Subgroups — D₃×#65313 #14418402

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₅×D₃×Q₈	C₂	1	1	yes	maximal, characteristic
2	#11751125	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65313	C₂	1	1	yes	maximal, characteristic, complemented
4	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic
5	D₃×C₄⋊#168	C₂	1	2	yes	maximal
6	D₃×#3935	C₂	1	2	yes	maximal
7	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic
8	#11746866	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746863	C₂	1	1	yes	maximal, characteristic, complemented
10	#11746858	C₂	1	2	yes	maximal, complemented
11	#11746850	C₂	1	2	yes	maximal, complemented
12	C₂×#65313	—	3	1	no	maximal, Hall
13	C₂×C₅×D₃×Q₈	C₄	1	1	yes	characteristic
14	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
16	C₅×D₃×C₄⋊C₄	C₄	1	2	yes	—
17	C₅×D₃×C₄⋊C₄	C₄	1	1	yes	characteristic
18	C₅×#887	C₄	1	1	yes	characteristic
19	C₅×#887	C₄	1	2	yes	—
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₄²×C₅×D₃	C₂²	1	2	yes	—
22	C₄×C₅×Dic₆	C₂²	1	2	yes	—
23	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
24	C₂×D₃×#168	C₂²	1	1	yes	characteristic
25	C₂×D₃×#168	C₂²	1	2	yes	—
26	C₂×D₃×#168	C₂²	1	1	yes	characteristic
27	C₄⋊(C₃⋊#168)	C₂²	1	2	yes	—
28	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
29	#91087	C₂²	1	2	yes	—
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₃×C₄⋊#168	C₂²	1	2	yes	—
32	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
33	C₃×#3935	C₂²	1	2	yes	—
34	C₃×C₄×#168	C₂²	1	1	yes	characteristic
35	Dic₃⋊#168	C₂²	1	2	yes	—
36	Dic₃⋊#168	C₂²	1	2	yes	—
37	Dic₃⋊#168	C₂²	1	2	yes	—
38	#90953	C₂²	1	2	yes	—
39	#90953	C₂²	1	2	yes	—
40	Dic₃×#168	C₂²	1	1	yes	characteristic
41	Dic₃×#168	C₂²	1	1	yes	characteristic
42	D₃×#446	—	5	1	no	maximal, Hall
43	C₂×C₄×C₅×Q₈	—	3	1	no	—
44	#65313	—	3	2	no	—
45	#65313	—	3	1	no	—
46	#65313	—	3	2	no	—
47	#65313	—	3	1	no	—
48	#65313	—	3	1	no	—
49	#65313	D₃	1	1	yes	characteristic, direct product factor
50	C₂×C₄⋊#168	—	3	1	no	—
51	C₂×C₄⋊#168	—	3	2	no	—
52	C₂×#3935	—	3	2	no	—
53	C₂×C₄×#168	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
55	C₅×D₃×Q₈	—	2	4	no	—
56	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
58	C₂×C₄×C₅×D₃	C₂×C₄	1	2	yes	—
59	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
61	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
62	C₂×C₅×Dic₆	C₂×C₄	1	2	yes	—
63	C₃×C₅×C₄⋊C₄	C₂×C₄	1	2	yes	—
64	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
68	C₂×C₃⋊#168	C₂³	1	2	yes	—
69	C₂×C₃⋊#168	C₂³	1	1	yes	characteristic
70	C₅×C₄⋊Dic₃	C₂×C₄	1	2	yes	—
71	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
72	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
76	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
77	C₄×C₅×Dic₃	C₂×C₄	1	2	yes	—
78	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
79	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
80	C₄×C₅×Dic₃	C₂³	1	2	yes	—
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	2	yes	—
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	D₃×#168	—	2	2	no	—
85	D₃×#168	—	2	4	no	—
86	D₃×#168	Q₈	1	4	yes	complemented
87	C₄×D₃×Q₈	D₅	1	1	yes	characteristic
88	C₃×#446	—	5	1	no	—
89	#5024	—	5	1	no	—
90	D₃×C₄⋊C₈	—	5	1	no	—
91	D₃×C₄⋊C₈	—	5	2	no	—
92	#4831	—	5	1	no	—
93	#4828	—	5	2	no	—
94	D₃×#97	—	5	2	no	—
95	#4701	—	5	2	no	—
96	C₄×D₃×C₈	—	5	1	no	—
97	#4679	—	5	1	no	—
98	C₂²×C₅×Q₈	—	3	1	no	—
99	C₄×C₅×Q₈	—	3	1	no	—
100	C₄×C₅×Q₈	—	3	2	no	—
101	C₄×C₅×Q₈	—	3	1	no	—
102	C₄×C₅×Q₈	—	3	2	no	—
103	C₄×C₅×Q₈	—	3	1	no	—
104	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	—	3	1	no	—
106	C₂×C₅×C₄⋊C₄	—	3	2	no	—
107	C₂×C₄²×C₅	—	3	1	no	—
108	C₂×C₄²×C₅	—	3	2	no	—
109	C₂²×#168	—	3	1	no	—
110	C₂²×#168	—	3	1	no	—
111	C₂²×#168	—	3	2	no	—
112	C₄⋊#168	—	3	2	no	—
113	C₄⋊#168	—	3	1	no	—
114	C₄⋊#168	—	3	2	no	—
115	C₄⋊#168	—	3	2	no	—
116	C₄⋊#168	—	3	2	no	—
117	C₄⋊#168	C₂×D₃	1	2	yes	—
118	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
119	#3935	—	3	2	no	—
120	#3935	—	3	2	no	—
121	#3935	—	3	2	no	—
122	#3935	C₂×D₃	1	2	yes	—
123	C₄×#168	—	3	1	no	—
124	C₄×#168	—	3	1	no	—
125	C₄×#168	—	3	1	no	—
126	C₄×#168	C₂×D₃	1	1	yes	characteristic
127	C₂×#446	—	15	1	no	Sylow
128	C₂²×C₅×D₃	C₂²×C₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
135	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
138	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₅×Dic₃	C₂²×C₄	1	1	yes	characteristic
140	C₄×C₅×D₃	—	2	4	no	—
141	C₄×C₅×D₃	—	2	2	no	—
142	C₄×C₅×D₃	—	2	4	no	—
143	C₄×C₅×D₃	M₁₆	1	4	yes	—
144	C₄×C₅×D₃	C₂×Q₈	1	2	yes	—
145	C₄×C₅×D₃	#41	1	2	yes	—
146	C₅×Dic₆	—	2	2	no	—
147	C₅×Dic₆	—	2	4	no	—
148	C₃⋊#168	—	2	1	no	—
149	C₃⋊#168	—	2	2	no	—
150	C₃⋊#168	C₂×Q₈	1	2	yes	complemented
151	C₃×#168	—	2	1	no	—
152	C₃×#168	—	2	2	no	—
153	C₃×#168	C₂×Q₈	1	2	yes	complemented
154	C₂×D₃×Q₈	Dic₅	1	1	yes	characteristic
155	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
156	Q₈×Dic₃	Dic₅	1	1	yes	characteristic
157	C₂×D₃×C₈	—	5	1	no	—
158	C₂×D₃×C₈	—	5	1	no	—
159	C₂×D₃×C₈	—	5	2	no	—
160	D₃×C₄⋊C₄	Dic₅	1	2	yes	—
161	D₃×C₄⋊C₄	Dic₅	1	1	yes	characteristic
162	#887	Dic₅	1	1	yes	characteristic
163	#887	Dic₅	1	2	yes	—
164	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
165	C₄²×D₃	C₂×D₅	1	2	yes	—
166	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
167	C₄×Dic₆	C₂×D₅	1	2	yes	—
168	C₃×C₄⋊C₈	—	5	2	no	—
169	C₃×C₄⋊C₈	—	5	1	no	—
170	C₃×#97	—	5	2	no	—
171	C₃×C₄×C₈	—	5	1	no	—
172	#815	—	5	2	no	—
173	#815	—	5	2	no	—
174	Dic₃⋊C₈	—	5	2	no	—
175	Dic₃⋊C₈	—	5	2	no	—
176	Dic₃⋊C₈	—	5	2	no	—
177	C₈×Dic₃	—	5	1	no	—
178	C₈×Dic₃	—	5	1	no	—
179	C₄⋊(C₃⋊C₈)	—	5	1	no	—
180	C₄⋊(C₃⋊C₈)	—	5	2	no	—
181	#803	—	5	2	no	—
182	C₄×C₃⋊C₈	—	5	1	no	—
183	C₂×C₅×Q₈	—	3	2	no	—
184	C₂×C₅×Q₈	—	3	1	no	—
185	C₂×C₅×Q₈	—	6	4	no	—
186	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	—	3	1	no	—
188	C₂²×C₄×C₅	—	3	1	no	—
189	C₂²×C₄×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	2	no	—
191	C₂²×C₄×C₅	—	3	2	no	—
192	C₅×C₄⋊C₄	—	3	2	no	—
193	C₅×C₄⋊C₄	—	3	2	no	—
194	C₅×C₄⋊C₄	—	3	2	no	—
195	C₅×C₄⋊C₄	—	3	2	no	—
196	C₅×C₄⋊C₄	—	3	1	no	—
197	C₅×C₄⋊C₄	C₄×D₃	1	2	yes	—
198	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
199	C₄²×C₅	—	3	1	no	—
200	C₄²×C₅	—	3	2	no	—
201	C₄²×C₅	—	3	1	no	—
202	C₄²×C₅	—	3	2	no	—
203	C₄²×C₅	—	3	1	no	—
204	C₄²×C₅	—	3	2	no	—
205	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₄²×C₅	C₂²×D₃	1	2	yes	—
207	C₂×#168	—	3	1	no	—
208	C₂×#168	—	3	4	no	—
209	C₂×#168	—	3	1	no	—
210	C₂×#168	—	3	2	no	—
211	C₂×#168	—	6	2	no	—
212	C₂×#168	—	6	4	no	—
213	C₂×#168	C₂²×D₃	1	1	yes	characteristic
214	C₂×#168	C₂²×D₃	1	2	yes	—
215	C₂×#168	C₂²×D₃	1	1	yes	characteristic
216	C₂×C₄×Q₈	—	3	1	no	—
217	#446	—	5	1	no	—
218	#446	—	15	1	no	—
219	#446	—	15	2	no	—
220	#446	—	15	2	no	—
221	#446	—	15	1	no	—
222	#446	—	15	1	no	—
223	C₂×C₄⋊C₈	—	15	1	no	—
224	C₂×C₄⋊C₈	—	15	2	no	—
225	C₂×#97	—	15	2	no	—
226	C₂×C₄×C₈	—	15	1	no	—
227	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₅×D₃	C₄×Q₈	1	2	yes	—
229	C₂×C₅×D₃	C₂×M₁₆	1	2	yes	—
230	C₂×C₅×D₃	#131	1	2	yes	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	2	1	no	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
235	C₃×C₄×C₅	C₂²×Q₈	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
237	C₅×Dic₃	—	2	2	no	—
238	C₅×Dic₃	—	2	1	no	—
239	C₅×Dic₃	—	2	2	no	—
240	C₅×Dic₃	C₄×Q₈	1	2	yes	—
241	C₅×Dic₃	C₂×M₁₆	1	2	yes	—
242	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
243	D₃×Q₈	—	2	4	no	—
244	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
245	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
246	C₂×C₄×D₃	C₂×Dic₅	1	2	yes	—
247	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
248	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
249	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
250	C₂×Dic₆	C₂×Dic₅	1	2	yes	—
251	C₂×C₃×C₈	—	5	1	no	—
252	C₂×C₃×C₈	—	5	1	no	—
253	C₂×C₃×C₈	—	5	2	no	—
254	C₃×C₄⋊C₄	C₂×Dic₅	1	2	yes	—
255	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
256	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
257	C₃×C₄²	C₂²×D₅	1	2	yes	—
258	C₄⋊Dic₃	C₂×Dic₅	1	2	yes	—
259	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
260	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
261	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
262	Dic₃⋊C₄	C₂×Dic₅	1	2	yes	—
263	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
264	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
265	C₄×Dic₃	C₂×Dic₅	1	2	yes	—
266	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
267	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
268	C₄×Dic₃	C₂²×D₅	1	2	yes	—
269	C₂×C₃⋊C₈	—	5	1	no	—
270	C₂×C₃⋊C₈	—	5	1	no	—
271	C₂×C₃⋊C₈	—	5	2	no	—
272	D₃×C₈	—	5	4	no	—
273	D₃×C₈	—	10	2	no	—
274	D₃×C₈	—	10	4	no	—
275	C₂³×C₅	—	3	1	no	—
276	C₅×Q₈	—	2	2	no	—
277	C₅×Q₈	—	6	4	no	—
278	C₅×Q₈	—	6	2	no	—
279	C₂×C₄×C₅	—	3	1	no	—
280	C₂×C₄×C₅	—	3	1	no	—
281	C₂×C₄×C₅	—	3	4	no	—
282	C₂×C₄×C₅	—	3	2	no	—
283	C₂×C₄×C₅	—	3	2	no	—
284	C₂×C₄×C₅	—	3	1	no	—
285	C₂×C₄×C₅	—	3	2	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	6	2	no	—
288	C₂×C₄×C₅	—	6	4	no	—
289	C₂×C₄×C₅	—	6	4	no	—
290	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
291	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
292	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
293	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
295	#168	—	2	1	no	—
296	#168	—	2	2	no	—
297	#168	—	3	2	no	—
298	#168	—	6	1	no	—
299	#168	—	6	2	no	—
300	#168	D₃×Q₈	1	2	yes	complemented
301	C₂²×Q₈	—	3	1	no	—
302	C₂²×C₈	—	15	1	no	—
303	C₂²×C₈	—	15	1	no	—
304	C₂²×C₈	—	15	2	no	—
305	C₄×Q₈	—	3	1	no	—
306	C₄×Q₈	—	3	2	no	—
307	C₄×Q₈	—	3	1	no	—
308	C₄×Q₈	—	3	2	no	—
309	C₄×Q₈	—	3	1	no	—
310	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	—	3	1	no	—
312	C₂×C₄⋊C₄	—	3	2	no	—
313	C₂×C₄²	—	3	1	no	—
314	C₂×C₄²	—	3	2	no	—
315	C₄⋊C₈	—	5	1	no	—
316	C₄⋊C₈	—	5	2	no	—
317	C₄⋊C₈	—	15	2	no	—
318	C₄⋊C₈	—	15	2	no	—
319	C₄⋊C₈	—	15	2	no	—
320	C₄⋊C₈	—	15	1	no	—
321	C₄⋊C₈	—	15	2	no	—
322	#97	—	5	2	no	—
323	#97	—	15	2	no	—
324	#97	—	15	2	no	—
325	#97	—	15	2	no	—
326	C₄×C₈	—	5	1	no	—
327	C₄×C₈	—	15	1	no	—
328	C₄×C₈	—	15	1	no	—
329	C₄×C₈	—	15	1	no	—
330	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
332	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
333	C₅×D₃	#446	1	4	yes	complemented
334	C₂²×D₃	C₂²×Dic₅	1	1	yes	characteristic
335	C₃×Q₈	—	2	2	no	—
336	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
337	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
338	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
339	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
340	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
341	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
342	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
343	C₂×Dic₃	C₂²×Dic₅	1	2	yes	—
344	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
345	C₂×Dic₃	C₂²×Dic₅	1	1	yes	characteristic
346	C₄×D₃	—	2	4	no	—
347	C₄×D₃	—	2	2	no	—
348	C₄×D₃	—	2	4	no	—
349	C₄×D₃	#681	1	4	yes	—
350	C₄×D₃	Q₈×D₅	1	2	yes	—
351	C₄×D₃	#713	1	2	yes	—
352	Dic₆	—	2	2	no	—
353	Dic₆	—	2	4	no	—
354	C₃×C₈	—	5	2	no	—
355	C₃×C₈	—	10	1	no	—
356	C₃×C₈	—	10	2	no	—
357	C₃⋊C₈	—	5	2	no	—
358	C₃⋊C₈	—	10	1	no	—
359	C₃⋊C₈	—	10	2	no	—
360	C₂²×C₅	—	3	2	no	—
361	C₂²×C₅	—	3	2	no	—
362	C₂²×C₅	—	3	2	no	—
363	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	1	no	—
366	C₄×C₅	—	2	2	no	—
367	C₄×C₅	—	3	2	no	—
368	C₄×C₅	—	3	2	no	—
369	C₄×C₅	—	6	2	no	—
370	C₄×C₅	—	6	1	no	—
371	C₄×C₅	—	6	2	no	—
372	C₄×C₅	D₃×M₁₆	1	2	yes	—
373	C₄×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
374	C₄×C₅	D₃×#41	1	1	yes	characteristic
375	C₂×Q₈	—	3	2	no	—
376	C₂×Q₈	—	3	1	no	—
377	C₂×Q₈	—	6	4	no	—
378	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
379	C₂²×C₄	—	3	1	no	—
380	C₂²×C₄	—	3	1	no	—
381	C₂²×C₄	—	3	1	no	—
382	C₂²×C₄	—	3	2	no	—
383	C₂²×C₄	—	3	2	no	—
384	C₂×C₈	—	5	1	no	—
385	C₂×C₈	—	5	1	no	—
386	C₂×C₈	—	5	2	no	—
387	C₂×C₈	—	15	4	no	—
388	C₂×C₈	—	15	1	no	—
389	C₂×C₈	—	15	1	no	—
390	C₂×C₈	—	15	2	no	—
391	C₂×C₈	—	30	2	no	—
392	C₂×C₈	—	30	4	no	—
393	C₄⋊C₄	—	3	2	no	—
394	C₄⋊C₄	—	3	2	no	—
395	C₄⋊C₄	—	3	2	no	—
396	C₄⋊C₄	—	3	2	no	—
397	C₄⋊C₄	—	3	1	no	—
398	C₄⋊C₄	D₃×Dic₅	1	2	yes	—
399	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
400	C₄²	—	3	1	no	—
401	C₄²	—	3	2	no	—
402	C₄²	—	3	1	no	—
403	C₄²	—	3	2	no	—
404	C₄²	—	3	1	no	—
405	C₄²	—	3	2	no	—
406	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
407	C₄²	C₂×D₃×D₅	1	2	yes	—
408	C₃×C₅	C₂×#446	1	1	yes	characteristic, complemented, Hall
409	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
410	C₂×D₃	C₂×#681	1	2	yes	—
411	C₂×D₃	Q₈×Dic₅	1	2	yes	—
412	C₂×D₃	#4094	1	2	yes	—
413	C₃×C₄	—	2	2	no	—
414	C₃×C₄	—	2	1	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	C₂×#681	1	2	yes	—
417	C₃×C₄	C₂×Q₈×D₅	1	1	yes	characteristic
418	C₃×C₄	C₂×#713	1	1	yes	characteristic
419	Dic₃	—	2	2	no	—
420	Dic₃	—	2	1	no	—
421	Dic₃	—	2	2	no	—
422	Dic₃	C₂×#681	1	2	yes	—
423	Dic₃	Q₈×Dic₅	1	2	yes	—
424	C₂×C₅	—	3	4	no	—
425	C₂×C₅	C₄×D₃×Q₈	1	1	yes	characteristic
426	C₂×C₅	C₂×D₃×M₁₆	1	1	yes	characteristic
427	C₂×C₅	D₃×#131	1	1	yes	characteristic
428	C₂³	—	3	1	no	—
429	Q₈	—	2	2	no	—
430	Q₈	—	6	4	no	—
431	Q₈	—	6	2	no	—
432	C₂×C₄	—	3	1	no	—
433	C₂×C₄	—	3	1	no	—
434	C₂×C₄	—	3	2	no	—
435	C₂×C₄	—	3	2	no	—
436	C₂×C₄	—	3	4	no	—
437	C₂×C₄	—	3	1	no	—
438	C₂×C₄	—	3	2	no	—
439	C₂×C₄	—	3	2	no	—
440	C₂×C₄	—	6	4	no	—
441	C₂×C₄	—	6	2	no	—
442	C₂×C₄	—	6	4	no	—
443	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
444	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
445	C₂×C₄	C₂×D₃×Dic₅	1	2	yes	—
446	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
447	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
448	C₈	—	5	2	no	—
449	C₈	—	10	1	no	—
450	C₈	—	10	2	no	—
451	C₈	—	15	2	no	—
452	C₈	—	30	1	no	—
453	C₈	—	30	2	no	—
454	C₂×C₃	C₂²×#681	1	1	yes	characteristic
455	C₂×C₃	C₂×Q₈×Dic₅	1	1	yes	characteristic
456	C₂×C₃	C₂×#4094	1	1	yes	characteristic
457	D₃	#65313	1	4	yes	direct product factor
458	C₅	D₃×#446	1	1	yes	characteristic, complemented, Sylow
459	C₂²	—	3	2	no	—
460	C₂²	—	3	2	no	—
461	C₂²	—	3	2	no	—
462	C₂²	C₂²×D₃×Dic₅	1	1	yes	characteristic
463	C₄	—	2	1	no	—
464	C₄	—	2	2	no	—
465	C₄	—	2	2	no	—
466	C₄	—	3	2	no	—
467	C₄	—	3	2	no	—
468	C₄	—	6	1	no	—
469	C₄	—	6	2	no	—
470	C₄	—	6	2	no	—
471	C₄	D₃×#681	1	2	yes	—
472	C₄	D₃×Q₈×D₅	1	1	yes	characteristic
473	C₄	D₃×#713	1	1	yes	characteristic
474	C₃	C₂×#65313	1	1	yes	characteristic, complemented, Sylow
475	C₂	—	3	4	no	—
476	C₂	C₂×D₃×#681	1	1	yes	characteristic
477	C₂	D₃×Q₈×Dic₅	1	1	yes	characteristic
478	C₂	D₃×#4094	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₃×D₅
commutator, socle	C₂²×C₃×C₅	C₂³×C₄
Fitting	C₃×C₄×C₅×Q₈	C₂²
prime radical	C₂²×C₅×D₃	C₂²×C₄
cosocle	C₂×C₃×C₄×C₅	C₂⁴
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#446
LCS	G ▷ C₂²×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #11751125	C₂	semidirect
3. C₃×#65313	C₂	semidirect
8. #11746866	C₂	semidirect
9. #11746863	C₂	semidirect
10. #11746858	C₂	semidirect
11. #11746850	C₂	semidirect
49. #65313	D₃	direct (N × H)
86. D₃×#168	Q₈	semidirect
150. C₃⋊#168	C₂×Q₈	semidirect
153. C₃×#168	C₂×Q₈	semidirect
300. #168	D₃×Q₈	semidirect
333. C₅×D₃	#446	semidirect
408. C₃×C₅	C₂×#446	semidirect
457. D₃	#65313	direct (N × H)
458. C₅	D₃×#446	semidirect
474. C₃	C₂×#65313	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×D₃×Q₈	2
#11751125	2
C₃×#65313	2
D₃×C₄⋊#168	2
D₃×#3935	2
C₄×D₃×#168	2
#11746866	2
#11746863	2
#11746858	2
#11746850	2
C₂×#65313	3
D₃×#446	5

Subgroups — D3×#65313 #14418402

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65313 #14418402