Subgroups — Dic₃×#4053 #14411481

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4053	C₂	1	1	yes	maximal, characteristic
2	Dic₃×#709	C₂	1	1	yes	maximal, characteristic
3	C₂×#91284	C₂	1	1	yes	maximal, characteristic
4	#11751223	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#11748324	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×Dic₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
8	#11748051	C₂	1	2	yes	maximal, complemented
9	#11747646	C₂	1	2	yes	maximal, complemented
10	Dic₃×#676	C₂	1	2	yes	maximal, complemented
11	C₈×D₅×Dic₃	C₂	1	2	yes	maximal, complemented
12	C₄×#4053	—	3	1	no	maximal, Hall
13	C₂×C₃×#709	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
15	#91815	C₂²	1	1	yes	characteristic
16	C₂²×C₃⋊#168	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₅×#208	C₂²	1	1	yes	characteristic
19	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
20	C₃×#4053	C₄	1	8	yes	complemented
21	C₂×C₃×#676	C₂²	1	2	yes	—
22	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
23	Dic₃×C₂²⋊D₅	C₄	1	4	yes	—
24	Dic₃×D₂₀	C₄	1	2	yes	—
25	C₄×D₅×Dic₃	C₂²	1	2	yes	—
26	#91357	C₂²	1	2	yes	—
27	Dic₃×Dic₁₀	C₄	1	2	yes	—
28	C₂×#6649	C₂²	1	2	yes	—
29	#91284	C₄	1	8	yes	complemented
30	C₂×D₅×C₃⋊C₈	C₂²	1	2	yes	—
31	#91099	C₂²	1	2	yes	—
32	C₈×Dic₁₅	C₂²	1	2	yes	—
33	C₅×#815	C₂²	1	2	yes	—
34	C₅×C₈×Dic₃	C₂²	1	2	yes	—
35	#90954	C₂²	1	2	yes	—
36	#90951	C₂²	1	2	yes	—
37	Dic₃×#168	C₂²	1	1	yes	characteristic
38	Dic₃×#168	C₂²	1	1	yes	characteristic
39	Dic₃×#168	C₂²	1	1	yes	characteristic
40	Dic₃×#168	C₂²	1	1	yes	characteristic
41	Dic₃×#131	—	5	1	no	maximal, Hall
42	C₂×#4053	—	3	1	no	—
43	C₂×#4053	D₃	1	1	yes	characteristic
44	C₄×#709	—	3	1	no	—
45	C₄×C₅×M₁₆	—	3	1	no	—
46	#65411	—	3	1	no	—
47	#65411	—	3	1	no	—
48	C₂×C₄×#168	—	3	1	no	—
49	#64997	—	3	2	no	—
50	#64997	—	3	2	no	—
51	C₄×#676	—	3	2	no	—
52	C₄×C₈×D₅	—	3	2	no	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
55	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	2	yes	—
56	C₃×#709	C₂×C₄	1	4	yes	—
57	C₃×#709	C₂×C₄	1	4	yes	—
58	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
60	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
61	C₂×D₅×Dic₃	C₂×C₄	1	4	yes	—
62	C₃×C₅×M₁₆	C₂×C₄	1	4	yes	complemented
63	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
64	#6719	C₂×C₄	1	2	yes	—
65	C₄⋊Dic₁₅	C₂×C₄	1	2	yes	—
66	C₄×Dic₁₅	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	C₂×C₄	1	4	yes	complemented
68	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
71	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
73	C₅×#208	C₂×C₄	1	4	yes	complemented
74	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
75	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
76	C₂×C₃×#168	C₂³	1	1	yes	characteristic
77	C₂×C₃×#168	C₂³	1	1	yes	characteristic
78	C₃×#676	C₂×C₄	1	8	yes	complemented
79	C₃×C₈×D₅	C₂×C₄	1	8	yes	complemented
80	#6668	C₂×C₄	1	4	yes	—
81	#6665	C₂×C₄	1	4	yes	—
82	Dic₃×Dic₅	C₂×C₄	1	4	yes	—
83	#6649	C₂×C₄	1	8	yes	complemented
84	D₅×C₃⋊C₈	C₂×C₄	1	8	yes	complemented
85	C₂×C₃×#131	—	5	1	no	—
86	Dic₃×#41	—	5	1	no	—
87	C₂×#948	—	5	1	no	—
88	#5122	—	5	1	no	—
89	#5122	—	5	2	no	—
90	Dic₃×M₁₆	—	5	2	no	—
91	Dic₃×M₁₆	D₅	1	1	yes	characteristic, complemented
92	#5101	—	5	1	no	—
93	#5101	—	5	2	no	—
94	C₂×C₈×Dic₃	—	5	1	no	—
95	C₂×C₈×Dic₃	—	5	2	no	—
96	C₂×#709	C₂×D₃	1	1	yes	characteristic
97	C₂×C₅×M₁₆	—	3	1	no	—
98	C₂×C₅×M₁₆	C₂×D₃	1	1	yes	characteristic
99	C₂×C₄²×C₅	—	3	1	no	—
100	C₄×C₂²⋊D₅	—	3	4	no	—
101	#4072	—	3	1	no	—
102	C₂²×#168	—	3	1	no	—
103	C₂²×#168	C₂×D₃	1	1	yes	characteristic
104	#4053	—	3	8	no	—
105	#4053	Dic₃	1	8	yes	direct product factor
106	C₂×#676	—	3	2	no	—
107	C₂×#676	C₂×D₃	1	2	yes	—
108	C₂×C₈×D₅	—	3	2	no	—
109	C₂×C₈×D₅	C₂×D₃	1	2	yes	—
110	C₄×D₂₀	—	3	2	no	—
111	#4018	—	3	2	no	—
112	C₄²×D₅	—	3	2	no	—
113	C₄×Dic₁₀	—	3	2	no	—
114	C₅×#97	—	3	2	no	—
115	C₄×C₅×C₈	—	3	2	no	—
116	#3947	—	3	2	no	—
117	#3947	—	3	2	no	—
118	C₈×Dic₅	—	3	2	no	—
119	C₈×Dic₅	—	3	2	no	—
120	C₄×#168	—	3	1	no	—
121	C₄×#168	—	3	1	no	—
122	C₄×#168	—	3	1	no	—
123	C₄×#168	—	3	1	no	—
124	C₄×#131	—	15	1	no	Sylow
125	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
131	C₂×Dic₁₅	C₂²×C₄	1	4	yes	—
132	C₂×C₅×Dic₃	—	2	4	no	—
133	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
134	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
135	C₃×C₂²⋊D₅	C₄²	1	8	yes	—
136	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
137	C₃×D₂₀	C₄²	1	4	yes	—
138	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
139	C₃×C₄×D₅	C₂²×C₄	1	4	yes	—
140	C₃×Dic₁₀	C₄²	1	4	yes	—
141	D₅×Dic₃	—	2	8	no	—
142	C₃×C₅×C₈	C₂²×C₄	1	4	yes	—
143	C₃⋊#168	C₂²×C₄	1	2	yes	—
144	C₃⋊#168	C₂²×C₄	1	2	yes	—
145	C₃×#168	C₂²×C₄	1	2	yes	—
146	C₃×#168	C₂²×C₄	1	2	yes	—
147	C₅×C₃⋊C₈	C₂²×C₄	1	4	yes	—
148	C₂×C₃×#41	—	5	1	no	—
149	C₃×#131	—	5	8	no	—
150	C₂×C₃×M₁₆	—	5	2	no	—
151	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
152	C₂²×C₃×C₈	—	5	1	no	—
153	C₂²×C₃×C₈	—	5	2	no	—
154	#948	—	5	8	no	—
155	Q₈×Dic₃	—	5	2	no	—
156	D₄×Dic₃	—	5	4	no	—
157	D₄×Dic₃	—	5	2	no	—
158	#926	—	5	1	no	—
159	#926	—	5	2	no	—
160	C₂×C₄×Dic₃	—	5	2	no	—
161	C₂×C₄×Dic₃	C₂×D₅	1	1	yes	characteristic
162	C₂×#208	—	5	2	no	—
163	C₂×#208	C₂×D₅	1	1	yes	characteristic
164	C₂²×C₃⋊C₈	—	5	1	no	—
165	C₂²×C₃⋊C₈	—	5	2	no	—
166	#815	—	5	2	no	—
167	#815	—	5	2	no	—
168	#815	C₂×D₅	1	2	yes	—
169	C₈×Dic₃	—	5	2	no	—
170	C₈×Dic₃	—	5	1	no	—
171	C₈×Dic₃	—	5	1	no	—
172	C₈×Dic₃	—	5	1	no	—
173	C₈×Dic₃	—	5	1	no	—
174	C₈×Dic₃	—	5	2	no	—
175	C₈×Dic₃	C₂×D₅	1	2	yes	—
176	C₂²×C₄×C₅	—	3	2	no	—
177	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
178	C₂×C₂²⋊D₅	C₄×D₃	1	2	yes	—
179	#709	C₄×D₃	1	4	yes	—
180	#709	C₂×Dic₃	1	4	yes	—
181	C₂×D₂₀	C₄×D₃	1	1	yes	characteristic
182	C₂×C₄×D₅	—	3	4	no	—
183	C₂×C₄×D₅	C₂²×D₃	1	2	yes	—
184	C₂×Dic₁₀	C₄×D₃	1	1	yes	characteristic
185	C₅×M₁₆	—	3	4	no	—
186	C₅×M₁₆	C₂×Dic₃	1	4	yes	complemented
187	C₂×C₅×C₈	—	3	2	no	—
188	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
189	C₄²×C₅	—	3	2	no	—
190	C₄²×C₅	—	3	1	no	—
191	C₄²×C₅	—	3	1	no	—
192	C₂²⋊Dic₅	—	3	2	no	—
193	#685	—	3	4	no	—
194	C₄⋊Dic₅	—	3	2	no	—
195	#683	—	3	4	no	—
196	C₄×Dic₅	—	3	2	no	—
197	C₄×Dic₅	—	3	4	no	—
198	C₂×#168	—	3	4	no	—
199	C₂×#168	—	3	1	no	—
200	C₂×#168	—	3	1	no	—
201	C₂×#168	C₂×Dic₃	1	4	yes	complemented
202	C₂×#168	C₂²×D₃	1	1	yes	characteristic
203	C₂×#168	C₂²×D₃	1	1	yes	characteristic
204	#676	—	3	8	no	—
205	#676	C₂×Dic₃	1	8	yes	complemented
206	C₈×D₅	—	3	8	no	—
207	C₈×D₅	C₂×Dic₃	1	8	yes	complemented
208	C₂×#131	—	5	1	no	—
209	C₂×#131	—	15	1	no	—
210	C₄×#41	—	15	1	no	—
211	#405	—	15	2	no	—
212	#405	—	15	2	no	—
213	#405	—	15	1	no	—
214	#405	—	15	1	no	—
215	C₄×M₁₆	—	3	1	no	—
216	C₄×M₁₆	—	15	2	no	—
217	C₂×C₄×C₈	—	15	2	no	—
218	C₂×C₄×C₈	—	15	1	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	C₂×C₄²	1	2	yes	—
221	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₃×D₅	—	2	4	no	—
223	C₂×C₃×D₅	C₂×C₄²	1	4	yes	—
224	C₃×C₄×C₅	C₂×C₄²	1	2	yes	—
225	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
226	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
227	Dic₁₅	—	2	4	no	—
228	C₃×Dic₅	C₂×C₄²	1	4	yes	—
229	C₅×Dic₃	—	2	2	no	—
230	C₅×Dic₃	#131	1	4	yes	complemented
231	C₃×#41	—	5	4	no	—
232	C₃×#41	—	5	4	no	—
233	C₂×C₃×Q₈	—	5	1	no	—
234	C₂×C₃×D₄	—	5	2	no	—
235	C₂×C₃×D₄	—	5	1	no	—
236	C₂²×C₃×C₄	—	5	2	no	—
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₂²×Dic₃	—	5	4	no	—
239	C₂²×Dic₃	C₄×D₅	1	2	yes	—
240	C₃×M₁₆	—	5	8	no	—
241	C₃×M₁₆	C₄×D₅	1	4	yes	complemented
242	C₂×C₃×C₈	—	5	4	no	—
243	C₂×C₃×C₈	—	5	1	no	—
244	C₂×C₃×C₈	—	5	1	no	—
245	C₂×C₃×C₈	—	5	8	no	—
246	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
247	#217	—	5	2	no	—
248	#217	—	5	4	no	—
249	C₄⋊Dic₃	—	5	2	no	—
250	C₄⋊Dic₃	—	5	4	no	—
251	C₄×Dic₃	—	5	2	no	—
252	C₄×Dic₃	—	5	4	no	—
253	C₄×Dic₃	C₄×D₅	1	2	yes	—
254	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
255	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
256	#208	—	5	8	no	—
257	#208	C₄×D₅	1	4	yes	complemented
258	C₂×C₃⋊C₈	—	5	4	no	—
259	C₂×C₃⋊C₈	—	5	1	no	—
260	C₂×C₃⋊C₈	—	5	1	no	—
261	C₂×C₃⋊C₈	—	5	8	no	—
262	C₂×C₃⋊C₈	C₂²×D₅	1	2	yes	—
263	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
264	C₂²×D₅	C₂×C₄×D₃	1	2	yes	—
265	C₂×C₄×C₅	—	3	2	no	—
266	C₂×C₄×C₅	—	3	2	no	—
267	C₂×C₄×C₅	—	6	4	no	—
268	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
269	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
270	C₂×C₄×C₅	C₂²×Dic₃	1	2	yes	—
271	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
272	C₂²⋊D₅	C₄×Dic₃	1	8	yes	—
273	C₂×Dic₅	—	3	4	no	—
274	C₂×Dic₅	C₂×C₄×D₃	1	2	yes	—
275	D₂₀	C₄×Dic₃	1	4	yes	—
276	C₄×D₅	—	6	8	no	—
277	C₄×D₅	C₂×C₄×D₃	1	4	yes	—
278	C₄×D₅	C₂²×Dic₃	1	4	yes	—
279	Dic₁₀	C₄×Dic₃	1	4	yes	—
280	C₅×C₈	—	3	4	no	—
281	C₅×C₈	C₂²×Dic₃	1	4	yes	—
282	#168	—	3	2	no	—
283	#168	—	3	2	no	—
284	#168	C₂²×Dic₃	1	2	yes	—
285	#168	C₂²×Dic₃	1	2	yes	—
286	C₂×#41	—	5	1	no	—
287	#131	—	5	8	no	—
288	#131	—	15	8	no	—
289	C₂×M₁₆	—	3	1	no	—
290	C₂×M₁₆	—	5	2	no	—
291	C₂×M₁₆	—	15	2	no	—
292	C₂×M₁₆	D₃×D₅	1	1	yes	characteristic
293	C₂²×C₈	—	5	1	no	—
294	C₂²×C₈	—	5	2	no	—
295	C₂²×C₈	—	15	2	no	—
296	C₂²×C₈	—	15	1	no	—
297	C₄×Q₈	—	15	2	no	—
298	C₄×D₄	—	15	2	no	—
299	C₄×D₄	—	15	4	no	—
300	#117	—	15	2	no	—
301	#117	—	15	1	no	—
302	C₂×C₄²	—	3	1	no	—
303	C₂×C₄²	—	15	2	no	—
304	#97	—	3	2	no	—
305	#97	—	15	2	no	—
306	#97	—	15	2	no	—
307	C₄×C₈	—	3	2	no	—
308	C₄×C₈	—	15	1	no	—
309	C₄×C₈	—	15	1	no	—
310	C₄×C₈	—	15	1	no	—
311	C₄×C₈	—	15	1	no	—
312	C₄×C₈	—	15	2	no	—
313	C₄×C₈	—	15	2	no	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
316	C₂×C₃×C₅	C₂×#131	1	2	yes	—
317	C₃×D₅	—	2	4	no	—
318	C₂³×C₃	—	5	2	no	—
319	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
320	C₃×Q₈	—	5	4	no	—
321	C₃×D₄	—	5	8	no	—
322	C₃×D₄	—	5	4	no	—
323	C₂×C₃×C₄	—	5	2	no	—
324	C₂×C₃×C₄	—	5	4	no	—
325	C₂×C₃×C₄	—	5	4	no	—
326	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
327	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
328	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
329	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
330	C₂×Dic₃	—	2	4	no	—
331	C₂×Dic₃	—	5	4	no	—
332	C₂×Dic₃	—	10	8	no	—
333	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
334	C₂×Dic₃	C₂×C₄×D₅	1	2	yes	—
335	C₃×C₈	—	5	2	no	—
336	C₃×C₈	—	5	2	no	—
337	C₃×C₈	C₂×C₄×D₅	1	4	yes	—
338	C₃⋊C₈	—	5	2	no	—
339	C₃⋊C₈	—	5	2	no	—
340	C₃⋊C₈	C₂×C₄×D₅	1	4	yes	—
341	C₂²×C₅	—	2	2	no	—
342	C₂²×C₅	C₂×C₄×Dic₃	1	2	yes	—
343	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
344	C₂×D₅	—	2	4	no	—
345	C₂×D₅	C₂×C₄×Dic₃	1	4	yes	—
346	C₄×C₅	—	3	4	no	—
347	C₄×C₅	—	6	2	no	—
348	C₄×C₅	C₂×C₄×Dic₃	1	2	yes	—
349	C₄×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
350	C₄×C₅	C₂³×Dic₃	1	1	yes	characteristic
351	Dic₅	—	6	4	no	—
352	Dic₅	C₂×C₄×Dic₃	1	4	yes	—
353	#41	—	5	4	no	—
354	#41	—	5	4	no	—
355	C₂×Q₈	—	5	1	no	—
356	C₂×D₄	—	5	2	no	—
357	C₂×D₄	—	5	1	no	—
358	C₂²×C₄	—	3	2	no	—
359	C₂²×C₄	—	5	2	no	—
360	C₂²×C₄	—	15	4	no	—
361	C₂²×C₄	C₂×D₃×D₅	1	1	yes	characteristic
362	M₁₆	—	3	4	no	—
363	M₁₆	—	5	8	no	—
364	M₁₆	—	15	8	no	—
365	M₁₆	D₅×Dic₃	1	4	yes	complemented
366	C₂×C₈	—	3	2	no	—
367	C₂×C₈	—	5	4	no	—
368	C₂×C₈	—	5	1	no	—
369	C₂×C₈	—	5	1	no	—
370	C₂×C₈	—	5	8	no	—
371	C₂×C₈	—	15	8	no	—
372	C₂×C₈	—	15	4	no	—
373	C₂×C₈	—	15	1	no	—
374	C₂×C₈	—	15	1	no	—
375	C₂×C₈	C₂×D₃×D₅	1	2	yes	—
376	C₄⋊C₄	—	15	4	no	—
377	C₄⋊C₄	—	15	2	no	—
378	C₂²⋊C₄	—	15	4	no	—
379	C₂²⋊C₄	—	15	2	no	—
380	C₄²	—	3	2	no	—
381	C₄²	—	3	1	no	—
382	C₄²	—	3	1	no	—
383	C₄²	—	15	4	no	—
384	C₄²	—	15	2	no	—
385	C₃×C₅	C₄×#131	1	1	yes	characteristic, complemented, Hall
386	C₂²×C₃	—	2	2	no	—
387	C₂²×C₃	—	5	4	no	—
388	C₂²×C₃	—	10	4	no	—
389	C₂²×C₃	C₄²×D₅	1	2	yes	—
390	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
391	C₃×C₄	—	5	4	no	—
392	C₃×C₄	C₄²×D₅	1	2	yes	—
393	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
394	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
395	Dic₃	—	2	2	no	—
396	Dic₃	—	10	4	no	—
397	Dic₃	#4053	1	4	yes	direct product factor
398	C₂×C₅	—	2	2	no	—
399	C₂×C₅	D₃×#131	1	2	yes	—
400	C₂×C₅	C₂²×C₄×Dic₃	1	1	yes	characteristic
401	D₅	—	2	4	no	—
402	C₂³	—	5	2	no	—
403	C₂³	C₄×D₃×D₅	1	1	yes	characteristic
404	Q₈	—	5	4	no	—
405	D₄	—	5	8	no	—
406	D₄	—	5	4	no	—
407	C₂×C₄	—	3	2	no	—
408	C₂×C₄	—	3	2	no	—
409	C₂×C₄	—	5	2	no	—
410	C₂×C₄	—	5	4	no	—
411	C₂×C₄	—	5	4	no	—
412	C₂×C₄	—	6	4	no	—
413	C₂×C₄	—	15	4	no	—
414	C₂×C₄	—	30	8	no	—
415	C₂×C₄	C₄×D₃×D₅	1	2	yes	—
416	C₂×C₄	C₄×D₃×D₅	1	1	yes	characteristic
417	C₂×C₄	C₂×D₅×Dic₃	1	2	yes	—
418	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
419	C₈	—	3	4	no	—
420	C₈	—	5	2	no	—
421	C₈	—	5	2	no	—
422	C₈	—	15	2	no	—
423	C₈	—	15	2	no	—
424	C₈	C₂×D₅×Dic₃	1	4	yes	—
425	C₂×C₃	—	2	2	no	—
426	C₂×C₃	—	10	4	no	—
427	C₂×C₃	C₂×C₄²×D₅	1	1	yes	characteristic
428	C₂×C₃	C₂×#4053	1	2	yes	—
429	C₅	Dic₃×#131	1	1	yes	characteristic, complemented, Sylow
430	C₂²	—	2	2	no	—
431	C₂²	—	5	4	no	—
432	C₂²	—	10	4	no	—
433	C₂²	C₄×D₅×Dic₃	1	2	yes	—
434	C₂²	C₂×C₄×D₃×D₅	1	1	yes	characteristic
435	C₄	—	3	4	no	—
436	C₄	—	5	4	no	—
437	C₄	—	6	2	no	—
438	C₄	—	30	4	no	—
439	C₄	C₄×D₅×Dic₃	1	2	yes	—
440	C₄	C₂×C₄×D₃×D₅	1	1	yes	characteristic
441	C₄	C₂²×D₅×Dic₃	1	1	yes	characteristic
442	C₃	C₄×#4053	1	1	yes	characteristic, complemented, Sylow
443	C₂	—	2	2	no	—
444	C₂	—	10	4	no	—
445	C₂	D₃×#4053	1	2	yes	—
446	C₂	C₂×C₄×D₅×Dic₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator	C₂×C₃×C₅	C₂²×C₄²
Fitting	C₂×C₃×C₅×M₁₆	C₂²
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂×C₃×#709	C₂²
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₂×M₁₆	D₃×D₅
hypocenter	C₃×C₅	C₄×#131
LCS	G ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
4. #11751223	C₂	semidirect
5. C₅×Dic₃×M₁₆	C₂	semidirect
6. #11748324	C₂	semidirect
7. C₂×Dic₃×#168	C₂	semidirect
8. #11748051	C₂	semidirect
9. #11747646	C₂	semidirect
10. Dic₃×#676	C₂	semidirect
11. C₈×D₅×Dic₃	C₂	semidirect
20. C₃×#4053	C₄	semidirect
29. #91284	C₄	semidirect
62. C₃×C₅×M₁₆	C₂×C₄	semidirect
67. C₂×C₃⋊#168	C₂×C₄	semidirect
73. C₅×#208	C₂×C₄	semidirect
75. C₂×C₃×#168	C₂×C₄	semidirect
78. C₃×#676	C₂×C₄	semidirect
79. C₃×C₈×D₅	C₂×C₄	semidirect
83. #6649	C₂×C₄	semidirect
84. D₅×C₃⋊C₈	C₂×C₄	semidirect
91. Dic₃×M₁₆	D₅	semidirect
105. #4053	Dic₃	direct (N × H)
186. C₅×M₁₆	C₂×Dic₃	semidirect
201. C₂×#168	C₂×Dic₃	semidirect
205. #676	C₂×Dic₃	semidirect
207. C₈×D₅	C₂×Dic₃	semidirect
230. C₅×Dic₃	#131	semidirect
241. C₃×M₁₆	C₄×D₅	semidirect
257. #208	C₄×D₅	semidirect
365. M₁₆	D₅×Dic₃	semidirect
385. C₃×C₅	C₄×#131	semidirect
397. Dic₃	#4053	direct (N × H)
429. C₅	Dic₃×#131	semidirect
442. C₃	C₄×#4053	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×#4053	2
Dic₃×#709	2
C₂×#91284	2
#11751223	2
C₅×Dic₃×M₁₆	2
#11748324	2
C₂×Dic₃×#168	2
#11748051	2
#11747646	2
Dic₃×#676	2
C₈×D₅×Dic₃	2
C₄×#4053	3
Dic₃×#131	5

Subgroups — Dic3×#4053 #14411481

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Dic₃×#4053 #14411481