Subgroups — #14578205

Order 2432.

1032 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11927298	C₂	1	2	yes	maximal, complemented
2	#11927288	C₂	1	2	yes	maximal, complemented
3	#11927267	C₂	1	2	yes	maximal, complemented
4	#11927217	C₂	1	4	yes	maximal, complemented
5	D₄×Dic₃₈	C₂	1	2	yes	maximal, complemented
6	#11927203	C₂	1	2	yes	maximal, complemented
7	#11927190	C₂	1	2	yes	maximal, complemented
8	#11927169	C₂	1	2	yes	maximal, complemented
9	#11927165	C₂	1	2	yes	maximal, complemented
10	#11927160	C₂	1	4	yes	maximal, complemented
11	#11927131	C₂	1	2	yes	maximal, complemented
12	#11927120	C₂	1	2	yes	maximal, complemented
13	#11927101	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#10597321	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#529	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#64541	C₂²	1	2	yes	—
17	C₂²×D₇₆	C₂²	1	1	yes	characteristic
18	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
19	C₂²×Dic₃₈	C₂²	1	2	yes	complemented
20	C₁₉×#126	C₂²	1	2	yes	complemented
21	C₁₉×#125	C₂²	1	1	yes	characteristic, complemented
22	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×#123	C₂²	1	2	yes	—
24	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₉×#121	C₂²	1	1	yes	characteristic
26	C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₁₉	C₂²	1	2	yes	—
28	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₁₉×#117	C₂²	1	2	yes	complemented
30	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
31	#10597392	C₂²	1	4	yes	complemented
32	#10597385	C₂²	1	4	yes	complemented
33	#10597383	C₂²	1	4	yes	—
34	D₄×Dic₁₉	C₂²	1	4	yes	—
35	#10597376	C₂²	1	2	yes	—
36	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
37	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	2	yes	—
38	#10597372	C₂²	1	2	yes	—
39	#10597370	C₂²	1	2	yes	—
40	#10597370	C₂²	1	2	yes	—
41	#10597370	C₂²	1	2	yes	complemented
42	#10597344	C₂²	1	4	yes	complemented
43	#10597344	C₂²	1	4	yes	complemented
44	#10597344	C₂²	1	4	yes	complemented
45	#10597343	C₂²	1	4	yes	complemented
46	#10597343	C₂²	1	4	yes	complemented
47	#10597342	C₂²	1	4	yes	complemented
48	#10597342	C₂²	1	4	yes	complemented
49	#10597340	C₂²	1	4	yes	—
50	#10597338	C₂²	1	4	yes	complemented
51	#10597334	C₂²	1	4	yes	complemented
52	#10597332	C₂²	1	4	yes	complemented
53	#10597332	C₂²	1	4	yes	complemented
54	#10597331	C₂²	1	4	yes	complemented
55	#10597331	C₂²	1	4	yes	complemented
56	#10597330	C₂²	1	4	yes	—
57	#10597329	C₂²	1	4	yes	complemented
58	(C₂²⋊D₁₉)⋊C₄	C₂²	1	4	yes	complemented
59	C₂²⋊C₄×D₁₉	C₂²	1	4	yes	—
60	#10597324	C₂²	1	4	yes	—
61	#10597324	C₂²	1	4	yes	complemented
62	#10597321	C₂²	1	2	yes	—
63	#10597321	C₂²	1	2	yes	—
64	#10597321	C₂²	1	2	yes	—
65	#10597321	C₂²	1	2	yes	—
66	#10597321	C₂²	1	2	yes	—
67	C₄×D₇₆	C₂²	1	2	yes	—
68	#10597316	C₂²	1	2	yes	complemented
69	#10597315	C₂²	1	1	yes	characteristic, complemented
70	#10597315	C₂²	1	1	yes	characteristic, complemented
71	#10597315	C₂²	1	2	yes	complemented
72	C₄×Dic₃₈	C₂²	1	2	yes	complemented
73	C₄×Dic₃₈	C₂²	1	2	yes	complemented
74	C₄×Dic₃₈	C₂²	1	2	yes	complemented
75	C₂³×D₁₉	C₂³	1	2	yes	—
76	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₁₉	C₂³	1	2	yes	—
78	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂³	1	2	yes	—
80	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
83	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
84	C₂×C₂²⋊D₁₉	C₂³	1	4	yes	—
85	C₂²×Dic₁₉	C₂³	1	2	yes	—
86	C₂²×Dic₁₉	C₂³	1	4	yes	—
87	#64541	—	4	4	no	—
88	C₂×D₇₆	—	4	2	no	—
89	C₂×D₇₆	C₂³	1	2	yes	—
90	C₂×D₇₆	C₂³	1	2	yes	—
91	C₂×C₄×D₁₉	C₂³	1	4	yes	—
92	C₂×C₄×D₁₉	C₂³	1	4	yes	—
93	C₂×Dic₃₈	—	4	2	no	—
94	C₂×Dic₃₈	—	4	4	no	—
95	C₂×Dic₃₈	C₂³	1	2	yes	—
96	C₂×Dic₃₈	C₂³	1	2	yes	—
97	C₂×Dic₃₈	C₂³	1	2	yes	—
98	C₂×Dic₃₈	C₂³	1	4	yes	—
99	C₂×Dic₃₈	C₂³	1	2	yes	—
100	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
101	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
102	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
103	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
104	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
106	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
107	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
108	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
109	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
110	C₂²⋊C₄×C₁₉	C₂³	1	2	yes	—
111	C₄²×C₁₉	C₂³	1	1	yes	characteristic
112	C₄²×C₁₉	C₂³	1	1	yes	characteristic
113	C₄²×C₁₉	C₂³	1	1	yes	characteristic
114	C₄²×C₁₉	C₂³	1	1	yes	characteristic
115	C₄²×C₁₉	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₉	C₂³	1	4	yes	—
118	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
119	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
120	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
121	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
122	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
123	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
124	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
125	(C₂×D₁₉)⋊C₄	C₂³	1	4	yes	—
126	C₄⋊Dic₁₉	C₂³	1	2	yes	—
127	C₄⋊Dic₁₉	C₂³	1	4	yes	—
128	C₄⋊Dic₁₉	C₂³	1	4	yes	—
129	C₄⋊Dic₁₉	C₂³	1	2	yes	—
130	C₄⋊Dic₁₉	C₂³	1	2	yes	—
131	C₄⋊Dic₁₉	C₂³	1	2	yes	—
132	Dic₁₉⋊C₄	C₂³	1	4	yes	—
133	Dic₁₉⋊C₄	C₂³	1	4	yes	—
134	Dic₁₉⋊C₄	C₂³	1	4	yes	—
135	Dic₁₉⋊C₄	C₂³	1	4	yes	—
136	C₄×Dic₁₉	C₂³	1	4	yes	—
137	C₄×Dic₁₉	C₂³	1	4	yes	—
138	C₂³×C₁₉	C₂⁴	1	2	yes	—
139	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
140	C₂²×D₁₉	—	2	4	no	—
141	C₂²×D₁₉	—	4	2	no	—
142	C₂²×D₁₉	—	4	2	no	—
143	C₂²×D₁₉	C₂⁴	1	4	yes	—
144	Q₈×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	2	4	no	—
146	D₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	2	4	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
153	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
156	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
157	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
160	C₂²⋊D₁₉	—	4	4	no	—
161	C₂²⋊D₁₉	—	4	4	no	—
162	C₂×Dic₁₉	—	4	2	no	—
163	C₂×Dic₁₉	—	4	4	no	—
164	C₂×Dic₁₉	C₂⁴	1	4	yes	—
165	C₂×Dic₁₉	C₂⁴	1	4	yes	—
166	C₂×Dic₁₉	C₂⁴	1	4	yes	—
167	D₇₆	—	2	4	no	—
168	D₇₆	—	4	2	no	—
169	C₄×D₁₉	—	4	4	no	—
170	C₄×D₁₉	—	4	4	no	—
171	Dic₃₈	—	2	4	no	—
172	Dic₃₈	—	2	4	no	—
173	Dic₃₈	—	4	2	no	—
174	Dic₃₈	—	4	4	no	—
175	Dic₃₈	—	4	2	no	—
176	#3561	—	19	1	no	maximal, Sylow
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	2₋¹⁺⁴	1	2	yes	—
183	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
184	C₂×D₁₉	—	2	4	no	—
185	C₂×D₁₉	—	2	4	no	—
186	C₂×D₁₉	—	2	4	no	—
187	C₂×D₁₉	—	8	4	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	1	no	—
190	C₄×C₁₉	—	2	1	no	—
191	C₄×C₁₉	—	2	1	no	—
192	C₄×C₁₉	—	2	2	no	—
193	C₄×C₁₉	—	2	1	no	—
194	C₄×C₁₉	—	2	2	no	—
195	C₄×C₁₉	—	2	1	no	—
196	C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
197	Dic₁₉	—	2	4	no	—
198	Dic₁₉	—	2	4	no	—
199	Dic₁₉	—	2	4	no	—
200	#563	—	19	2	no	—
201	#562	—	19	2	no	—
202	#556	—	19	2	no	—
203	#551	—	19	4	no	—
204	D₄×Q₈	—	19	2	no	—
205	#548	—	19	2	no	—
206	#546	—	19	2	no	—
207	#543	—	19	2	no	—
208	#542	—	19	4	no	—
209	#542	—	19	2	no	—
210	#538	—	19	2	no	—
211	#536	—	19	2	no	—
212	#533	—	19	1	no	—
213	#529	D₁₉	1	1	yes	characteristic, complemented
214	C₂×#124	—	19	1	no	—
215	C₂×C₁₉	—	2	2	no	—
216	C₂×C₁₉	—	4	2	no	—
217	C₂×C₁₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
218	C₂×C₁₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
219	C₂×C₁₉	#585	1	1	yes	characteristic
220	D₁₉	—	4	4	no	—
221	C₂×#41	—	19	2	no	—
222	C₂²×Q₈	—	19	1	no	—
223	C₂²×Q₈	—	19	2	no	—
224	C₂²×D₄	—	19	1	no	—
225	C₄⋊Q₈	—	19	4	no	—
226	C₄⋊Q₈	—	19	1	no	—
227	C₄⋊Q₈	—	19	1	no	—
228	C₄⋊Q₈	—	19	2	no	—
229	#126	—	19	4	no	—
230	#126	—	19	4	no	—
231	#126	—	19	4	no	—
232	#126	C₂×D₁₉	1	2	yes	complemented
233	#125	—	19	2	no	—
234	#125	C₂×D₁₉	1	1	yes	characteristic, complemented
235	#124	—	19	4	no	—
236	#124	—	19	4	no	—
237	#124	—	19	2	no	—
238	#124	—	19	2	no	—
239	#124	—	19	2	no	—
240	#124	—	19	2	no	—
241	#124	—	19	2	no	—
242	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
243	#123	—	19	4	no	—
244	#123	—	19	4	no	—
245	#123	—	19	4	no	—
246	#123	—	19	4	no	—
247	#123	C₂×D₁₉	1	2	yes	—
248	C₂²⋊Q₈	—	19	4	no	—
249	C₂²⋊Q₈	—	19	2	no	—
250	C₂²⋊Q₈	—	19	2	no	—
251	C₂²⋊Q₈	—	19	2	no	—
252	C₂²⋊Q₈	—	19	4	no	—
253	C₂²⋊Q₈	—	19	4	no	—
254	C₂²⋊Q₈	—	19	4	no	—
255	C₂²⋊Q₈	—	19	4	no	—
256	C₂²⋊Q₈	—	19	4	no	—
257	C₂²⋊Q₈	—	19	4	no	—
258	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
259	#121	—	19	4	no	—
260	#121	—	19	2	no	—
261	#121	—	19	4	no	—
262	#121	C₂×D₁₉	1	1	yes	characteristic
263	#120	—	19	4	no	—
264	C₄×Q₈	—	19	2	no	—
265	C₄×Q₈	—	19	2	no	—
266	C₄×Q₈	—	19	2	no	—
267	C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
268	C₄×D₄	—	19	4	no	—
269	C₄×D₄	—	19	4	no	—
270	C₄×D₄	—	19	2	no	—
271	C₄×D₄	C₂×D₁₉	1	2	yes	—
272	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
273	#117	—	19	2	no	—
274	#117	—	19	4	no	—
275	#117	C₂×D₁₉	1	2	yes	complemented
276	C₂×C₂²⋊C₄	—	19	2	no	—
277	C₂×C₂²⋊C₄	—	19	2	no	—
278	C₂×C₂²⋊C₄	—	19	4	no	—
279	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
280	C₁₉	#3561	1	1	yes	characteristic, complemented, Sylow
281	C₂⁴	—	19	2	no	—
282	#41	—	76	4	no	—
283	C₂×Q₈	—	19	2	no	—
284	C₂×Q₈	—	19	2	no	—
285	C₂×Q₈	—	19	2	no	—
286	C₂×Q₈	—	19	4	no	—
287	C₂×Q₈	—	19	2	no	—
288	C₂×Q₈	—	76	2	no	—
289	C₂×Q₈	—	76	4	no	—
290	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
291	C₂×D₄	—	19	4	no	—
292	C₂×D₄	—	19	4	no	—
293	C₂×D₄	—	19	2	no	—
294	C₂×D₄	—	19	2	no	—
295	C₂×D₄	—	76	2	no	—
296	C₂×D₄	C₂²×D₁₉	1	2	yes	—
297	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
298	C₂²×C₄	—	19	2	no	—
299	C₂²×C₄	—	19	4	no	—
300	C₂²×C₄	—	19	4	no	—
301	C₂²×C₄	—	19	4	no	—
302	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₁₉	1	2	yes	—
305	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
306	C₄⋊C₄	—	19	4	no	—
307	C₄⋊C₄	—	19	4	no	—
308	C₄⋊C₄	—	19	4	no	—
309	C₄⋊C₄	—	19	4	no	—
310	C₄⋊C₄	—	19	4	no	—
311	C₄⋊C₄	—	19	2	no	—
312	C₄⋊C₄	—	19	2	no	—
313	C₄⋊C₄	—	19	2	no	—
314	C₄⋊C₄	—	19	4	no	—
315	C₄⋊C₄	—	19	2	no	—
316	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
317	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
318	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
319	C₄⋊C₄	C₂²×D₁₉	1	2	yes	—
320	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
321	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
322	C₂²⋊C₄	—	19	4	no	—
323	C₂²⋊C₄	—	19	4	no	—
324	C₂²⋊C₄	—	19	4	no	—
325	C₂²⋊C₄	—	19	4	no	—
326	C₂²⋊C₄	—	19	4	no	—
327	C₂²⋊C₄	—	19	4	no	—
328	C₂²⋊C₄	—	19	4	no	—
329	C₂²⋊C₄	—	19	4	no	—
330	C₂²⋊C₄	—	19	4	no	—
331	C₂²⋊C₄	—	19	4	no	—
332	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
333	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
334	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
335	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
336	C₂²⋊C₄	C₂²×D₁₉	1	2	yes	—
337	C₄²	—	19	4	no	—
338	C₄²	—	19	4	no	—
339	C₄²	C₂²×D₁₉	1	1	yes	characteristic
340	C₄²	C₂²×D₁₉	1	1	yes	characteristic
341	C₄²	C₂²×D₁₉	1	1	yes	characteristic
342	C₄²	C₂²×D₁₉	1	1	yes	characteristic
343	C₄²	C₂²×D₁₉	1	2	yes	—
344	C₂³	—	19	4	no	—
345	C₂³	—	38	4	no	—
346	C₂³	—	76	2	no	—
347	C₂³	—	76	2	no	—
348	C₂³	C₂³×D₁₉	1	2	yes	—
349	C₂³	C₂³×D₁₉	1	1	yes	characteristic
350	Q₈	—	4	1	no	—
351	Q₈	—	38	4	no	—
352	Q₈	—	38	4	no	—
353	Q₈	—	76	4	no	—
354	Q₈	—	76	2	no	—
355	Q₈	—	76	2	no	—
356	D₄	—	2	4	no	—
357	D₄	—	4	1	no	—
358	D₄	—	38	4	no	—
359	D₄	—	76	2	no	—
360	D₄	—	76	4	no	—
361	D₄	—	76	4	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	4	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	19	4	no	—
367	C₂×C₄	—	19	4	no	—
368	C₂×C₄	—	19	4	no	—
369	C₂×C₄	—	76	4	no	—
370	C₂×C₄	—	76	4	no	—
371	C₂×C₄	—	76	4	no	—
372	C₂×C₄	—	76	2	no	—
373	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
374	C₂×C₄	C₂³×D₁₉	1	2	yes	—
375	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
376	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
377	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
378	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
379	C₂×C₄	C₂³×D₁₉	1	2	yes	—
380	C₂×C₄	C₂³×D₁₉	1	2	yes	—
381	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	2	2	no	—
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	38	4	no	—
388	C₂²	—	38	4	no	—
389	C₂²	—	38	4	no	—
390	C₂²	—	152	4	no	—
391	C₂²	#10597436	1	2	yes	—
392	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
393	C₄	—	2	2	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	1	no	—
399	C₄	—	2	1	no	—
400	C₄	—	2	2	no	—
401	C₄	—	38	4	no	—
402	C₄	—	38	4	no	—
403	C₄	—	38	4	no	—
404	C₄	#10597435	1	2	yes	—
405	C₂	—	2	2	no	—
406	C₂	—	4	2	no	—
407	C₂	—	76	4	no	—
408	C₂	C₂×#10597435	1	1	yes	characteristic
409	C₂	C₂×#10597436	1	1	yes	characteristic
410	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Fitting	C₁₉×#529	C₂
hypercenter	#529	D₁₉
hypocenter	C₁₉	#3561
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #11927298	C₂	semidirect
2. #11927288	C₂	semidirect
3. #11927267	C₂	semidirect
4. #11927217	C₂	semidirect
5. D₄×Dic₃₈	C₂	semidirect
6. #11927203	C₂	semidirect
7. #11927190	C₂	semidirect
8. #11927169	C₂	semidirect
9. #11927165	C₂	semidirect
10. #11927160	C₂	semidirect
11. #11927131	C₂	semidirect
12. #11927120	C₂	semidirect
13. #11927101	C₂	semidirect
14. C₂×#10597321	C₂	semidirect
15. C₁₉×#529	C₂	semidirect
19. C₂²×Dic₃₈	C₂²	semidirect
20. C₁₉×#126	C₂²	semidirect
21. C₁₉×#125	C₂²	semidirect
22. C₁₉×#124	C₂²	semidirect
26. C₄×Q₈×C₁₉	C₂²	semidirect
28. C₄×D₄×C₁₉	C₂²	semidirect
29. C₁₉×#117	C₂²	semidirect
31. #10597392	C₂²	semidirect
32. #10597385	C₂²	semidirect
41. #10597370	C₂²	semidirect
42. #10597344	C₂²	semidirect
43. #10597344	C₂²	semidirect
44. #10597344	C₂²	semidirect
45. #10597343	C₂²	semidirect
46. #10597343	C₂²	semidirect
47. #10597342	C₂²	semidirect
48. #10597342	C₂²	semidirect
50. #10597338	C₂²	semidirect
51. #10597334	C₂²	semidirect
52. #10597332	C₂²	semidirect
53. #10597332	C₂²	semidirect
54. #10597331	C₂²	semidirect
55. #10597331	C₂²	semidirect
57. #10597329	C₂²	semidirect
58. (C₂²⋊D₁₉)⋊C₄	C₂²	semidirect
61. #10597324	C₂²	semidirect
68. #10597316	C₂²	semidirect
69. #10597315	C₂²	semidirect
70. #10597315	C₂²	semidirect
71. #10597315	C₂²	semidirect
72. C₄×Dic₃₈	C₂²	semidirect
73. C₄×Dic₃₈	C₂²	semidirect
74. C₄×Dic₃₈	C₂²	semidirect
213. #529	D₁₉	semidirect
232. #126	C₂×D₁₉	semidirect
234. #125	C₂×D₁₉	semidirect
242. #124	C₂×D₁₉	semidirect
267. C₄×Q₈	C₂×D₁₉	semidirect
272. C₄×D₄	C₂×D₁₉	semidirect
275. #117	C₂×D₁₉	semidirect
280. C₁₉	#3561	semidirect

Maximal subgroups

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

subgroup	index
#11927298	2
#11927288	2
#11927267	2
#11927217	2
D₄×Dic₃₈	2
#11927203	2
#11927190	2
#11927169	2
#11927165	2
#11927160	2
#11927131	2
#11927120	2
#11927101	2
C₂×#10597321	2
C₁₉×#529	2
#3561	19