no	—
390	C₂×C₃×D₄	—	4	1	no	—
391	C₂×C₃×D₄	—	4	1	no	—
392	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
393	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
394	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
395	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
396	C₂²×C₃×C₄	—	2	1	no	—
397	C₂²×C₃×C₄	—	2	1	no	—
398	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
399	C₃×Q₁₆	—	4	1	no	—
400	C₃×SD₁₆	—	4	1	no	—
401	C₃×SD₁₆	—	4	1	no	—
402	C₃×SD₁₆	—	4	1	no	—
403	C₃×SD₁₆	—	4	1	no	—
404	C₃×D₈	—	4	1	no	—
405	C₃×D₈	—	4	1	no	—
406	C₃×D₈	—	4	1	no	—
407	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
408	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
409	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
410	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
411	C₃×C₄⋊C₄	—	2	1	no	—
412	C₃×C₄⋊C₄	—	2	1	no	—
413	C₃×C₄⋊C₄	—	2	1	no	—
414	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
415	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
416	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
417	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
418	C₃×C₂²⋊C₄	—	2	1	no	—
419	C₃×C₂²⋊C₄	—	2	1	no	—
420	C₃×C₂²⋊C₄	—	2	1	no	—
421	C₃×C₂²⋊C₄	—	2	1	no	—
422	C₃×C₂²⋊C₄	—	2	1	no	—
423	C₃×C₂²⋊C₄	—	2	1	no	—
424	C₃×C₂²⋊C₄	—	2	1	no	—
425	C₃×C₂²⋊C₄	—	2	1	no	—
426	C₃×C₂²⋊C₄	—	2	1	no	—
427	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
428	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
429	C₃×C₄²	—	2	1	no	—
430	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
431	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
432	C₂³×C₅	—	2	1	no	—
433	C₂³×C₅	—	2	1	no	—
434	C₂³×C₅	—	2	1	no	—
435	C₂³×C₅	—	2	1	no	—
436	C₂³×C₅	—	4	2	no	—
437	C₂³×C₅	—	8	1	no	—
438	C₂³×C₅	—	8	1	no	—
439	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
440	C₅×Q₈	—	2	1	no	—
441	C₅×Q₈	—	2	1	no	—
442	C₅×Q₈	—	2	1	no	—
443	C₅×Q₈	—	2	1	no	—
444	C₅×Q₈	—	8	1	no	—
445	C₅×D₄	—	2	1	no	—
446	C₅×D₄	—	2	1	no	—
447	C₅×D₄	—	2	1	no	—
448	C₅×D₄	—	2	1	no	—
449	C₅×D₄	—	2	1	no	—
450	C₅×D₄	—	2	1	no	—
451	C₅×D₄	—	2	1	no	—
452	C₅×D₄	—	2	1	no	—
453	C₅×D₄	—	4	2	no	—
454	C₅×D₄	—	4	2	no	—
455	C₅×D₄	—	8	1	no	—
456	C₅×D₄	—	8	1	no	—
457	C₅×D₄	—	8	1	no	—
458	C₅×D₄	—	8	1	no	—
459	C₅×D₄	—	8	1	no	—
460	C₂×C₄×C₅	—	2	1	no	—
461	C₂×C₄×C₅	—	2	1	no	—
462	C₂×C₄×C₅	—	2	1	no	—
463	C₂×C₄×C₅	—	2	1	no	—
464	C₂×C₄×C₅	—	2	1	no	—
465	C₂×C₄×C₅	—	2	1	no	—
466	C₂×C₄×C₅	—	4	2	no	—
467	C₂×C₄×C₅	—	8	1	no	—
468	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
469	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
470	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
471	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
472	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
473	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
474	C₅×C₈	—	2	1	no	—
475	C₅×C₈	—	2	1	no	—
476	C₅×C₈	—	2	1	no	—
477	C₅×C₈	—	2	1	no	—
478	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
479	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
480	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
481	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
482	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
483	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
484	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
485	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
486	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
487	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
488	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
489	#127	C₂²×C₃×C₅	1	1	yes	characteristic
490	#127	C₂²×C₃×C₅	1	1	yes	characteristic
491	#126	—	2	1	no	—
492	#124	—	2	1	no	—
493	#124	C₂²×C₃×C₅	1	1	yes	characteristic
494	#124	C₂²×C₃×C₅	1	1	yes	characteristic
495	#124	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
496	#123	—	2	1	no	—
497	C₂²⋊Q₈	—	2	1	no	—
498	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
499	#121	—	2	1	no	—
500	#121	—	2	1	no	—
501	#121	C₂²×C₃×C₅	1	1	yes	characteristic
502	#120	—	2	1	no	—
503	#120	—	2	1	no	—
504	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
505	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
506	#117	C₂²×C₃×C₅	1	1	yes	characteristic
507	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
508	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
509	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
510	#103	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
511	#102	C₂²×C₃×C₅	1	1	yes	characteristic
512	#102	C₂²×C₃×C₅	1	1	yes	characteristic
513	#102	C₂²×C₃×C₅	1	1	yes	characteristic
514	#102	C₂²×C₃×C₅	1	1	yes	characteristic
515	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
516	#102	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
517	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
518	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
519	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
520	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
521	C₂×C₃×C₅	—	4	1	no	—
522	C₂×C₃×C₅	—	8	1	no	—
523	C₂×C₃×C₅	—	8	1	no	—
524	C₂×C₃×C₅	—	8	1	no	—
525	C₂×C₃×C₅	—	8	1	no	—
526	C₂×C₃×C₅	#535	1	1	yes	characteristic
527	C₂×C₃×C₅	#576	1	1	yes	characteristic
528	C₂×C₃×C₅	#577	1	1	yes	characteristic
529	C₂³×C₃	—	2	1	no	—
530	C₂³×C₃	—	2	1	no	—
531	C₂³×C₃	—	2	1	no	—
532	C₂³×C₃	—	2	1	no	—
533	C₂³×C₃	—	4	2	no	—
534	C₂³×C₃	—	8	1	no	—
535	C₂³×C₃	—	8	1	no	—
536	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
537	C₃×Q₈	—	2	1	no	—
538	C₃×Q₈	—	2	1	no	—
539	C₃×Q₈	—	2	1	no	—
540	C₃×Q₈	—	2	1	no	—
541	C₃×Q₈	—	8	1	no	—
542	C₃×D₄	—	2	1	no	—
543	C₃×D₄	—	2	1	no	—
544	C₃×D₄	—	2	1	no	—
545	C₃×D₄	—	2	1	no	—
546	C₃×D₄	—	2	1	no	—
547	C₃×D₄	—	2	1	no	—
548	C₃×D₄	—	2	1	no	—
549	C₃×D₄	—	2	1	no	—
550	C₃×D₄	—	4	2	no	—
551	C₃×D₄	—	4	2	no	—
552	C₃×D₄	—	8	1	no	—
553	C₃×D₄	—	8	1	no	—
554	C₃×D₄	—	8	1	no	—
555	C₃×D₄	—	8	1	no	—
556	C₃×D₄	—	8	1	no	—
557	C₂×C₃×C₄	—	2	1	no	—
558	C₂×C₃×C₄	—	2	1	no	—
559	C₂×C₃×C₄	—	2	1	no	—
560	C₂×C₃×C₄	—	2	1	no	—
561	C₂×C₃×C₄	—	2	1	no	—
562	C₂×C₃×C₄	—	2	1	no	—
563	C₂×C₃×C₄	—	4	2	no	—
564	C₂×C₃×C₄	—	8	1	no	—
565	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
566	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
567	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
568	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
570	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
571	C₃×C₈	—	2	1	no	—
572	C₃×C₈	—	2	1	no	—
573	C₃×C₈	—	2	1	no	—
574	C₃×C₈	—	2	1	no	—
575	C₂²×C₅	—	2	1	no	—
576	C₂²×C₅	—	2	1	no	—
577	C₂²×C₅	—	2	1	no	—
578	C₂²×C₅	—	4	1	no	—
579	C₂²×C₅	—	4	1	no	—
580	C₂²×C₅	—	4	1	no	—
581	C₂²×C₅	—	4	1	no	—
582	C₂²×C₅	—	4	1	no	—
583	C₂²×C₅	—	4	1	no	—
584	C₂²×C₅	—	4	1	no	—
585	C₂²×C₅	—	4	1	no	—
586	C₂²×C₅	—	4	1	no	—
587	C₂²×C₅	—	4	1	no	—
588	C₂²×C₅	—	4	1	no	—
589	C₂²×C₅	—	4	1	no	—
590	C₂²×C₅	—	8	4	no	—
591	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
592	C₄×C₅	—	2	1	no	—
593	C₄×C₅	—	2	1	no	—
594	C₄×C₅	—	2	1	no	—
595	C₄×C₅	—	2	1	no	—
596	C₄×C₅	—	2	1	no	—
597	C₄×C₅	—	4	1	no	—
598	C₄×C₅	—	4	1	no	—
599	C₄×C₅	—	4	1	no	—
600	C₄×C₅	—	4	1	no	—
601	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
602	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
603	C₂⁴	—	2	1	no	—
604	#41	—	4	1	no	—
605	#41	—	4	1	no	—
606	C₂×Q₈	—	2	1	no	—
607	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
608	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	2	1	no	—
611	C₂×D₄	—	2	1	no	—
612	C₂×D₄	—	2	1	no	—
613	C₂×D₄	—	2	1	no	—
614	C₂×D₄	—	2	1	no	—
615	C₂×D₄	—	2	1	no	—
616	C₂×D₄	—	4	1	no	—
617	C₂×D₄	—	4	1	no	—
618	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
619	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
620	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
621	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
622	C₂²×C₄	—	2	1	no	—
623	C₂²×C₄	—	2	1	no	—
624	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
625	Q₁₆	—	4	1	no	—
626	SD₁₆	—	4	1	no	—
627	SD₁₆	—	4	1	no	—
628	SD₁₆	—	4	1	no	—
629	SD₁₆	—	4	1	no	—
630	D₈	—	4	1	no	—
631	D₈	—	4	1	no	—
632	D₈	—	4	1	no	—
633	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
634	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
635	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
636	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
637	C₄⋊C₄	—	2	1	no	—
638	C₄⋊C₄	—	2	1	no	—
639	C₄⋊C₄	—	2	1	no	—
640	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
641	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
642	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
643	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
644	C₂²⋊C₄	—	2	1	no	—
645	C₂²⋊C₄	—	2	1	no	—
646	C₂²⋊C₄	—	2	1	no	—
647	C₂²⋊C₄	—	2	1	no	—
648	C₂²⋊C₄	—	2	1	no	—
649	C₂²⋊C₄	—	2	1	no	—
650	C₂²⋊C₄	—	2	1	no	—
651	C₂²⋊C₄	—	2	1	no	—
652	C₂²⋊C₄	—	2	1	no	—
653	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
654	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
655	C₄²	—	2	1	no	—
656	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
657	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
658	C₃×C₅	#3224	1	1	yes	characteristic, direct product factor, Hall
659	C₂²×C₃	—	2	1	no	—
660	C₂²×C₃	—	2	1	no	—
661	C₂²×C₃	—	2	1	no	—
662	C₂²×C₃	—	4	1	no	—
663	C₂²×C₃	—	4	1	no	—
664	C₂²×C₃	—	4	1	no	—
665	C₂²×C₃	—	4	1	no	—
666	C₂²×C₃	—	4	1	no	—
667	C₂²×C₃	—	4	1	no	—
668	C₂²×C₃	—	4	1	no	—
669	C₂²×C₃	—	4	1	no	—
670	C₂²×C₃	—	4	1	no	—
671	C₂²×C₃	—	4	1	no	—
672	C₂²×C₃	—	4	1	no	—
673	C₂²×C₃	—	4	1	no	—
674	C₂²×C₃	—	8	4	no	—
675	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
676	C₃×C₄	—	2	1	no	—
677	C₃×C₄	—	2	1	no	—
678	C₃×C₄	—	2	1	no	—
679	C₃×C₄	—	2	1	no	—
680	C₃×C₄	—	2	1	no	—
681	C₃×C₄	—	4	1	no	—
682	C₃×C₄	—	4	1	no	—
683	C₃×C₄	—	4	1	no	—
684	C₃×C₄	—	4	1	no	—
685	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
686	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
687	C₂×C₅	—	4	1	no	—
688	C₂×C₅	—	8	1	no	—
689	C₂×C₅	—	8	1	no	—
690	C₂×C₅	—	8	1	no	—
691	C₂×C₅	—	8	1	no	—
692	C₂×C₅	C₃×#535	1	1	yes	characteristic
693	C₂×C₅	C₃×#576	1	1	yes	characteristic
694	C₂×C₅	C₃×#577	1	1	yes	characteristic
695	C₂³	—	2	1	no	—
696	C₂³	—	2	1	no	—
697	C₂³	—	2	1	no	—
698	C₂³	—	2	1	no	—
699	C₂³	—	4	2	no	—
700	C₂³	—	8	1	no	—
701	C₂³	—	8	1	no	—
702	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
703	Q₈	—	2	1	no	—
704	Q₈	—	2	1	no	—
705	Q₈	—	2	1	no	—
706	Q₈	—	2	1	no	—
707	Q₈	—	8	1	no	—
708	D₄	—	2	1	no	—
709	D₄	—	2	1	no	—
710	D₄	—	2	1	no	—
711	D₄	—	2	1	no	—
712	D₄	—	2	1	no	—
713	D₄	—	2	1	no	—
714	D₄	—	2	1	no	—
715	D₄	—	2	1	no	—
716	D₄	—	4	2	no	—
717	D₄	—	4	2	no	—
718	D₄	—	8	1	no	—
719	D₄	—	8	1	no	—
720	D₄	—	8	1	no	—
721	D₄	—	8	1	no	—
722	D₄	—	8	1	no	—
723	C₂×C₄	—	2	1	no	—
724	C₂×C₄	—	2	1	no	—
725	C₂×C₄	—	2	1	no	—
726	C₂×C₄	—	2	1	no	—
727	C₂×C₄	—	2	1	no	—
728	C₂×C₄	—	2	1	no	—
729	C₂×C₄	—	4	2	no	—
730	C₂×C₄	—	8	1	no	—
731	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
732	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
733	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
734	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
735	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
736	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
737	C₈	—	2	1	no	—
738	C₈	—	2	1	no	—
739	C₈	—	2	1	no	—
740	C₈	—	2	1	no	—
741	C₂×C₃	—	4	1	no	—
742	C₂×C₃	—	8	1	no	—
743	C₂×C₃	—	8	1	no	—
744	C₂×C₃	—	8	1	no	—
745	C₂×C₃	—	8	1	no	—
746	C₂×C₃	C₅×#535	1	1	yes	characteristic
747	C₂×C₃	C₅×#576	1	1	yes	characteristic
748	C₂×C₃	C₅×#577	1	1	yes	characteristic
749	C₅	C₃×#3224	1	1	yes	characteristic, direct product factor, Sylow
750	C₂²	—	2	1	no	—
751	C₂²	—	2	1	no	—
752	C₂²	—	2	1	no	—
753	C₂²	—	4	1	no	—
754	C₂²	—	4	1	no	—
755	C₂²	—	4	1	no	—
756	C₂²	—	4	1	no	—
757	C₂²	—	4	1	no	—
758	C₂²	—	4	1	no	—
759	C₂²	—	4	1	no	—
760	C₂²	—	4	1	no	—
761	C₂²	—	4	1	no	—
762	C₂²	—	4	1	no	—
763	C₂²	—	4	1	no	—
764	C₂²	—	4	1	no	—
765	C₂²	—	8	4	no	—
766	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
767	C₄	—	2	1	no	—
768	C₄	—	2	1	no	—
769	C₄	—	2	1	no	—
770	C₄	—	2	1	no	—
771	C₄	—	2	1	no	—
772	C₄	—	4	1	no	—
773	C₄	—	4	1	no	—
774	C₄	—	4	1	no	—
775	C₄	—	4	1	no	—
776	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
777	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
778	C₃	C₅×#3224	1	1	yes	characteristic, direct product factor, Sylow
779	C₂	—	4	1	no	—
780	C₂	—	8	1	no	—
781	C₂	—	8	1	no	—
782	C₂	—	8	1	no	—
783	C₂	—	8	1	no	—
784	C₂	C₃×C₅×#535	1	1	yes	characteristic
785	C₂	C₃×C₅×#576	1	1	yes	characteristic
786	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
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×#535	C₂	semidirect
3. C₃×C₅×#496	C₂	semidirect
4. C₃×C₅×#495	C₂	semidirect
5. C₃×C₅×#489	C₂	semidirect
6. C₃×C₅×#486	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#463	C₂	semidirect
9. C₃×C₅×#460	C₂	semidirect
10. C₃×C₅×#459	C₂	semidirect
11. C₃×C₅×#452	C₂	semidirect
12. C₃×C₅×#450	C₂	semidirect
13. C₃×C₅×#449	C₂	semidirect
14. C₃×C₅×#447	C₂	semidirect
15. C₃×C₅×#433	C₂	semidirect
16. C₅×#3224	C₃	direct (N × H)
19. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
22. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
23. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
26. C₂×C₃×C₅×D₈	C₂²	semidirect
27. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
34. C₃×C₅×#124	C₂²	semidirect
43. C₃×C₄×C₅×Q₈	C₂²	semidirect
44. C₃×C₄×C₅×D₄	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×#3224	C₅	direct (N × H)
61. C₅×#542	C₂×C₃	semidirect
62. C₅×#535	C₂×C₃	semidirect
63. C₅×#496	C₂×C₃	semidirect
64. C₅×#495	C₂×C₃	semidirect
65. C₅×#489	C₂×C₃	semidirect
66. C₅×#486	C₂×C₃	semidirect
67. C₅×#464	C₂×C₃	semidirect
68. C₅×#463	C₂×C₃	semidirect
69. C₅×#460	C₂×C₃	semidirect
70. C₅×#459	C₂×C₃	semidirect
71. C₅×#452	C₂×C₃	semidirect
72. C₅×#450	C₂×C₃	semidirect
73. C₅×#449	C₂×C₃	semidirect
74. C₅×#447	C₂×C₃	semidirect
75. C₅×#433	C₂×C₃	semidirect
131. C₃×#542	C₂×C₅	semidirect
132. C₃×#535	C₂×C₅	semidirect
133. C₃×#496	C₂×C₅	semidirect
134. C₃×#495	C₂×C₅	semidirect
135. C₃×#489	C₂×C₅	semidirect
136. C₃×#486	C₂×C₅	semidirect
137. C₃×#464	C₂×C₅	semidirect
138. C₃×#463	C₂×C₅	semidirect
139. C₃×#460	C₂×C₅	semidirect
140. C₃×#459	C₂×C₅	semidirect
141. C₃×#452	C₂×C₅	semidirect
142. C₃×#450	C₂×C₅	semidirect
143. C₃×#449	C₂×C₅	semidirect
144. C₃×#447	C₂×C₅	semidirect
145. C₃×#433	C₂×C₅	semidirect
148. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
151. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
152. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
155. C₂×C₅×D₈	C₂²×C₃	semidirect
156. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
163. C₅×#124	C₂²×C₃	semidirect
172. C₄×C₅×Q₈	C₂²×C₃	semidirect
173. C₄×C₅×D₄	C₂²×C₃	semidirect
175. C₅×C₄⋊C₈	C₂²×C₃	semidirect
176. C₅×C₄⋊C₈	C₂²×C₃	semidirect
177. C₅×#103	C₂²×C₃	semidirect
178. C₅×#103	C₂²×C₃	semidirect
183. C₅×#102	C₂²×C₃	semidirect
184. C₅×#102	C₂²×C₃	semidirect
187. C₅×#97	C₂²×C₃	semidirect
188. C₄×C₅×C₈	C₂²×C₃	semidirect
189. #3224	C₃×C₅	direct (N × H)
238. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
241. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
242. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
245. C₂×C₃×D₈	C₂²×C₅	semidirect
246. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
253. C₃×#124	C₂²×C₅	semidirect
262. C₃×C₄×Q₈	C₂²×C₅	semidirect
263. C₃×C₄×D₄	C₂²×C₅	semidirect
265. C₃×C₄⋊C₈	C₂²×C₅	semidirect
266. C₃×C₄⋊C₈	C₂²×C₅	semidirect
267. C₃×#103	C₂²×C₅	semidirect
268. C₃×#103	C₂²×C₅	semidirect
273. C₃×#102	C₂²×C₅	semidirect
274. C₃×#102	C₂²×C₅	semidirect
277. C₃×#97	C₂²×C₅	semidirect
278. C₃×C₄×C₈	C₂²×C₅	semidirect
334. #542	C₂×C₃×C₅	semidirect
335. #535	C₂×C₃×C₅	semidirect
336. #496	C₂×C₃×C₅	semidirect
337. #495	C₂×C₃×C₅	semidirect
338. #489	C₂×C₃×C₅	semidirect
339. #486	C₂×C₃×C₅	semidirect
340. #464	C₂×C₃×C₅	semidirect
341. #463	C₂×C₃×C₅	semidirect
342. #460	C₂×C₃×C₅	semidirect
343. #459	C₂×C₃×C₅	semidirect
344. #452	C₂×C₃×C₅	semidirect
345. #450	C₂×C₃×C₅	semidirect
346. #449	C₂×C₃×C₅	semidirect
347. #447	C₂×C₃×C₅	semidirect
348. #433	C₂×C₃×C₅	semidirect
480. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
483. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
484. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
487. C₂×D₈	C₂²×C₃×C₅	semidirect
488. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
495. #124	C₂²×C₃×C₅	semidirect
504. C₄×Q₈	C₂²×C₃×C₅	semidirect
505. C₄×D₄	C₂²×C₃×C₅	semidirect
507. C₄⋊C₈	C₂²×C₃×C₅	semidirect
508. C₄⋊C₈	C₂²×C₃×C₅	semidirect
509. #103	C₂²×C₃×C₅	semidirect
510. #103	C₂²×C₃×C₅	semidirect
515. #102	C₂²×C₃×C₅	semidirect
516. #102	C₂²×C₃×C₅	semidirect
519. #97	C₂²×C₃×C₅	semidirect
520. C₄×C₈	C₂²×C₃×C₅	semidirect
658. C₃×C₅	#3224	direct (N × H)
749. C₅	C₃×#3224	direct (N × H)
778. C₃	C₅×#3224	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×#535	2
C₃×C₅×#496	2
C₃×C₅×#495	2
C₃×C₅×#489	2
C₃×C₅×#486	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#460	2
C₃×C₅×#459	2
C₃×C₅×#452	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₅×#447	2
C₃×C₅×#433	2
C₅×#3224	3
C₃×#3224	5

Subgroups — C3×C5×#3224 #14276258

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3224 #14276258