Subgroups — #18075906

Order 4864.

496 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	#14566031	C₂	1	1	yes	maximal, characteristic
2	#14563612	C₂	1	1	yes	maximal, characteristic
3	C₄×(C₂×D₁₉)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561475	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561474	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄²×D₁₉	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
11	C₂×(C₂×D₁₉)⋊C₈	—	2	1	no	—
12	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
13	#11926411	—	2	1	no	—
14	#11926409	C₄	1	1	yes	characteristic
15	#11926409	C₄	1	1	yes	characteristic
16	#11926406	—	2	1	no	—
17	#11926401	C₄	1	1	yes	characteristic
18	#11926401	C₄	1	1	yes	characteristic
19	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
20	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
21	#11926390	—	2	1	no	—
22	#11926298	—	2	1	no	—
23	#11926298	—	2	1	no	—
24	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₉	D₄	1	1	yes	characteristic
30	C₂²×C₈×C₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₉	—	2	1	no	—
35	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
36	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄×Dic₁₉	—	2	1	no	—
41	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	C₄²×D₁₉	—	2	1	no	—
47	C₄²×D₁₉	—	2	1	no	—
48	C₄²×D₁₉	—	2	1	no	—
49	C₄²×D₁₉	—	2	1	no	—
50	C₁₉×C₄⋊C₈	—	2	1	no	—
51	C₁₉×C₄⋊C₈	—	2	1	no	—
52	C₄×C₈×C₁₉	—	2	1	no	—
53	C₄×C₈×C₁₉	—	2	1	no	—
54	C₁₉×#95	—	2	1	no	—
55	C₁₉⋊#95	—	2	1	no	—
56	C₁₉⋊#95	—	2	1	no	—
57	C₁₉⋊#95	—	2	1	no	—
58	C₁₉⋊#95	—	2	1	no	—
59	C₁₉⋊#95	—	2	1	no	—
60	C₁₉⋊#95	—	2	1	no	—
61	C₁₉⋊#95	—	2	1	no	—
62	(C₂×D₁₉)⋊C₈	—	2	4	no	—
63	(C₂×D₁₉)⋊C₈	—	4	2	no	—
64	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
65	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
66	C₄×C₁₉⋊C₈	—	2	1	no	—
67	C₄×C₁₉⋊C₈	—	2	1	no	—
68	C₂³×D₁₉	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×Dic₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
79	C₂×C₄×D₁₉	—	2	2	no	—
80	C₂×C₄×D₁₉	—	2	1	no	—
81	C₂×C₄×D₁₉	—	2	1	no	—
82	C₂×C₄×D₁₉	—	2	1	no	—
83	C₂×C₄×D₁₉	—	2	1	no	—
84	C₂×C₄×D₁₉	—	2	1	no	—
85	C₂×C₄×D₁₉	—	2	1	no	—
86	C₂×C₄×D₁₉	—	2	1	no	—
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	—	2	1	no	—
92	C₂×C₄×D₁₉	—	2	1	no	—
93	C₂×C₄×D₁₉	—	2	1	no	—
94	C₂×C₄×D₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	—	2	2	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₂×C₈×C₁₉	—	4	1	no	—
99	C₂×C₈×C₁₉	—	4	1	no	—
100	C₂×C₈×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	2	1	no	—
102	C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	#41	1	1	yes	characteristic
108	C₄²×C₁₉	#41	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	2	no	—
112	(C₂×D₁₉)⋊C₄	—	4	2	no	—
113	C₄⋊Dic₁₉	—	2	1	no	—
114	C₄⋊Dic₁₉	—	2	1	no	—
115	C₄⋊Dic₁₉	—	2	1	no	—
116	C₄⋊Dic₁₉	—	2	1	no	—
117	C₄×Dic₁₉	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	—	2	1	no	—
120	C₄×Dic₁₉	—	2	1	no	—
121	C₄×Dic₁₉	—	2	1	no	—
122	C₄×Dic₁₉	—	2	1	no	—
123	C₄×Dic₁₉	—	4	1	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	C₂×C₁₉⋊C₈	—	2	2	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	#8711	—	19	1	no	maximal, Sylow
132	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
133	C₂²×D₁₉	—	2	1	no	—
134	C₂²×D₁₉	—	2	1	no	—
135	C₂²×D₁₉	—	2	1	no	—
136	C₂²×D₁₉	—	2	1	no	—
137	C₂²×D₁₉	—	2	1	no	—
138	C₂²×D₁₉	—	2	1	no	—
139	C₂²×D₁₉	#104	1	2	yes	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
149	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
150	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
162	C₂×Dic₁₉	—	2	1	no	—
163	C₂×Dic₁₉	—	2	1	no	—
164	C₂×Dic₁₉	—	2	1	no	—
165	C₂×Dic₁₉	—	2	1	no	—
166	C₂×Dic₁₉	—	2	1	no	—
167	C₂×Dic₁₉	—	2	1	no	—
168	C₂×Dic₁₉	—	2	1	no	—
169	C₂×Dic₁₉	—	2	1	no	—
170	C₂×Dic₁₉	—	2	1	no	—
171	C₂×Dic₁₉	—	4	1	no	—
172	C₂×Dic₁₉	—	4	1	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	C₄×D₁₉	—	4	2	no	—
178	C₄×D₁₉	—	4	2	no	—
179	C₄×D₁₉	—	4	1	no	—
180	C₄×D₁₉	—	4	1	no	—
181	C₄×D₁₉	—	4	1	no	—
182	C₄×D₁₉	—	4	1	no	—
183	C₄×D₁₉	—	4	1	no	—
184	C₄×D₁₉	—	4	1	no	—
185	C₄×D₁₉	—	4	1	no	—
186	C₄×D₁₉	—	4	1	no	—
187	C₈×C₁₉	—	4	2	no	—
188	C₈×C₁₉	—	8	1	no	—
189	C₁₉⋊C₈	—	4	2	no	—
190	C₁₉⋊C₈	—	8	1	no	—
191	#2283	—	19	1	no	—
192	#1797	—	19	1	no	—
193	C₄×C₂²⋊C₈	—	19	1	no	—
194	#1279	—	19	1	no	—
195	#1279	—	19	1	no	—
196	#1279	—	19	1	no	—
197	#1279	D₁₉	1	1	yes	characteristic, complemented
198	C₂²×C₁₉	#381	1	1	yes	characteristic
199	C₂²×C₁₉	#408	1	1	yes	characteristic
200	C₂²×C₁₉	#408	1	1	yes	characteristic
201	C₂²×C₁₉	#416	1	1	yes	characteristic
202	C₂²×C₁₉	#417	1	1	yes	characteristic
203	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
204	C₂²×C₁₉	#421	1	1	yes	characteristic
205	C₂×D₁₉	—	2	2	no	—
206	C₂×D₁₉	—	2	2	no	—
207	C₂×D₁₉	—	2	2	no	—
208	C₂×D₁₉	—	4	1	no	—
209	C₂×D₁₉	—	4	1	no	—
210	C₂×D₁₉	—	4	1	no	—
211	C₂×D₁₉	—	4	1	no	—
212	C₄×C₁₉	—	2	1	no	—
213	C₄×C₁₉	—	2	1	no	—
214	C₄×C₁₉	—	8	1	no	—
215	C₄×C₁₉	—	8	1	no	—
216	C₄×C₁₉	#433	1	1	yes	characteristic
217	C₄×C₁₉	#433	1	1	yes	characteristic
218	C₄×C₁₉	#433	1	1	yes	characteristic
219	C₄×C₁₉	#433	1	1	yes	characteristic
220	C₄×C₁₉	#482	1	1	yes	characteristic
221	C₄×C₁₉	#482	1	1	yes	characteristic
222	C₄×C₁₉	#485	1	1	yes	characteristic
223	C₄×C₁₉	#485	1	1	yes	characteristic
224	Dic₁₉	—	4	1	no	—
225	Dic₁₉	—	4	1	no	—
226	Dic₁₉	—	4	1	no	—
227	Dic₁₉	—	8	1	no	—
228	Dic₁₉	—	8	1	no	—
229	C₂²×C₄²	—	19	1	no	—
230	C₂×C₄⋊C₈	—	19	1	no	—
231	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
232	C₂×C₂²⋊C₈	—	38	1	no	—
233	C₂×C₂²⋊C₈	—	38	1	no	—
234	C₂×C₄×C₈	—	19	1	no	—
235	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
236	#383	—	38	1	no	—
237	#382	—	19	1	no	—
238	#382	—	19	1	no	—
239	#381	—	38	1	no	—
240	#380	—	19	1	no	—
241	#380	—	19	1	no	—
242	C₄×C₄⋊C₄	—	19	1	no	—
243	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
244	C₄×C₂²⋊C₄	—	38	1	no	—
245	#376	—	38	1	no	—
246	#336	—	38	1	no	—
247	#336	—	38	1	no	—
248	C₂×C₁₉	#1482	1	1	yes	characteristic
249	C₂×C₁₉	#1483	1	1	yes	characteristic
250	C₂×C₁₉	#1494	1	1	yes	characteristic
251	C₂×C₁₉	#1495	1	1	yes	characteristic
252	C₂×C₁₉	#1818	1	1	yes	characteristic
253	C₂×C₁₉	#1825	1	1	yes	characteristic
254	C₂×C₁₉	#1826	1	1	yes	characteristic
255	D₁₉	—	4	2	no	—
256	C₂³×C₄	—	19	1	no	—
257	C₂³×C₄	—	19	1	no	—
258	C₂³×C₄	—	19	1	no	—
259	C₂²×C₈	—	2	1	no	—
260	C₂²×C₈	—	2	1	no	—
261	C₂²×C₈	—	38	1	no	—
262	C₂²×C₈	—	38	1	no	—
263	C₂×C₄⋊C₄	—	19	1	no	—
264	C₂×C₄⋊C₄	—	19	1	no	—
265	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
266	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	—	38	1	no	—
268	C₂×C₂²⋊C₄	—	38	1	no	—
269	C₂×C₄²	—	2	1	no	—
270	C₂×C₄²	—	19	1	no	—
271	C₂×C₄²	—	19	1	no	—
272	C₂×C₄²	—	19	1	no	—
273	C₂×C₄²	—	38	1	no	—
274	C₂×C₄²	—	38	1	no	—
275	C₂×C₄²	—	38	1	no	—
276	C₂×C₄²	—	38	1	no	—
277	C₂×C₄²	—	38	1	no	—
278	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
279	C₄⋊C₈	—	2	1	no	—
280	C₄⋊C₈	—	2	1	no	—
281	C₄⋊C₈	—	38	1	no	—
282	C₄⋊C₈	—	38	1	no	—
283	C₂²⋊C₈	—	38	4	no	—
284	C₂²⋊C₈	—	76	2	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	38	1	no	—
288	C₄×C₈	—	38	1	no	—
289	#95	—	2	1	no	—
290	#95	—	38	1	no	—
291	#95	—	38	1	no	—
292	#95	—	38	1	no	—
293	#95	—	38	1	no	—
294	#95	—	38	1	no	—
295	#95	—	38	1	no	—
296	#95	—	38	1	no	—
297	C₁₉	#8711	1	1	yes	characteristic, complemented, Sylow
298	C₂⁴	—	19	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	19	1	no	—
302	C₂²×C₄	—	19	1	no	—
303	C₂²×C₄	—	19	1	no	—
304	C₂²×C₄	—	38	2	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	—	38	1	no	—
307	C₂²×C₄	—	38	1	no	—
308	C₂²×C₄	—	38	1	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	—	38	1	no	—
312	C₂²×C₄	—	38	1	no	—
313	C₂²×C₄	—	38	1	no	—
314	C₂²×C₄	—	38	1	no	—
315	C₂²×C₄	—	38	1	no	—
316	C₂²×C₄	—	38	1	no	—
317	C₂²×C₄	—	38	1	no	—
318	C₂²×C₄	—	38	1	no	—
319	C₂²×C₄	—	38	1	no	—
320	C₂²×C₄	—	38	1	no	—
321	C₂²×C₄	—	76	1	no	—
322	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
325	C₂×C₈	—	2	2	no	—
326	C₂×C₈	—	4	1	no	—
327	C₂×C₈	—	4	1	no	—
328	C₂×C₈	—	4	1	no	—
329	C₂×C₈	—	4	1	no	—
330	C₂×C₈	—	4	1	no	—
331	C₂×C₈	—	38	2	no	—
332	C₂×C₈	—	76	1	no	—
333	C₂×C₈	—	76	1	no	—
334	C₂×C₈	—	76	1	no	—
335	C₂×C₈	—	76	1	no	—
336	C₂×C₈	—	76	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	38	1	no	—
342	C₄⋊C₄	—	38	1	no	—
343	C₄⋊C₄	—	38	1	no	—
344	C₄⋊C₄	—	38	1	no	—
345	C₂²⋊C₄	—	76	2	no	—
346	C₂²⋊C₄	—	76	2	no	—
347	C₄²	—	4	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	38	1	no	—
350	C₄²	—	38	1	no	—
351	C₄²	—	38	1	no	—
352	C₄²	—	38	1	no	—
353	C₄²	—	38	1	no	—
354	C₄²	—	38	1	no	—
355	C₄²	—	76	1	no	—
356	C₄²	—	76	1	no	—
357	C₄²	#64541	1	1	yes	characteristic
358	C₄²	#64541	1	1	yes	characteristic
359	C₄²	#64543	1	1	yes	characteristic
360	C₄²	#64545	1	1	yes	characteristic
361	C₂³	—	19	2	no	—
362	C₂³	—	38	1	no	—
363	C₂³	—	38	1	no	—
364	C₂³	—	38	1	no	—
365	C₂³	—	38	1	no	—
366	C₂³	—	38	1	no	—
367	C₂³	—	38	1	no	—
368	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	1	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	38	1	no	—
382	C₂×C₄	—	38	1	no	—
383	C₂×C₄	—	38	1	no	—
384	C₂×C₄	—	38	1	no	—
385	C₂×C₄	—	38	1	no	—
386	C₂×C₄	—	76	2	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	1	no	—
389	C₂×C₄	—	76	1	no	—
390	C₂×C₄	—	76	1	no	—
391	C₂×C₄	—	76	1	no	—
392	C₂×C₄	—	76	1	no	—
393	C₂×C₄	—	76	1	no	—
394	C₂×C₄	—	76	1	no	—
395	C₂×C₄	—	76	1	no	—
396	C₂×C₄	—	76	1	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	#10597318	1	1	yes	characteristic
403	C₂×C₄	#10597329	1	1	yes	characteristic
404	C₂×C₄	#10597329	1	1	yes	characteristic
405	C₂×C₄	#10597338	1	1	yes	characteristic
406	C₂×C₄	#10597340	1	1	yes	characteristic
407	C₂×C₄	#10597340	1	1	yes	characteristic
408	C₂×C₄	#10597347	1	1	yes	characteristic
409	C₂×C₄	#10597347	1	1	yes	characteristic
410	C₂×C₄	#10597353	1	1	yes	characteristic
411	C₂×C₄	#10597353	1	1	yes	characteristic
412	C₂×C₄	#10597358	1	1	yes	characteristic
413	C₂×C₄	#10597360	1	1	yes	characteristic
414	C₂×C₄	#10597362	1	1	yes	characteristic
415	C₂×C₄	#10597364	1	1	yes	characteristic
416	C₈	—	4	2	no	—
417	C₈	—	8	1	no	—
418	C₈	—	76	2	no	—
419	C₈	—	152	1	no	—
420	C₂²	—	38	2	no	—
421	C₂²	—	38	2	no	—
422	C₂²	—	38	2	no	—
423	C₂²	—	76	1	no	—
424	C₂²	—	76	1	no	—
425	C₂²	—	76	1	no	—
426	C₂²	—	76	1	no	—
427	C₂²	#11926406	1	1	yes	characteristic
428	C₂²	#11926509	1	1	yes	characteristic
429	C₂²	#11926509	1	1	yes	characteristic
430	C₂²	#11926537	1	1	yes	characteristic
431	C₂²	#11926544	1	1	yes	characteristic
432	C₂²	#104×D₁₉	1	1	yes	characteristic
433	C₂²	#11926559	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	1	no	—
438	C₄	—	76	1	no	—
439	C₄	—	76	1	no	—
440	C₄	—	76	1	no	—
441	C₄	—	152	1	no	—
442	C₄	—	152	1	no	—
443	C₄	#11926603	1	1	yes	characteristic
444	C₄	#11926604	1	1	yes	characteristic
445	C₄	#11926604	1	1	yes	characteristic
446	C₄	#11926606	1	1	yes	characteristic
447	C₄	#11926866	1	1	yes	characteristic
448	C₄	#11926870	1	1	yes	characteristic
449	C₄	#11926883	1	1	yes	characteristic
450	C₄	#11926887	1	1	yes	characteristic
451	C₂	—	76	2	no	—
452	C₂	#14562040	1	1	yes	characteristic
453	C₂	#14562047	1	1	yes	characteristic
454	C₂	#14562092	1	1	yes	characteristic
455	C₂	#14562099	1	1	yes	characteristic
456	C₂	#14563705	1	1	yes	characteristic
457	C₂	#14563728	1	1	yes	characteristic
458	C₂	#14563733	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1279	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂³×D₁₉	C₂²⋊C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8711
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #14561476	C₂	semidirect
5. #14561475	C₂	semidirect
6. #14561474	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
197. #1279	D₁₉	semidirect
297. C₁₉	#8711	semidirect

Maximal subgroups

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

subgroup	index
#14566031	2
#14563612	2
C₄×(C₂×D₁₉)⋊C₈	2
#14561476	2
#14561475	2
#14561474	2
C₁₉×#1279	2
#8711	19