Subgroups — #18077378

Order 4864.

608 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926750	C₂	1	1	yes	maximal, characteristic
2	#14566586	C₂	1	1	yes	maximal, characteristic
3	#14564595	C₂	1	1	yes	maximal, characteristic, complemented
4	#14564586	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1296	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64516	—	2	1	no	—
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	C₂×#10597338	—	2	1	no	—
12	#11926750	—	2	2	no	—
13	#11926750	C₄	1	4	yes	complemented
14	C₂×#10597273	—	2	1	no	—
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926445	—	2	1	no	—
17	#11926434	—	2	2	no	—
18	#11926401	—	2	1	no	—
19	C₄⋊C₄×Dic₁₉	—	2	1	no	—
20	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
21	#11926307	—	2	1	no	—
22	#11926307	—	2	1	no	—
23	#11926306	—	2	2	no	—
24	#11926271	—	2	2	no	—
25	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₁₉×#384	C₂²	1	1	yes	characteristic
28	C₂²×D₇₆	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	—	2	1	no	—
30	C₂²×Dic₃₈	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
35	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
39	C₂×(C₂×D₁₉)⋊C₄	—	2	2	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	1	yes	characteristic
44	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₉	—	2	2	no	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	—	2	1	no	—
48	C₂×#64516	—	2	4	no	—
49	C₂×#64516	—	4	2	no	—
50	C₂×#64516	—	4	2	no	—
51	#10597338	—	4	2	no	—
52	#10597338	—	4	2	no	—
53	C₄×D₇₆	—	2	1	no	—
54	C₄×D₇₆	—	2	1	no	—
55	C₄×D₇₆	C₂×C₄	1	2	yes	—
56	C₄×D₇₆	D₄	1	2	yes	—
57	#10597315	—	2	1	no	—
58	#10597315	—	2	1	no	—
59	#10597315	—	2	1	no	—
60	#10597315	C₂×C₄	1	2	yes	—
61	C₁₉×C₄⋊C₈	—	2	1	no	—
62	C₁₉×C₄⋊C₈	—	2	1	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
65	C₁₉⋊#95	—	2	2	no	—
66	C₁₉⋊#95	—	2	1	no	—
67	#10597273	—	2	4	no	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₂³×D₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	—	2	1	no	—
77	C₂²×Dic₁₉	—	2	1	no	—
78	C₂²×Dic₁₉	—	4	1	no	—
79	C₂×D₇₆	—	2	1	no	—
80	C₂×D₇₆	—	2	1	no	—
81	C₂×D₇₆	—	2	1	no	—
82	C₂×D₇₆	—	2	1	no	—
83	C₂×D₇₆	—	2	1	no	—
84	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
85	C₂×C₄×D₁₉	—	2	2	no	—
86	C₂×C₄×D₁₉	—	2	2	no	—
87	C₂×C₄×D₁₉	—	4	1	no	—
88	C₂×C₄×D₁₉	—	4	1	no	—
89	C₂×C₄×D₁₉	—	4	1	no	—
90	C₂×C₄×D₁₉	—	4	1	no	—
91	C₂×Dic₃₈	—	2	2	no	—
92	C₂×Dic₃₈	—	4	1	no	—
93	C₂×Dic₃₈	—	4	1	no	—
94	C₂×Dic₃₈	—	4	1	no	—
95	C₂×Dic₃₈	—	4	1	no	—
96	C₂×Dic₃₈	—	4	1	no	—
97	C₂×C₈×C₁₉	—	2	2	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₂×C₈×C₁₉	—	4	1	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	2	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	#41	1	1	yes	characteristic
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	(C₂×D₁₉)⋊C₄	—	2	2	no	—
113	(C₂×D₁₉)⋊C₄	—	2	2	no	—
114	(C₂×D₁₉)⋊C₄	—	4	4	no	—
115	(C₂×D₁₉)⋊C₄	—	8	2	no	—
116	C₄⋊Dic₁₉	—	2	1	no	—
117	C₄⋊Dic₁₉	—	2	1	no	—
118	C₄⋊Dic₁₉	—	2	2	no	—
119	C₄⋊Dic₁₉	—	2	2	no	—
120	C₄⋊Dic₁₉	—	2	1	no	—
121	C₄⋊Dic₁₉	—	2	1	no	—
122	C₄⋊Dic₁₉	—	4	1	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
125	C₄⋊Dic₁₉	SD₁₆	1	2	yes	complemented
126	C₄×Dic₁₉	—	4	4	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	C₄×Dic₁₉	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	2	2	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	#64516	—	4	8	no	—
133	#8988	—	19	1	no	maximal, Sylow
134	C₂³×C₁₉	#120	1	1	yes	characteristic
135	C₂²×D₁₉	—	2	2	no	—
136	C₂²×D₁₉	—	4	1	no	—
137	C₂²×D₁₉	—	4	1	no	—
138	C₂²×D₁₉	—	4	1	no	—
139	C₂²×D₁₉	—	4	1	no	—
140	C₂²×D₁₉	—	4	1	no	—
141	C₂²×D₁₉	—	4	1	no	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	2	no	—
147	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#123	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	#135	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×C₄×C₁₉	#137	1	1	yes	characteristic
161	C₂×Dic₁₉	—	2	2	no	—
162	C₂×Dic₁₉	—	2	2	no	—
163	C₂×Dic₁₉	—	4	1	no	—
164	C₂×Dic₁₉	—	4	1	no	—
165	C₂×Dic₁₉	—	4	1	no	—
166	C₂×Dic₁₉	—	4	1	no	—
167	C₂×Dic₁₉	—	4	2	no	—
168	C₂×Dic₁₉	—	4	1	no	—
169	C₂×Dic₁₉	—	4	1	no	—
170	C₂×Dic₁₉	—	4	1	no	—
171	C₂×Dic₁₉	—	8	1	no	—
172	C₂×Dic₁₉	—	8	1	no	—
173	D₇₆	—	2	2	no	—
174	D₇₆	—	2	2	no	—
175	D₇₆	—	4	1	no	—
176	D₇₆	—	4	1	no	—
177	C₄×D₁₉	—	4	2	no	—
178	C₄×D₁₉	—	4	2	no	—
179	C₄×D₁₉	—	4	2	no	—
180	C₄×D₁₉	—	4	2	no	—
181	Dic₃₈	—	4	2	no	—
182	Dic₃₈	—	4	2	no	—
183	Dic₃₈	—	8	1	no	—
184	Dic₃₈	—	8	1	no	—
185	C₈×C₁₉	—	4	2	no	—
186	C₈×C₁₉	—	8	1	no	—
187	C₁₉⋊C₈	—	4	2	no	—
188	C₂×#461	—	19	1	no	—
189	#2354	—	19	1	no	—
190	#1990	—	19	1	no	—
191	#1988	—	19	1	no	—
192	C₂×D₄⋊C₈	—	19	1	no	—
193	#1296	D₁₉	1	1	yes	characteristic, complemented
194	#1279	—	19	1	no	—
195	C₂²×C₁₉	#386	1	1	yes	characteristic
196	C₂²×C₁₉	#449	1	1	yes	characteristic
197	C₂²×C₁₉	#449	1	1	yes	characteristic
198	C₂²×C₁₉	#450	1	1	yes	characteristic
199	C₂²×C₁₉	#452	1	1	yes	characteristic
200	C₂²×C₁₉	#455	1	1	yes	characteristic
201	C₂²×C₁₉	#456	1	1	yes	characteristic
202	C₂×D₁₉	—	4	2	no	—
203	C₂×D₁₉	—	4	2	no	—
204	C₂×D₁₉	—	4	2	no	—
205	C₂×D₁₉	—	8	1	no	—
206	C₂×D₁₉	—	8	1	no	—
207	C₂×D₁₉	—	8	1	no	—
208	C₂×D₁₉	—	8	1	no	—
209	C₄×C₁₉	—	2	1	no	—
210	C₄×C₁₉	—	2	1	no	—
211	C₄×C₁₉	—	8	2	no	—
212	C₄×C₁₉	#416	1	1	yes	characteristic
213	C₄×C₁₉	#418	1	1	yes	characteristic
214	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
215	C₄×C₁₉	#440	1	1	yes	characteristic
216	C₄×C₁₉	#461	1	1	yes	characteristic
217	C₄×C₁₉	#463	1	1	yes	characteristic
218	C₄×C₁₉	#482	1	1	yes	characteristic
219	C₄×C₁₉	#482	1	1	yes	characteristic
220	Dic₁₉	—	4	2	no	—
221	Dic₁₉	—	4	2	no	—
222	Dic₁₉	—	8	2	no	—
223	Dic₁₉	—	8	1	no	—
224	C₂²×SD₁₆	—	38	1	no	—
225	C₂×C₄⋊Q₈	—	19	1	no	—
226	C₂×C₄×D₄	—	19	1	no	—
227	C₂×#117	—	38	1	no	—
228	#461	—	19	4	no	—
229	#461	—	38	2	no	—
230	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
232	C₂×#103	—	38	1	no	—
233	C₂×C₄×C₈	—	19	1	no	—
234	#390	—	38	1	no	—
235	#388	—	38	2	no	—
236	#384	C₂×D₁₉	1	1	yes	characteristic
237	#380	—	38	1	no	—
238	C₄×C₄⋊C₄	—	19	1	no	—
239	C₄×C₄⋊C₄	—	38	1	no	—
240	#340	—	38	1	no	—
241	#340	—	38	1	no	—
242	#340	—	38	2	no	—
243	D₄⋊C₈	—	38	2	no	—
244	C₂×C₁₉	#1642	1	1	yes	characteristic
245	C₂×C₁₉	#1646	1	1	yes	characteristic
246	C₂×C₁₉	#1650	1	1	yes	characteristic
247	C₂×C₁₉	#1654	1	1	yes	characteristic
248	C₂×C₁₉	#1875	1	1	yes	characteristic
249	C₂×C₁₉	#1877	1	1	yes	characteristic
250	C₂×C₁₉	#1882	1	1	yes	characteristic
251	D₁₉	—	8	2	no	—
252	C₂²×Q₈	—	38	1	no	—
253	C₂²×D₄	—	19	1	no	—
254	C₂³×C₄	—	38	1	no	—
255	C₂×SD₁₆	—	38	4	no	—
256	C₂×SD₁₆	—	76	2	no	—
257	C₂×SD₁₆	—	76	2	no	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	38	1	no	—
261	C₄⋊Q₈	—	19	2	no	—
262	C₄⋊Q₈	—	38	1	no	—
263	C₄⋊Q₈	—	38	1	no	—
264	C₄⋊Q₈	—	38	1	no	—
265	C₄×D₄	—	19	2	no	—
266	C₄×D₄	—	19	2	no	—
267	C₄×D₄	—	38	1	no	—
268	C₄×D₄	—	38	1	no	—
269	#117	—	76	2	no	—
270	#117	—	76	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	19	1	no	—
274	C₂×C₄⋊C₄	—	19	1	no	—
275	C₂×C₄⋊C₄	—	19	1	no	—
276	C₂×C₄⋊C₄	—	38	1	no	—
277	C₂×C₄⋊C₄	—	38	1	no	—
278	C₂×C₄⋊C₄	D₇₆	1	2	yes	—
279	C₂×C₂²⋊C₄	—	38	1	no	—
280	C₂×C₂²⋊C₄	—	38	2	no	—
281	C₂×C₂²⋊C₄	—	38	2	no	—
282	C₂×C₄²	—	38	2	no	—
283	C₂×C₄²	—	38	1	no	—
284	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
285	C₄⋊C₈	—	2	1	no	—
286	C₄⋊C₈	—	2	1	no	—
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
289	#103	—	38	4	no	—
290	C₄×C₈	—	38	1	no	—
291	C₄×C₈	—	38	1	no	—
292	#95	—	38	2	no	—
293	#95	—	38	1	no	—
294	C₁₉	#8988	1	1	yes	characteristic, complemented, Sylow
295	C₂⁴	—	38	1	no	—
296	C₂×Q₈	—	38	2	no	—
297	C₂×Q₈	—	76	1	no	—
298	C₂×Q₈	—	76	1	no	—
299	C₂×Q₈	—	76	1	no	—
300	C₂×Q₈	—	76	1	no	—
301	C₂×Q₈	—	76	1	no	—
302	C₂×D₄	—	19	2	no	—
303	C₂×D₄	—	38	1	no	—
304	C₂×D₄	—	38	1	no	—
305	C₂×D₄	—	38	1	no	—
306	C₂×D₄	—	38	1	no	—
307	C₂×D₄	—	38	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	—	38	2	no	—
312	C₂²×C₄	—	38	2	no	—
313	C₂²×C₄	—	38	1	no	—
314	C₂²×C₄	—	76	1	no	—
315	C₂²×C₄	—	76	1	no	—
316	C₂²×C₄	—	76	1	no	—
317	C₂²×C₄	—	76	1	no	—
318	C₂²×C₄	—	76	1	no	—
319	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
320	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
322	SD₁₆	—	76	8	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	4	1	no	—
325	C₂×C₈	—	4	1	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	38	2	no	—
330	C₂×C₈	—	76	1	no	—
331	C₂×C₈	—	76	1	no	—
332	C₄⋊C₄	—	4	2	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	4	1	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	19	2	no	—
338	C₄⋊C₄	—	19	2	no	—
339	C₄⋊C₄	—	38	1	no	—
340	C₄⋊C₄	—	38	1	no	—
341	C₄⋊C₄	—	38	2	no	—
342	C₄⋊C₄	—	38	2	no	—
343	C₄⋊C₄	—	38	1	no	—
344	C₄⋊C₄	—	38	1	no	—
345	C₄⋊C₄	—	76	1	no	—
346	C₄⋊C₄	—	76	1	no	—
347	C₂²⋊C₄	—	38	2	no	—
348	C₂²⋊C₄	—	38	2	no	—
349	C₂²⋊C₄	—	76	4	no	—
350	C₂²⋊C₄	—	152	2	no	—
351	C₄²	—	76	4	no	—
352	C₄²	—	76	1	no	—
353	C₄²	—	76	1	no	—
354	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
355	C₄²	#64541	1	1	yes	characteristic
356	C₄²	D₄×D₁₉	1	1	yes	characteristic
357	C₄²	#64545	1	1	yes	characteristic
358	C₂³	—	38	2	no	—
359	C₂³	—	76	1	no	—
360	C₂³	—	76	1	no	—
361	C₂³	—	76	1	no	—
362	C₂³	—	76	1	no	—
363	C₂³	—	76	1	no	—
364	C₂³	—	76	1	no	—
365	C₂³	#10597328	1	1	yes	characteristic
366	Q₈	—	76	2	no	—
367	Q₈	—	76	2	no	—
368	Q₈	—	152	1	no	—
369	Q₈	—	152	1	no	—
370	D₄	—	38	2	no	—
371	D₄	—	38	2	no	—
372	D₄	—	76	1	no	—
373	D₄	—	76	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	38	2	no	—
380	C₂×C₄	—	38	2	no	—
381	C₂×C₄	—	76	1	no	—
382	C₂×C₄	—	76	1	no	—
383	C₂×C₄	—	76	1	no	—
384	C₂×C₄	—	76	1	no	—
385	C₂×C₄	—	76	2	no	—
386	C₂×C₄	—	76	2	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	2	no	—
389	C₂×C₄	—	76	2	no	—
390	C₂×C₄	—	76	1	no	—
391	C₂×C₄	—	76	1	no	—
392	C₂×C₄	—	76	1	no	—
393	C₂×C₄	—	152	1	no	—
394	C₂×C₄	—	152	1	no	—
395	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
396	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
397	C₂×C₄	#10597330	1	1	yes	characteristic
398	C₂×C₄	#10597339	1	1	yes	characteristic
399	C₂×C₄	#10597340	1	1	yes	characteristic
400	C₂×C₄	#10597341	1	1	yes	characteristic
401	C₂×C₄	#10597357	1	1	yes	characteristic
402	C₂×C₄	#10597357	1	1	yes	characteristic
403	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
404	C₂×C₄	#10597360	1	1	yes	characteristic
405	C₂×C₄	#10597362	1	1	yes	characteristic
406	C₂×C₄	#10597362	1	1	yes	characteristic
407	C₂×C₄	#10597364	1	1	yes	characteristic
408	C₂×C₄	#10597365	1	1	yes	characteristic
409	C₈	—	4	2	no	—
410	C₈	—	8	1	no	—
411	C₈	—	76	2	no	—
412	C₂²	—	76	2	no	—
413	C₂²	—	76	2	no	—
414	C₂²	—	76	2	no	—
415	C₂²	—	152	1	no	—
416	C₂²	—	152	1	no	—
417	C₂²	—	152	1	no	—
418	C₂²	—	152	1	no	—
419	C₂²	#11926422	1	1	yes	characteristic
420	C₂²	#11926690	1	1	yes	characteristic
421	C₂²	#11926692	1	1	yes	characteristic
422	C₂²	#11926696	1	1	yes	characteristic
423	C₂²	#11926709	1	1	yes	characteristic
424	C₂²	#11926724	1	1	yes	characteristic
425	C₂²	#11926729	1	1	yes	characteristic
426	C₄	—	2	1	no	—
427	C₄	—	2	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	76	2	no	—
430	C₄	—	76	2	no	—
431	C₄	—	152	1	no	—
432	C₄	—	152	2	no	—
433	C₄	#11926539	1	1	yes	characteristic
434	C₄	#11926547	1	1	yes	characteristic
435	C₄	#11926631	1	1	yes	characteristic
436	C₄	#11926643	1	1	yes	characteristic
437	C₄	#11926748	1	1	yes	characteristic
438	C₄	#11926758	1	1	yes	characteristic
439	C₄	#11926870	1	1	yes	characteristic
440	C₄	#11926871	1	1	yes	characteristic
441	C₂	—	152	2	no	—
442	C₂	#14562836	1	1	yes	characteristic
443	C₂	#14562864	1	1	yes	characteristic
444	C₂	#14562892	1	1	yes	characteristic
445	C₂	#14562920	1	1	yes	characteristic
446	C₂	#14563956	1	1	yes	characteristic
447	C₂	#14563970	1	1	yes	characteristic
448	C₂	#14564003	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1296	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1296	D₁₉
hypocenter	C₁₉	#8988
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1296

Complements

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

N	H ≅ G/N	type
3. #14564595	C₂	semidirect
4. #14564586	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1296	C₂	semidirect
13. #11926750	C₄	semidirect
125. C₄⋊Dic₁₉	SD₁₆	semidirect
193. #1296	D₁₉	semidirect
294. C₁₉	#8988	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926750	2
#14566586	2
#14564595	2
#14564586	2
C₂×#11926271	2
#14561474	2
C₁₉×#1296	2
#8988	19