Subgroups — D₃×#65367 #14439815

Order 1920.

848 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×D₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	D₃×#4015	C₂	1	1	yes	maximal, characteristic
3	#11751179	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65367	C₂	1	1	yes	maximal, characteristic, complemented
5	D₃×#3939	C₂	1	4	yes	maximal
6	#11747146	C₂	1	4	yes	maximal, complemented
7	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic
8	#11746962	C₂	1	1	yes	maximal, characteristic, complemented
9	#11746955	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#65367	—	3	1	no	maximal, Hall
11	C₂×C₅×D₃×Q₈	—	2	1	no	—
12	C₂×D₃×Dic₁₀	—	2	1	no	—
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	#91758	C₂²	1	1	yes	characteristic
15	C₅×#944	—	2	1	no	—
16	C₅×D₃×C₄⋊C₄	—	2	1	no	—
17	C₅×D₃×C₄⋊C₄	C₂²	1	2	yes	—
18	C₅×#888	—	2	1	no	—
19	C₅×#888	C₂²	1	2	yes	—
20	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₅×#869	C₂²	1	1	yes	characteristic
22	C₃×#4015	C₂²	1	1	yes	characteristic
23	#91469	—	2	1	no	—
24	#91469	C₂²	1	2	yes	—
25	D₃×C₄⋊Dic₅	—	2	1	no	—
26	D₃×C₄⋊Dic₅	C₂²	1	2	yes	—
27	#91389	—	2	1	no	—
28	C₂×D₃×#168	C₂²	1	2	yes	—
29	#91091	C₂²	1	4	yes	—
30	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
31	C₃×#3939	C₂²	1	4	yes	—
32	C₃×C₄×#168	C₂²	1	1	yes	characteristic
33	#90989	C₂²	1	4	yes	—
34	#90988	C₂²	1	4	yes	—
35	Dic₃×#168	C₂²	1	2	yes	—
36	D₃×#500	—	5	1	no	maximal, Hall
37	C₂×C₅×C₄⋊Q₈	—	3	1	no	—
38	C₂×#4015	—	3	1	no	—
39	#65367	—	3	1	no	—
40	#65367	—	3	4	no	—
41	#65367	—	3	1	no	—
42	#65367	—	3	1	no	—
43	#65367	D₃	1	1	yes	characteristic, direct product factor
44	C₂×#3939	—	3	4	no	—
45	C₂×C₄×#168	—	3	1	no	—
46	C₂×C₃×C₅×Q₈	—	2	1	no	—
47	C₂×Dic₃₀	—	2	1	no	—
48	C₅×D₃×Q₈	—	4	4	no	—
49	C₂×C₄×C₅×D₃	—	2	2	no	—
50	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
51	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
52	C₂×C₄×C₅×D₃	C₂³	1	1	yes	characteristic
53	C₂×C₅×Dic₆	—	2	1	no	—
54	C₂×C₅×Dic₆	—	2	2	no	—
55	C₂×C₃×Dic₁₀	—	2	1	no	—
56	C₂×#1204	—	2	2	no	—
57	C₂×D₃×Dic₅	—	2	2	no	—
58	D₃×Dic₁₀	—	4	4	no	—
59	C₃×C₅×C₄⋊C₄	—	2	1	no	—
60	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₄⋊Dic₁₅	—	2	1	no	—
63	C₄⋊Dic₁₅	C₂³	1	2	yes	—
64	C₂×C₃⋊#168	C₂³	1	2	yes	—
65	C₅×C₄⋊Dic₃	—	2	1	no	—
66	C₅×C₄⋊Dic₃	C₂³	1	2	yes	—
67	C₅×Dic₃⋊C₄	—	2	2	no	—
68	C₅×Dic₃⋊C₄	—	2	2	no	—
69	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
70	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
71	C₄×C₅×Dic₃	C₂³	1	1	yes	characteristic
72	C₃×C₄⋊Dic₅	—	2	1	no	—
73	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
74	C₂×C₃×#168	C₂³	1	2	yes	—
75	Dic₃⋊Dic₅	—	2	2	no	—
76	Dic₃⋊Dic₅	—	2	2	no	—
77	D₃×#168	Q₈	1	8	yes	complemented
78	D₃×C₄⋊Q₈	—	5	1	no	—
79	D₃×C₄⋊Q₈	D₅	1	1	yes	characteristic
80	C₃×#500	—	5	1	no	—
81	#5078	—	5	1	no	—
82	#5078	—	5	1	no	—
83	D₃×#107	—	5	4	no	—
84	#4874	—	5	4	no	—
85	C₄×D₃×C₈	—	5	1	no	—
86	#4682	—	5	1	no	—
87	C₂²×C₅×Q₈	—	6	1	no	—
88	C₂²×Dic₁₀	—	6	1	no	—
89	C₅×C₄⋊Q₈	—	3	2	no	—
90	C₅×C₄⋊Q₈	—	3	1	no	—
91	C₅×C₄⋊Q₈	—	6	1	no	—
92	C₅×C₄⋊Q₈	—	6	1	no	—
93	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	—	3	2	no	—
95	C₂×C₅×C₄⋊C₄	—	6	1	no	—
96	C₂×C₄²×C₅	—	3	1	no	—
97	C₂×C₄⋊Dic₅	—	3	2	no	—
98	C₂×C₄⋊Dic₅	—	6	1	no	—
99	C₂²×#168	—	3	2	no	—
100	#4015	—	3	1	no	—
101	#4015	—	3	2	no	—
102	#4015	—	6	1	no	—
103	#4015	—	6	1	no	—
104	#4015	C₂×D₃	1	1	yes	characteristic
105	#3939	—	3	4	no	—
106	#3939	—	3	4	no	—
107	#3939	—	3	4	no	—
108	#3939	C₂×D₃	1	4	yes	—
109	C₄×#168	—	3	1	no	—
110	C₄×#168	—	3	2	no	—
111	C₄×#168	C₂×D₃	1	1	yes	characteristic
112	C₂×#500	—	15	1	no	Sylow
113	C₂²×C₅×D₃	C₂×D₄	1	1	yes	characteristic
114	C₃×C₅×Q₈	—	4	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₂×Dic₁₅	—	2	2	no	—
120	Dic₃₀	—	4	2	no	—
121	C₂×C₅×Dic₃	—	2	2	no	—
122	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₅×Dic₃	C₂×D₄	1	1	yes	characteristic
125	C₄×C₅×D₃	—	4	4	no	—
126	C₄×C₅×D₃	D₈	1	4	yes	—
127	C₄×C₅×D₃	Q₁₆	1	4	yes	—
128	C₄×C₅×D₃	C₂×Q₈	1	4	yes	—
129	C₅×Dic₆	—	4	2	no	—
130	C₅×Dic₆	—	4	4	no	—
131	C₂×C₃×Dic₅	—	2	2	no	—
132	C₃×Dic₁₀	—	4	2	no	—
133	#1204	—	4	4	no	—
134	D₃×Dic₅	—	4	4	no	—
135	C₃⋊#168	C₂×Q₈	1	4	yes	complemented
136	C₃×#168	C₂×Q₈	1	4	yes	complemented
137	C₂×D₃×Q₈	—	2	1	no	—
138	C₂×D₃×Q₈	—	10	1	no	—
139	C₃×C₄⋊Q₈	—	5	1	no	—
140	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
141	#944	—	2	1	no	—
142	#944	—	10	1	no	—
143	C₂×D₃×C₈	—	5	2	no	—
144	D₃×C₄⋊C₄	—	2	1	no	—
145	D₃×C₄⋊C₄	—	5	2	no	—
146	D₃×C₄⋊C₄	—	10	1	no	—
147	D₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
148	#888	—	2	1	no	—
149	#888	—	5	2	no	—
150	#888	—	10	1	no	—
151	#888	C₂×D₅	1	2	yes	—
152	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
153	#869	—	5	1	no	—
154	#869	C₂×D₅	1	1	yes	characteristic
155	C₃×#107	—	5	4	no	—
156	C₃×C₄×C₈	—	5	1	no	—
157	#818	—	5	4	no	—
158	C₈×Dic₃	—	5	2	no	—
159	#807	—	5	4	no	—
160	#807	—	5	4	no	—
161	C₄×C₃⋊C₈	—	5	1	no	—
162	C₂×C₅×Q₈	—	2	1	no	—
163	C₂×C₅×Q₈	—	6	2	no	—
164	C₂×C₅×Q₈	—	6	1	no	—
165	C₂×C₅×Q₈	—	12	4	no	—
166	C₂²×C₄×C₅	—	3	1	no	—
167	C₂²×C₄×C₅	—	3	1	no	—
168	C₂²×C₄×C₅	—	3	1	no	—
169	C₂²×C₄×C₅	—	6	2	no	—
170	C₂²×Dic₅	—	6	2	no	—
171	C₂×Dic₁₀	—	2	1	no	—
172	C₂×Dic₁₀	—	6	2	no	—
173	C₂×Dic₁₀	—	6	1	no	—
174	C₂×Dic₁₀	—	12	4	no	—
175	C₅×C₄⋊C₄	—	2	1	no	—
176	C₅×C₄⋊C₄	—	3	2	no	—
177	C₅×C₄⋊C₄	—	6	2	no	—
178	C₅×C₄⋊C₄	—	6	2	no	—
179	C₅×C₄⋊C₄	—	6	1	no	—
180	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
181	C₄²×C₅	—	3	1	no	—
182	C₄²×C₅	—	3	1	no	—
183	C₄²×C₅	—	3	1	no	—
184	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
185	C₄⋊Dic₅	—	2	1	no	—
186	C₄⋊Dic₅	—	3	2	no	—
187	C₄⋊Dic₅	—	6	2	no	—
188	C₄⋊Dic₅	—	6	2	no	—
189	C₄⋊Dic₅	—	6	1	no	—
190	C₄⋊Dic₅	C₂²×D₃	1	2	yes	—
191	C₂×#168	—	3	2	no	—
192	C₂×#168	—	3	8	no	—
193	C₂×#168	C₂²×D₃	1	2	yes	—
194	C₂×C₄⋊Q₈	—	3	1	no	—
195	C₂×C₄⋊Q₈	—	15	1	no	—
196	#500	—	5	1	no	—
197	#500	—	15	1	no	—
198	#500	—	15	4	no	—
199	#500	—	15	1	no	—
200	#500	—	15	1	no	—
201	C₂×#107	—	15	4	no	—
202	C₂×C₄×C₈	—	15	1	no	—
203	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₅×D₃	C₄⋊Q₈	1	2	yes	—
205	C₂×C₅×D₃	C₂×D₈	1	2	yes	—
206	C₂×C₅×D₃	C₂×Q₁₆	1	2	yes	—
207	C₃×C₄×C₅	—	4	2	no	—
208	C₃×C₄×C₅	C₂×D₈	1	2	yes	—
209	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
210	C₃×C₄×C₅	C₂²×Q₈	1	2	yes	—
211	Dic₁₅	—	4	2	no	—
212	C₃×Dic₅	—	4	2	no	—
213	C₅×Dic₃	—	4	2	no	—
214	C₅×Dic₃	C₄⋊Q₈	1	2	yes	—
215	C₅×Dic₃	C₂×D₈	1	2	yes	—
216	C₅×Dic₃	C₂×Q₁₆	1	2	yes	—
217	C₂×C₃×Q₈	—	2	1	no	—
218	C₂×C₃×Q₈	—	10	1	no	—
219	D₃×Q₈	—	4	4	no	—
220	D₃×Q₈	—	20	4	no	—
221	C₂×C₄×D₃	—	2	2	no	—
222	C₂×C₄×D₃	—	10	2	no	—
223	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
224	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
225	C₂×C₄×D₃	C₂²×D₅	1	1	yes	characteristic
226	C₂×Dic₆	—	2	1	no	—
227	C₂×Dic₆	—	2	2	no	—
228	C₂×Dic₆	—	10	1	no	—
229	C₂×Dic₆	—	10	2	no	—
230	C₂×C₃×C₈	—	5	2	no	—
231	C₃×C₄⋊C₄	—	2	1	no	—
232	C₃×C₄⋊C₄	—	5	2	no	—
233	C₃×C₄⋊C₄	—	10	1	no	—
234	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
235	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
236	C₄⋊Dic₃	—	2	1	no	—
237	C₄⋊Dic₃	—	5	2	no	—
238	C₄⋊Dic₃	—	10	1	no	—
239	C₄⋊Dic₃	C₂²×D₅	1	2	yes	—
240	Dic₃⋊C₄	—	2	2	no	—
241	Dic₃⋊C₄	—	2	2	no	—
242	Dic₃⋊C₄	—	10	2	no	—
243	Dic₃⋊C₄	—	10	2	no	—
244	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
245	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
246	C₄×Dic₃	C₂²×D₅	1	1	yes	characteristic
247	C₂×C₃⋊C₈	—	5	2	no	—
248	D₃×C₈	—	5	8	no	—
249	C₂³×C₅	—	3	1	no	—
250	C₅×Q₈	—	4	2	no	—
251	C₅×Q₈	—	12	4	no	—
252	C₅×Q₈	—	12	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	3	1	no	—
255	C₂×C₄×C₅	—	3	1	no	—
256	C₂×C₄×C₅	—	3	1	no	—
257	C₂×C₄×C₅	—	3	4	no	—
258	C₂×C₄×C₅	—	3	4	no	—
259	C₂×C₄×C₅	—	3	4	no	—
260	C₂×C₄×C₅	—	6	2	no	—
261	C₂×C₄×C₅	—	12	4	no	—
262	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
263	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
265	C₂×Dic₅	—	2	2	no	—
266	C₂×Dic₅	—	6	2	no	—
267	C₂×Dic₅	—	12	4	no	—
268	Dic₁₀	—	4	2	no	—
269	Dic₁₀	—	12	4	no	—
270	Dic₁₀	—	12	2	no	—
271	#168	—	3	4	no	—
272	#168	D₃×Q₈	1	4	yes	complemented
273	C₂²×Q₈	—	6	1	no	—
274	C₂²×Q₈	—	30	1	no	—
275	C₂²×C₈	—	15	2	no	—
276	C₄⋊Q₈	—	3	2	no	—
277	C₄⋊Q₈	—	3	1	no	—
278	C₄⋊Q₈	—	5	1	no	—
279	C₄⋊Q₈	—	6	1	no	—
280	C₄⋊Q₈	—	6	1	no	—
281	C₄⋊Q₈	—	15	2	no	—
282	C₄⋊Q₈	—	15	1	no	—
283	C₄⋊Q₈	—	30	1	no	—
284	C₄⋊Q₈	—	30	1	no	—
285	C₄⋊Q₈	D₃×D₅	1	1	yes	characteristic
286	C₂×C₄⋊C₄	—	3	2	no	—
287	C₂×C₄⋊C₄	—	6	1	no	—
288	C₂×C₄⋊C₄	—	15	2	no	—
289	C₂×C₄⋊C₄	—	30	1	no	—
290	C₂×C₄²	—	3	1	no	—
291	#107	—	5	4	no	—
292	#107	—	15	4	no	—
293	#107	—	15	4	no	—
294	#107	—	15	4	no	—
295	C₄×C₈	—	5	1	no	—
296	C₄×C₈	—	15	2	no	—
297	C₄×C₈	—	15	1	no	—
298	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
299	C₂×C₃×C₅	C₂²×D₈	1	1	yes	characteristic
300	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
301	C₅×D₃	#500	1	4	yes	complemented
302	C₂²×D₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
303	C₃×Q₈	—	4	2	no	—
304	C₃×Q₈	—	20	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	10	2	no	—
307	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
310	C₂×Dic₃	—	2	2	no	—
311	C₂×Dic₃	—	10	2	no	—
312	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
313	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
314	C₂×Dic₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
315	C₄×D₃	—	4	4	no	—
316	C₄×D₃	—	20	4	no	—
317	C₄×D₃	#686	1	4	yes	—
318	C₄×D₃	#689	1	4	yes	—
319	C₄×D₃	Q₈×D₅	1	4	yes	—
320	Dic₆	—	4	2	no	—
321	Dic₆	—	4	4	no	—
322	Dic₆	—	20	2	no	—
323	Dic₆	—	20	4	no	—
324	C₃×C₈	—	5	4	no	—
325	C₃⋊C₈	—	5	4	no	—
326	C₂²×C₅	—	3	2	no	—
327	C₂²×C₅	—	3	2	no	—
328	C₂²×C₅	—	3	2	no	—
329	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
330	C₄×C₅	—	3	2	no	—
331	C₄×C₅	—	3	2	no	—
332	C₄×C₅	—	3	2	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	—	12	2	no	—
335	C₄×C₅	D₃×D₈	1	2	yes	—
336	C₄×C₅	D₃×Q₁₆	1	2	yes	—
337	C₄×C₅	C₂×D₃×Q₈	1	2	yes	—
338	Dic₅	—	4	2	no	—
339	Dic₅	—	12	2	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	6	2	no	—
342	C₂×Q₈	—	6	1	no	—
343	C₂×Q₈	—	10	1	no	—
344	C₂×Q₈	—	12	4	no	—
345	C₂×Q₈	—	30	2	no	—
346	C₂×Q₈	—	30	1	no	—
347	C₂×Q₈	—	60	4	no	—
348	C₂²×C₄	—	3	1	no	—
349	C₂²×C₄	—	3	1	no	—
350	C₂²×C₄	—	3	1	no	—
351	C₂²×C₄	—	6	2	no	—
352	C₂²×C₄	—	30	2	no	—
353	C₂×C₈	—	5	2	no	—
354	C₂×C₈	—	15	8	no	—
355	C₂×C₈	—	15	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	3	2	no	—
358	C₄⋊C₄	—	5	2	no	—
359	C₄⋊C₄	—	6	2	no	—
360	C₄⋊C₄	—	6	2	no	—
361	C₄⋊C₄	—	6	1	no	—
362	C₄⋊C₄	—	10	1	no	—
363	C₄⋊C₄	—	15	2	no	—
364	C₄⋊C₄	—	30	2	no	—
365	C₄⋊C₄	—	30	2	no	—
366	C₄⋊C₄	—	30	1	no	—
367	C₄⋊C₄	C₂×D₃×D₅	1	2	yes	—
368	C₄²	—	3	1	no	—
369	C₄²	—	3	1	no	—
370	C₄²	—	3	1	no	—
371	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
372	C₃×C₅	C₂×#500	1	1	yes	characteristic, complemented, Hall
373	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
374	C₂×D₃	C₂×#686	1	2	yes	—
375	C₂×D₃	C₂×#689	1	2	yes	—
376	C₂×D₃	#4090	1	2	yes	—
377	C₃×C₄	—	4	2	no	—
378	C₃×C₄	—	20	2	no	—
379	C₃×C₄	C₂×#686	1	2	yes	—
380	C₃×C₄	C₂×#689	1	2	yes	—
381	C₃×C₄	C₂×Q₈×D₅	1	2	yes	—
382	Dic₃	—	4	2	no	—
383	Dic₃	—	20	2	no	—
384	Dic₃	C₂×#686	1	2	yes	—
385	Dic₃	C₂×#689	1	2	yes	—
386	Dic₃	#4090	1	2	yes	—
387	C₂×C₅	—	3	4	no	—
388	C₂×C₅	D₃×C₄⋊Q₈	1	1	yes	characteristic
389	C₂×C₅	C₂×D₃×D₈	1	1	yes	characteristic
390	C₂×C₅	C₂×D₃×Q₁₆	1	1	yes	characteristic
391	C₂³	—	3	1	no	—
392	Q₈	—	4	2	no	—
393	Q₈	—	12	4	no	—
394	Q₈	—	12	2	no	—
395	Q₈	—	20	2	no	—
396	Q₈	—	60	4	no	—
397	Q₈	—	60	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	3	1	no	—
400	C₂×C₄	—	3	1	no	—
401	C₂×C₄	—	3	1	no	—
402	C₂×C₄	—	3	4	no	—
403	C₂×C₄	—	3	4	no	—
404	C₂×C₄	—	3	4	no	—
405	C₂×C₄	—	6	2	no	—
406	C₂×C₄	—	10	2	no	—
407	C₂×C₄	—	12	4	no	—
408	C₂×C₄	—	30	2	no	—
409	C₂×C₄	—	60	4	no	—
410	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
411	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
412	C₂×C₄	C₂²×D₃×D₅	1	1	yes	characteristic
413	C₈	—	5	4	no	—
414	C₈	—	15	4	no	—
415	C₂×C₃	C₂²×#686	1	1	yes	characteristic
416	C₂×C₃	C₂²×#689	1	1	yes	characteristic
417	C₂×C₃	C₂×#4090	1	1	yes	characteristic
418	D₃	#65367	1	4	yes	direct product factor
419	C₅	D₃×#500	1	1	yes	characteristic, complemented, Sylow
420	C₂²	—	3	2	no	—
421	C₂²	—	3	2	no	—
422	C₂²	—	3	2	no	—
423	C₂²	C₂×D₃×C₂²⋊D₅	1	1	yes	characteristic
424	C₄	—	3	2	no	—
425	C₄	—	3	2	no	—
426	C₄	—	3	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	12	2	no	—
429	C₄	—	20	2	no	—
430	C₄	—	60	2	no	—
431	C₄	D₃×#686	1	2	yes	—
432	C₄	D₃×#689	1	2	yes	—
433	C₄	D₃×Q₈×D₅	1	2	yes	—
434	C₃	C₂×#65367	1	1	yes	characteristic, complemented, Sylow
435	C₂	—	3	4	no	—
436	C₂	C₂×D₃×#686	1	1	yes	characteristic
437	C₂	C₂×D₃×#689	1	1	yes	characteristic
438	C₂	D₃×#4090	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₃×C₂²⋊D₅
commutator, cosocle	C₂×C₃×C₄×C₅	C₂⁴
Frattini	C₂×C₄	C₂²×D₃×D₅
Fitting	C₃×C₅×C₄⋊Q₈	C₂²
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₅×D₃	C₂×D₄
hypercenter	C₄⋊Q₈	D₃×D₅
hypocenter	C₃×C₅	C₂×#500
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
3. #11751179	C₂	semidirect
4. C₃×#65367	C₂	semidirect
6. #11747146	C₂	semidirect
8. #11746962	C₂	semidirect
9. #11746955	C₂	semidirect
43. #65367	D₃	direct (N × H)
77. D₃×#168	Q₈	semidirect
135. C₃⋊#168	C₂×Q₈	semidirect
136. C₃×#168	C₂×Q₈	semidirect
272. #168	D₃×Q₈	semidirect
301. C₅×D₃	#500	semidirect
372. C₃×C₅	C₂×#500	semidirect
418. D₃	#65367	direct (N × H)
419. C₅	D₃×#500	semidirect
434. C₃	C₂×#65367	semidirect

Maximal subgroups

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

subgroup	index
C₅×D₃×C₄⋊Q₈	2
D₃×#4015	2
#11751179	2
C₃×#65367	2
D₃×#3939	2
#11747146	2
C₄×D₃×#168	2
#11746962	2
#11746955	2
C₂×#65367	3
D₃×#500	5

Subgroups — D3×#65367 #14439815

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₃×#65367 #14439815