Subgroups — #18076976

Order 4864.

644 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566699	C₂	1	1	yes	maximal, characteristic
2	#14564440	C₂	1	1	yes	maximal, characteristic
3	#14564396	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926287	C₂	1	1	yes	maximal, characteristic
5	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1948	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597320	C₂²	1	1	yes	characteristic
9	C₂×C₄×D₇₆	—	2	1	no	—
10	C₂×#10597339	—	2	1	no	—
11	C₂×#10597265	—	2	1	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597266	—	2	2	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#11926446	—	2	1	no	—
16	#11926445	—	2	1	no	—
17	#11926422	—	2	2	no	—
18	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
19	#11926306	—	2	1	no	—
20	#11926287	C₄	1	4	yes	complemented
21	C₂×C₁₉×#106	—	2	1	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₁₉×#384	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#340	—	2	1	no	—
26	C₂²×D₇₆	—	2	1	no	—
27	C₂²×D₇₆	—	2	1	no	—
28	C₂²×D₇₆	D₄	1	2	yes	—
29	C₂²×C₄×D₁₉	—	2	2	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₉	—	2	1	no	—
37	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
38	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
39	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
40	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
41	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₉	—	2	1	no	—
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	#10597339	—	4	2	no	—
47	#10597339	—	4	2	no	—
48	#10597320	—	2	1	no	—
49	#10597320	—	2	1	no	—
50	#10597320	C₂×C₄	1	2	yes	—
51	#10597320	Q₈	1	2	yes	—
52	C₄×D₇₆	—	4	2	no	—
53	C₄×D₇₆	—	4	2	no	—
54	C₁₉×#106	—	4	2	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
57	C₁₉×#95	—	2	1	no	—
58	C₁₉⋊#95	—	2	1	no	—
59	#10597266	—	4	4	no	—
60	#10597265	—	4	2	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₂³×D₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	4	1	no	—
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×Dic₁₉	—	2	1	no	—
73	C₂²×Dic₁₉	—	2	1	no	—
74	C₂×D₇₆	—	2	2	no	—
75	C₂×D₇₆	—	2	2	no	—
76	C₂×D₇₆	—	2	2	no	—
77	C₂×D₇₆	—	2	2	no	—
78	C₂×D₇₆	—	2	2	no	—
79	C₂×D₇₆	—	4	1	no	—
80	C₂×D₇₆	—	4	1	no	—
81	C₂×D₇₆	—	4	1	no	—
82	C₂×D₇₆	—	4	1	no	—
83	C₂×D₇₆	—	4	1	no	—
84	C₂×D₇₆	—	4	1	no	—
85	C₂×D₇₆	—	4	1	no	—
86	C₂×D₇₆	—	4	1	no	—
87	C₂×D₇₆	—	4	2	no	—
88	C₂×D₇₆	—	4	2	no	—
89	C₂×D₇₆	C₄⋊C₄	1	4	yes	—
90	C₂×C₄×D₁₉	—	4	4	no	—
91	C₂×C₄×D₁₉	—	4	4	no	—
92	C₂×C₄×D₁₉	—	8	2	no	—
93	C₂×C₈×C₁₉	—	2	2	no	—
94	C₂×C₈×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	4	2	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
109	C₄²×C₁₉	#41	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	(C₂×D₁₉)⋊C₄	—	4	4	no	—
112	(C₂×D₁₉)⋊C₄	—	4	4	no	—
113	(C₂×D₁₉)⋊C₄	—	8	2	no	—
114	C₄⋊Dic₁₉	—	2	1	no	—
115	C₄⋊Dic₁₉	—	2	1	no	—
116	C₄⋊Dic₁₉	—	2	1	no	—
117	C₄⋊Dic₁₉	SD₁₆	1	2	yes	—
118	C₄×Dic₁₉	—	4	1	no	—
119	C₄×Dic₁₉	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	2	2	no	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	#8924	—	19	1	no	maximal, Sylow
127	C₂³×C₁₉	#120	1	1	yes	characteristic
128	C₂²×D₁₉	—	2	4	no	—
129	C₂²×D₁₉	—	4	2	no	—
130	C₂²×D₁₉	—	4	2	no	—
131	C₂²×D₁₉	—	4	2	no	—
132	C₂²×D₁₉	—	4	2	no	—
133	C₂²×D₁₉	—	4	2	no	—
134	C₂²×D₁₉	—	4	2	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	2	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	8	1	no	—
144	C₂×C₄×C₁₉	—	8	1	no	—
145	C₂×C₄×C₁₉	—	8	1	no	—
146	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
153	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
156	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
157	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
158	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×Dic₁₉	—	2	2	no	—
161	C₂×Dic₁₉	—	4	1	no	—
162	C₂×Dic₁₉	—	4	1	no	—
163	C₂×Dic₁₉	—	4	1	no	—
164	C₂×Dic₁₉	—	4	1	no	—
165	C₂×Dic₁₉	—	4	1	no	—
166	D₇₆	—	4	4	no	—
167	D₇₆	—	4	2	no	—
168	D₇₆	—	4	2	no	—
169	D₇₆	—	4	2	no	—
170	D₇₆	—	4	2	no	—
171	D₇₆	—	4	2	no	—
172	D₇₆	—	4	2	no	—
173	D₇₆	—	4	2	no	—
174	D₇₆	—	4	2	no	—
175	D₇₆	—	8	2	no	—
176	C₄×D₁₉	—	8	8	no	—
177	C₈×C₁₉	—	4	2	no	—
178	C₁₉⋊C₈	—	4	2	no	—
179	C₁₉⋊C₈	—	4	2	no	—
180	#2366	—	19	1	no	—
181	#1957	—	19	1	no	—
182	#1948	—	19	1	no	—
183	#1948	D₁₉	1	1	yes	characteristic, complemented
184	C₂×#331	—	19	1	no	—
185	#1279	—	19	1	no	—
186	#1279	—	19	1	no	—
187	C₂²×C₁₉	#385	1	1	yes	characteristic
188	C₂²×C₁₉	#449	1	1	yes	characteristic
189	C₂²×C₁₉	#449	1	1	yes	characteristic
190	C₂²×C₁₉	#450	1	1	yes	characteristic
191	C₂²×C₁₉	#450	1	1	yes	characteristic
192	C₂²×C₁₉	#453	1	1	yes	characteristic
193	C₂²×C₁₉	#455	1	1	yes	characteristic
194	C₂×D₁₉	—	4	4	no	—
195	C₂×D₁₉	—	4	4	no	—
196	C₂×D₁₉	—	4	4	no	—
197	C₂×D₁₉	—	8	2	no	—
198	C₂×D₁₉	—	8	2	no	—
199	C₂×D₁₉	—	8	2	no	—
200	C₂×D₁₉	—	8	2	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	4	2	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	—	16	1	no	—
206	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
207	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
208	C₄×C₁₉	#442	1	1	yes	characteristic
209	C₄×C₁₉	#442	1	1	yes	characteristic
210	C₄×C₁₉	#476	1	1	yes	characteristic
211	C₄×C₁₉	#476	1	1	yes	characteristic
212	C₄×C₁₉	#478	1	1	yes	characteristic
213	C₄×C₁₉	#478	1	1	yes	characteristic
214	Dic₁₉	—	4	2	no	—
215	Dic₁₉	—	8	1	no	—
216	C₂×#127	—	19	1	no	—
217	C₂×C₄×D₄	—	38	1	no	—
218	C₂×C₄×D₄	—	38	1	no	—
219	C₂×#106	—	2	1	no	—
220	C₂×#106	—	38	1	no	—
221	C₂×C₄⋊C₈	—	19	1	no	—
222	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
223	C₂×#102	—	38	2	no	—
224	C₂×C₄×C₈	—	19	1	no	—
225	#390	—	38	1	no	—
226	#390	—	38	1	no	—
227	#386	—	38	2	no	—
228	#384	C₂×D₁₉	1	1	yes	characteristic
229	C₄×C₄⋊C₄	—	19	1	no	—
230	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
231	#340	—	2	1	no	—
232	#340	—	38	1	no	—
233	#331	—	19	4	no	—
234	C₂×C₁₉	#1620	1	1	yes	characteristic
235	C₂×C₁₉	#1629	1	1	yes	characteristic
236	C₂×C₁₉	#1642	1	1	yes	characteristic
237	C₂×C₁₉	#1642	1	1	yes	characteristic
238	C₂×C₁₉	#1856	1	1	yes	characteristic
239	C₂×C₁₉	#1864	1	1	yes	characteristic
240	C₂×C₁₉	#1864	1	1	yes	characteristic
241	D₁₉	—	8	4	no	—
242	C₂²×D₄	—	19	2	no	—
243	C₂²×D₄	—	38	1	no	—
244	C₂²×D₄	—	38	1	no	—
245	C₂³×C₄	—	38	2	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	38	1	no	—
248	C₂²×C₈	—	38	1	no	—
249	#127	—	19	2	no	—
250	#127	—	19	2	no	—
251	#127	—	38	1	no	—
252	#127	—	38	1	no	—
253	C₄×D₄	—	76	2	no	—
254	C₄×D₄	—	76	2	no	—
255	C₄×D₄	—	76	2	no	—
256	C₄×D₄	—	76	2	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄⋊C₄	—	19	1	no	—
261	C₂×C₄⋊C₄	—	19	1	no	—
262	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	—	38	2	no	—
265	C₂×C₂²⋊C₄	—	38	2	no	—
266	C₂×C₂²⋊C₄	—	38	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	—	38	1	no	—
269	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
270	#106	—	4	2	no	—
271	#106	—	76	2	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	19	2	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	C₄×D₁₉	1	2	yes	complemented
276	#102	—	76	4	no	—
277	C₄×C₈	—	38	1	no	—
278	C₄×C₈	—	38	1	no	—
279	#95	—	2	1	no	—
280	#95	—	38	1	no	—
281	C₁₉	#8924	1	1	yes	characteristic, complemented, Sylow
282	C₂⁴	—	38	2	no	—
283	C₂×D₄	—	19	4	no	—
284	C₂×D₄	—	38	2	no	—
285	C₂×D₄	—	38	2	no	—
286	C₂×D₄	—	38	2	no	—
287	C₂×D₄	—	38	2	no	—
288	C₂×D₄	—	38	2	no	—
289	C₂×D₄	—	76	2	no	—
290	C₂×D₄	—	76	2	no	—
291	C₂×D₄	—	76	1	no	—
292	C₂×D₄	—	76	1	no	—
293	C₂×D₄	—	76	1	no	—
294	C₂×D₄	—	76	1	no	—
295	C₂×D₄	—	76	1	no	—
296	C₂×D₄	—	76	1	no	—
297	C₂×D₄	—	76	1	no	—
298	C₂×D₄	—	76	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	38	1	no	—
303	C₂²×C₄	—	38	1	no	—
304	C₂²×C₄	—	76	4	no	—
305	C₂²×C₄	—	76	4	no	—
306	C₂²×C₄	—	152	2	no	—
307	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
308	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	38	2	no	—
314	C₂×C₈	—	38	2	no	—
315	C₂×C₈	—	76	1	no	—
316	C₂×C₈	—	76	1	no	—
317	C₂×C₈	—	76	1	no	—
318	C₂×C₈	—	76	1	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	4	1	no	—
324	C₄⋊C₄	—	4	1	no	—
325	C₄⋊C₄	—	4	1	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	19	2	no	—
328	C₄⋊C₄	—	38	1	no	—
329	C₄⋊C₄	—	38	1	no	—
330	C₄⋊C₄	—	38	1	no	—
331	C₄⋊C₄	#64527	1	2	yes	—
332	C₂²⋊C₄	—	76	4	no	—
333	C₂²⋊C₄	—	76	4	no	—
334	C₂²⋊C₄	—	152	2	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	4	1	no	—
337	C₄²	—	76	1	no	—
338	C₄²	—	76	1	no	—
339	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
340	C₄²	#64541	1	1	yes	characteristic
341	C₄²	Q₈×D₁₉	1	1	yes	characteristic
342	C₄²	#64545	1	1	yes	characteristic
343	C₂³	—	38	4	no	—
344	C₂³	—	76	2	no	—
345	C₂³	—	76	2	no	—
346	C₂³	—	76	2	no	—
347	C₂³	—	76	2	no	—
348	C₂³	—	76	2	no	—
349	C₂³	—	76	2	no	—
350	C₂³	#10597383	1	1	yes	characteristic
351	D₄	—	76	4	no	—
352	D₄	—	76	2	no	—
353	D₄	—	76	2	no	—
354	D₄	—	76	2	no	—
355	D₄	—	76	2	no	—
356	D₄	—	76	2	no	—
357	D₄	—	76	2	no	—
358	D₄	—	76	2	no	—
359	D₄	—	76	2	no	—
360	D₄	—	152	2	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	8	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	38	2	no	—
373	C₂×C₄	—	76	1	no	—
374	C₂×C₄	—	76	1	no	—
375	C₂×C₄	—	76	1	no	—
376	C₂×C₄	—	76	1	no	—
377	C₂×C₄	—	76	1	no	—
378	C₂×C₄	—	152	8	no	—
379	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
380	C₂×C₄	#10597339	1	1	yes	characteristic
381	C₂×C₄	#10597340	1	1	yes	characteristic
382	C₂×C₄	#10597342	1	1	yes	characteristic
383	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
384	C₂×C₄	#10597360	1	1	yes	characteristic
385	C₂×C₄	#10597360	1	1	yes	characteristic
386	C₂×C₄	#10597362	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
388	C₂×C₄	#10597378	1	1	yes	characteristic
389	C₂×C₄	C₂×#64527	1	1	yes	characteristic
390	C₂×C₄	#10597392	1	1	yes	characteristic
391	C₂×C₄	#10597395	1	1	yes	characteristic
392	C₂×C₄	#10597396	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	76	2	no	—
395	C₈	—	76	2	no	—
396	C₂²	—	76	4	no	—
397	C₂²	—	76	4	no	—
398	C₂²	—	76	4	no	—
399	C₂²	—	152	2	no	—
400	C₂²	—	152	2	no	—
401	C₂²	—	152	2	no	—
402	C₂²	—	152	2	no	—
403	C₂²	#11926415	1	1	yes	characteristic
404	C₂²	#11926687	1	1	yes	characteristic
405	C₂²	#11926688	1	1	yes	characteristic
406	C₂²	#11926693	1	1	yes	characteristic
407	C₂²	#11926694	1	1	yes	characteristic
408	C₂²	#11926710	1	1	yes	characteristic
409	C₂²	#11926720	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	4	2	no	—
413	C₄	—	8	1	no	—
414	C₄	—	16	1	no	—
415	C₄	—	76	2	no	—
416	C₄	—	152	1	no	—
417	C₄	#11926631	1	1	yes	characteristic
418	C₄	C₄×#64527	1	1	yes	characteristic
419	C₄	#11926654	1	1	yes	characteristic
420	C₄	#11926655	1	1	yes	characteristic
421	C₄	#11926831	1	1	yes	characteristic
422	C₄	#11926833	1	1	yes	characteristic
423	C₄	#11926841	1	1	yes	characteristic
424	C₄	#11926843	1	1	yes	characteristic
425	C₂	—	152	4	no	—
426	C₂	#14562693	1	1	yes	characteristic
427	C₂	#14562750	1	1	yes	characteristic
428	C₂	#14562833	1	1	yes	characteristic
429	C₂	#14562834	1	1	yes	characteristic
430	C₂	#14563843	1	1	yes	characteristic
431	C₂	#14563893	1	1	yes	characteristic
432	C₂	#14563895	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1948	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1948	D₁₉
hypocenter	C₁₉	#8924
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1948

Complements

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

N	H ≅ G/N	type
3. #14564396	C₂	semidirect
5. #14561476	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1948	C₂	semidirect
20. #11926287	C₄	semidirect
56. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
62. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
183. #1948	D₁₉	semidirect
275. C₄⋊C₈	C₄×D₁₉	semidirect
281. C₁₉	#8924	semidirect

Maximal subgroups

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

subgroup	index
#14566699	2
#14564440	2
#14564396	2
C₂×#11926287	2
#14561476	2
#14561474	2
C₁₉×#1948	2
#8924	19