Subgroups — #18077830

Order 4864.

738 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926918	C₂	1	1	yes	maximal, characteristic
2	#14566699	C₂	1	1	yes	maximal, characteristic
3	#14564584	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×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	2	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₇₆	—	2	1	no	—
11	C₂×#10597339	—	2	1	no	—
12	#11926918	—	2	2	no	—
13	#11926918	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
16	#11926446	—	2	1	no	—
17	#11926445	—	2	1	no	—
18	#11926422	—	2	2	no	—
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	#11926306	—	2	1	no	—
21	#11926306	—	2	1	no	—
22	#11926287	—	2	2	no	—
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₁₉×#340	—	2	1	no	—
27	C₁₉×#340	—	2	1	no	—
28	C₂²×Q₈×C₁₉	—	2	1	no	—
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×D₇₆	—	2	1	no	—
31	C₂²×D₇₆	D₄	1	2	yes	—
32	C₂²×C₄×D₁₉	—	2	2	no	—
33	C₂²×C₈×C₁₉	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
42	C₂×C₄²×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
44	C₂×#64527	—	2	8	no	—
45	C₂×#64527	—	4	4	no	—
46	C₂×#64527	—	4	4	no	—
47	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
48	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
49	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
50	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	#10597339	—	4	2	no	—
56	#10597339	—	4	2	no	—
57	#10597320	—	2	1	no	—
58	#10597320	—	2	1	no	—
59	#10597320	C₂×C₄	1	2	yes	—
60	#10597320	D₄	1	2	yes	—
61	C₄×D₇₆	—	4	2	no	—
62	C₄×D₇₆	—	4	2	no	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	C₁₉⋊#95	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄×C₁₉⋊C₈	—	2	1	no	—
70	C₄×C₁₉⋊C₈	C₂×C₄	1	2	yes	complemented
71	C₂³×D₁₉	—	2	2	no	—
72	C₂×Q₈×C₁₉	—	2	2	no	—
73	C₂×Q₈×C₁₉	—	4	2	no	—
74	C₂×Q₈×C₁₉	—	4	2	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	—	2	1	no	—
77	C₂²×C₄×C₁₉	—	2	1	no	—
78	C₂²×C₄×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	—	2	1	no	—
83	C₂²×Dic₁₉	—	2	1	no	—
84	C₂×D₇₆	—	2	2	no	—
85	C₂×D₇₆	—	2	2	no	—
86	C₂×D₇₆	—	2	2	no	—
87	C₂×D₇₆	—	2	2	no	—
88	C₂×D₇₆	—	2	2	no	—
89	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	1	no	—
93	C₂×D₇₆	—	4	1	no	—
94	C₂×D₇₆	—	4	1	no	—
95	C₂×D₇₆	—	4	1	no	—
96	C₂×D₇₆	—	4	1	no	—
97	C₂×D₇₆	—	4	2	no	—
98	C₂×D₇₆	—	4	2	no	—
99	C₂×D₇₆	C₂²⋊C₄	1	4	yes	—
100	C₂×C₄×D₁₉	—	4	4	no	—
101	C₂×C₄×D₁₉	—	4	4	no	—
102	C₂×C₄×D₁₉	—	8	2	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₂×C₈×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	2	1	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
118	C₄²×C₁₉	#41	1	1	yes	characteristic
119	C₄²×C₁₉	#41	1	1	yes	characteristic
120	#64527	—	4	16	no	—
121	(C₂×D₁₉)⋊C₄	—	4	4	no	—
122	(C₂×D₁₉)⋊C₄	—	4	4	no	—
123	(C₂×D₁₉)⋊C₄	—	8	2	no	—
124	C₄⋊Dic₁₉	—	2	1	no	—
125	C₄⋊Dic₁₉	—	2	1	no	—
126	C₄⋊Dic₁₉	—	2	1	no	—
127	C₄⋊Dic₁₉	SD₁₆	1	2	yes	complemented
128	C₄×Dic₁₉	—	4	1	no	—
129	C₄×Dic₁₉	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	2	2	no	—
131	C₂×C₁₉⋊C₈	—	2	2	no	—
132	C₂×C₁₉⋊C₈	—	2	2	no	—
133	C₂×C₁₉⋊C₈	—	4	1	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	1	no	—
136	#9064	—	19	1	no	maximal, Sylow
137	C₂³×C₁₉	#120	1	1	yes	characteristic
138	C₂²×D₁₉	—	2	4	no	—
139	C₂²×D₁₉	—	4	2	no	—
140	C₂²×D₁₉	—	4	2	no	—
141	C₂²×D₁₉	—	4	2	no	—
142	C₂²×D₁₉	—	4	2	no	—
143	C₂²×D₁₉	—	4	2	no	—
144	C₂²×D₁₉	—	4	2	no	—
145	Q₈×C₁₉	—	4	4	no	—
146	Q₈×C₁₉	—	8	2	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	8	1	no	—
157	C₂×C₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
168	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
172	C₂×Dic₁₉	—	2	2	no	—
173	C₂×Dic₁₉	—	4	1	no	—
174	C₂×Dic₁₉	—	4	1	no	—
175	C₂×Dic₁₉	—	4	1	no	—
176	C₂×Dic₁₉	—	4	1	no	—
177	C₂×Dic₁₉	—	4	1	no	—
178	D₇₆	—	4	4	no	—
179	D₇₆	—	4	2	no	—
180	D₇₆	—	4	2	no	—
181	D₇₆	—	4	2	no	—
182	D₇₆	—	4	2	no	—
183	D₇₆	—	4	2	no	—
184	D₇₆	—	4	2	no	—
185	D₇₆	—	4	2	no	—
186	D₇₆	—	4	2	no	—
187	D₇₆	—	8	2	no	—
188	C₄×D₁₉	—	8	8	no	—
189	C₈×C₁₉	—	8	1	no	—
190	C₁₉⋊C₈	—	2	4	no	—
191	C₁₉⋊C₈	—	8	1	no	—
192	C₂×#492	—	19	1	no	—
193	#2366	—	19	1	no	—
194	#1987	—	19	1	no	—
195	#1987	D₁₉	1	1	yes	characteristic, complemented
196	C₂×#331	—	19	1	no	—
197	#1279	—	19	1	no	—
198	#1279	—	19	1	no	—
199	C₂²×C₁₉	#386	1	1	yes	characteristic
200	C₂²×C₁₉	#450	1	1	yes	characteristic
201	C₂²×C₁₉	#450	1	1	yes	characteristic
202	C₂²×C₁₉	#452	1	1	yes	characteristic
203	C₂²×C₁₉	#452	1	1	yes	characteristic
204	C₂²×C₁₉	#453	1	1	yes	characteristic
205	C₂²×C₁₉	#453	1	1	yes	characteristic
206	C₂×D₁₉	—	4	4	no	—
207	C₂×D₁₉	—	4	4	no	—
208	C₂×D₁₉	—	4	4	no	—
209	C₂×D₁₉	—	8	2	no	—
210	C₂×D₁₉	—	8	2	no	—
211	C₂×D₁₉	—	8	2	no	—
212	C₂×D₁₉	—	8	2	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	4	2	no	—
216	C₄×C₁₉	—	8	1	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
219	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
220	C₄×C₁₉	#440	1	1	yes	characteristic
221	C₄×C₁₉	#440	1	1	yes	characteristic
222	C₄×C₁₉	#461	1	1	yes	characteristic
223	C₄×C₁₉	#461	1	1	yes	characteristic
224	C₄×C₁₉	#463	1	1	yes	characteristic
225	C₄×C₁₉	#463	1	1	yes	characteristic
226	Dic₁₉	—	4	2	no	—
227	Dic₁₉	—	8	1	no	—
228	C₂²×SD₁₆	—	38	2	no	—
229	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
230	C₂×#127	—	19	1	no	—
231	C₂×C₄×D₄	—	38	1	no	—
232	C₂×C₄×D₄	—	38	1	no	—
233	#492	—	19	4	no	—
234	#492	—	38	2	no	—
235	C₂×C₄⋊C₈	—	19	1	no	—
236	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
237	C₂×C₄×C₈	—	19	1	no	—
238	#390	—	38	1	no	—
239	#390	—	38	1	no	—
240	#386	—	38	2	no	—
241	C₄×C₄⋊C₄	—	19	1	no	—
242	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
243	#340	—	2	1	no	—
244	#340	—	2	1	no	—
245	#340	—	38	1	no	—
246	#340	—	38	1	no	—
247	#331	—	38	2	no	—
248	C₂×C₁₉	#1629	1	1	yes	characteristic
249	C₂×C₁₉	#1630	1	1	yes	characteristic
250	C₂×C₁₉	#1631	1	1	yes	characteristic
251	C₂×C₁₉	#1631	1	1	yes	characteristic
252	C₂×C₁₉	#1877	1	1	yes	characteristic
253	C₂×C₁₉	#1877	1	1	yes	characteristic
254	C₂×C₁₉	#1887	1	1	yes	characteristic
255	D₁₉	—	8	4	no	—
256	C₂²×Q₈	—	2	1	no	—
257	C₂²×D₄	—	19	2	no	—
258	C₂²×D₄	—	38	1	no	—
259	C₂²×D₄	—	38	1	no	—
260	C₂³×C₄	—	38	2	no	—
261	C₂×SD₁₆	—	38	8	no	—
262	C₂×SD₁₆	—	76	4	no	—
263	C₂×SD₁₆	—	76	4	no	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	—	38	1	no	—
266	C₂²×C₈	—	38	1	no	—
267	C₄⋊Q₈	—	2	1	no	—
268	C₄⋊Q₈	—	2	1	no	—
269	C₄⋊Q₈	—	2	1	no	—
270	C₄⋊Q₈	C₄×D₁₉	1	2	yes	complemented
271	#127	—	19	2	no	—
272	#127	—	19	2	no	—
273	#127	—	38	1	no	—
274	#127	—	38	1	no	—
275	C₄×D₄	—	76	2	no	—
276	C₄×D₄	—	76	2	no	—
277	C₄×D₄	—	76	2	no	—
278	C₄×D₄	—	76	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	19	1	no	—
282	C₂×C₄⋊C₄	—	19	1	no	—
283	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	—	38	2	no	—
286	C₂×C₂²⋊C₄	—	38	2	no	—
287	C₂×C₂²⋊C₄	—	38	2	no	—
288	C₂×C₄²	—	2	1	no	—
289	C₂×C₄²	—	38	1	no	—
290	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
291	C₄⋊C₈	—	2	1	no	—
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	38	1	no	—
294	C₄⋊C₈	—	38	1	no	—
295	C₄×C₈	—	19	2	no	—
296	C₄×C₈	—	38	1	no	—
297	#95	—	2	1	no	—
298	#95	—	38	1	no	—
299	C₁₉	#9064	1	1	yes	characteristic, complemented, Sylow
300	C₂⁴	—	38	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×D₄	—	19	4	no	—
306	C₂×D₄	—	38	2	no	—
307	C₂×D₄	—	38	2	no	—
308	C₂×D₄	—	38	2	no	—
309	C₂×D₄	—	38	2	no	—
310	C₂×D₄	—	38	2	no	—
311	C₂×D₄	—	76	2	no	—
312	C₂×D₄	—	76	2	no	—
313	C₂×D₄	—	76	1	no	—
314	C₂×D₄	—	76	1	no	—
315	C₂×D₄	—	76	1	no	—
316	C₂×D₄	—	76	1	no	—
317	C₂×D₄	—	76	1	no	—
318	C₂×D₄	—	76	1	no	—
319	C₂×D₄	—	76	1	no	—
320	C₂×D₄	—	76	1	no	—
321	C₂²×C₄	—	2	1	no	—
322	C₂²×C₄	—	2	1	no	—
323	C₂²×C₄	—	4	1	no	—
324	C₂²×C₄	—	38	1	no	—
325	C₂²×C₄	—	38	1	no	—
326	C₂²×C₄	—	76	4	no	—
327	C₂²×C₄	—	76	4	no	—
328	C₂²×C₄	—	152	2	no	—
329	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
332	SD₁₆	—	76	16	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	38	2	no	—
337	C₂×C₈	—	38	2	no	—
338	C₂×C₈	—	38	2	no	—
339	C₂×C₈	—	76	1	no	—
340	C₂×C₈	—	76	1	no	—
341	C₂×C₈	—	76	1	no	—
342	C₄⋊C₄	—	2	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₄⋊C₄	—	4	1	no	—
349	C₄⋊C₄	—	19	2	no	—
350	C₄⋊C₄	—	38	1	no	—
351	C₄⋊C₄	—	38	1	no	—
352	C₄⋊C₄	—	38	1	no	—
353	C₄⋊C₄	#64527	1	2	yes	complemented
354	C₂²⋊C₄	—	76	4	no	—
355	C₂²⋊C₄	—	76	4	no	—
356	C₂²⋊C₄	—	152	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	76	1	no	—
360	C₄²	—	76	1	no	—
361	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
362	C₄²	#64541	1	1	yes	characteristic
363	C₄²	D₄×D₁₉	1	1	yes	characteristic
364	C₄²	#64543	1	1	yes	characteristic
365	C₂³	—	38	4	no	—
366	C₂³	—	76	2	no	—
367	C₂³	—	76	2	no	—
368	C₂³	—	76	2	no	—
369	C₂³	—	76	2	no	—
370	C₂³	—	76	2	no	—
371	C₂³	—	76	2	no	—
372	C₂³	#10597383	1	1	yes	characteristic
373	Q₈	—	4	4	no	—
374	Q₈	—	8	2	no	—
375	D₄	—	76	4	no	—
376	D₄	—	76	2	no	—
377	D₄	—	76	2	no	—
378	D₄	—	76	2	no	—
379	D₄	—	76	2	no	—
380	D₄	—	76	2	no	—
381	D₄	—	76	2	no	—
382	D₄	—	76	2	no	—
383	D₄	—	76	2	no	—
384	D₄	—	152	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	8	1	no	—
395	C₂×C₄	—	8	1	no	—
396	C₂×C₄	—	38	2	no	—
397	C₂×C₄	—	76	1	no	—
398	C₂×C₄	—	76	1	no	—
399	C₂×C₄	—	76	1	no	—
400	C₂×C₄	—	76	1	no	—
401	C₂×C₄	—	76	1	no	—
402	C₂×C₄	—	152	8	no	—
403	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
404	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
405	C₂×C₄	#10597329	1	1	yes	characteristic
406	C₂×C₄	#10597330	1	1	yes	characteristic
407	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
408	C₂×C₄	#10597360	1	1	yes	characteristic
409	C₂×C₄	#10597364	1	1	yes	characteristic
410	C₂×C₄	#10597365	1	1	yes	characteristic
411	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
412	C₂×C₄	#10597384	1	1	yes	characteristic
413	C₂×C₄	C₂×#64527	1	1	yes	characteristic
414	C₂×C₄	#10597388	1	1	yes	characteristic
415	C₂×C₄	#10597395	1	1	yes	characteristic
416	C₂×C₄	#10597396	1	1	yes	characteristic
417	C₈	—	8	1	no	—
418	C₈	—	38	4	no	—
419	C₈	—	152	1	no	—
420	C₂²	—	76	4	no	—
421	C₂²	—	76	4	no	—
422	C₂²	—	76	4	no	—
423	C₂²	—	152	2	no	—
424	C₂²	—	152	2	no	—
425	C₂²	—	152	2	no	—
426	C₂²	—	152	2	no	—
427	C₂²	#11926420	1	1	yes	characteristic
428	C₂²	#11926693	1	1	yes	characteristic
429	C₂²	#11926694	1	1	yes	characteristic
430	C₂²	#11926704	1	1	yes	characteristic
431	C₂²	#11926705	1	1	yes	characteristic
432	C₂²	#11926710	1	1	yes	characteristic
433	C₂²	#11926710	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	4	2	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	1	no	—
439	C₄	—	76	2	no	—
440	C₄	—	152	1	no	—
441	C₄	#11926629	1	1	yes	characteristic
442	C₄	C₄×#64527	1	1	yes	characteristic
443	C₄	#11926642	1	1	yes	characteristic
444	C₄	#11926647	1	1	yes	characteristic
445	C₄	#11926746	1	1	yes	characteristic
446	C₄	#11926748	1	1	yes	characteristic
447	C₄	#11926756	1	1	yes	characteristic
448	C₄	#11926762	1	1	yes	characteristic
449	C₂	—	152	4	no	—
450	C₂	#14562750	1	1	yes	characteristic
451	C₂	#14562755	1	1	yes	characteristic
452	C₂	#14562760	1	1	yes	characteristic
453	C₂	#14562761	1	1	yes	characteristic
454	C₂	#14563966	1	1	yes	characteristic
455	C₂	#14563972	1	1	yes	characteristic
456	C₂	#14564030	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1987	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1987	D₁₉
hypocenter	C₁₉	#9064
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1987

Complements

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

N	H ≅ G/N	type
3. #14564584	C₂	semidirect
5. #14561476	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1987	C₂	semidirect
13. #11926918	C₄	semidirect
37. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
70. C₄×C₁₉⋊C₈	C₂×C₄	semidirect
113. C₄⋊C₄×C₁₉	SD₁₆	semidirect
127. C₄⋊Dic₁₉	SD₁₆	semidirect
195. #1987	D₁₉	semidirect
270. C₄⋊Q₈	C₄×D₁₉	semidirect
299. C₁₉	#9064	semidirect
353. C₄⋊C₄	#64527	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926918	2
#14566699	2
#14564584	2
C₂×#11926287	2
#14561476	2
#14561474	2
C₁₉×#1987	2
#9064	19