Subgroups — #14281663

Order 1920.

528 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	C₄×C₅×#239	C₂	1	1	yes	maximal, characteristic
2	D₃×C₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
3	#11746876	C₂	1	1	yes	maximal, characteristic, complemented
4	#11746356	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×Q₈⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745837	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745836	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602432	—	3	1	no	maximal, Hall
9	C₂×C₅×#239	C₄	1	1	yes	characteristic
10	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₅×Q₈×Dic₃	C₄	1	1	yes	characteristic
12	C₅×#893	—	2	1	no	—
13	C₅×#893	C₄	1	1	yes	characteristic
14	C₅×#892	—	2	1	no	—
15	C₅×#892	C₄	1	1	yes	characteristic
16	C₄×C₅×D₁₂	—	2	1	no	—
17	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
18	C₄²×C₅×D₃	—	2	1	no	—
19	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂×D₃×#168	—	2	1	no	—
21	C₄⋊(C₃⋊#168)	C₂²	1	1	yes	characteristic
22	C₄×C₃⋊#168	C₂²	1	1	yes	characteristic
23	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
24	C₃×C₄×#168	C₂²	1	1	yes	characteristic
25	Dic₃⋊#168	—	2	1	no	—
26	Dic₃⋊#168	—	2	1	no	—
27	(C₂×D₃)⋊#168	—	2	1	no	—
28	#68230	—	5	1	no	maximal, Hall
29	C₄×C₅×#41	—	3	1	no	—
30	#65214	—	3	1	no	—
31	C₂×C₄⋊#168	—	3	1	no	—
32	Q₈⋊#168	—	3	1	no	—
33	Q₈⋊#168	D₃	1	1	yes	characteristic, complemented
34	D₄⋊#168	—	3	1	no	—
35	D₄⋊#168	—	3	1	no	—
36	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
37	C₅×#239	—	2	2	no	—
38	C₅×#239	C₈	1	4	yes	complemented
39	C₂×C₅×D₁₂	—	2	1	no	—
40	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	—	2	1	no	—
42	C₂×C₄×C₅×D₃	—	2	1	no	—
43	C₂×C₄×C₅×D₃	—	2	1	no	—
44	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
46	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
47	C₃×C₅×C₄⋊C₄	—	2	1	no	—
48	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
49	C₃×C₄²×C₅	—	2	1	no	—
50	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃⋊#168	—	2	1	no	—
52	C₂×C₃⋊#168	—	2	1	no	—
53	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
55	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
58	C₄×C₅×Dic₃	—	2	1	no	—
59	C₄×C₅×Dic₃	—	2	1	no	—
60	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
61	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
62	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
63	C₂×C₃×#168	—	2	1	no	—
64	C₂×C₃×#168	—	2	1	no	—
65	D₃×#168	—	4	2	no	—
66	C₄×#239	D₅	1	1	yes	characteristic
67	D₃×C₄⋊C₈	—	5	1	no	—
68	#4685	—	5	1	no	—
69	C₃×Q₈⋊C₈	—	5	1	no	—
70	#4535	—	5	1	no	—
71	#4483	—	5	1	no	—
72	#4459	—	5	1	no	—
73	C₂×C₅×#41	—	3	1	no	—
74	C₄×C₅×Q₈	—	3	1	no	—
75	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
76	C₄×C₅×D₄	—	3	1	no	—
77	C₄×C₅×D₄	—	3	1	no	—
78	C₄×C₅×D₄	—	6	1	no	—
79	C₄×C₅×D₄	—	6	1	no	—
80	C₅×#117	—	3	1	no	—
81	C₅×#117	—	6	1	no	—
82	C₂×C₄²×C₅	—	3	1	no	—
83	C₂×C₄²×C₅	—	6	1	no	—
84	C₂²×#168	—	6	1	no	—
85	C₂²⋊#168	—	6	1	no	—
86	C₄⋊#168	—	3	1	no	—
87	C₄⋊#168	—	6	1	no	—
88	C₄⋊#168	—	6	1	no	—
89	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
90	C₄×#168	—	3	1	no	—
91	C₄×#168	C₂×D₃	1	1	yes	characteristic
92	#1477	—	15	1	no	Sylow
93	C₂²×C₅×D₃	—	2	1	no	—
94	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
95	C₃×C₅×Q₈	—	2	1	no	—
96	C₃×C₅×Q₈	C₂×C₈	1	2	yes	complemented
97	C₂×C₃×C₄×C₅	—	2	1	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₅×D₁₂	—	2	4	no	—
107	C₅×D₁₂	—	2	1	no	—
108	C₅×D₁₂	C₂×C₈	1	2	yes	complemented
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	2	1	no	—
111	C₄×C₅×D₃	—	2	4	no	—
112	C₄×C₅×D₃	—	4	1	no	—
113	C₄×C₅×D₃	—	4	2	no	—
114	C₄×C₅×D₃	—	4	1	no	—
115	C₄×C₅×D₃	—	4	1	no	—
116	C₄×C₅×D₃	C₂×C₈	1	2	yes	—
117	C₄×C₅×D₃	M₁₆	1	2	yes	—
118	C₃⋊#168	—	4	1	no	—
119	C₃⋊#168	—	4	1	no	—
120	C₃×#168	—	4	1	no	—
121	C₃×#168	—	4	1	no	—
122	C₂×#239	Dic₅	1	1	yes	characteristic
123	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
124	Q₈×Dic₃	Dic₅	1	1	yes	characteristic
125	C₂×D₃×C₈	—	10	1	no	—
126	#893	—	2	1	no	—
127	#893	Dic₅	1	1	yes	characteristic
128	#892	—	2	1	no	—
129	#892	Dic₅	1	1	yes	characteristic
130	C₄×D₁₂	—	2	1	no	—
131	C₄×D₁₂	C₂×D₅	1	1	yes	characteristic
132	C₄²×D₃	—	2	1	no	—
133	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
134	C₃×C₄⋊C₈	—	5	1	no	—
135	C₃×C₄×C₈	—	5	1	no	—
136	(C₂×D₃)⋊C₈	—	10	1	no	—
137	Dic₃⋊C₈	—	10	1	no	—
138	Dic₃⋊C₈	—	10	1	no	—
139	C₄⋊(C₃⋊C₈)	—	5	1	no	—
140	C₄×C₃⋊C₈	—	5	1	no	—
141	C₅×#41	—	3	4	no	—
142	C₅×#41	—	6	2	no	—
143	C₂×C₅×Q₈	C₄×D₃	1	1	yes	characteristic
144	C₂×C₅×D₄	—	3	1	no	—
145	C₂×C₅×D₄	—	6	1	no	—
146	C₂²×C₄×C₅	—	3	1	no	—
147	C₂²×C₄×C₅	—	3	1	no	—
148	C₂²×C₄×C₅	—	3	1	no	—
149	C₂²×C₄×C₅	—	6	1	no	—
150	C₂²×C₄×C₅	—	6	1	no	—
151	C₂²×C₄×C₅	—	6	1	no	—
152	C₅×C₄⋊C₄	—	2	1	no	—
153	C₅×C₄⋊C₄	—	3	1	no	—
154	C₅×C₄⋊C₄	—	6	1	no	—
155	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
156	C₅×C₂²⋊C₄	—	6	1	no	—
157	C₅×C₂²⋊C₄	—	6	1	no	—
158	C₅×C₂²⋊C₄	—	6	1	no	—
159	C₄²×C₅	—	2	1	no	—
160	C₄²×C₅	—	3	1	no	—
161	C₄²×C₅	—	3	1	no	—
162	C₄²×C₅	—	3	1	no	—
163	C₄²×C₅	—	6	1	no	—
164	C₄²×C₅	—	6	1	no	—
165	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
166	C₂×#168	—	2	1	no	—
167	C₂×#168	—	2	1	no	—
168	C₂×#168	—	6	1	no	—
169	C₂×#168	—	6	1	no	—
170	C₂×#168	—	12	2	no	—
171	C₄×#41	—	3	1	no	—
172	#431	—	15	1	no	—
173	C₂×C₄⋊C₈	—	15	1	no	—
174	Q₈⋊C₈	—	5	1	no	—
175	Q₈⋊C₈	—	15	1	no	—
176	D₄⋊C₈	—	15	1	no	—
177	D₄⋊C₈	—	15	1	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂×C₅×D₃	—	2	1	no	—
180	C₂×C₅×D₃	—	2	1	no	—
181	C₂×C₅×D₃	—	2	2	no	—
182	C₂×C₅×D₃	—	4	1	no	—
183	C₂×C₅×D₃	—	4	1	no	—
184	C₂×C₅×D₃	C₂²⋊C₈	1	2	yes	—
185	C₃×C₄×C₅	—	2	2	no	—
186	C₃×C₄×C₅	—	2	1	no	—
187	C₃×C₄×C₅	—	4	1	no	—
188	C₃×C₄×C₅	C₂²×C₈	1	1	yes	characteristic
189	C₃×C₄×C₅	C₂×M₁₆	1	1	yes	characteristic
190	C₃×C₄×C₅	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₃×C₄×C₅	#137	1	1	yes	characteristic
192	C₅×Dic₃	—	2	1	no	—
193	C₅×Dic₃	—	2	1	no	—
194	C₅×Dic₃	—	4	1	no	—
195	C₅×Dic₃	C₂²⋊C₈	1	2	yes	—
196	C₂×C₃×Q₈	C₂×Dic₅	1	1	yes	characteristic
197	#239	—	2	2	no	—
198	#239	#168	1	4	yes	complemented
199	C₂×D₁₂	—	2	1	no	—
200	C₂×D₁₂	C₂×Dic₅	1	1	yes	characteristic
201	C₂×C₄×D₃	—	2	1	no	—
202	C₂×C₄×D₃	—	2	1	no	—
203	C₂×C₄×D₃	—	2	1	no	—
204	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
205	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
206	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
207	C₂×C₃×C₈	—	10	1	no	—
208	C₂×C₃×C₈	—	10	1	no	—
209	C₃×C₄⋊C₄	—	2	1	no	—
210	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
211	C₃×C₄²	—	2	1	no	—
212	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
213	(C₂×D₃)⋊C₄	—	2	1	no	—
214	(C₂×D₃)⋊C₄	—	2	1	no	—
215	(C₂×D₃)⋊C₄	—	2	1	no	—
216	C₄⋊Dic₃	—	2	1	no	—
217	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
218	C₄×Dic₃	—	2	1	no	—
219	C₄×Dic₃	—	2	1	no	—
220	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
221	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
222	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
223	C₂×C₃⋊C₈	—	10	1	no	—
224	C₂×C₃⋊C₈	—	10	1	no	—
225	D₃×C₈	—	20	2	no	—
226	C₂³×C₅	—	3	1	no	—
227	C₂³×C₅	—	6	1	no	—
228	C₅×Q₈	—	2	1	no	—
229	C₅×Q₈	D₃×C₈	1	2	yes	complemented
230	C₅×D₄	—	3	2	no	—
231	C₅×D₄	—	6	4	no	—
232	C₅×D₄	—	6	1	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	3	1	no	—
236	C₂×C₄×C₅	—	3	2	no	—
237	C₂×C₄×C₅	—	3	2	no	—
238	C₂×C₄×C₅	—	3	1	no	—
239	C₂×C₄×C₅	—	3	1	no	—
240	C₂×C₄×C₅	—	6	4	no	—
241	C₂×C₄×C₅	—	6	1	no	—
242	C₂×C₄×C₅	—	6	1	no	—
243	C₂×C₄×C₅	—	6	1	no	—
244	C₂×C₄×C₅	—	12	1	no	—
245	C₂×C₄×C₅	—	12	2	no	—
246	C₂×C₄×C₅	—	12	1	no	—
247	C₂×C₄×C₅	—	12	1	no	—
248	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
249	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
250	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
251	#168	—	4	1	no	—
252	#168	—	4	1	no	—
253	#168	—	12	1	no	—
254	#168	—	12	1	no	—
255	C₂×#41	—	3	1	no	—
256	C₂²×C₈	—	30	1	no	—
257	C₄×Q₈	—	3	1	no	—
258	C₄×Q₈	D₃×D₅	1	1	yes	characteristic
259	C₄×D₄	—	3	1	no	—
260	C₄×D₄	—	3	1	no	—
261	C₄×D₄	—	6	1	no	—
262	C₄×D₄	—	6	1	no	—
263	#117	—	3	1	no	—
264	#117	—	6	1	no	—
265	C₂×C₄²	—	3	1	no	—
266	C₂×C₄²	—	6	1	no	—
267	C₄⋊C₈	—	5	1	no	—
268	C₄⋊C₈	—	15	1	no	—
269	C₄⋊C₈	—	30	1	no	—
270	C₄⋊C₈	—	30	1	no	—
271	C₂²⋊C₈	—	30	1	no	—
272	C₄×C₈	—	5	1	no	—
273	C₄×C₈	—	15	1	no	—
274	C₂×C₃×C₅	C₂×C₂²⋊C₈	1	1	yes	characteristic
275	C₂×C₃×C₅	#417	1	1	yes	characteristic
276	C₂×C₃×C₅	#421	1	1	yes	characteristic
277	C₅×D₃	—	2	2	no	—
278	C₅×D₃	—	4	2	no	—
279	C₂²×D₃	—	2	1	no	—
280	C₂²×D₃	C₂²⋊Dic₅	1	1	yes	characteristic
281	C₃×Q₈	—	2	1	no	—
282	C₃×Q₈	C₂×#168	1	2	yes	complemented
283	C₂×C₃×C₄	—	2	1	no	—
284	C₂×C₃×C₄	—	2	1	no	—
285	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
288	C₂×Dic₃	—	2	1	no	—
289	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
290	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
291	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
292	D₁₂	—	2	4	no	—
293	D₁₂	—	2	1	no	—
294	D₁₂	C₂×#168	1	2	yes	complemented
295	C₄×D₃	—	2	1	no	—
296	C₄×D₃	—	2	1	no	—
297	C₄×D₃	—	2	4	no	—
298	C₄×D₃	—	4	1	no	—
299	C₄×D₃	—	4	2	no	—
300	C₄×D₃	—	4	1	no	—
301	C₄×D₃	—	4	1	no	—
302	C₄×D₃	C₂×#168	1	2	yes	—
303	C₄×D₃	#681	1	2	yes	—
304	C₃×C₈	—	20	1	no	—
305	C₃×C₈	—	20	1	no	—
306	C₃⋊C₈	—	20	1	no	—
307	C₃⋊C₈	—	20	1	no	—
308	C₂²×C₅	—	3	2	no	—
309	C₂²×C₅	—	6	1	no	—
310	C₂²×C₅	—	6	1	no	—
311	C₂²×C₅	—	6	2	no	—
312	C₂²×C₅	—	12	1	no	—
313	C₂²×C₅	—	12	1	no	—
314	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
315	C₄×C₅	—	2	2	no	—
316	C₄×C₅	—	2	1	no	—
317	C₄×C₅	—	3	2	no	—
318	C₄×C₅	—	4	1	no	—
319	C₄×C₅	—	6	1	no	—
320	C₄×C₅	—	6	1	no	—
321	C₄×C₅	—	12	1	no	—
322	C₄×C₅	C₂×D₃×C₈	1	1	yes	characteristic
323	C₄×C₅	D₃×M₁₆	1	1	yes	characteristic
324	C₄×C₅	#914	1	1	yes	characteristic
325	C₄×C₅	#918	1	1	yes	characteristic
326	#41	—	3	4	no	—
327	#41	—	6	2	no	—
328	C₂×Q₈	D₃×Dic₅	1	1	yes	characteristic
329	C₂×D₄	—	3	1	no	—
330	C₂×D₄	—	6	1	no	—
331	C₂²×C₄	—	3	1	no	—
332	C₂²×C₄	—	3	1	no	—
333	C₂²×C₄	—	3	1	no	—
334	C₂²×C₄	—	6	1	no	—
335	C₂²×C₄	—	6	1	no	—
336	C₂²×C₄	—	6	1	no	—
337	C₂×C₈	—	10	1	no	—
338	C₂×C₈	—	10	1	no	—
339	C₂×C₈	—	30	1	no	—
340	C₂×C₈	—	30	1	no	—
341	C₂×C₈	—	60	2	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	3	1	no	—
344	C₄⋊C₄	—	6	1	no	—
345	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
346	C₂²⋊C₄	—	6	1	no	—
347	C₂²⋊C₄	—	6	1	no	—
348	C₂²⋊C₄	—	6	1	no	—
349	C₄²	—	2	1	no	—
350	C₄²	—	3	1	no	—
351	C₄²	—	3	1	no	—
352	C₄²	—	3	1	no	—
353	C₄²	—	6	1	no	—
354	C₄²	—	6	1	no	—
355	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
356	C₃×C₅	#1477	1	1	yes	characteristic, complemented, Hall
357	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
358	C₂×D₃	—	2	1	no	—
359	C₂×D₃	—	2	1	no	—
360	C₂×D₃	—	2	2	no	—
361	C₂×D₃	—	4	1	no	—
362	C₂×D₃	—	4	1	no	—
363	C₂×D₃	C₂²⋊#168	1	2	yes	—
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	1	no	—
366	C₃×C₄	—	4	1	no	—
367	C₃×C₄	C₂²×#168	1	1	yes	characteristic
368	C₃×C₄	C₂×#681	1	1	yes	characteristic
369	C₃×C₄	#4095	1	1	yes	characteristic
370	C₃×C₄	#4097	1	1	yes	characteristic
371	Dic₃	—	2	1	no	—
372	Dic₃	—	2	1	no	—
373	Dic₃	—	4	1	no	—
374	Dic₃	C₂²⋊#168	1	2	yes	—
375	C₂×C₅	—	6	2	no	—
376	C₂×C₅	—	12	2	no	—
377	C₂×C₅	D₃×C₂²⋊C₈	1	1	yes	characteristic
378	C₂×C₅	#4803	1	1	yes	characteristic
379	C₂×C₅	#4821	1	1	yes	characteristic
380	C₂³	—	3	1	no	—
381	C₂³	—	6	1	no	—
382	Q₈	—	2	1	no	—
383	Q₈	D₃×#168	1	2	yes	complemented
384	D₄	—	3	2	no	—
385	D₄	—	6	4	no	—
386	D₄	—	6	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	3	1	no	—
390	C₂×C₄	—	3	2	no	—
391	C₂×C₄	—	3	2	no	—
392	C₂×C₄	—	3	1	no	—
393	C₂×C₄	—	3	1	no	—
394	C₂×C₄	—	6	4	no	—
395	C₂×C₄	—	6	1	no	—
396	C₂×C₄	—	6	1	no	—
397	C₂×C₄	—	6	1	no	—
398	C₂×C₄	—	12	1	no	—
399	C₂×C₄	—	12	2	no	—
400	C₂×C₄	—	12	1	no	—
401	C₂×C₄	—	12	1	no	—
402	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
403	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
404	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
405	C₈	—	20	1	no	—
406	C₈	—	20	1	no	—
407	C₈	—	60	1	no	—
408	C₈	—	60	1	no	—
409	C₂×C₃	C₂×C₂²⋊#168	1	1	yes	characteristic
410	C₂×C₃	#65521	1	1	yes	characteristic
411	C₂×C₃	#65525	1	1	yes	characteristic
412	D₃	—	2	2	no	—
413	D₃	—	4	2	no	—
414	C₅	#68230	1	1	yes	characteristic, complemented, Sylow
415	C₂²	—	3	2	no	—
416	C₂²	—	6	1	no	—
417	C₂²	—	6	1	no	—
418	C₂²	—	6	2	no	—
419	C₂²	—	12	1	no	—
420	C₂²	—	12	1	no	—
421	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	2	no	—
424	C₄	—	3	2	no	—
425	C₄	—	4	1	no	—
426	C₄	—	6	1	no	—
427	C₄	—	6	1	no	—
428	C₄	—	12	1	no	—
429	C₄	C₂×D₃×#168	1	1	yes	characteristic
430	C₄	D₃×#681	1	1	yes	characteristic
431	C₄	#91504	1	1	yes	characteristic
432	C₄	#91510	1	1	yes	characteristic
433	C₃	#10602432	1	1	yes	characteristic, complemented, Sylow
434	C₂	—	6	2	no	—
435	C₂	—	12	2	no	—
436	C₂	D₃×C₂²⋊#168	1	1	yes	characteristic
437	C₂	#11749201	1	1	yes	characteristic
438	C₂	#11749429	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₃×C₄×C₅	C₂²×C₈
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₄×C₅×Q₈	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#239	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄×Q₈	D₃×D₅
hypocenter	C₃×C₅	#1477
LCS	G ▷ C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. D₃×C₄⋊#168	C₂	semidirect
3. #11746876	C₂	semidirect
4. #11746356	C₂	semidirect
5. C₃×Q₈⋊#168	C₂	semidirect
6. #11745837	C₂	semidirect
7. #11745836	C₂	semidirect
33. Q₈⋊#168	D₃	semidirect
38. C₅×#239	C₈	semidirect
96. C₃×C₅×Q₈	C₂×C₈	semidirect
108. C₅×D₁₂	C₂×C₈	semidirect
198. #239	#168	semidirect
229. C₅×Q₈	D₃×C₈	semidirect
282. C₃×Q₈	C₂×#168	semidirect
294. D₁₂	C₂×#168	semidirect
356. C₃×C₅	#1477	semidirect
383. Q₈	D₃×#168	semidirect
414. C₅	#68230	semidirect
433. C₃	#10602432	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₅×#239	2
D₃×C₄⋊#168	2
#11746876	2
#11746356	2
C₃×Q₈⋊#168	2
#11745837	2
#11745836	2
#10602432	3
#68230	5