Subgroups — D₁₅×#433 #14413819

Order 1920.

824 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₅×#117	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#433	C₂	1	1	yes	maximal, characteristic, complemented
3	#11751101	C₂	1	1	yes	maximal, characteristic, complemented
4	#11750941	C₂	1	2	yes	maximal, complemented
5	D₁₅×C₄⋊C₈	C₂	1	2	yes	maximal, complemented
6	D₁₅×C₂²⋊C₈	C₂	1	2	yes	maximal
7	#11750821	C₂	1	2	yes	maximal, complemented
8	#11750810	C₂	1	1	yes	maximal, characteristic, complemented
9	D₁₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
10	#11750791	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×C₈×D₁₅	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#433	—	3	1	no	maximal, Hall
13	C₂²×C₄×D₁₅	C₂²	1	1	yes	characteristic
14	C₃×C₅×#117	C₂²	1	1	yes	characteristic
15	#91815	C₂²	1	1	yes	characteristic
16	C₂×C₈×D₁₅	C₂²	1	2	yes	—
17	C₂×C₈×D₁₅	C₂²	1	2	yes	—
18	#91781	C₄	1	2	yes	—
19	C₄⋊C₄×D₁₅	C₄	1	2	yes	—
20	C₂²⋊C₄×D₁₅	C₄	1	2	yes	—
21	#91766	C₄	1	2	yes	—
22	#91761	C₂²	1	1	yes	characteristic
23	#91761	C₂²	1	1	yes	characteristic
24	C₄²×D₁₅	C₂²	1	1	yes	characteristic
25	C₄²×D₁₅	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
27	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
28	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
30	#91114	C₂²	1	2	yes	—
31	#91104	C₂²	1	2	yes	—
32	#91104	C₂²	1	2	yes	—
33	#91099	C₂²	1	2	yes	complemented
34	#91098	C₂²	1	2	yes	complemented
35	#91098	C₂²	1	2	yes	complemented
36	C₈×Dic₁₅	C₂²	1	2	yes	complemented
37	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	complemented
38	#91087	C₂²	1	1	yes	characteristic, complemented
39	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic, complemented
40	D₃×#433	—	5	1	no	maximal, Hall
41	D₅×#117	—	3	1	no	—
42	C₅×#433	D₃	1	1	yes	characteristic, complemented
43	#65289	—	3	1	no	—
44	#65129	—	3	2	no	—
45	D₅×C₄⋊C₈	—	3	2	no	—
46	D₅×C₂²⋊C₈	—	3	2	no	—
47	#65009	—	3	2	no	—
48	#64998	—	3	1	no	—
49	D₅×#97	—	3	1	no	—
50	#64979	—	3	1	no	—
51	C₄×C₈×D₅	—	3	1	no	—
52	C₂³×D₁₅	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×Dic₁₅	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×D₁₅	—	2	4	no	—
56	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
57	C₂×C₄×D₁₅	C₂×C₄	1	2	yes	—
58	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×D₁₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
61	C₂×C₄×D₁₅	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	—
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
68	#6719	C₂×C₄	1	2	yes	—
69	#6714	C₂×C₄	1	2	yes	—
70	#6714	C₂×C₄	1	2	yes	—
71	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
72	#6712	C₂×C₄	1	2	yes	—
73	#6712	C₂×C₄	1	2	yes	—
74	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
75	C₄×Dic₁₅	C₂×C₄	1	2	yes	—
76	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
77	C₄×Dic₁₅	C₂³	1	1	yes	characteristic
78	C₂×C₃⋊#168	C₂³	1	2	yes	—
79	C₂×C₃⋊#168	C₂³	1	2	yes	—
80	C₈×D₁₅	—	2	4	no	—
81	C₈×D₁₅	—	2	4	no	—
82	D₃×#117	—	5	1	no	—
83	C₃×#433	D₅	1	1	yes	characteristic, complemented
84	#5000	—	5	1	no	—
85	#4840	—	5	2	no	—
86	D₃×C₄⋊C₈	—	5	2	no	—
87	D₃×C₂²⋊C₈	—	5	2	no	—
88	#4720	—	5	2	no	—
89	#4709	—	5	1	no	—
90	D₃×#97	—	5	1	no	—
91	#4690	—	5	1	no	—
92	C₄×D₃×C₈	—	5	1	no	—
93	C₂²×C₄×D₅	—	3	1	no	—
94	C₅×#117	C₂×D₃	1	1	yes	characteristic
95	#4072	—	3	1	no	—
96	C₂×C₈×D₅	—	3	2	no	—
97	C₂×C₈×D₅	—	3	2	no	—
98	#4038	—	3	2	no	—
99	D₅×C₄⋊C₄	—	3	2	no	—
100	D₅×C₂²⋊C₄	—	3	2	no	—
101	#4023	—	3	2	no	—
102	#4018	—	3	1	no	—
103	#4018	—	3	1	no	—
104	C₄²×D₅	—	3	1	no	—
105	C₄²×D₅	—	3	1	no	—
106	C₅×C₄⋊C₈	C₂×D₃	1	2	yes	complemented
107	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
108	C₅×#97	C₂×D₃	1	1	yes	characteristic, complemented
109	C₄×C₅×C₈	C₂×D₃	1	1	yes	characteristic, complemented
110	C₂²⋊#168	—	3	2	no	—
111	#3952	—	3	2	no	—
112	#3952	—	3	2	no	—
113	#3947	—	3	2	no	—
114	#3946	—	3	2	no	—
115	#3946	—	3	2	no	—
116	C₈×Dic₅	—	3	2	no	—
117	C₄⋊#168	—	3	2	no	—
118	#3935	—	3	1	no	—
119	C₄×#168	—	3	1	no	—
120	C₂×#433	—	15	1	no	Sylow
121	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₁₅	—	2	2	no	—
123	C₂²×D₁₅	—	2	4	no	—
124	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
125	C₂²×D₁₅	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×Dic₁₅	—	2	2	no	—
132	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
133	C₂×Dic₁₅	C₂²×C₄	1	2	yes	—
134	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×Dic₁₅	C₂²×C₄	1	1	yes	characteristic
136	C₄×D₁₅	—	2	2	no	—
137	C₄×D₁₅	—	2	4	no	—
138	C₄×D₁₅	—	2	4	no	—
139	C₄×D₁₅	—	2	2	no	—
140	C₄×D₁₅	—	2	2	no	—
141	C₄×D₁₅	#41	1	4	yes	—
142	C₃×C₅×C₈	—	2	2	no	—
143	C₃×C₅×C₈	—	2	2	no	—
144	C₃⋊#168	—	2	2	no	—
145	C₃⋊#168	—	2	2	no	—
146	C₂²×C₄×D₃	—	5	1	no	—
147	C₃×#117	C₂×D₅	1	1	yes	characteristic
148	#926	—	5	1	no	—
149	C₂×D₃×C₈	—	5	2	no	—
150	C₂×D₃×C₈	—	5	2	no	—
151	#892	—	5	2	no	—
152	D₃×C₄⋊C₄	—	5	2	no	—
153	D₃×C₂²⋊C₄	—	5	2	no	—
154	#877	—	5	2	no	—
155	#872	—	5	1	no	—
156	#872	—	5	1	no	—
157	C₄²×D₃	—	5	1	no	—
158	C₄²×D₃	—	5	1	no	—
159	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
160	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
161	C₃×#97	C₂×D₅	1	1	yes	characteristic, complemented
162	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
163	#830	—	5	2	no	—
164	(C₂×D₃)⋊C₈	—	5	2	no	—
165	(C₂×D₃)⋊C₈	—	5	2	no	—
166	#815	—	5	2	no	—
167	Dic₃⋊C₈	—	5	2	no	—
168	Dic₃⋊C₈	—	5	2	no	—
169	C₈×Dic₃	—	5	2	no	—
170	C₄⋊(C₃⋊C₈)	—	5	2	no	—
171	#803	—	5	1	no	—
172	C₄×C₃⋊C₈	—	5	1	no	—
173	C₂³×D₅	—	3	1	no	—
174	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
175	C₂²×Dic₅	—	3	1	no	—
176	C₂×C₄×D₅	—	3	1	no	—
177	C₂×C₄×D₅	—	3	1	no	—
178	C₂×C₄×D₅	—	3	1	no	—
179	C₂×C₄×D₅	—	3	2	no	—
180	C₂×C₄×D₅	—	3	2	no	—
181	C₂×C₄×D₅	—	3	1	no	—
182	C₂×C₄×D₅	—	6	4	no	—
183	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
184	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
185	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
186	C₅×C₂²⋊C₄	C₄×D₃	1	2	yes	—
187	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
188	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
189	C₂²⋊Dic₅	—	3	2	no	—
190	#685	—	3	2	no	—
191	#685	—	3	2	no	—
192	C₄⋊Dic₅	—	3	2	no	—
193	#683	—	3	2	no	—
194	#683	—	3	2	no	—
195	C₄×Dic₅	—	3	2	no	—
196	C₄×Dic₅	—	3	2	no	—
197	C₄×Dic₅	—	3	1	no	—
198	C₄×Dic₅	—	3	1	no	—
199	C₂×#168	—	3	2	no	—
200	C₂×#168	—	3	2	no	—
201	C₈×D₅	—	6	4	no	—
202	C₈×D₅	—	6	4	no	—
203	C₂×#117	—	15	1	no	—
204	#433	—	15	1	no	—
205	#433	—	15	2	no	—
206	#433	—	15	2	no	—
207	#433	—	15	1	no	—
208	#433	—	15	1	no	—
209	#433	D₁₅	1	1	yes	characteristic, direct product factor
210	C₂×C₄⋊C₈	—	15	2	no	—
211	C₂×C₂²⋊C₈	—	15	2	no	—
212	C₂×#97	—	15	1	no	—
213	C₂×C₄×C₈	—	15	1	no	—
214	C₂²×C₃×C₅	—	2	1	no	—
215	C₂²×C₃×C₅	—	2	2	no	—
216	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
217	C₂×D₁₅	—	2	1	no	—
218	C₂×D₁₅	—	2	2	no	—
219	C₂×D₁₅	—	4	4	no	—
220	C₂×D₁₅	#117	1	2	yes	—
221	C₂×D₁₅	#131	1	4	yes	—
222	C₃×C₄×C₅	—	2	1	no	—
223	C₃×C₄×C₅	—	2	2	no	—
224	C₃×C₄×C₅	—	2	2	no	—
225	C₃×C₄×C₅	C₂×#41	1	2	yes	—
226	Dic₁₅	—	2	1	no	—
227	Dic₁₅	—	2	2	no	—
228	Dic₁₅	—	2	2	no	—
229	Dic₁₅	#117	1	2	yes	—
230	C₂³×D₃	—	5	1	no	—
231	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
232	C₂²×Dic₃	—	5	1	no	—
233	C₂×C₄×D₃	—	5	1	no	—
234	C₂×C₄×D₃	—	5	2	no	—
235	C₂×C₄×D₃	—	5	2	no	—
236	C₂×C₄×D₃	—	5	1	no	—
237	C₂×C₄×D₃	—	5	1	no	—
238	C₂×C₄×D₃	—	5	1	no	—
239	C₂×C₄×D₃	—	10	4	no	—
240	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
241	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
242	C₃×C₄⋊C₄	C₄×D₅	1	2	yes	—
243	C₃×C₂²⋊C₄	C₄×D₅	1	2	yes	—
244	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
245	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
246	#217	—	5	2	no	—
247	(C₂×D₃)⋊C₄	—	5	2	no	—
248	(C₂×D₃)⋊C₄	—	5	2	no	—
249	C₄⋊Dic₃	—	5	2	no	—
250	Dic₃⋊C₄	—	5	2	no	—
251	Dic₃⋊C₄	—	5	2	no	—
252	C₄×Dic₃	—	5	2	no	—
253	C₄×Dic₃	—	5	2	no	—
254	C₄×Dic₃	—	5	1	no	—
255	C₄×Dic₃	—	5	1	no	—
256	C₂×C₃⋊C₈	—	5	2	no	—
257	C₂×C₃⋊C₈	—	5	2	no	—
258	D₃×C₈	—	10	4	no	—
259	D₃×C₈	—	10	4	no	—
260	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
261	C₂²×D₅	—	3	1	no	—
262	C₂²×D₅	—	3	1	no	—
263	C₂²×D₅	—	6	2	no	—
264	C₂²×D₅	—	6	4	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
267	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
270	C₂×Dic₅	—	3	1	no	—
271	C₂×Dic₅	—	3	2	no	—
272	C₂×Dic₅	—	3	2	no	—
273	C₂×Dic₅	—	3	1	no	—
274	C₂×Dic₅	—	6	2	no	—
275	C₄×D₅	—	3	4	no	—
276	C₄×D₅	—	6	2	no	—
277	C₄×D₅	—	6	4	no	—
278	C₄×D₅	—	6	4	no	—
279	C₄×D₅	—	6	2	no	—
280	C₄×D₅	—	6	2	no	—
281	C₅×C₈	—	2	2	no	—
282	C₅×C₈	—	2	2	no	—
283	#168	—	6	2	no	—
284	#168	—	6	2	no	—
285	C₂³×C₄	—	15	1	no	—
286	C₂²×C₈	—	15	2	no	—
287	C₂²×C₈	—	15	2	no	—
288	#117	—	15	1	no	—
289	#117	—	15	2	no	—
290	#117	—	15	2	no	—
291	#117	—	15	1	no	—
292	#117	—	15	1	no	—
293	#117	C₂×D₁₅	1	1	yes	characteristic
294	C₂×C₄⋊C₄	—	15	2	no	—
295	C₂×C₂²⋊C₄	—	15	2	no	—
296	C₂×C₄²	—	15	1	no	—
297	C₂×C₄²	—	15	1	no	—
298	C₄⋊C₈	—	15	2	no	—
299	C₄⋊C₈	—	15	2	no	—
300	C₄⋊C₈	—	15	2	no	—
301	C₄⋊C₈	C₂×D₁₅	1	2	yes	complemented
302	C₂²⋊C₈	—	15	2	no	—
303	C₂²⋊C₈	—	15	2	no	—
304	C₂²⋊C₈	—	15	2	no	—
305	C₂²⋊C₈	C₂×D₁₅	1	2	yes	—
306	#97	—	15	2	no	—
307	#97	—	15	1	no	—
308	#97	C₂×D₁₅	1	1	yes	characteristic, complemented
309	C₄×C₈	—	15	2	no	—
310	C₄×C₈	—	15	1	no	—
311	C₄×C₈	C₂×D₁₅	1	1	yes	characteristic, complemented
312	C₂×C₃×C₅	—	4	1	no	—
313	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
314	C₂×C₃×C₅	C₂×#131	1	2	yes	—
315	D₁₅	—	4	1	no	—
316	D₁₅	#433	1	4	yes	direct product factor
317	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
318	C₂²×D₃	—	5	1	no	—
319	C₂²×D₃	—	5	1	no	—
320	C₂²×D₃	—	10	2	no	—
321	C₂²×D₃	—	10	4	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
324	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
325	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
326	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
327	C₂×Dic₃	—	5	1	no	—
328	C₂×Dic₃	—	5	2	no	—
329	C₂×Dic₃	—	5	2	no	—
330	C₂×Dic₃	—	5	1	no	—
331	C₂×Dic₃	—	10	2	no	—
332	C₄×D₃	—	5	4	no	—
333	C₄×D₃	—	10	2	no	—
334	C₄×D₃	—	10	4	no	—
335	C₄×D₃	—	10	4	no	—
336	C₄×D₃	—	10	2	no	—
337	C₄×D₃	—	10	2	no	—
338	C₃×C₈	—	2	2	no	—
339	C₃×C₈	—	2	2	no	—
340	C₃⋊C₈	—	10	2	no	—
341	C₃⋊C₈	—	10	2	no	—
342	C₂²×C₅	—	2	2	no	—
343	C₂²×C₅	—	2	1	no	—
344	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
345	C₂×D₅	—	3	4	no	—
346	C₂×D₅	—	3	2	no	—
347	C₂×D₅	—	6	2	no	—
348	C₂×D₅	—	6	1	no	—
349	C₂×D₅	—	12	4	no	—
350	C₄×C₅	—	2	2	no	—
351	C₄×C₅	—	2	2	no	—
352	C₄×C₅	—	2	1	no	—
353	C₄×C₅	D₃×#41	1	2	yes	—
354	Dic₅	—	3	2	no	—
355	Dic₅	—	6	2	no	—
356	Dic₅	—	6	2	no	—
357	Dic₅	—	6	1	no	—
358	C₂⁴	—	15	1	no	—
359	C₂²×C₄	—	15	1	no	—
360	C₂²×C₄	—	15	1	no	—
361	C₂²×C₄	—	15	2	no	—
362	C₂²×C₄	—	15	2	no	—
363	C₂²×C₄	—	15	1	no	—
364	C₂²×C₄	—	15	1	no	—
365	C₂²×C₄	—	15	1	no	—
366	C₂²×C₄	—	30	4	no	—
367	C₂²×C₄	C₂²×D₁₅	1	1	yes	characteristic
368	C₂×C₈	—	15	2	no	—
369	C₂×C₈	—	15	2	no	—
370	C₂×C₈	—	30	4	no	—
371	C₂×C₈	—	30	4	no	—
372	C₂×C₈	C₂²×D₁₅	1	2	yes	—
373	C₂×C₈	C₂²×D₁₅	1	2	yes	—
374	C₄⋊C₄	—	15	2	no	—
375	C₄⋊C₄	—	15	2	no	—
376	C₄⋊C₄	—	15	2	no	—
377	C₄⋊C₄	C₄×D₁₅	1	2	yes	—
378	C₂²⋊C₄	—	15	2	no	—
379	C₂²⋊C₄	—	15	2	no	—
380	C₂²⋊C₄	—	15	2	no	—
381	C₂²⋊C₄	C₄×D₁₅	1	2	yes	—
382	C₄²	—	15	2	no	—
383	C₄²	—	15	2	no	—
384	C₄²	—	15	1	no	—
385	C₄²	—	15	1	no	—
386	C₄²	C₂²×D₁₅	1	1	yes	characteristic
387	C₄²	C₂²×D₁₅	1	1	yes	characteristic
388	C₃×C₅	C₂×#433	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	1	no	—
391	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
392	C₂×D₃	—	5	4	no	—
393	C₂×D₃	—	5	2	no	—
394	C₂×D₃	—	10	2	no	—
395	C₂×D₃	—	10	1	no	—
396	C₂×D₃	—	20	4	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	2	no	—
399	C₃×C₄	—	2	1	no	—
400	C₃×C₄	D₅×#41	1	2	yes	—
401	Dic₃	—	5	2	no	—
402	Dic₃	—	10	2	no	—
403	Dic₃	—	10	2	no	—
404	Dic₃	—	10	1	no	—
405	C₂×C₅	—	4	1	no	—
406	C₂×C₅	D₃×#117	1	1	yes	characteristic
407	C₂×C₅	D₃×#131	1	2	yes	—
408	D₅	—	3	4	no	—
409	D₅	—	12	1	no	—
410	C₂³	—	15	1	no	—
411	C₂³	—	15	1	no	—
412	C₂³	—	30	2	no	—
413	C₂³	—	30	4	no	—
414	C₂³	C₂×C₄×D₁₅	1	1	yes	characteristic
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	15	1	no	—
417	C₂×C₄	—	15	4	no	—
418	C₂×C₄	—	15	2	no	—
419	C₂×C₄	—	15	2	no	—
420	C₂×C₄	—	15	1	no	—
421	C₂×C₄	—	30	2	no	—
422	C₂×C₄	—	30	2	no	—
423	C₂×C₄	—	30	4	no	—
424	C₂×C₄	—	30	4	no	—
425	C₂×C₄	—	30	2	no	—
426	C₂×C₄	—	30	2	no	—
427	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
428	C₂×C₄	C₂×C₄×D₁₅	1	2	yes	—
429	C₂×C₄	C₂×C₄×D₁₅	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₁₅	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	30	2	no	—
434	C₈	—	30	2	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	D₅×#117	1	1	yes	characteristic
437	C₂×C₃	D₅×#131	1	2	yes	—
438	D₃	—	5	4	no	—
439	D₃	—	20	1	no	—
440	C₅	D₃×#433	1	1	yes	characteristic, complemented, Sylow
441	C₂²	—	2	2	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	15	4	no	—
444	C₂²	—	15	2	no	—
445	C₂²	—	30	2	no	—
446	C₂²	—	30	1	no	—
447	C₂²	—	60	4	no	—
448	C₂²	C₂²×C₄×D₁₅	1	1	yes	characteristic
449	C₄	—	2	2	no	—
450	C₄	—	2	2	no	—
451	C₄	—	2	1	no	—
452	C₄	—	15	2	no	—
453	C₄	—	30	2	no	—
454	C₄	—	30	2	no	—
455	C₄	—	30	1	no	—
456	C₄	#41×D₁₅	1	2	yes	—
457	C₃	D₅×#433	1	1	yes	characteristic, complemented, Sylow
458	C₂	—	4	1	no	—
459	C₂	—	15	4	no	—
460	C₂	—	60	1	no	—
461	C₂	D₁₅×#117	1	1	yes	characteristic
462	C₂	D₁₅×#131	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₅×#433	C₂
prime radical	C₂³×D₁₅	C₂×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	#433	D₁₅
hypocenter	C₃×C₅	C₂×#433
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#433	C₂	semidirect
3. #11751101	C₂	semidirect
4. #11750941	C₂	semidirect
5. D₁₅×C₄⋊C₈	C₂	semidirect
7. #11750821	C₂	semidirect
8. #11750810	C₂	semidirect
9. D₁₅×#97	C₂	semidirect
10. #11750791	C₂	semidirect
11. C₄×C₈×D₁₅	C₂	semidirect
26. C₃×C₅×C₄⋊C₈	C₂²	semidirect
28. C₃×C₅×#97	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
33. #91099	C₂²	semidirect
34. #91098	C₂²	semidirect
35. #91098	C₂²	semidirect
36. C₈×Dic₁₅	C₂²	semidirect
37. C₄⋊(C₃⋊#168)	C₂²	semidirect
38. #91087	C₂²	semidirect
39. C₄×C₃⋊#168	C₂²	semidirect
42. C₅×#433	D₃	semidirect
83. C₃×#433	D₅	semidirect
106. C₅×C₄⋊C₈	C₂×D₃	semidirect
108. C₅×#97	C₂×D₃	semidirect
109. C₄×C₅×C₈	C₂×D₃	semidirect
159. C₃×C₄⋊C₈	C₂×D₅	semidirect
161. C₃×#97	C₂×D₅	semidirect
162. C₃×C₄×C₈	C₂×D₅	semidirect
209. #433	D₁₅	direct (N × H)
301. C₄⋊C₈	C₂×D₁₅	semidirect
308. #97	C₂×D₁₅	semidirect
311. C₄×C₈	C₂×D₁₅	semidirect
316. D₁₅	#433	direct (N × H)
388. C₃×C₅	C₂×#433	semidirect
440. C₅	D₃×#433	semidirect
457. C₃	D₅×#433	semidirect

Maximal subgroups

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

subgroup	index
D₁₅×#117	2
C₃×C₅×#433	2
#11751101	2
#11750941	2
D₁₅×C₄⋊C₈	2
D₁₅×C₂²⋊C₈	2
#11750821	2
#11750810	2
D₁₅×#97	2
#11750791	2
C₄×C₈×D₁₅	2
D₅×#433	3
D₃×#433	5

Subgroups — D15×#433 #14413819

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₅×#433 #14413819