Subgroups — #14282479

Order 1920.

460 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5557	C₂	1	1	yes	maximal, characteristic
2	C₄×D₃×#168	C₂	1	1	yes	maximal, characteristic, complemented
3	#11746875	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄⋊(C₃⋊#168)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×D₄⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
6	#11745843	C₂	1	1	yes	maximal, characteristic, complemented
7	#11745842	C₂	1	1	yes	maximal, characteristic, complemented
8	#10602545	—	3	1	no	maximal, Hall
9	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₅×#938	C₄	1	1	yes	characteristic
11	C₅×#936	C₄	1	1	yes	characteristic
12	C₄×C₅×#67	—	2	1	no	—
13	C₅×#926	—	2	1	no	—
14	C₅×#897	C₄	1	1	yes	characteristic
15	C₅×#890	C₄	1	1	yes	characteristic
16	C₅×#883	—	2	1	no	—
17	C₅×#879	—	2	1	no	—
18	C₄²×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₄×C₅×Dic₆	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	(C₂×D₃)⋊#168	—	2	1	no	—
26	#90953	—	2	1	no	—
27	Dic₃×#168	—	2	1	no	—
28	#68177	—	5	1	no	maximal, Hall
29	C₅×#529	—	3	1	no	—
30	#65215	—	3	1	no	—
31	C₂×C₄×#168	—	3	1	no	—
32	Q₈⋊#168	—	3	1	no	—
33	Q₈⋊#168	—	3	1	no	—
34	D₄⋊#168	—	3	1	no	—
35	D₄⋊#168	D₃	1	1	yes	characteristic, complemented
36	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	—	2	1	no	—
38	C₂×C₅×#67	—	2	1	no	—
39	C₂×C₄×C₅×D₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
41	C₂×C₄×C₅×D₃	D₄	1	1	yes	characteristic
42	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
43	C₃×C₅×C₄⋊C₄	C₂×C₄	1	1	yes	characteristic
44	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
45	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
46	C₂×C₃⋊#168	—	2	1	no	—
47	C₂×C₃⋊#168	—	2	1	no	—
48	C₅×#217	—	2	1	no	—
49	C₅×#217	—	2	1	no	—
50	C₅×#217	—	2	1	no	—
51	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
52	C₅×C₄⋊Dic₃	—	2	1	no	—
53	C₅×C₄⋊Dic₃	—	2	1	no	—
54	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
55	C₅×Dic₃⋊C₄	—	2	1	no	—
56	C₅×Dic₃⋊C₄	—	2	1	no	—
57	C₄×C₅×Dic₃	—	2	1	no	—
58	C₄×C₅×Dic₃	C₂×C₄	1	1	yes	characteristic
59	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
60	C₄×C₅×Dic₃	D₄	1	1	yes	characteristic
61	C₂×C₃×#168	—	2	1	no	—
62	C₂×C₃×#168	—	2	1	no	—
63	D₃×#168	—	2	4	no	—
64	#5557	D₅	1	1	yes	characteristic
65	#4835	—	5	1	no	—
66	C₄×D₃×C₈	—	5	1	no	—
67	C₃×D₄⋊C₈	—	5	1	no	—
68	D₄⋊(C₃⋊C₈)	—	5	1	no	—
69	#4484	—	5	1	no	—
70	#4456	—	5	1	no	—
71	C₅×#126	—	6	1	no	—
72	C₅×#125	—	3	1	no	—
73	C₅×#124	—	3	1	no	—
74	C₅×#123	—	6	1	no	—
75	C₅×C₂²⋊Q₈	—	3	1	no	—
76	C₅×#121	—	3	1	no	—
77	C₄×C₅×Q₈	—	3	1	no	—
78	C₄×C₅×D₄	—	6	1	no	—
79	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
80	C₅×#117	—	6	1	no	—
81	C₂×C₄²×C₅	—	3	1	no	—
82	C₂²×#168	—	6	1	no	—
83	C₂²⋊#168	—	6	1	no	—
84	C₄⋊#168	—	3	1	no	—
85	C₄⋊#168	C₂×D₃	1	1	yes	characteristic
86	#3935	—	6	1	no	—
87	C₄×#168	—	3	1	no	—
88	C₄×#168	—	6	1	no	—
89	C₄×#168	C₂×D₃	1	1	yes	characteristic
90	#1494	—	15	1	no	Sylow
91	C₂³×C₃×C₅	—	2	1	no	—
92	C₂²×C₅×D₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₃×C₅×D₄	—	2	1	no	—
94	C₃×C₅×D₄	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	4	1	no	—
97	C₂×C₃×C₄×C₅	—	4	1	no	—
98	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
99	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
100	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
101	C₅×#67	—	4	2	no	—
102	C₂×C₅×Dic₃	—	2	1	no	—
103	C₂×C₅×Dic₃	—	2	1	no	—
104	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
105	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₅×Dic₃	C₂²⋊C₄	1	1	yes	characteristic
107	C₄×C₅×D₃	—	2	2	no	—
108	C₄×C₅×D₃	—	2	1	no	—
109	C₄×C₅×D₃	—	2	1	no	—
110	C₄×C₅×D₃	—	2	1	no	—
111	C₄×C₅×D₃	—	2	1	no	—
112	C₅×Dic₆	—	2	1	no	—
113	C₅×Dic₆	—	2	1	no	—
114	C₃⋊#168	—	2	2	no	—
115	C₃⋊#168	—	4	1	no	—
116	C₃×#168	—	2	2	no	—
117	C₃×#168	—	4	1	no	—
118	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
119	#938	Dic₅	1	1	yes	characteristic
120	#936	Dic₅	1	1	yes	characteristic
121	C₄×#67	—	2	1	no	—
122	#926	—	2	1	no	—
123	C₂×D₃×C₈	—	10	1	no	—
124	#897	Dic₅	1	1	yes	characteristic
125	#890	Dic₅	1	1	yes	characteristic
126	#883	—	2	1	no	—
127	#879	—	2	1	no	—
128	C₄²×D₃	C₂×D₅	1	1	yes	characteristic
129	C₄×Dic₆	C₂×D₅	1	1	yes	characteristic
130	C₃×C₄⋊C₈	—	5	1	no	—
131	C₃×C₄×C₈	—	5	1	no	—
132	(C₂×D₃)⋊C₈	—	10	1	no	—
133	#815	—	10	1	no	—
134	C₈×Dic₃	—	10	1	no	—
135	C₄⋊(C₃⋊C₈)	—	5	1	no	—
136	C₄×C₃⋊C₈	—	5	1	no	—
137	C₂×C₅×Q₈	—	3	1	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂×C₅×D₄	C₄×D₃	1	1	yes	characteristic
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	3	1	no	—
142	C₂²×C₄×C₅	—	3	1	no	—
143	C₂²×C₄×C₅	—	3	1	no	—
144	C₅×C₄⋊C₄	—	3	1	no	—
145	C₅×C₄⋊C₄	—	6	1	no	—
146	C₅×C₄⋊C₄	—	6	1	no	—
147	C₅×C₄⋊C₄	—	6	1	no	—
148	C₅×C₄⋊C₄	—	6	1	no	—
149	C₅×C₄⋊C₄	C₄×D₃	1	1	yes	characteristic
150	C₅×C₂²⋊C₄	—	2	1	no	—
151	C₅×C₂²⋊C₄	—	6	1	no	—
152	C₅×C₂²⋊C₄	—	6	1	no	—
153	C₅×C₂²⋊C₄	—	6	1	no	—
154	C₅×C₂²⋊C₄	—	6	1	no	—
155	C₄²×C₅	—	3	1	no	—
156	C₄²×C₅	—	3	1	no	—
157	C₄²×C₅	—	3	1	no	—
158	C₄²×C₅	—	6	1	no	—
159	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
160	C₂×#168	—	2	1	no	—
161	C₂×#168	—	2	1	no	—
162	C₂×#168	—	6	4	no	—
163	C₂×#168	—	6	1	no	—
164	C₂×#168	—	6	1	no	—
165	#529	—	3	1	no	—
166	#432	—	15	1	no	—
167	C₂×C₄×C₈	—	15	1	no	—
168	Q₈⋊C₈	—	15	1	no	—
169	Q₈⋊C₈	—	15	1	no	—
170	D₄⋊C₈	—	5	1	no	—
171	D₄⋊C₈	—	15	1	no	—
172	C₂²×C₃×C₅	—	4	1	no	—
173	C₂²×C₃×C₅	—	4	1	no	—
174	C₂²×C₃×C₅	—	4	1	no	—
175	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂×C₅×D₃	—	2	1	no	—
177	C₂×C₅×D₃	—	2	1	no	—
178	C₂×C₅×D₃	#104	1	2	yes	—
179	C₃×C₄×C₅	—	2	1	no	—
180	C₃×C₄×C₅	—	4	1	no	—
181	C₃×C₄×C₅	#131	1	1	yes	characteristic
182	C₃×C₄×C₅	#131	1	1	yes	characteristic
183	C₃×C₄×C₅	#135	1	1	yes	characteristic
184	C₃×C₄×C₅	#135	1	1	yes	characteristic
185	C₅×Dic₃	—	2	1	no	—
186	C₅×Dic₃	—	2	1	no	—
187	C₅×Dic₃	—	2	1	no	—
188	C₅×Dic₃	—	4	1	no	—
189	C₅×Dic₃	—	4	1	no	—
190	C₂×C₃×D₄	C₂×Dic₅	1	1	yes	characteristic
191	C₂²×C₃×C₄	—	2	1	no	—
192	C₂×#67	—	2	1	no	—
193	C₂×C₄×D₃	C₂×Dic₅	1	1	yes	characteristic
194	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
195	C₂×C₄×D₃	C₂²⋊D₅	1	1	yes	characteristic
196	C₂×Dic₆	C₂×Dic₅	1	1	yes	characteristic
197	C₂×C₃×C₈	—	10	1	no	—
198	C₂×C₃×C₈	—	10	1	no	—
199	C₃×C₄⋊C₄	C₂×Dic₅	1	1	yes	characteristic
200	C₃×C₂²⋊C₄	—	2	1	no	—
201	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
202	#217	—	2	1	no	—
203	#217	—	2	1	no	—
204	#217	—	2	1	no	—
205	(C₂×D₃)⋊C₄	—	2	1	no	—
206	C₄⋊Dic₃	—	2	1	no	—
207	C₄⋊Dic₃	—	2	1	no	—
208	C₄⋊Dic₃	C₂×Dic₅	1	1	yes	characteristic
209	Dic₃⋊C₄	—	2	1	no	—
210	Dic₃⋊C₄	—	2	1	no	—
211	C₄×Dic₃	—	2	1	no	—
212	C₄×Dic₃	C₂×Dic₅	1	1	yes	characteristic
213	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
214	C₄×Dic₃	C₂²⋊D₅	1	1	yes	characteristic
215	C₂×C₃⋊C₈	—	10	1	no	—
216	C₂×C₃⋊C₈	—	10	1	no	—
217	D₃×C₈	—	10	4	no	—
218	C₂³×C₅	—	2	1	no	—
219	C₂³×C₅	—	3	1	no	—
220	C₅×Q₈	—	6	1	no	—
221	C₅×Q₈	—	6	1	no	—
222	C₅×D₄	—	2	1	no	—
223	C₅×D₄	—	2	1	no	—
224	C₅×D₄	—	12	2	no	—
225	C₂×C₄×C₅	—	2	1	no	—
226	C₂×C₄×C₅	—	3	1	no	—
227	C₂×C₄×C₅	—	3	1	no	—
228	C₂×C₄×C₅	—	3	1	no	—
229	C₂×C₄×C₅	—	4	1	no	—
230	C₂×C₄×C₅	—	4	1	no	—
231	C₂×C₄×C₅	—	6	2	no	—
232	C₂×C₄×C₅	—	6	1	no	—
233	C₂×C₄×C₅	—	6	1	no	—
234	C₂×C₄×C₅	—	6	1	no	—
235	C₂×C₄×C₅	—	6	1	no	—
236	C₂×C₄×C₅	—	6	1	no	—
237	C₂×C₄×C₅	—	6	1	no	—
238	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
239	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	D₃×D₄	1	1	yes	characteristic
241	#168	—	2	2	no	—
242	#168	—	4	1	no	—
243	#168	—	6	2	no	—
244	#168	—	12	1	no	—
245	C₂²×C₈	—	30	1	no	—
246	#126	—	6	1	no	—
247	#125	—	3	1	no	—
248	#124	—	3	1	no	—
249	#123	—	6	1	no	—
250	C₂²⋊Q₈	—	3	1	no	—
251	#121	—	3	1	no	—
252	C₄×Q₈	—	3	1	no	—
253	C₄×D₄	—	6	1	no	—
254	C₄×D₄	D₃×D₅	1	1	yes	characteristic
255	#117	—	6	1	no	—
256	C₂×C₄²	—	3	1	no	—
257	C₄⋊C₈	—	5	1	no	—
258	C₄⋊C₈	—	15	1	no	—
259	C₂²⋊C₈	—	30	1	no	—
260	#97	—	30	1	no	—
261	C₄×C₈	—	5	1	no	—
262	C₄×C₈	—	15	1	no	—
263	C₄×C₈	—	30	1	no	—
264	C₂×C₃×C₅	—	8	1	no	—
265	C₂×C₃×C₅	#408	1	1	yes	characteristic
266	C₂×C₃×C₅	#416	1	1	yes	characteristic
267	C₂×C₃×C₅	C₂×#104	1	1	yes	characteristic
268	C₅×D₃	—	2	2	no	—
269	C₂³×C₃	—	2	1	no	—
270	C₂²×D₃	C₂²⋊Dic₅	1	1	yes	characteristic
271	C₃×D₄	—	2	1	no	—
272	C₃×D₄	—	2	1	no	—
273	C₂×C₃×C₄	—	2	1	no	—
274	C₂×C₃×C₄	—	4	1	no	—
275	C₂×C₃×C₄	—	4	1	no	—
276	C₂×C₃×C₄	C₂²×Dic₅	1	1	yes	characteristic
277	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
278	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
279	#67	—	4	2	no	—
280	C₂×Dic₃	—	2	1	no	—
281	C₂×Dic₃	—	2	1	no	—
282	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
283	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
284	C₂×Dic₃	C₂²⋊Dic₅	1	1	yes	characteristic
285	C₄×D₃	—	2	2	no	—
286	C₄×D₃	—	2	1	no	—
287	C₄×D₃	—	2	1	no	—
288	C₄×D₃	—	2	1	no	—
289	C₄×D₃	—	2	1	no	—
290	Dic₆	—	2	1	no	—
291	Dic₆	—	2	1	no	—
292	C₃×C₈	—	10	2	no	—
293	C₃×C₈	—	20	1	no	—
294	C₃⋊C₈	—	10	2	no	—
295	C₃⋊C₈	—	20	1	no	—
296	C₂²×C₅	—	3	2	no	—
297	C₂²×C₅	—	4	1	no	—
298	C₂²×C₅	—	4	1	no	—
299	C₂²×C₅	—	4	1	no	—
300	C₂²×C₅	—	6	1	no	—
301	C₂²×C₅	—	6	1	no	—
302	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
303	C₄×C₅	—	2	1	no	—
304	C₄×C₅	—	4	1	no	—
305	C₄×C₅	—	6	1	no	—
306	C₄×C₅	—	6	1	no	—
307	C₄×C₅	—	6	1	no	—
308	C₄×C₅	—	12	1	no	—
309	C₄×C₅	—	12	1	no	—
310	C₄×C₅	#901	1	1	yes	characteristic
311	C₄×C₅	#907	1	1	yes	characteristic
312	C₄×C₅	#912	1	1	yes	characteristic
313	C₄×C₅	#916	1	1	yes	characteristic
314	C₂×Q₈	—	3	1	no	—
315	C₂×D₄	—	6	1	no	—
316	C₂×D₄	D₃×Dic₅	1	1	yes	characteristic
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	3	1	no	—
319	C₂²×C₄	—	3	1	no	—
320	C₂²×C₄	—	3	1	no	—
321	C₂×C₈	—	10	1	no	—
322	C₂×C₈	—	10	1	no	—
323	C₂×C₈	—	30	4	no	—
324	C₂×C₈	—	30	1	no	—
325	C₂×C₈	—	30	1	no	—
326	C₄⋊C₄	—	3	1	no	—
327	C₄⋊C₄	—	6	1	no	—
328	C₄⋊C₄	—	6	1	no	—
329	C₄⋊C₄	—	6	1	no	—
330	C₄⋊C₄	—	6	1	no	—
331	C₄⋊C₄	D₃×Dic₅	1	1	yes	characteristic
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	6	1	no	—
334	C₂²⋊C₄	—	6	1	no	—
335	C₂²⋊C₄	—	6	1	no	—
336	C₂²⋊C₄	—	6	1	no	—
337	C₄²	—	3	1	no	—
338	C₄²	—	3	1	no	—
339	C₄²	—	3	1	no	—
340	C₄²	—	6	1	no	—
341	C₄²	C₂×D₃×D₅	1	1	yes	characteristic
342	C₃×C₅	#1494	1	1	yes	characteristic, complemented, Hall
343	C₂²×C₃	—	4	1	no	—
344	C₂²×C₃	—	4	1	no	—
345	C₂²×C₃	—	4	1	no	—
346	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
347	C₂×D₃	—	2	1	no	—
348	C₂×D₃	—	2	1	no	—
349	C₂×D₃	#3969	1	2	yes	—
350	C₃×C₄	—	2	1	no	—
351	C₃×C₄	—	4	1	no	—
352	C₃×C₄	#4094	1	1	yes	characteristic
353	C₃×C₄	#4094	1	1	yes	characteristic
354	C₃×C₄	#4096	1	1	yes	characteristic
355	C₃×C₄	#4096	1	1	yes	characteristic
356	Dic₃	—	2	1	no	—
357	Dic₃	—	2	1	no	—
358	Dic₃	—	2	1	no	—
359	Dic₃	—	4	1	no	—
360	Dic₃	—	4	1	no	—
361	C₂×C₅	—	6	2	no	—
362	C₂×C₅	—	8	1	no	—
363	C₂×C₅	#4727	1	1	yes	characteristic
364	C₂×C₅	#4772	1	1	yes	characteristic
365	C₂×C₅	D₃×#104	1	1	yes	characteristic
366	C₂³	—	2	1	no	—
367	C₂³	—	3	1	no	—
368	Q₈	—	6	1	no	—
369	Q₈	—	6	1	no	—
370	D₄	—	2	1	no	—
371	D₄	—	2	1	no	—
372	D₄	—	12	2	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	3	1	no	—
375	C₂×C₄	—	3	1	no	—
376	C₂×C₄	—	3	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	6	2	no	—
380	C₂×C₄	—	6	1	no	—
381	C₂×C₄	—	6	1	no	—
382	C₂×C₄	—	6	1	no	—
383	C₂×C₄	—	6	1	no	—
384	C₂×C₄	—	6	1	no	—
385	C₂×C₄	—	6	1	no	—
386	C₂×C₄	C₂×D₃×Dic₅	1	1	yes	characteristic
387	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
388	C₂×C₄	D₃×C₂²⋊D₅	1	1	yes	characteristic
389	C₈	—	10	2	no	—
390	C₈	—	20	1	no	—
391	C₈	—	30	2	no	—
392	C₈	—	60	1	no	—
393	C₂×C₃	—	8	1	no	—
394	C₂×C₃	#65522	1	1	yes	characteristic
395	C₂×C₃	#65523	1	1	yes	characteristic
396	C₂×C₃	C₂×#3969	1	1	yes	characteristic
397	D₃	—	2	2	no	—
398	C₅	#68177	1	1	yes	characteristic, complemented, Sylow
399	C₂²	—	3	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	6	1	no	—
404	C₂²	—	6	1	no	—
405	C₂²	D₃×C₂²⋊Dic₅	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	4	1	no	—
408	C₄	—	6	1	no	—
409	C₄	—	6	1	no	—
410	C₄	—	6	1	no	—
411	C₄	—	12	1	no	—
412	C₄	—	12	1	no	—
413	C₄	#91286	1	1	yes	characteristic
414	C₄	#91288	1	1	yes	characteristic
415	C₄	#91493	1	1	yes	characteristic
416	C₄	#91495	1	1	yes	characteristic
417	C₃	#10602545	1	1	yes	characteristic, complemented, Sylow
418	C₂	—	6	2	no	—
419	C₂	—	8	1	no	—
420	C₂	#11748490	1	1	yes	characteristic
421	C₂	#11748965	1	1	yes	characteristic
422	C₂	D₃×#3969	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₃×C₂²⋊D₅
commutator	C₂×C₃×C₄×C₅	C₂²×C₄
Frattini	C₄²	C₂×D₃×D₅
Fitting	C₃×C₄×C₅×D₄	C₂²
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₅×#938	C₄
cosocle	C₃×C₄²×C₅	C₂³
hypercenter	C₄×D₄	D₃×D₅
hypocenter	C₃×C₅	#1494
LCS	G ▷ C₂×C₃×C₄×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₄×D₃×#168	C₂	semidirect
3. #11746875	C₂	semidirect
4. D₄⋊(C₃⋊#168)	C₂	semidirect
5. C₃×D₄⋊#168	C₂	semidirect
6. #11745843	C₂	semidirect
7. #11745842	C₂	semidirect
35. D₄⋊#168	D₃	semidirect
342. C₃×C₅	#1494	semidirect
398. C₅	#68177	semidirect
417. C₃	#10602545	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5557	2
C₄×D₃×#168	2
#11746875	2
D₄⋊(C₃⋊#168)	2
C₃×D₄⋊#168	2
#11745843	2
#11745842	2
#10602545	3
#68177	5