Subgroups — #18077359

Order 4864.

680 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926746	C₂	1	1	yes	maximal, characteristic
2	C₄⋊C₄×D₇₆	C₂	1	1	yes	maximal, characteristic
3	#14564597	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
5	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂×C₄×D₇₆	—	2	1	no	—
10	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊C₄×D₁₉	—	2	1	no	—
12	#11926746	—	2	2	no	—
13	#11926746	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#10597292	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	#11926442	—	2	1	no	—
18	#11926418	—	2	2	no	—
19	#11926414	C₂²	1	1	yes	characteristic
20	#11926401	—	2	1	no	—
21	#11926306	—	2	2	no	—
22	#11926271	—	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	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×C₄×D₁₉	—	2	2	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	C₂×C₄	1	2	yes	complemented
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#64527	—	2	4	no	—
44	C₂×#64527	—	4	2	no	—
45	C₂×#64527	—	4	2	no	—
46	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
47	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
52	C₂×Dic₁₉⋊C₄	—	2	2	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	—	2	1	no	—
55	C₄⋊C₄×D₁₉	—	4	2	no	—
56	C₄⋊C₄×D₁₉	—	4	2	no	—
57	C₄×D₇₆	—	2	1	no	—
58	C₄×D₇₆	—	2	1	no	—
59	C₄×D₇₆	—	4	2	no	—
60	C₄×D₇₆	—	4	2	no	—
61	C₄×D₇₆	C₂×C₄	1	2	yes	—
62	C₄×D₇₆	D₄	1	2	yes	—
63	C₁₉×C₄⋊C₈	—	2	1	no	—
64	C₁₉×C₄⋊C₈	—	2	1	no	—
65	C₁₉×#95	—	2	1	no	—
66	#10597292	—	2	4	no	—
67	C₁₉⋊#95	—	2	2	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	C₂×C₄	1	2	yes	complemented
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₂³×D₁₉	—	2	1	no	—
73	C₂×Q₈×C₁₉	—	2	2	no	—
74	C₂×Q₈×C₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	4	1	no	—
76	C₂×Q₈×C₁₉	—	4	1	no	—
77	C₂×Q₈×C₁₉	—	4	1	no	—
78	C₂×Q₈×C₁₉	—	4	1	no	—
79	C₂²×C₄×C₁₉	—	2	1	no	—
80	C₂²×C₄×C₁₉	—	2	1	no	—
81	C₂²×C₄×C₁₉	—	4	1	no	—
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₁₉	—	2	1	no	—
86	C₂²×Dic₁₉	—	2	2	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×D₇₆	—	2	1	no	—
90	C₂×D₇₆	C₂²⋊C₄	1	2	yes	—
91	C₂×D₇₆	D₈	1	2	yes	—
92	C₂×D₇₆	SD₁₆	1	2	yes	—
93	C₂×C₄×D₁₉	—	2	2	no	—
94	C₂×C₄×D₁₉	—	2	2	no	—
95	C₂×C₄×D₁₉	—	4	1	no	—
96	C₂×C₄×D₁₉	—	4	1	no	—
97	C₂×C₄×D₁₉	—	4	1	no	—
98	C₂×C₄×D₁₉	—	4	1	no	—
99	C₂×C₄×D₁₉	—	4	4	no	—
100	C₂×C₄×D₁₉	—	4	4	no	—
101	C₂×C₄×D₁₉	—	8	2	no	—
102	C₂×C₈×C₁₉	—	4	1	no	—
103	C₂×C₈×C₁₉	—	4	1	no	—
104	C₂×C₈×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	complemented
113	C₄²×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₁₉	#41	1	1	yes	characteristic
118	C₄²×C₁₉	#41	1	1	yes	characteristic
119	#64527	—	4	8	no	—
120	(C₂×D₁₉)⋊C₄	—	2	2	no	—
121	(C₂×D₁₉)⋊C₄	—	2	2	no	—
122	(C₂×D₁₉)⋊C₄	—	4	4	no	—
123	C₄⋊Dic₁₉	—	2	1	no	—
124	C₄⋊Dic₁₉	—	4	1	no	—
125	C₄⋊Dic₁₉	—	4	1	no	—
126	C₄⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	4	1	no	—
128	C₄⋊Dic₁₉	—	4	2	no	—
129	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
130	Dic₁₉⋊C₄	—	4	4	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	C₂×C₁₉⋊C₈	—	4	1	no	—
137	#8985	—	19	1	no	maximal, Sylow
138	C₂³×C₁₉	#120	1	1	yes	characteristic
139	C₂²×D₁₉	—	2	2	no	—
140	C₂²×D₁₉	—	2	2	no	—
141	C₂²×D₁₉	—	2	2	no	—
142	C₂²×D₁₉	—	4	1	no	—
143	C₂²×D₁₉	—	4	1	no	—
144	C₂²×D₁₉	—	4	1	no	—
145	C₂²×D₁₉	—	4	1	no	—
146	Q₈×C₁₉	—	4	2	no	—
147	Q₈×C₁₉	—	4	2	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	Q₈×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	—	2	1	no	—
151	C₂×C₄×C₁₉	—	2	1	no	—
152	C₂×C₄×C₁₉	—	2	2	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	1	no	—
158	C₂×C₄×C₁₉	—	4	1	no	—
159	C₂×C₄×C₁₉	—	8	1	no	—
160	C₂×C₄×C₁₉	—	8	1	no	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
171	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
175	C₂×Dic₁₉	—	2	2	no	—
176	C₂×Dic₁₉	—	4	1	no	—
177	C₂×Dic₁₉	—	4	1	no	—
178	C₂×Dic₁₉	—	4	2	no	—
179	C₂×Dic₁₉	—	4	2	no	—
180	C₂×Dic₁₉	—	4	2	no	—
181	D₇₆	—	2	2	no	—
182	D₇₆	—	2	2	no	—
183	D₇₆	—	2	2	no	—
184	D₇₆	#102	1	4	yes	—
185	C₄×D₁₉	—	4	2	no	—
186	C₄×D₁₉	—	4	2	no	—
187	C₄×D₁₉	—	4	2	no	—
188	C₄×D₁₉	—	4	2	no	—
189	C₄×D₁₉	—	8	8	no	—
190	C₈×C₁₉	—	8	1	no	—
191	C₁₉⋊C₈	—	4	2	no	—
192	C₁₉⋊C₈	—	4	2	no	—
193	C₂×#461	—	19	1	no	—
194	D₄×C₄⋊C₄	—	19	1	no	—
195	#1990	—	19	1	no	—
196	#1988	D₁₉	1	1	yes	characteristic, complemented
197	C₂×D₄⋊C₈	—	19	1	no	—
198	#1296	—	19	1	no	—
199	#1279	—	19	1	no	—
200	C₂²×C₁₉	#386	1	1	yes	characteristic
201	C₂²×C₁₉	#447	1	1	yes	characteristic
202	C₂²×C₁₉	#448	1	1	yes	characteristic
203	C₂²×C₁₉	#450	1	1	yes	characteristic
204	C₂²×C₁₉	#452	1	1	yes	characteristic
205	C₂²×C₁₉	#455	1	1	yes	characteristic
206	C₂²×C₁₉	#456	1	1	yes	characteristic
207	C₂×D₁₉	—	2	4	no	—
208	C₂×D₁₉	—	4	2	no	—
209	C₂×D₁₉	—	4	2	no	—
210	C₂×D₁₉	—	4	2	no	—
211	C₂×D₁₉	—	4	2	no	—
212	C₂×D₁₉	—	4	2	no	—
213	C₂×D₁₉	—	4	2	no	—
214	C₄×C₁₉	—	2	1	no	—
215	C₄×C₁₉	—	2	1	no	—
216	C₄×C₁₉	—	4	2	no	—
217	C₄×C₁₉	—	8	2	no	—
218	C₄×C₁₉	—	8	1	no	—
219	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
220	C₄×C₁₉	#417	1	1	yes	characteristic
221	C₄×C₁₉	C₄×SD₁₆	1	1	yes	characteristic
222	C₄×C₁₉	#440	1	1	yes	characteristic
223	C₄×C₁₉	#461	1	1	yes	characteristic
224	C₄×C₁₉	#463	1	1	yes	characteristic
225	C₄×C₁₉	#480	1	1	yes	characteristic
226	C₄×C₁₉	#481	1	1	yes	characteristic
227	Dic₁₉	—	4	2	no	—
228	Dic₁₉	—	8	2	no	—
229	C₂²×SD₁₆	—	38	1	no	—
230	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
231	C₂×C₄×D₄	—	19	1	no	—
232	C₂×C₄×D₄	—	38	1	no	—
233	C₂²×C₄⋊C₄	—	38	1	no	—
234	#461	—	19	4	no	—
235	#461	—	38	2	no	—
236	C₂×C₄⋊C₈	—	19	1	no	—
237	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
238	C₂×#103	—	38	1	no	—
239	C₂×C₄×C₈	—	19	1	no	—
240	#389	—	38	1	no	—
241	#385	—	38	2	no	—
242	#384	—	19	1	no	—
243	#380	—	38	1	no	—
244	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
245	#340	—	2	1	no	—
246	#340	—	2	1	no	—
247	#340	—	38	2	no	—
248	D₄⋊C₈	—	38	2	no	—
249	C₂×C₁₉	#1639	1	1	yes	characteristic
250	C₂×C₁₉	#1643	1	1	yes	characteristic
251	C₂×C₁₉	#1647	1	1	yes	characteristic
252	C₂×C₁₉	#1651	1	1	yes	characteristic
253	C₂×C₁₉	#1874	1	1	yes	characteristic
254	C₂×C₁₉	#1877	1	1	yes	characteristic
255	C₂×C₁₉	#1882	1	1	yes	characteristic
256	D₁₉	—	4	4	no	—
257	C₂²×Q₈	—	2	1	no	—
258	C₂²×D₄	—	19	1	no	—
259	C₂³×C₄	—	38	2	no	—
260	C₂³×C₄	—	38	1	no	—
261	C₂×SD₁₆	—	38	4	no	—
262	C₂×SD₁₆	—	76	2	no	—
263	C₂×SD₁₆	—	76	2	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	C₄×D₄	—	19	2	no	—
272	C₄×D₄	—	19	2	no	—
273	C₄×D₄	—	38	1	no	—
274	C₄×D₄	—	38	1	no	—
275	C₄×D₄	—	76	2	no	—
276	C₄×D₄	—	76	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	19	1	no	—
280	C₂×C₄⋊C₄	—	19	2	no	—
281	C₂×C₄⋊C₄	—	38	2	no	—
282	C₂×C₄⋊C₄	—	38	1	no	—
283	C₂×C₄⋊C₄	—	38	1	no	—
284	C₂×C₄⋊C₄	—	76	2	no	—
285	C₂×C₄⋊C₄	—	76	2	no	—
286	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	—	38	1	no	—
289	C₂×C₂²⋊C₄	—	38	2	no	—
290	C₂×C₄²	—	2	1	no	—
291	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
292	C₄⋊C₈	—	2	1	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	19	2	no	—
295	C₄⋊C₈	—	38	1	no	—
296	#103	—	38	4	no	—
297	C₄×C₈	—	38	1	no	—
298	C₄×C₈	—	38	1	no	—
299	#95	—	2	1	no	—
300	#95	—	38	2	no	—
301	C₁₉	#8985	1	1	yes	characteristic, complemented, Sylow
302	C₂⁴	—	38	1	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	4	1	no	—
305	C₂×Q₈	—	4	1	no	—
306	C₂×Q₈	—	4	1	no	—
307	C₂×Q₈	—	4	1	no	—
308	C₂×Q₈	—	4	1	no	—
309	C₂×D₄	—	19	2	no	—
310	C₂×D₄	—	19	2	no	—
311	C₂×D₄	—	19	2	no	—
312	C₂×D₄	—	38	1	no	—
313	C₂×D₄	—	38	1	no	—
314	C₂×D₄	—	38	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	4	1	no	—
318	C₂²×C₄	—	38	1	no	—
319	C₂²×C₄	—	38	2	no	—
320	C₂²×C₄	—	38	2	no	—
321	C₂²×C₄	—	38	2	no	—
322	C₂²×C₄	—	76	4	no	—
323	C₂²×C₄	—	76	4	no	—
324	C₂²×C₄	—	76	1	no	—
325	C₂²×C₄	—	76	1	no	—
326	C₂²×C₄	—	76	1	no	—
327	C₂²×C₄	—	76	1	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	8	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	—	76	1	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	—	76	2	no	—
352	C₄⋊C₄	—	76	4	no	—
353	C₄⋊C₄	—	76	1	no	—
354	C₄⋊C₄	—	76	1	no	—
355	C₄⋊C₄	—	76	1	no	—
356	C₄⋊C₄	—	76	1	no	—
357	C₄⋊C₄	#64527	1	2	yes	complemented
358	C₂²⋊C₄	—	38	2	no	—
359	C₂²⋊C₄	—	38	2	no	—
360	C₂²⋊C₄	—	76	4	no	—
361	C₄²	—	4	1	no	—
362	C₄²	—	4	1	no	—
363	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
364	C₄²	#64541	1	1	yes	characteristic
365	C₄²	D₄×D₁₉	1	1	yes	characteristic
366	C₄²	#64543	1	1	yes	characteristic
367	C₂³	—	38	2	no	—
368	C₂³	—	38	2	no	—
369	C₂³	—	38	2	no	—
370	C₂³	—	76	1	no	—
371	C₂³	—	76	1	no	—
372	C₂³	—	76	1	no	—
373	C₂³	—	76	1	no	—
374	C₂³	#10597383	1	1	yes	characteristic
375	Q₈	—	4	2	no	—
376	Q₈	—	4	2	no	—
377	Q₈	—	8	1	no	—
378	Q₈	—	8	1	no	—
379	D₄	—	19	4	no	—
380	D₄	—	38	2	no	—
381	D₄	—	38	2	no	—
382	D₄	—	38	2	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	4	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	8	1	no	—
393	C₂×C₄	—	8	1	no	—
394	C₂×C₄	—	38	2	no	—
395	C₂×C₄	—	76	1	no	—
396	C₂×C₄	—	76	1	no	—
397	C₂×C₄	—	76	2	no	—
398	C₂×C₄	—	76	2	no	—
399	C₂×C₄	—	76	2	no	—
400	C₂×C₄	—	76	2	no	—
401	C₂×C₄	—	76	2	no	—
402	C₂×C₄	—	76	2	no	—
403	C₂×C₄	—	76	2	no	—
404	C₂×C₄	—	152	8	no	—
405	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
406	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
407	C₂×C₄	#10597329	1	1	yes	characteristic
408	C₂×C₄	#10597330	1	1	yes	characteristic
409	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
410	C₂×C₄	#10597357	1	1	yes	characteristic
411	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
412	C₂×C₄	#10597361	1	1	yes	characteristic
413	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
414	C₂×C₄	#10597384	1	1	yes	characteristic
415	C₂×C₄	C₂×#64527	1	1	yes	characteristic
416	C₂×C₄	#10597388	1	1	yes	characteristic
417	C₂×C₄	#10597395	1	1	yes	characteristic
418	C₂×C₄	#10597396	1	1	yes	characteristic
419	C₈	—	8	1	no	—
420	C₈	—	76	2	no	—
421	C₈	—	76	2	no	—
422	C₂²	—	38	4	no	—
423	C₂²	—	76	2	no	—
424	C₂²	—	76	2	no	—
425	C₂²	—	76	2	no	—
426	C₂²	—	76	2	no	—
427	C₂²	—	76	2	no	—
428	C₂²	—	76	2	no	—
429	C₂²	#11926420	1	1	yes	characteristic
430	C₂²	#11926676	1	1	yes	characteristic
431	C₂²	#11926681	1	1	yes	characteristic
432	C₂²	#11926694	1	1	yes	characteristic
433	C₂²	#11926704	1	1	yes	characteristic
434	C₂²	#11926720	1	1	yes	characteristic
435	C₂²	#11926725	1	1	yes	characteristic
436	C₄	—	2	1	no	—
437	C₄	—	2	1	no	—
438	C₄	—	4	2	no	—
439	C₄	—	8	1	no	—
440	C₄	—	8	2	no	—
441	C₄	—	76	2	no	—
442	C₄	—	152	2	no	—
443	C₄	#102×D₁₉	1	1	yes	characteristic
444	C₄	#11926542	1	1	yes	characteristic
445	C₄	C₄×#64527	1	1	yes	characteristic
446	C₄	#11926642	1	1	yes	characteristic
447	C₄	#11926746	1	1	yes	characteristic
448	C₄	#11926756	1	1	yes	characteristic
449	C₄	#11926856	1	1	yes	characteristic
450	C₄	#11926861	1	1	yes	characteristic
451	C₂	—	76	4	no	—
452	C₂	#14562813	1	1	yes	characteristic
453	C₂	#14562841	1	1	yes	characteristic
454	C₂	#14562869	1	1	yes	characteristic
455	C₂	#14562897	1	1	yes	characteristic
456	C₂	#14563949	1	1	yes	characteristic
457	C₂	#14563972	1	1	yes	characteristic
458	C₂	#14564001	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597383
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1988	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂²×D₇₆	D₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1988	D₁₉
hypocenter	C₁₉	#8985
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1988

Complements

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

N	H ≅ G/N	type
3. #14564597	C₂	semidirect
5. #14561519	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#1988	C₂	semidirect
13. #11926746	C₄	semidirect
36. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
69. C₄⋊(C₁₉⋊C₈)	C₂×C₄	semidirect
112. C₄⋊C₄×C₁₉	SD₁₆	semidirect
196. #1988	D₁₉	semidirect
270. C₄⋊Q₈	C₄×D₁₉	semidirect
301. C₁₉	#8985	semidirect
357. 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×#11926746	2
C₄⋊C₄×D₇₆	2
#14564597	2
C₂×#11926271	2
#14561519	2
#14561476	2
C₁₉×#1988	2
#8985	19