Subgroups — D₃×#6817 #13089362

Order 1440.

696 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10624283	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#6817	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×#1220	C₂	1	2	yes	maximal, complemented
5	#10624207	C₂	1	2	yes	maximal, complemented
6	D₃×D₆₀	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×D₃×D₁₅	C₂	1	2	yes	maximal, complemented
8	#10624199	C₂	1	2	yes	maximal, complemented
9	#10624197	C₂	1	1	yes	maximal, characteristic, complemented
10	D₃×Dic₃₀	C₂	1	1	yes	maximal, characteristic, complemented
11	#10624193	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#6817	—	3	1	no	maximal
13	D₃×#709	—	3	1	no	maximal
14	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂×D₃×D₁₅	C₂²	1	2	yes	—
16	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic, complemented
17	#67184	C₂²	1	2	yes	complemented
18	C₄⋊(C₃⋊D₁₅)	C₂²	1	1	yes	characteristic, complemented
19	C₄×C₃⋊D₁₅	C₂²	1	2	yes	complemented
20	#67180	C₂²	1	1	yes	characteristic, complemented
21	C₃×#1220	C₂²	1	2	yes	complemented
22	C₃×D₆₀	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₄×D₁₅	C₂²	1	2	yes	complemented
24	C₃×Dic₃₀	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
29	C₃×C₄×C₅×D₃	C₂²	1	1	yes	characteristic, complemented
30	#67153	C₂²	1	2	yes	complemented
31	#67152	C₂²	1	2	yes	complemented
32	#67151	C₂²	1	2	yes	complemented
33	#67150	C₂²	1	2	yes	complemented
34	#67149	C₂²	1	2	yes	complemented
35	D₃×Dic₁₅	C₂²	1	2	yes	—
36	Dic₃×D₁₅	C₂²	1	2	yes	complemented
37	D₃×#235	—	5	1	no	maximal, Hall
38	C₂²×C₃×C₄×C₅	—	3	1	no	—
39	C₂×#1220	—	3	2	no	—
40	#6817	—	3	1	no	—
41	#6817	—	3	1	no	—
42	#6817	—	3	2	no	—
43	#6817	—	3	1	no	—
44	#6817	—	3	2	no	—
45	#6817	—	3	1	no	—
46	#6817	—	6	1	no	—
47	#6817	D₃	1	1	yes	characteristic, direct product factor
48	C₂×D₆₀	—	3	1	no	—
49	C₂×C₄×D₁₅	—	3	2	no	—
50	C₂×Dic₃₀	—	3	1	no	—
51	C₂×C₄×C₅×D₃	D₃	1	1	yes	characteristic, complemented
52	C₃×#709	—	3	1	no	—
53	D₃×C₂²⋊D₅	—	3	2	no	—
54	#6779	—	3	2	no	—
55	D₃×D₂₀	—	3	1	no	—
56	C₄×D₃×D₅	—	3	2	no	—
57	#6771	—	3	2	no	—
58	#6769	—	3	1	no	—
59	D₃×Dic₁₀	—	3	1	no	—
60	#6765	—	3	1	no	—
61	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
62	C₂×C₃⋊D₁₅	C₂³	1	2	yes	—
63	C₂×C₃×D₁₅	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₃	—	2	2	no	—
65	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₃	C₂³	1	1	yes	characteristic
67	D₃×D₁₅	—	2	4	no	—
68	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₃²×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₃⋊Dic₁₅	C₂³	1	2	yes	—
71	C₃×Dic₁₅	C₂³	1	2	yes	—
72	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₃×C₅×Dic₃	C₂³	1	1	yes	characteristic
74	C₂×#709	—	9	1	no	Hall
75	#3828	—	5	1	no	—
76	C₃×#235	—	5	1	no	—
77	C₂×C₃×C₄×D₃	D₅	1	1	yes	characteristic, complemented
78	D₃×#67	—	5	2	no	—
79	#3804	—	5	2	no	—
80	D₃×D₁₂	—	5	1	no	—
81	C₄×D₃²	—	5	2	no	—
82	#3799	—	5	1	no	—
83	#3798	—	5	2	no	—
84	#3795	—	5	1	no	—
85	D₃×Dic₆	—	5	1	no	—
86	C₂³×C₃×C₅	—	3	1	no	—
87	C₂²×D₁₅	—	3	2	no	—
88	C₂²×C₅×D₃	C₂×D₃	1	1	yes	characteristic
89	C₂×D₃×D₅	—	3	2	no	—
90	C₂×C₃×C₄×C₅	—	2	1	no	—
91	C₂×C₃×C₄×C₅	—	3	1	no	—
92	C₂×C₃×C₄×C₅	—	3	1	no	—
93	C₂×C₃×C₄×C₅	—	3	1	no	—
94	C₂×C₃×C₄×C₅	—	3	1	no	—
95	C₂×C₃×C₄×C₅	—	3	1	no	—
96	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
97	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic, complemented
98	#1220	—	3	2	no	—
99	#1220	—	3	2	no	—
100	#1220	—	3	2	no	—
101	#1220	—	3	2	no	—
102	#1220	—	6	2	no	—
103	#1220	C₂×D₃	1	2	yes	complemented
104	C₂×Dic₁₅	—	3	2	no	—
105	D₆₀	—	3	2	no	—
106	D₆₀	—	3	1	no	—
107	D₆₀	—	3	1	no	—
108	D₆₀	—	6	1	no	—
109	D₆₀	C₂×D₃	1	1	yes	characteristic, complemented
110	C₄×D₁₅	—	3	2	no	—
111	C₄×D₁₅	—	3	2	no	—
112	C₄×D₁₅	—	3	2	no	—
113	C₄×D₁₅	—	3	2	no	—
114	C₄×D₁₅	—	6	2	no	—
115	C₄×D₁₅	C₂×D₃	1	2	yes	complemented
116	Dic₃₀	—	3	1	no	—
117	Dic₃₀	—	3	1	no	—
118	Dic₃₀	—	3	2	no	—
119	Dic₃₀	—	6	1	no	—
120	Dic₃₀	C₂×D₃	1	1	yes	characteristic, complemented
121	C₂×C₅×Dic₃	C₂×D₃	1	1	yes	characteristic, complemented
122	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic
123	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic
124	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
125	C₄×C₅×D₃	C₂×D₃	1	1	yes	characteristic, complemented
126	C₃×C₂²⋊D₅	—	3	2	no	—
127	C₃×D₂₀	—	3	1	no	—
128	C₃×C₄×D₅	—	3	2	no	—
129	C₃×Dic₁₀	—	3	1	no	—
130	#1204	—	3	2	no	—
131	#1203	—	3	2	no	—
132	#1202	—	3	2	no	—
133	#1201	—	3	2	no	—
134	#1200	—	3	2	no	—
135	D₃×Dic₅	—	3	2	no	—
136	D₅×Dic₃	—	3	2	no	—
137	D₃×#41	—	15	1	no	—
138	C₂×#235	—	15	1	no	—
139	C₂×C₃²×C₅	—	2	1	no	—
140	C₂×C₃²×C₅	C₂⁴	1	1	yes	characteristic
141	C₃⋊D₁₅	—	2	2	no	—
142	C₃×D₁₅	—	2	2	no	—
143	C₃×C₅×D₃	—	2	1	no	—
144	C₃×C₅×D₃	#41	1	2	yes	complemented
145	C₂²×C₄×C₅	—	3	1	no	—
146	C₂×C₂²⋊D₅	—	9	2	no	—
147	#709	—	3	1	no	—
148	#709	—	9	1	no	—
149	#709	—	9	2	no	—
150	#709	—	9	1	no	—
151	#709	—	9	2	no	—
152	#709	—	9	1	no	—
153	C₂×D₂₀	—	9	1	no	—
154	C₂×C₄×D₅	—	9	2	no	—
155	C₂×Dic₁₀	—	9	1	no	—
156	C₂²×C₃×D₃	C₂×D₅	1	1	yes	characteristic
157	C₂×D₃²	—	5	2	no	—
158	C₂×C₃²×C₄	C₂×D₅	1	1	yes	characteristic, complemented
159	#638	—	5	2	no	—
160	C₄⋊(C₃⋊D₃)	—	5	1	no	—
161	C₄×C₃⋊D₃	—	5	2	no	—
162	#634	—	5	1	no	—
163	C₃×#67	—	5	2	no	—
164	C₂×C₃×Dic₃	C₂×D₅	1	1	yes	characteristic, complemented
165	C₃×D₁₂	—	5	1	no	—
166	C₃×C₄×D₃	—	5	2	no	—
167	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic
168	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic
169	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic, complemented
170	C₃×C₄×D₃	C₂×D₅	1	1	yes	characteristic, complemented
171	C₃×Dic₆	—	5	1	no	—
172	#627	—	5	2	no	—
173	#626	—	5	2	no	—
174	#626	—	5	2	no	—
175	#625	—	5	2	no	—
176	#624	—	5	2	no	—
177	D₃×Dic₃	—	5	2	no	—
178	D₃×Dic₃	—	5	2	no	—
179	C₂²×C₃×C₅	—	2	1	no	—
180	C₂²×C₃×C₅	—	3	1	no	—
181	C₂²×C₃×C₅	—	3	1	no	—
182	C₂²×C₃×C₅	—	6	2	no	—
183	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₂×D₁₅	—	3	2	no	—
186	C₂×D₁₅	—	3	2	no	—
187	C₂×D₁₅	—	6	2	no	—
188	C₂×D₁₅	—	6	4	no	—
189	C₂×D₁₅	C₂²×D₃	1	2	yes	—
190	C₂×C₅×D₃	—	2	2	no	—
191	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
192	C₂×C₅×D₃	C₂²×D₃	1	1	yes	characteristic
193	C₂×C₃×D₅	—	3	2	no	—
194	D₃×D₅	—	6	4	no	—
195	C₃×C₄×C₅	—	2	1	no	—
196	C₃×C₄×C₅	—	2	1	no	—
197	C₃×C₄×C₅	—	3	1	no	—
198	C₃×C₄×C₅	—	3	1	no	—
199	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
201	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₃×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
203	Dic₁₅	—	3	2	no	—
204	Dic₁₅	—	3	2	no	—
205	Dic₁₅	—	6	2	no	—
206	Dic₁₅	C₂²×D₃	1	2	yes	—
207	C₃×Dic₅	—	3	2	no	—
208	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
209	C₅×Dic₃	C₂²×D₃	1	1	yes	characteristic
210	C₃×#41	—	15	1	no	—
211	C₂²×C₃×C₄	—	3	1	no	—
212	C₂×#67	—	15	2	no	—
213	#239	—	15	1	no	—
214	D₃×Q₈	—	15	1	no	—
215	#237	—	15	2	no	—
216	#237	—	15	1	no	—
217	D₃×D₄	—	15	2	no	—
218	D₃×D₄	—	15	1	no	—
219	#235	—	5	1	no	—
220	#235	—	15	1	no	—
221	#235	—	15	2	no	—
222	#235	—	15	1	no	—
223	#235	—	15	2	no	—
224	#235	—	15	1	no	—
225	#235	—	15	1	no	—
226	#235	—	15	2	no	—
227	#235	—	30	1	no	—
228	C₂×D₁₂	—	15	1	no	—
229	C₂×C₄×D₃	—	15	2	no	—
230	C₂×C₄×D₃	—	15	2	no	—
231	C₂×C₄×D₃	D₁₅	1	1	yes	characteristic, complemented
232	C₂×Dic₆	—	15	1	no	—
233	C₃²×C₅	C₂×#41	1	1	yes	characteristic, complemented, Hall
234	C₂³×C₅	—	3	1	no	—
235	C₂²×D₅	—	9	2	no	—
236	C₂×C₄×C₅	—	3	1	no	—
237	C₂×C₄×C₅	—	3	1	no	—
238	C₂×C₄×C₅	—	3	1	no	—
239	C₂×C₄×C₅	—	3	1	no	—
240	C₂×C₄×C₅	—	3	1	no	—
241	C₂×C₄×C₅	D₃²	1	1	yes	characteristic, complemented
242	C₂²⋊D₅	—	3	2	no	—
243	C₂²⋊D₅	—	9	2	no	—
244	C₂²⋊D₅	—	9	2	no	—
245	C₂²⋊D₅	—	9	2	no	—
246	C₂×Dic₅	—	9	2	no	—
247	D₂₀	—	3	1	no	—
248	D₂₀	—	9	2	no	—
249	D₂₀	—	9	1	no	—
250	C₄×D₅	—	3	2	no	—
251	C₄×D₅	—	9	2	no	—
252	C₄×D₅	—	9	2	no	—
253	C₄×D₅	—	9	2	no	—
254	Dic₁₀	—	3	1	no	—
255	Dic₁₀	—	9	2	no	—
256	Dic₁₀	—	9	1	no	—
257	C₂²×C₃²	C₂²×D₅	1	1	yes	characteristic
258	C₂×C₃⋊D₃	—	5	2	no	—
259	C₂×C₃×D₃	—	2	2	no	—
260	C₂×C₃×D₃	—	5	2	no	—
261	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
262	C₂×C₃×D₃	C₂²×D₅	1	1	yes	characteristic
263	D₃²	—	10	4	no	—
264	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
265	C₃²×C₄	C₂²×D₅	1	1	yes	characteristic
266	C₃⋊Dic₃	—	5	2	no	—
267	C₃×Dic₃	—	5	2	no	—
268	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
269	C₃×Dic₃	C₂²×D₅	1	1	yes	characteristic
270	C₂×#41	—	45	1	no	Sylow
271	C₂×C₃×C₅	—	2	1	no	—
272	C₂×C₃×C₅	—	2	1	no	—
273	C₂×C₃×C₅	—	2	1	no	—
274	C₂×C₃×C₅	—	3	2	no	—
275	C₂×C₃×C₅	—	4	1	no	—
276	C₂×C₃×C₅	—	6	1	no	—
277	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
278	C₂×C₃×C₅	C₂³×D₃	1	1	yes	characteristic
279	D₁₅	—	2	2	no	—
280	D₁₅	—	6	2	no	—
281	D₁₅	—	6	2	no	—
282	D₁₅	—	12	2	no	—
283	C₃×D₅	—	6	2	no	—
284	C₅×D₃	—	2	1	no	—
285	C₅×D₃	#235	1	2	yes	complemented
286	C₂³×C₃	—	3	1	no	—
287	C₂²×D₃	—	15	2	no	—
288	C₂²×D₃	—	15	2	no	—
289	C₂²×D₃	C₂×D₁₅	1	1	yes	characteristic
290	C₃×Q₈	—	15	1	no	—
291	C₃×D₄	—	15	2	no	—
292	C₃×D₄	—	15	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	3	1	no	—
295	C₂×C₃×C₄	—	3	1	no	—
296	C₂×C₃×C₄	—	3	1	no	—
297	C₂×C₃×C₄	—	3	1	no	—
298	C₂×C₃×C₄	—	3	1	no	—
299	C₂×C₃×C₄	—	15	2	no	—
300	C₂×C₃×C₄	D₃×D₅	1	1	yes	characteristic, complemented
301	C₂×C₃×C₄	C₂×D₁₅	1	1	yes	characteristic, complemented
302	#67	—	5	2	no	—
303	#67	—	15	2	no	—
304	#67	—	15	2	no	—
305	#67	—	15	2	no	—
306	#67	—	15	2	no	—
307	#67	—	15	2	no	—
308	#67	—	15	2	no	—
309	#67	—	30	2	no	—
310	C₂×Dic₃	—	15	2	no	—
311	C₂×Dic₃	—	15	2	no	—
312	C₂×Dic₃	C₂×D₁₅	1	1	yes	characteristic, complemented
313	D₁₂	—	5	1	no	—
314	D₁₂	—	15	2	no	—
315	D₁₂	—	15	2	no	—
316	D₁₂	—	15	1	no	—
317	D₁₂	—	15	1	no	—
318	D₁₂	—	30	1	no	—
319	C₄×D₃	—	5	2	no	—
320	C₄×D₃	—	15	2	no	—
321	C₄×D₃	—	15	2	no	—
322	C₄×D₃	—	15	2	no	—
323	C₄×D₃	—	15	2	no	—
324	C₄×D₃	—	15	2	no	—
325	C₄×D₃	—	15	2	no	—
326	C₄×D₃	—	30	2	no	—
327	C₄×D₃	C₂×D₁₅	1	1	yes	characteristic
328	C₄×D₃	C₂×D₁₅	1	1	yes	characteristic
329	C₄×D₃	C₂×D₁₅	1	1	yes	characteristic, complemented
330	C₄×D₃	C₂×D₁₅	1	1	yes	characteristic, complemented
331	Dic₆	—	5	1	no	—
332	Dic₆	—	15	2	no	—
333	Dic₆	—	15	1	no	—
334	Dic₆	—	15	1	no	—
335	Dic₆	—	15	2	no	—
336	Dic₆	—	30	1	no	—
337	C₂²×C₅	—	3	1	no	—
338	C₂²×C₅	—	3	1	no	—
339	C₂²×C₅	—	6	2	no	—
340	C₂²×C₅	C₂×D₃²	1	1	yes	characteristic
341	C₂×D₅	—	3	2	no	—
342	C₂×D₅	—	9	2	no	—
343	C₂×D₅	—	18	4	no	—
344	C₄×C₅	—	3	1	no	—
345	C₄×C₅	—	3	1	no	—
346	C₄×C₅	C₂×D₃²	1	1	yes	characteristic
347	C₄×C₅	C₂×D₃²	1	1	yes	characteristic
348	Dic₅	—	3	2	no	—
349	Dic₅	—	9	2	no	—
350	C₂×C₃²	—	2	1	no	—
351	C₂×C₃²	C₂³×D₅	1	1	yes	characteristic
352	C₃⋊D₃	—	10	2	no	—
353	C₃×D₃	—	2	1	no	—
354	C₃×D₃	—	10	2	no	—
355	C₃×D₃	#709	1	2	yes	complemented
356	#41	—	15	1	no	—
357	#41	—	45	2	no	—
358	#41	—	45	2	no	—
359	#41	—	45	1	no	—
360	#41	—	45	1	no	—
361	#41	—	45	1	no	—
362	C₂×Q₈	—	45	1	no	—
363	C₂×D₄	—	45	1	no	—
364	C₂×D₄	—	45	2	no	—
365	C₂²×C₄	—	3	1	no	—
366	C₂²×C₄	—	45	2	no	—
367	C₃×C₅	—	2	1	no	—
368	C₃×C₅	C₂×#235	1	1	yes	characteristic, complemented
369	C₃×C₅	D₃×#41	1	1	yes	characteristic, complemented
370	C₂²×C₃	—	2	1	no	—
371	C₂²×C₃	—	3	1	no	—
372	C₂²×C₃	—	3	1	no	—
373	C₂²×C₃	—	6	2	no	—
374	C₂²×C₃	—	15	2	no	—
375	C₂²×C₃	C₂×D₃×D₅	1	1	yes	characteristic
376	C₂²×C₃	C₂²×D₁₅	1	1	yes	characteristic
377	C₂×D₃	—	2	2	no	—
378	C₂×D₃	—	5	2	no	—
379	C₂×D₃	—	15	2	no	—
380	C₂×D₃	—	15	2	no	—
381	C₂×D₃	—	30	2	no	—
382	C₂×D₃	—	30	4	no	—
383	C₂×D₃	—	30	4	no	—
384	C₂×D₃	C₂²×D₁₅	1	1	yes	characteristic
385	C₂×D₃	C₂²×D₁₅	1	1	yes	characteristic
386	C₃×C₄	—	2	1	no	—
387	C₃×C₄	—	2	1	no	—
388	C₃×C₄	—	3	1	no	—
389	C₃×C₄	—	3	1	no	—
390	C₃×C₄	—	15	2	no	—
391	C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
392	C₃×C₄	C₂×D₃×D₅	1	1	yes	characteristic
393	C₃×C₄	C₂²×D₁₅	1	1	yes	characteristic
394	C₃×C₄	C₂²×D₁₅	1	1	yes	characteristic
395	Dic₃	—	5	2	no	—
396	Dic₃	—	15	2	no	—
397	Dic₃	—	15	2	no	—
398	Dic₃	—	30	2	no	—
399	Dic₃	C₂²×D₁₅	1	1	yes	characteristic
400	Dic₃	C₂²×D₁₅	1	1	yes	characteristic
401	C₂×C₅	—	2	1	no	—
402	C₂×C₅	—	3	2	no	—
403	C₂×C₅	—	6	1	no	—
404	C₂×C₅	C₂²×D₃²	1	1	yes	characteristic
405	D₅	—	6	2	no	—
406	D₅	—	18	2	no	—
407	C₃²	C₂×#709	1	1	yes	characteristic, complemented, Sylow
408	C₂³	—	3	1	no	—
409	C₂³	—	45	2	no	—
410	Q₈	—	15	1	no	—
411	Q₈	—	45	2	no	—
412	Q₈	—	45	1	no	—
413	D₄	—	15	2	no	—
414	D₄	—	15	1	no	—
415	D₄	—	45	2	no	—
416	D₄	—	45	2	no	—
417	D₄	—	45	2	no	—
418	D₄	—	45	2	no	—
419	D₄	—	45	1	no	—
420	C₂×C₄	—	3	1	no	—
421	C₂×C₄	—	3	1	no	—
422	C₂×C₄	—	3	1	no	—
423	C₂×C₄	—	3	1	no	—
424	C₂×C₄	—	3	1	no	—
425	C₂×C₄	—	15	2	no	—
426	C₂×C₄	—	45	2	no	—
427	C₂×C₄	—	45	2	no	—
428	C₂×C₄	—	45	2	no	—
429	C₂×C₄	—	45	2	no	—
430	C₂×C₄	D₃×D₁₅	1	1	yes	characteristic, complemented
431	C₂×C₃	—	2	1	no	—
432	C₂×C₃	—	2	1	no	—
433	C₂×C₃	—	2	1	no	—
434	C₂×C₃	—	3	2	no	—
435	C₂×C₃	—	4	1	no	—
436	C₂×C₃	—	6	1	no	—
437	C₂×C₃	—	30	2	no	—
438	C₂×C₃	C₂²×D₃×D₅	1	1	yes	characteristic
439	C₂×C₃	C₂³×D₁₅	1	1	yes	characteristic
440	D₃	—	2	1	no	—
441	D₃	—	10	2	no	—
442	D₃	—	30	2	no	—
443	D₃	—	30	2	no	—
444	D₃	—	60	2	no	—
445	D₃	#6817	1	2	yes	direct product factor
446	C₅	D₃×#235	1	1	yes	characteristic, complemented, Sylow
447	C₂²	—	3	1	no	—
448	C₂²	—	3	1	no	—
449	C₂²	—	6	2	no	—
450	C₂²	—	15	2	no	—
451	C₂²	—	45	2	no	—
452	C₂²	—	90	4	no	—
453	C₂²	C₂×D₃×D₁₅	1	1	yes	characteristic
454	C₄	—	3	1	no	—
455	C₄	—	3	1	no	—
456	C₄	—	15	2	no	—
457	C₄	—	45	2	no	—
458	C₄	C₂×D₃×D₁₅	1	1	yes	characteristic
459	C₄	C₂×D₃×D₁₅	1	1	yes	characteristic
460	C₃	—	2	1	no	—
461	C₃	D₃×#709	1	1	yes	characteristic, complemented
462	C₃	C₂×#6817	1	1	yes	characteristic, complemented
463	C₂	—	2	1	no	—
464	C₂	—	3	2	no	—
465	C₂	—	6	1	no	—
466	C₂	—	30	2	no	—
467	C₂	—	90	2	no	—
468	C₂	C₂²×D₃×D₁₅	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₃×D₁₅
commutator, socle, cosocle	C₂×C₃²×C₅	C₂⁴
Frattini	C₂	C₂²×D₃×D₁₅
Fitting	C₂×C₃²×C₄×C₅	C₂²
hypercenter	C₂×C₄	D₃×D₁₅
hypocenter	C₃²×C₅	C₂×#41
LCS	G ▷ C₂×C₃²×C₅ ▷ C₃²×C₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #10624283	C₂	semidirect
2. C₃×#6817	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
4. D₃×#1220	C₂	semidirect
5. #10624207	C₂	semidirect
6. D₃×D₆₀	C₂	semidirect
7. C₄×D₃×D₁₅	C₂	semidirect
8. #10624199	C₂	semidirect
9. #10624197	C₂	semidirect
10. D₃×Dic₃₀	C₂	semidirect
11. #10624193	C₂	semidirect
16. C₂×C₃²×C₄×C₅	C₂²	semidirect
17. #67184	C₂²	semidirect
18. C₄⋊(C₃⋊D₁₅)	C₂²	semidirect
19. C₄×C₃⋊D₁₅	C₂²	semidirect
20. #67180	C₂²	semidirect
21. C₃×#1220	C₂²	semidirect
22. C₃×D₆₀	C₂²	semidirect
23. C₃×C₄×D₁₅	C₂²	semidirect
24. C₃×Dic₃₀	C₂²	semidirect
25. C₂×C₃×C₅×Dic₃	C₂²	semidirect
28. C₃×C₄×C₅×D₃	C₂²	semidirect
29. C₃×C₄×C₅×D₃	C₂²	semidirect
30. #67153	C₂²	semidirect
31. #67152	C₂²	semidirect
32. #67151	C₂²	semidirect
33. #67150	C₂²	semidirect
34. #67149	C₂²	semidirect
36. Dic₃×D₁₅	C₂²	semidirect
47. #6817	D₃	direct (N × H)
51. C₂×C₄×C₅×D₃	D₃	semidirect
77. C₂×C₃×C₄×D₃	D₅	semidirect
96. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
97. C₂×C₃×C₄×C₅	C₂×D₃	semidirect
103. #1220	C₂×D₃	semidirect
109. D₆₀	C₂×D₃	semidirect
115. C₄×D₁₅	C₂×D₃	semidirect
120. Dic₃₀	C₂×D₃	semidirect
121. C₂×C₅×Dic₃	C₂×D₃	semidirect
124. C₄×C₅×D₃	C₂×D₃	semidirect
125. C₄×C₅×D₃	C₂×D₃	semidirect
144. C₃×C₅×D₃	#41	semidirect
158. C₂×C₃²×C₄	C₂×D₅	semidirect
164. C₂×C₃×Dic₃	C₂×D₅	semidirect
169. C₃×C₄×D₃	C₂×D₅	semidirect
170. C₃×C₄×D₃	C₂×D₅	semidirect
231. C₂×C₄×D₃	D₁₅	semidirect
233. C₃²×C₅	C₂×#41	semidirect
241. C₂×C₄×C₅	D₃²	semidirect
285. C₅×D₃	#235	semidirect
300. C₂×C₃×C₄	D₃×D₅	semidirect
301. C₂×C₃×C₄	C₂×D₁₅	semidirect
312. C₂×Dic₃	C₂×D₁₅	semidirect
329. C₄×D₃	C₂×D₁₅	semidirect
330. C₄×D₃	C₂×D₁₅	semidirect
355. C₃×D₃	#709	semidirect
368. C₃×C₅	C₂×#235	semidirect
369. C₃×C₅	D₃×#41	semidirect
407. C₃²	C₂×#709	semidirect
430. C₂×C₄	D₃×D₁₅	semidirect
445. D₃	#6817	direct (N × H)
446. C₅	D₃×#235	semidirect
461. C₃	D₃×#709	semidirect
462. C₃	C₂×#6817	semidirect

Maximal subgroups

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

subgroup	index
#10624283	2
C₃×#6817	2
C₂×C₃×C₄×C₅×D₃	2
D₃×#1220	2
#10624207	2
D₃×D₆₀	2
C₄×D₃×D₁₅	2
#10624199	2
#10624197	2
D₃×Dic₃₀	2
#10624193	2
C₂×#6817	3
D₃×#709	3
D₃×#235	5

Subgroups — D3×#6817 #13089362

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#6817 #13089362