Subgroups — #18076786

Order 4864.

602 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	C₄⋊C₄×D₇₆	C₂	1	1	yes	maximal, characteristic
2	#14564398	C₂	1	1	yes	maximal, characteristic, complemented
3	#14563763	C₂	1	1	yes	maximal, characteristic, complemented
4	#14563636	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	—	2	1	no	—
9	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×D₁₉	—	2	1	no	—
11	C₂×#10597265	—	2	1	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×#10597278	—	2	1	no	—
14	#11926442	—	2	1	no	—
15	#11926418	—	2	2	no	—
16	#11926414	C₂²	1	1	yes	characteristic
17	#11926414	C₂²	1	1	yes	characteristic
18	#11926401	—	2	1	no	—
19	#11926307	—	2	1	no	—
20	#11926307	—	2	2	no	—
21	#11926306	—	2	1	no	—
22	#11926273	C₄	1	4	yes	complemented
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂²×D₇₆	D₄	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	—	2	1	no	—
28	C₂²×C₄×D₁₉	—	2	2	no	—
29	C₂²×C₈×C₁₉	—	2	1	no	—
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
32	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₉	—	2	1	no	—
34	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
35	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
36	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
37	C₂×C₄⋊Dic₁₉	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	—	2	1	no	—
39	C₂×C₄⋊Dic₁₉	—	2	1	no	—
40	C₂×C₄⋊Dic₁₉	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
44	C₂×Dic₁₉⋊C₄	—	2	2	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₄⋊C₄×D₁₉	—	4	2	no	—
47	C₄⋊C₄×D₁₉	—	4	2	no	—
48	C₄×D₇₆	—	2	1	no	—
49	C₄×D₇₆	—	2	1	no	—
50	C₄×D₇₆	—	4	2	no	—
51	C₄×D₇₆	—	4	2	no	—
52	C₄×D₇₆	C₂×C₄	1	2	yes	—
53	C₄×D₇₆	Q₈	1	2	yes	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₄×C₈×C₁₉	—	2	1	no	—
57	C₄×C₈×C₁₉	C₂×C₄	1	2	yes	complemented
58	C₁₉×#95	—	2	1	no	—
59	C₁₉⋊#95	—	2	2	no	—
60	#10597278	—	4	2	no	—
61	#10597265	—	4	2	no	—
62	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
63	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
64	C₂³×D₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
70	C₂²×Dic₁₉	—	2	1	no	—
71	C₂²×Dic₁₉	—	2	2	no	—
72	C₂²×Dic₁₉	—	4	1	no	—
73	C₂×D₇₆	—	2	1	no	—
74	C₂×D₇₆	—	2	1	no	—
75	C₂×D₇₆	—	2	1	no	—
76	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
77	C₂×D₇₆	SD₁₆	1	2	yes	—
78	C₂×D₇₆	SD₁₆	1	2	yes	—
79	C₂×C₄×D₁₉	—	2	2	no	—
80	C₂×C₄×D₁₉	—	2	2	no	—
81	C₂×C₄×D₁₉	—	4	1	no	—
82	C₂×C₄×D₁₉	—	4	1	no	—
83	C₂×C₄×D₁₉	—	4	1	no	—
84	C₂×C₄×D₁₉	—	4	1	no	—
85	C₂×C₄×D₁₉	—	4	4	no	—
86	C₂×C₄×D₁₉	—	4	4	no	—
87	C₂×C₄×D₁₉	—	8	2	no	—
88	C₂×C₈×C₁₉	—	2	2	no	—
89	C₂×C₈×C₁₉	—	4	1	no	—
90	C₂×C₈×C₁₉	—	4	1	no	—
91	C₂×C₈×C₁₉	—	4	1	no	—
92	C₂×C₈×C₁₉	—	4	1	no	—
93	C₂×C₈×C₁₉	—	4	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	2	1	no	—
96	C₄⋊C₄×C₁₉	—	2	1	no	—
97	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
98	C₄²×C₁₉	—	4	1	no	—
99	C₄²×C₁₉	—	4	1	no	—
100	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
101	C₄²×C₁₉	C₂×Q₈	1	1	yes	characteristic
102	C₄²×C₁₉	#41	1	1	yes	characteristic
103	C₄²×C₁₉	#41	1	1	yes	characteristic
104	(C₂×D₁₉)⋊C₄	—	2	2	no	—
105	(C₂×D₁₉)⋊C₄	—	2	2	no	—
106	(C₂×D₁₉)⋊C₄	—	4	4	no	—
107	C₄⋊Dic₁₉	—	2	1	no	—
108	C₄⋊Dic₁₉	—	4	1	no	—
109	C₄⋊Dic₁₉	—	4	1	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	2	no	—
113	C₄⋊Dic₁₉	—	4	2	no	—
114	C₄⋊Dic₁₉	—	4	1	no	—
115	C₄⋊Dic₁₉	—	4	1	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
119	Dic₁₉⋊C₄	—	4	4	no	—
120	C₂×C₁₉⋊C₈	—	2	2	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	#8894	—	19	1	no	maximal, Sylow
124	C₂³×C₁₉	#120	1	1	yes	characteristic
125	C₂²×D₁₉	—	2	2	no	—
126	C₂²×D₁₉	—	2	2	no	—
127	C₂²×D₁₉	—	2	2	no	—
128	C₂²×D₁₉	—	4	1	no	—
129	C₂²×D₁₉	—	4	1	no	—
130	C₂²×D₁₉	—	4	1	no	—
131	C₂²×D₁₉	—	4	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
144	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
145	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
146	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
150	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
154	C₂×Dic₁₉	—	2	2	no	—
155	C₂×Dic₁₉	—	4	1	no	—
156	C₂×Dic₁₉	—	4	1	no	—
157	C₂×Dic₁₉	—	4	2	no	—
158	C₂×Dic₁₉	—	4	2	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	—	8	1	no	—
161	C₂×Dic₁₉	—	8	1	no	—
162	C₂×Dic₁₉	—	8	1	no	—
163	D₇₆	—	2	2	no	—
164	D₇₆	—	2	2	no	—
165	D₇₆	—	2	2	no	—
166	D₇₆	#106	1	4	yes	complemented
167	C₄×D₁₉	—	4	2	no	—
168	C₄×D₁₉	—	4	2	no	—
169	C₄×D₁₉	—	4	2	no	—
170	C₄×D₁₉	—	4	2	no	—
171	C₄×D₁₉	—	8	8	no	—
172	C₈×C₁₉	—	4	2	no	—
173	C₈×C₁₉	—	8	1	no	—
174	C₁₉⋊C₈	—	4	2	no	—
175	D₄×C₄⋊C₄	—	19	1	no	—
176	#1948	—	19	1	no	—
177	#1834	—	19	1	no	—
178	#1802	—	19	1	no	—
179	C₂×D₄⋊C₈	—	19	1	no	—
180	#1296	—	19	1	no	—
181	#1279	D₁₉	1	1	yes	characteristic, complemented
182	C₂²×C₁₉	#385	1	1	yes	characteristic
183	C₂²×C₁₉	#447	1	1	yes	characteristic
184	C₂²×C₁₉	#448	1	1	yes	characteristic
185	C₂²×C₁₉	#450	1	1	yes	characteristic
186	C₂²×C₁₉	#452	1	1	yes	characteristic
187	C₂²×C₁₉	#454	1	1	yes	characteristic
188	C₂²×C₁₉	#455	1	1	yes	characteristic
189	C₂×D₁₉	—	2	4	no	—
190	C₂×D₁₉	—	4	2	no	—
191	C₂×D₁₉	—	4	2	no	—
192	C₂×D₁₉	—	4	2	no	—
193	C₂×D₁₉	—	4	2	no	—
194	C₂×D₁₉	—	4	2	no	—
195	C₂×D₁₉	—	4	2	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	8	1	no	—
200	C₄×C₁₉	C₂×#106	1	1	yes	characteristic
201	C₄×C₁₉	#428	1	1	yes	characteristic
202	C₄×C₁₉	C₄×D₈	1	1	yes	characteristic
203	C₄×C₁₉	#440	1	1	yes	characteristic
204	C₄×C₁₉	#474	1	1	yes	characteristic
205	C₄×C₁₉	#478	1	1	yes	characteristic
206	C₄×C₁₉	#481	1	1	yes	characteristic
207	C₄×C₁₉	#483	1	1	yes	characteristic
208	Dic₁₉	—	4	2	no	—
209	Dic₁₉	—	8	2	no	—
210	Dic₁₉	—	16	1	no	—
211	C₂×C₄×D₄	—	19	1	no	—
212	C₂×C₄×D₄	—	38	1	no	—
213	C₂²×C₄⋊C₄	—	38	1	no	—
214	C₂×#106	—	38	1	no	—
215	C₂×C₄⋊C₈	—	19	1	no	—
216	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
217	C₂×#102	—	38	1	no	—
218	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
219	#389	—	38	1	no	—
220	#385	—	38	2	no	—
221	#384	—	19	1	no	—
222	#384	—	19	1	no	—
223	#380	—	38	1	no	—
224	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
225	#340	—	38	1	no	—
226	#340	—	38	2	no	—
227	#340	—	38	1	no	—
228	D₄⋊C₈	—	19	4	no	—
229	C₂×C₁₉	#1627	1	1	yes	characteristic
230	C₂×C₁₉	#1635	1	1	yes	characteristic
231	C₂×C₁₉	#1639	1	1	yes	characteristic
232	C₂×C₁₉	#1643	1	1	yes	characteristic
233	C₂×C₁₉	#1853	1	1	yes	characteristic
234	C₂×C₁₉	#1860	1	1	yes	characteristic
235	C₂×C₁₉	#1862	1	1	yes	characteristic
236	D₁₉	—	4	4	no	—
237	C₂²×D₄	—	19	1	no	—
238	C₂³×C₄	—	38	2	no	—
239	C₂³×C₄	—	38	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	2	1	no	—
242	C₂²×C₈	—	38	1	no	—
243	C₄×D₄	—	19	2	no	—
244	C₄×D₄	—	19	2	no	—
245	C₄×D₄	—	38	1	no	—
246	C₄×D₄	—	38	1	no	—
247	C₄×D₄	—	76	2	no	—
248	C₄×D₄	—	76	2	no	—
249	C₂×C₄⋊C₄	—	19	1	no	—
250	C₂×C₄⋊C₄	—	19	2	no	—
251	C₂×C₄⋊C₄	—	38	2	no	—
252	C₂×C₄⋊C₄	—	38	1	no	—
253	C₂×C₄⋊C₄	—	38	1	no	—
254	C₂×C₄⋊C₄	—	38	1	no	—
255	C₂×C₄⋊C₄	—	38	1	no	—
256	C₂×C₄⋊C₄	—	38	1	no	—
257	C₂×C₄⋊C₄	—	76	2	no	—
258	C₂×C₄⋊C₄	—	76	2	no	—
259	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
260	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
261	C₂×C₂²⋊C₄	—	38	1	no	—
262	C₂×C₂²⋊C₄	—	38	2	no	—
263	C₂×C₄²	—	2	1	no	—
264	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
265	#106	—	76	2	no	—
266	C₄⋊C₈	—	2	1	no	—
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	19	2	no	—
269	C₄⋊C₈	—	38	1	no	—
270	#102	—	76	2	no	—
271	C₄×C₈	—	2	1	no	—
272	C₄×C₈	C₄×D₁₉	1	2	yes	complemented
273	#95	—	2	1	no	—
274	#95	—	38	2	no	—
275	C₁₉	#8894	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	—	38	1	no	—
277	C₂×D₄	—	19	2	no	—
278	C₂×D₄	—	19	2	no	—
279	C₂×D₄	—	19	2	no	—
280	C₂×D₄	—	38	1	no	—
281	C₂×D₄	—	38	1	no	—
282	C₂×D₄	—	38	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	38	1	no	—
286	C₂²×C₄	—	38	2	no	—
287	C₂²×C₄	—	38	2	no	—
288	C₂²×C₄	—	38	2	no	—
289	C₂²×C₄	—	76	4	no	—
290	C₂²×C₄	—	76	4	no	—
291	C₂²×C₄	—	76	1	no	—
292	C₂²×C₄	—	76	1	no	—
293	C₂²×C₄	—	76	1	no	—
294	C₂²×C₄	—	76	1	no	—
295	C₂²×C₄	—	76	1	no	—
296	C₂²×C₄	—	152	2	no	—
297	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
298	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
299	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	4	1	no	—
303	C₂×C₈	—	4	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	38	2	no	—
307	C₂×C₈	—	76	1	no	—
308	C₂×C₈	—	76	1	no	—
309	C₄⋊C₄	—	2	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	19	2	no	—
313	C₄⋊C₄	—	38	1	no	—
314	C₄⋊C₄	—	76	2	no	—
315	C₄⋊C₄	—	76	4	no	—
316	C₄⋊C₄	—	76	2	no	—
317	C₄⋊C₄	—	76	1	no	—
318	C₄⋊C₄	—	76	1	no	—
319	C₄⋊C₄	—	76	1	no	—
320	C₄⋊C₄	—	76	1	no	—
321	C₄⋊C₄	—	76	1	no	—
322	C₄⋊C₄	—	76	1	no	—
323	C₄⋊C₄	—	76	1	no	—
324	C₄⋊C₄	—	76	1	no	—
325	C₄⋊C₄	D₁₅₂	1	2	yes	—
326	C₂²⋊C₄	—	38	2	no	—
327	C₂²⋊C₄	—	38	2	no	—
328	C₂²⋊C₄	—	76	4	no	—
329	C₄²	—	4	1	no	—
330	C₄²	—	4	1	no	—
331	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
332	C₄²	#64541	1	1	yes	characteristic
333	C₄²	#64543	1	1	yes	characteristic
334	C₄²	Q₈×D₁₉	1	1	yes	characteristic
335	C₂³	—	38	2	no	—
336	C₂³	—	38	2	no	—
337	C₂³	—	38	2	no	—
338	C₂³	—	76	1	no	—
339	C₂³	—	76	1	no	—
340	C₂³	—	76	1	no	—
341	C₂³	—	76	1	no	—
342	C₂³	#10597328	1	1	yes	characteristic
343	D₄	—	19	4	no	—
344	D₄	—	38	2	no	—
345	D₄	—	38	2	no	—
346	D₄	—	38	2	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	1	no	—
355	C₂×C₄	—	38	2	no	—
356	C₂×C₄	—	76	1	no	—
357	C₂×C₄	—	76	1	no	—
358	C₂×C₄	—	76	2	no	—
359	C₂×C₄	—	76	2	no	—
360	C₂×C₄	—	76	2	no	—
361	C₂×C₄	—	76	2	no	—
362	C₂×C₄	—	76	2	no	—
363	C₂×C₄	—	76	2	no	—
364	C₂×C₄	—	76	2	no	—
365	C₂×C₄	—	152	8	no	—
366	C₂×C₄	—	152	1	no	—
367	C₂×C₄	—	152	1	no	—
368	C₂×C₄	—	152	1	no	—
369	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
370	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
371	C₂×C₄	#10597329	1	1	yes	characteristic
372	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
373	C₂×C₄	#10597342	1	1	yes	characteristic
374	C₂×C₄	#10597343	1	1	yes	characteristic
375	C₂×C₄	C₂×D₁₅₂	1	1	yes	characteristic
376	C₂×C₄	#10597350	1	1	yes	characteristic
377	C₂×C₄	#10597354	1	1	yes	characteristic
378	C₂×C₄	#10597355	1	1	yes	characteristic
379	C₂×C₄	#10597357	1	1	yes	characteristic
380	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
381	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
382	C₂×C₄	#10597364	1	1	yes	characteristic
383	C₈	—	4	2	no	—
384	C₈	—	8	1	no	—
385	C₈	—	76	2	no	—
386	C₂²	—	38	4	no	—
387	C₂²	—	76	2	no	—
388	C₂²	—	76	2	no	—
389	C₂²	—	76	2	no	—
390	C₂²	—	76	2	no	—
391	C₂²	—	76	2	no	—
392	C₂²	—	76	2	no	—
393	C₂²	#11926418	1	1	yes	characteristic
394	C₂²	#11926680	1	1	yes	characteristic
395	C₂²	#11926684	1	1	yes	characteristic
396	C₂²	#11926696	1	1	yes	characteristic
397	C₂²	#11926708	1	1	yes	characteristic
398	C₂²	#11926718	1	1	yes	characteristic
399	C₂²	#11926723	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	8	1	no	—
404	C₄	—	304	1	no	—
405	C₄	—	76	2	no	—
406	C₄	—	152	2	no	—
407	C₄	#106×D₁₉	1	1	yes	characteristic
408	C₄	#11926585	1	1	yes	characteristic
409	C₄	C₄×D₁₅₂	1	1	yes	characteristic
410	C₄	#11926646	1	1	yes	characteristic
411	C₄	#11926825	1	1	yes	characteristic
412	C₄	#11926845	1	1	yes	characteristic
413	C₄	#11926861	1	1	yes	characteristic
414	C₄	#11926873	1	1	yes	characteristic
415	C₂	—	76	4	no	—
416	C₂	#14562740	1	1	yes	characteristic
417	C₂	#14562789	1	1	yes	characteristic
418	C₂	#14562816	1	1	yes	characteristic
419	C₂	#14562845	1	1	yes	characteristic
420	C₂	#14563829	1	1	yes	characteristic
421	C₂	#14563869	1	1	yes	characteristic
422	C₂	#14563885	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8894
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
2. #14564398	C₂	semidirect
3. #14563763	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
22. #11926273	C₄	semidirect
57. C₄×C₈×C₁₉	C₂×C₄	semidirect
63. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
166. D₇₆	#106	semidirect
181. #1279	D₁₉	semidirect
272. C₄×C₈	C₄×D₁₉	semidirect
275. C₁₉	#8894	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₄×D₇₆	2
#14564398	2
#14563763	2
#14563636	2
C₂×#11926273	2
#14561519	2
C₁₉×#1279	2
#8894	19