Subgroups — C₃×C₅×#3300 #14276334

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#548	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#488	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#485	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#480	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#479	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#465	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#464	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#452	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#451	C₂	1	1	yes	maximal, characteristic, complemented
12	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
13	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
14	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
16	C₅×#3300	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×#126	—	2	1	no	—
25	C₃×C₅×#125	—	2	1	no	—
26	C₃×C₅×#125	C₂²	1	1	yes	characteristic
27	C₃×C₅×#124	—	2	1	no	—
28	C₃×C₅×#124	C₂²	1	1	yes	characteristic
29	C₃×C₅×#123	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#121	—	2	1	no	—
35	C₃×C₅×#121	C₂²	1	1	yes	characteristic
36	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
37	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
38	C₃×C₄×C₅×D₄	—	2	1	no	—
39	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
40	C₃×C₅×#117	—	2	1	no	—
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic
42	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
43	C₃×C₅×#107	C₂²	1	1	yes	characteristic
44	C₃×C₅×#107	C₂²	1	1	yes	characteristic
45	C₃×C₅×#106	C₂²	1	1	yes	characteristic
46	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₃×C₅×#103	C₂²	1	1	yes	characteristic
48	C₃×C₅×#103	C₂²	1	1	yes	characteristic
49	C₃×C₅×#103	C₂²	1	1	yes	characteristic
50	C₃×C₅×#103	C₂²	1	1	yes	characteristic
51	C₃×C₅×#103	C₂²	1	1	yes	characteristic
52	C₃×C₅×#103	C₂²	1	1	yes	characteristic
53	C₃×C₅×#103	C₂²	1	1	yes	characteristic
54	C₃×C₅×#102	C₂²	1	1	yes	characteristic
55	C₃×C₅×#102	C₂²	1	1	yes	characteristic
56	C₃×C₅×#102	C₂²	1	1	yes	characteristic
57	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
58	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
59	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
60	C₃×#3300	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
61	C₅×#552	C₂×C₃	1	1	yes	characteristic, complemented
62	C₅×#548	C₂×C₃	1	1	yes	characteristic
63	C₅×#488	C₂×C₃	1	1	yes	characteristic, complemented
64	C₅×#485	C₂×C₃	1	1	yes	characteristic, complemented
65	C₅×#480	C₂×C₃	1	1	yes	characteristic, complemented
66	C₅×#479	C₂×C₃	1	1	yes	characteristic, complemented
67	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
68	C₅×#465	C₂×C₃	1	1	yes	characteristic, complemented
69	C₅×#464	C₂×C₃	1	1	yes	characteristic, complemented
70	C₅×#452	C₂×C₃	1	1	yes	characteristic, complemented
71	C₅×#451	C₂×C₃	1	1	yes	characteristic, complemented
72	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
73	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
74	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
75	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
76	C₃×C₅×#41	—	2	2	no	—
77	C₃×C₅×#41	—	4	1	no	—
78	C₂×C₃×C₅×Q₈	—	2	1	no	—
79	C₂×C₃×C₅×Q₈	—	2	2	no	—
80	C₂×C₃×C₅×Q₈	—	4	1	no	—
81	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
82	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
83	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
84	C₂×C₃×C₅×D₄	—	2	1	no	—
85	C₂×C₃×C₅×D₄	—	2	1	no	—
86	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
87	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
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	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
93	C₃×C₅×Q₁₆	—	2	2	no	—
94	C₃×C₅×Q₁₆	—	4	1	no	—
95	C₃×C₅×SD₁₆	—	4	1	no	—
96	C₂×C₃×C₅×C₈	—	4	1	no	—
97	C₂×C₃×C₅×C₈	—	4	1	no	—
98	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
99	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
100	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
101	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
102	C₃×C₅×C₄⋊C₄	—	2	1	no	—
103	C₃×C₅×C₄⋊C₄	—	2	1	no	—
104	C₃×C₅×C₄⋊C₄	—	2	1	no	—
105	C₃×C₅×C₄⋊C₄	—	2	1	no	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	1	no	—
108	C₃×C₅×C₄⋊C₄	—	2	1	no	—
109	C₃×C₅×C₄⋊C₄	—	2	1	no	—
110	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
111	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
114	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
120	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
121	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
122	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
123	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
124	C₃×C₄²×C₅	—	2	1	no	—
125	C₃×C₄²×C₅	—	2	1	no	—
126	C₃×C₄²×C₅	—	2	1	no	—
127	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
128	C₃×#552	C₂×C₅	1	1	yes	characteristic, complemented
129	C₃×#548	C₂×C₅	1	1	yes	characteristic
130	C₃×#488	C₂×C₅	1	1	yes	characteristic, complemented
131	C₃×#485	C₂×C₅	1	1	yes	characteristic, complemented
132	C₃×#480	C₂×C₅	1	1	yes	characteristic, complemented
133	C₃×#479	C₂×C₅	1	1	yes	characteristic, complemented
134	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
135	C₃×#465	C₂×C₅	1	1	yes	characteristic, complemented
136	C₃×#464	C₂×C₅	1	1	yes	characteristic, complemented
137	C₃×#452	C₂×C₅	1	1	yes	characteristic, complemented
138	C₃×#451	C₂×C₅	1	1	yes	characteristic, complemented
139	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
140	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
141	C₃×#416	C₂×C₅	1	1	yes	characteristic, complemented
142	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
143	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
144	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
145	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
146	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
147	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
148	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
149	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
150	C₅×#126	—	2	1	no	—
151	C₅×#125	—	2	1	no	—
152	C₅×#125	C₂²×C₃	1	1	yes	characteristic
153	C₅×#124	—	2	1	no	—
154	C₅×#124	C₂²×C₃	1	1	yes	characteristic
155	C₅×#123	—	2	1	no	—
156	C₅×C₂²⋊Q₈	—	2	1	no	—
157	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
158	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
159	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
160	C₅×#121	—	2	1	no	—
161	C₅×#121	C₂²×C₃	1	1	yes	characteristic
162	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
163	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
164	C₄×C₅×D₄	—	2	1	no	—
165	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
166	C₅×#117	—	2	1	no	—
167	C₅×#117	C₂²×C₃	1	1	yes	characteristic
168	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
169	C₅×#107	C₂²×C₃	1	1	yes	characteristic
170	C₅×#107	C₂²×C₃	1	1	yes	characteristic
171	C₅×#106	C₂²×C₃	1	1	yes	characteristic
172	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
173	C₅×#103	C₂²×C₃	1	1	yes	characteristic
174	C₅×#103	C₂²×C₃	1	1	yes	characteristic
175	C₅×#103	C₂²×C₃	1	1	yes	characteristic
176	C₅×#103	C₂²×C₃	1	1	yes	characteristic
177	C₅×#103	C₂²×C₃	1	1	yes	characteristic
178	C₅×#103	C₂²×C₃	1	1	yes	characteristic
179	C₅×#103	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×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
184	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
185	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
186	#3300	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
187	C₂³×C₃×C₅	—	2	1	no	—
188	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
189	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
190	C₃×C₅×Q₈	—	2	1	no	—
191	C₃×C₅×Q₈	—	2	1	no	—
192	C₃×C₅×Q₈	—	2	1	no	—
193	C₃×C₅×Q₈	—	2	1	no	—
194	C₃×C₅×Q₈	—	2	1	no	—
195	C₃×C₅×Q₈	—	4	2	no	—
196	C₃×C₅×Q₈	#41	1	2	yes	—
197	C₃×C₅×D₄	—	2	2	no	—
198	C₃×C₅×D₄	—	2	1	no	—
199	C₃×C₅×D₄	—	2	1	no	—
200	C₃×C₅×D₄	—	4	2	no	—
201	C₃×C₅×D₄	—	4	2	no	—
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	—	2	1	no	—
210	C₂×C₃×C₄×C₅	—	2	1	no	—
211	C₂×C₃×C₄×C₅	—	2	1	no	—
212	C₂×C₃×C₄×C₅	—	2	1	no	—
213	C₂×C₃×C₄×C₅	—	4	2	no	—
214	C₂×C₃×C₄×C₅	—	4	2	no	—
215	C₂×C₃×C₄×C₅	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
220	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
221	C₃×C₅×C₈	—	2	1	no	—
222	C₃×C₅×C₈	—	2	1	no	—
223	C₃×C₅×C₈	—	2	1	no	—
224	C₃×C₅×C₈	—	2	1	no	—
225	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
226	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
227	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
228	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
229	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
230	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
231	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
232	C₃×#126	—	2	1	no	—
233	C₃×#125	—	2	1	no	—
234	C₃×#125	C₂²×C₅	1	1	yes	characteristic
235	C₃×#124	—	2	1	no	—
236	C₃×#124	C₂²×C₅	1	1	yes	characteristic
237	C₃×#123	—	2	1	no	—
238	C₃×C₂²⋊Q₈	—	2	1	no	—
239	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
240	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
241	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
242	C₃×#121	—	2	1	no	—
243	C₃×#121	C₂²×C₅	1	1	yes	characteristic
244	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
245	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
246	C₃×C₄×D₄	—	2	1	no	—
247	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
248	C₃×#117	—	2	1	no	—
249	C₃×#117	C₂²×C₅	1	1	yes	characteristic
250	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
251	C₃×#107	C₂²×C₅	1	1	yes	characteristic
252	C₃×#107	C₂²×C₅	1	1	yes	characteristic
253	C₃×#106	C₂²×C₅	1	1	yes	characteristic
254	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
255	C₃×#103	C₂²×C₅	1	1	yes	characteristic
256	C₃×#103	C₂²×C₅	1	1	yes	characteristic
257	C₃×#103	C₂²×C₅	1	1	yes	characteristic
258	C₃×#103	C₂²×C₅	1	1	yes	characteristic
259	C₃×#103	C₂²×C₅	1	1	yes	characteristic
260	C₃×#103	C₂²×C₅	1	1	yes	characteristic
261	C₃×#103	C₂²×C₅	1	1	yes	characteristic
262	C₃×#102	C₂²×C₅	1	1	yes	characteristic
263	C₃×#102	C₂²×C₅	1	1	yes	characteristic
264	C₃×#102	C₂²×C₅	1	1	yes	characteristic
265	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
266	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
267	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
268	C₅×#41	—	2	2	no	—
269	C₅×#41	—	4	1	no	—
270	C₂×C₅×Q₈	—	2	1	no	—
271	C₂×C₅×Q₈	—	2	2	no	—
272	C₂×C₅×Q₈	—	4	1	no	—
273	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
274	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
275	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
276	C₂×C₅×D₄	—	2	1	no	—
277	C₂×C₅×D₄	—	2	1	no	—
278	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
279	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
280	C₂²×C₄×C₅	—	2	1	no	—
281	C₂²×C₄×C₅	—	2	1	no	—
282	C₂²×C₄×C₅	—	2	1	no	—
283	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
284	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
285	C₅×Q₁₆	—	2	2	no	—
286	C₅×Q₁₆	—	4	1	no	—
287	C₅×SD₁₆	—	4	1	no	—
288	C₂×C₅×C₈	—	4	1	no	—
289	C₂×C₅×C₈	—	4	1	no	—
290	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
291	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
292	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
293	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
294	C₅×C₄⋊C₄	—	2	1	no	—
295	C₅×C₄⋊C₄	—	2	1	no	—
296	C₅×C₄⋊C₄	—	2	1	no	—
297	C₅×C₄⋊C₄	—	2	1	no	—
298	C₅×C₄⋊C₄	—	2	1	no	—
299	C₅×C₄⋊C₄	—	2	1	no	—
300	C₅×C₄⋊C₄	—	2	1	no	—
301	C₅×C₄⋊C₄	—	2	1	no	—
302	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
303	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
304	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
305	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
306	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
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	—	2	1	no	—
311	C₅×C₂²⋊C₄	—	2	1	no	—
312	C₅×C₂²⋊C₄	—	2	1	no	—
313	C₅×C₂²⋊C₄	—	2	1	no	—
314	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
315	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
316	C₄²×C₅	—	2	1	no	—
317	C₄²×C₅	—	2	1	no	—
318	C₄²×C₅	—	2	1	no	—
319	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
320	#552	C₂×C₃×C₅	1	1	yes	characteristic, complemented
321	#548	C₂×C₃×C₅	1	1	yes	characteristic
322	#488	C₂×C₃×C₅	1	1	yes	characteristic, complemented
323	#485	C₂×C₃×C₅	1	1	yes	characteristic, complemented
324	#480	C₂×C₃×C₅	1	1	yes	characteristic, complemented
325	#479	C₂×C₃×C₅	1	1	yes	characteristic, complemented
326	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
327	#465	C₂×C₃×C₅	1	1	yes	characteristic, complemented
328	#464	C₂×C₃×C₅	1	1	yes	characteristic, complemented
329	#452	C₂×C₃×C₅	1	1	yes	characteristic, complemented
330	#451	C₂×C₃×C₅	1	1	yes	characteristic, complemented
331	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
332	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
333	#416	C₂×C₃×C₅	1	1	yes	characteristic, complemented
334	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
335	C₂²×C₃×C₅	—	2	1	no	—
336	C₂²×C₃×C₅	—	2	1	no	—
337	C₂²×C₃×C₅	—	2	1	no	—
338	C₂²×C₃×C₅	—	2	1	no	—
339	C₂²×C₃×C₅	—	2	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	#135	1	2	yes	—
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	2	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	—	4	1	no	—
356	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
357	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
358	C₃×#41	—	2	2	no	—
359	C₃×#41	—	4	1	no	—
360	C₂×C₃×Q₈	—	2	1	no	—
361	C₂×C₃×Q₈	—	2	2	no	—
362	C₂×C₃×Q₈	—	4	1	no	—
363	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
365	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
366	C₂×C₃×D₄	—	2	1	no	—
367	C₂×C₃×D₄	—	2	1	no	—
368	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
369	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
370	C₂²×C₃×C₄	—	2	1	no	—
371	C₂²×C₃×C₄	—	2	1	no	—
372	C₂²×C₃×C₄	—	2	1	no	—
373	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
374	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
375	C₃×Q₁₆	—	2	2	no	—
376	C₃×Q₁₆	—	4	1	no	—
377	C₃×SD₁₆	—	4	1	no	—
378	C₂×C₃×C₈	—	4	1	no	—
379	C₂×C₃×C₈	—	4	1	no	—
380	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
381	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
382	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
383	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
384	C₃×C₄⋊C₄	—	2	1	no	—
385	C₃×C₄⋊C₄	—	2	1	no	—
386	C₃×C₄⋊C₄	—	2	1	no	—
387	C₃×C₄⋊C₄	—	2	1	no	—
388	C₃×C₄⋊C₄	—	2	1	no	—
389	C₃×C₄⋊C₄	—	2	1	no	—
390	C₃×C₄⋊C₄	—	2	1	no	—
391	C₃×C₄⋊C₄	—	2	1	no	—
392	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
393	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
394	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
395	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
396	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
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	—	2	1	no	—
401	C₃×C₂²⋊C₄	—	2	1	no	—
402	C₃×C₂²⋊C₄	—	2	1	no	—
403	C₃×C₂²⋊C₄	—	2	1	no	—
404	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
405	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
406	C₃×C₄²	—	2	1	no	—
407	C₃×C₄²	—	2	1	no	—
408	C₃×C₄²	—	2	1	no	—
409	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
410	C₂³×C₅	—	2	1	no	—
411	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
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	—	2	1	no	—
416	C₅×Q₈	—	2	1	no	—
417	C₅×Q₈	—	2	1	no	—
418	C₅×Q₈	—	4	2	no	—
419	C₅×Q₈	C₃×#41	1	2	yes	—
420	C₅×D₄	—	2	2	no	—
421	C₅×D₄	—	2	1	no	—
422	C₅×D₄	—	2	1	no	—
423	C₅×D₄	—	4	2	no	—
424	C₅×D₄	—	4	2	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	—	2	1	no	—
432	C₂×C₄×C₅	—	2	1	no	—
433	C₂×C₄×C₅	—	2	1	no	—
434	C₂×C₄×C₅	—	2	1	no	—
435	C₂×C₄×C₅	—	2	1	no	—
436	C₂×C₄×C₅	—	4	2	no	—
437	C₂×C₄×C₅	—	4	2	no	—
438	C₂×C₄×C₅	—	4	2	no	—
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	C₂×C₃×D₄	1	1	yes	characteristic
442	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
443	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
444	C₅×C₈	—	2	1	no	—
445	C₅×C₈	—	2	1	no	—
446	C₅×C₈	—	2	1	no	—
447	C₅×C₈	—	2	1	no	—
448	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
449	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
450	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
451	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
452	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
453	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
454	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
455	#126	—	2	1	no	—
456	#125	—	2	1	no	—
457	#125	C₂²×C₃×C₅	1	1	yes	characteristic
458	#124	—	2	1	no	—
459	#124	C₂²×C₃×C₅	1	1	yes	characteristic
460	#123	—	2	1	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
463	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
464	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
465	#121	—	2	1	no	—
466	#121	C₂²×C₃×C₅	1	1	yes	characteristic
467	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
468	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
469	C₄×D₄	—	2	1	no	—
470	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
471	#117	—	2	1	no	—
472	#117	C₂²×C₃×C₅	1	1	yes	characteristic
473	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
474	#107	C₂²×C₃×C₅	1	1	yes	characteristic
475	#107	C₂²×C₃×C₅	1	1	yes	characteristic
476	#106	C₂²×C₃×C₅	1	1	yes	characteristic
477	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
478	#103	C₂²×C₃×C₅	1	1	yes	characteristic
479	#103	C₂²×C₃×C₅	1	1	yes	characteristic
480	#103	C₂²×C₃×C₅	1	1	yes	characteristic
481	#103	C₂²×C₃×C₅	1	1	yes	characteristic
482	#103	C₂²×C₃×C₅	1	1	yes	characteristic
483	#103	C₂²×C₃×C₅	1	1	yes	characteristic
484	#103	C₂²×C₃×C₅	1	1	yes	characteristic
485	#102	C₂²×C₃×C₅	1	1	yes	characteristic
486	#102	C₂²×C₃×C₅	1	1	yes	characteristic
487	#102	C₂²×C₃×C₅	1	1	yes	characteristic
488	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
489	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
490	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
491	C₂×C₃×C₅	—	2	2	no	—
492	C₂×C₃×C₅	—	4	1	no	—
493	C₂×C₃×C₅	—	8	1	no	—
494	C₂×C₃×C₅	#546	1	1	yes	characteristic
495	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
496	C₂×C₃×C₅	#578	1	1	yes	characteristic
497	C₂³×C₃	—	2	1	no	—
498	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
499	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
500	C₃×Q₈	—	2	1	no	—
501	C₃×Q₈	—	2	1	no	—
502	C₃×Q₈	—	2	1	no	—
503	C₃×Q₈	—	2	1	no	—
504	C₃×Q₈	—	2	1	no	—
505	C₃×Q₈	—	4	2	no	—
506	C₃×Q₈	C₅×#41	1	2	yes	—
507	C₃×D₄	—	2	2	no	—
508	C₃×D₄	—	2	1	no	—
509	C₃×D₄	—	2	1	no	—
510	C₃×D₄	—	4	2	no	—
511	C₃×D₄	—	4	2	no	—
512	C₂×C₃×C₄	—	2	1	no	—
513	C₂×C₃×C₄	—	2	1	no	—
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	—	2	1	no	—
522	C₂×C₃×C₄	—	2	1	no	—
523	C₂×C₃×C₄	—	4	2	no	—
524	C₂×C₃×C₄	—	4	2	no	—
525	C₂×C₃×C₄	—	4	2	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	C₂⁴×C₅	1	1	yes	characteristic
531	C₃×C₈	—	2	1	no	—
532	C₃×C₈	—	2	1	no	—
533	C₃×C₈	—	2	1	no	—
534	C₃×C₈	—	2	1	no	—
535	C₂²×C₅	—	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	1	no	—
540	C₂²×C₅	—	4	1	no	—
541	C₂²×C₅	—	4	1	no	—
542	C₂²×C₅	—	4	1	no	—
543	C₂²×C₅	C₃×#135	1	2	yes	—
544	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
545	C₄×C₅	—	2	1	no	—
546	C₄×C₅	—	2	1	no	—
547	C₄×C₅	—	2	1	no	—
548	C₄×C₅	—	2	1	no	—
549	C₄×C₅	—	2	2	no	—
550	C₄×C₅	—	4	1	no	—
551	C₄×C₅	—	4	1	no	—
552	C₄×C₅	—	4	1	no	—
553	C₄×C₅	—	4	1	no	—
554	C₄×C₅	—	4	1	no	—
555	C₄×C₅	—	4	1	no	—
556	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
557	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
558	#41	—	2	2	no	—
559	#41	—	4	1	no	—
560	C₂×Q₈	—	2	1	no	—
561	C₂×Q₈	—	2	2	no	—
562	C₂×Q₈	—	4	1	no	—
563	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
564	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
565	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
566	C₂×D₄	—	2	1	no	—
567	C₂×D₄	—	2	1	no	—
568	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
569	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	1	no	—
572	C₂²×C₄	—	2	1	no	—
573	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
574	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
575	Q₁₆	—	2	2	no	—
576	Q₁₆	—	4	1	no	—
577	SD₁₆	—	4	1	no	—
578	C₂×C₈	—	4	1	no	—
579	C₂×C₈	—	4	1	no	—
580	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
581	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
582	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
583	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	C₃×C₅×D₄	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	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
596	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
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	C₃×C₅×D₄	1	1	yes	characteristic
605	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
606	C₄²	—	2	1	no	—
607	C₄²	—	2	1	no	—
608	C₄²	—	2	1	no	—
609	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
610	C₃×C₅	#3300	1	1	yes	characteristic, direct product factor, Hall
611	C₂²×C₃	—	2	1	no	—
612	C₂²×C₃	—	2	1	no	—
613	C₂²×C₃	—	2	1	no	—
614	C₂²×C₃	—	2	1	no	—
615	C₂²×C₃	—	2	1	no	—
616	C₂²×C₃	—	4	1	no	—
617	C₂²×C₃	—	4	1	no	—
618	C₂²×C₃	—	4	1	no	—
619	C₂²×C₃	C₅×#135	1	2	yes	—
620	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
621	C₃×C₄	—	2	1	no	—
622	C₃×C₄	—	2	1	no	—
623	C₃×C₄	—	2	2	no	—
624	C₃×C₄	—	2	1	no	—
625	C₃×C₄	—	2	1	no	—
626	C₃×C₄	—	4	1	no	—
627	C₃×C₄	—	4	1	no	—
628	C₃×C₄	—	4	1	no	—
629	C₃×C₄	—	4	1	no	—
630	C₃×C₄	—	4	1	no	—
631	C₃×C₄	—	4	1	no	—
632	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
633	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
634	C₂×C₅	—	2	2	no	—
635	C₂×C₅	—	4	1	no	—
636	C₂×C₅	—	8	1	no	—
637	C₂×C₅	C₃×#546	1	1	yes	characteristic
638	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
639	C₂×C₅	C₃×#578	1	1	yes	characteristic
640	C₂³	—	2	1	no	—
641	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
642	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
643	Q₈	—	2	1	no	—
644	Q₈	—	2	1	no	—
645	Q₈	—	2	1	no	—
646	Q₈	—	2	1	no	—
647	Q₈	—	2	1	no	—
648	Q₈	—	4	2	no	—
649	Q₈	C₃×C₅×#41	1	2	yes	—
650	D₄	—	2	2	no	—
651	D₄	—	2	1	no	—
652	D₄	—	2	1	no	—
653	D₄	—	4	2	no	—
654	D₄	—	4	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	1	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	1	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	2	1	no	—
661	C₂×C₄	—	2	1	no	—
662	C₂×C₄	—	2	1	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	4	2	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	2	no	—
669	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
670	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
671	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
672	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
673	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
674	C₈	—	2	1	no	—
675	C₈	—	2	1	no	—
676	C₈	—	2	1	no	—
677	C₈	—	2	1	no	—
678	C₂×C₃	—	2	2	no	—
679	C₂×C₃	—	4	1	no	—
680	C₂×C₃	—	8	1	no	—
681	C₂×C₃	C₅×#546	1	1	yes	characteristic
682	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
683	C₂×C₃	C₅×#578	1	1	yes	characteristic
684	C₅	C₃×#3300	1	1	yes	characteristic, direct product factor, Sylow
685	C₂²	—	2	1	no	—
686	C₂²	—	2	1	no	—
687	C₂²	—	2	1	no	—
688	C₂²	—	2	1	no	—
689	C₂²	—	2	1	no	—
690	C₂²	—	4	1	no	—
691	C₂²	—	4	1	no	—
692	C₂²	—	4	1	no	—
693	C₂²	C₃×C₅×#135	1	2	yes	—
694	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
695	C₄	—	2	1	no	—
696	C₄	—	2	1	no	—
697	C₄	—	2	2	no	—
698	C₄	—	2	1	no	—
699	C₄	—	2	1	no	—
700	C₄	—	4	1	no	—
701	C₄	—	4	1	no	—
702	C₄	—	4	1	no	—
703	C₄	—	4	1	no	—
704	C₄	—	4	1	no	—
705	C₄	—	4	1	no	—
706	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
707	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
708	C₃	C₅×#3300	1	1	yes	characteristic, direct product factor, Sylow
709	C₂	—	2	2	no	—
710	C₂	—	4	1	no	—
711	C₂	—	8	1	no	—
712	C₂	C₃×C₅×#546	1	1	yes	characteristic
713	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
714	C₂	C₃×C₅×#578	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×#548	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#552	C₂	semidirect
3. C₃×C₅×#488	C₂	semidirect
4. C₃×C₅×#485	C₂	semidirect
5. C₃×C₅×#480	C₂	semidirect
6. C₃×C₅×#479	C₂	semidirect
7. C₃×C₅×#467	C₂	semidirect
8. C₃×C₅×#465	C₂	semidirect
9. C₃×C₅×#464	C₂	semidirect
10. C₃×C₅×#452	C₂	semidirect
11. C₃×C₅×#451	C₂	semidirect
12. C₃×C₄×C₅×Q₁₆	C₂	semidirect
13. C₃×C₅×C₈×D₄	C₂	semidirect
14. C₃×C₅×#416	C₂	semidirect
15. C₂×C₃×C₅×#103	C₂	semidirect
16. C₅×#3300	C₃	direct (N × H)
60. C₃×#3300	C₅	direct (N × H)
61. C₅×#552	C₂×C₃	semidirect
63. C₅×#488	C₂×C₃	semidirect
64. C₅×#485	C₂×C₃	semidirect
65. C₅×#480	C₂×C₃	semidirect
66. C₅×#479	C₂×C₃	semidirect
67. C₅×#467	C₂×C₃	semidirect
68. C₅×#465	C₂×C₃	semidirect
69. C₅×#464	C₂×C₃	semidirect
70. C₅×#452	C₂×C₃	semidirect
71. C₅×#451	C₂×C₃	semidirect
72. C₄×C₅×Q₁₆	C₂×C₃	semidirect
73. C₅×C₈×D₄	C₂×C₃	semidirect
74. C₅×#416	C₂×C₃	semidirect
75. C₂×C₅×#103	C₂×C₃	semidirect
128. C₃×#552	C₂×C₅	semidirect
130. C₃×#488	C₂×C₅	semidirect
131. C₃×#485	C₂×C₅	semidirect
132. C₃×#480	C₂×C₅	semidirect
133. C₃×#479	C₂×C₅	semidirect
134. C₃×#467	C₂×C₅	semidirect
135. C₃×#465	C₂×C₅	semidirect
136. C₃×#464	C₂×C₅	semidirect
137. C₃×#452	C₂×C₅	semidirect
138. C₃×#451	C₂×C₅	semidirect
139. C₃×C₄×Q₁₆	C₂×C₅	semidirect
140. C₃×C₈×D₄	C₂×C₅	semidirect
141. C₃×#416	C₂×C₅	semidirect
142. C₂×C₃×#103	C₂×C₅	semidirect
186. #3300	C₃×C₅	direct (N × H)
320. #552	C₂×C₃×C₅	semidirect
322. #488	C₂×C₃×C₅	semidirect
323. #485	C₂×C₃×C₅	semidirect
324. #480	C₂×C₃×C₅	semidirect
325. #479	C₂×C₃×C₅	semidirect
326. #467	C₂×C₃×C₅	semidirect
327. #465	C₂×C₃×C₅	semidirect
328. #464	C₂×C₃×C₅	semidirect
329. #452	C₂×C₃×C₅	semidirect
330. #451	C₂×C₃×C₅	semidirect
331. C₄×Q₁₆	C₂×C₃×C₅	semidirect
332. C₈×D₄	C₂×C₃×C₅	semidirect
333. #416	C₂×C₃×C₅	semidirect
334. C₂×#103	C₂×C₃×C₅	semidirect
610. C₃×C₅	#3300	direct (N × H)
684. C₅	C₃×#3300	direct (N × H)
708. C₃	C₅×#3300	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×#552	2
C₃×C₅×#548	2
C₃×C₅×#488	2
C₃×C₅×#485	2
C₃×C₅×#480	2
C₃×C₅×#479	2
C₃×C₅×#467	2
C₃×C₅×#465	2
C₃×C₅×#464	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#416	2
C₂×C₃×C₅×#103	2
C₅×#3300	3
C₃×#3300	5

Subgroups — C3×C5×#3300 #14276334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3300 #14276334