Subgroups — #18075241

Order 4864.

568 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566096	C₂	1	1	yes	maximal, characteristic
2	#14563786	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×Dic₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926273	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926271	C₂	1	1	yes	maximal, characteristic
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₇₆	C₂²	1	1	yes	characteristic
9	C₂×#10597318	—	2	1	no	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₁₉⋊C₈	—	2	1	no	—
12	C₂×Dic₁₉⋊C₈	—	2	1	no	—
13	C₂×Dic₁₉⋊C₈	—	2	1	no	—
14	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
15	#11926445	C₄	1	1	yes	characteristic
16	#11926445	C₄	1	1	yes	characteristic
17	#11926440	C₄	1	1	yes	characteristic
18	#11926440	C₄	1	1	yes	characteristic
19	#11926433	—	2	1	no	—
20	#11926433	—	2	1	no	—
21	C₄×(C₂×D₁₉)⋊C₄	—	2	1	no	—
22	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
23	#11926298	—	2	1	no	—
24	#11926273	—	2	2	no	—
25	#11926271	—	2	2	no	—
26	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×D₇₆	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₉	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₂²×C₈×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₉	—	2	1	no	—
36	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
37	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
38	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
39	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
40	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
41	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
43	C₂×Dic₁₉⋊C₄	—	2	1	no	—
44	C₂×Dic₁₉⋊C₄	—	2	1	no	—
45	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₉	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
51	C₂²×C₁₉⋊C₈	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₄×D₇₆	—	2	1	no	—
54	C₄×D₇₆	—	2	1	no	—
55	C₄×D₇₆	D₄	1	2	yes	—
56	C₄×D₇₆	Q₈	1	2	yes	—
57	#10597318	—	4	2	no	—
58	#10597318	—	4	2	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	—	2	1	no	—
61	C₄×C₈×C₁₉	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₁₉×#95	—	2	1	no	—
64	C₁₉⋊#95	—	2	1	no	—
65	C₁₉⋊#95	—	2	1	no	—
66	Dic₁₉⋊C₈	—	2	4	no	—
67	Dic₁₉⋊C₈	—	4	2	no	—
68	Dic₁₉⋊C₈	—	4	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₂³×D₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	2	1	no	—
76	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₁₉	—	2	1	no	—
80	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×Dic₁₉	C₂²⋊C₄	1	1	yes	characteristic
84	C₂×D₇₆	—	2	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	—	2	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	—	2	1	no	—
89	C₂×D₇₆	C₄⋊C₄	1	2	yes	—
90	C₂×C₄×D₁₉	—	2	2	no	—
91	C₂×C₄×D₁₉	—	2	2	no	—
92	C₂×C₄×D₁₉	—	4	1	no	—
93	C₂×C₄×D₁₉	—	4	1	no	—
94	C₂×C₄×D₁₉	—	4	1	no	—
95	C₂×C₄×D₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	2	2	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	C₂×C₈×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	2	1	no	—
103	C₄⋊C₄×C₁₉	—	2	1	no	—
104	C₄⋊C₄×C₁₉	—	2	1	no	—
105	C₄⋊C₄×C₁₉	—	2	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₁₉	C₂×Q₈	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	2	no	—
115	(C₂×D₁₉)⋊C₄	—	4	2	no	—
116	(C₂×D₁₉)⋊C₄	—	4	2	no	—
117	(C₂×D₁₉)⋊C₄	—	4	2	no	—
118	C₄⋊Dic₁₉	—	2	1	no	—
119	C₄⋊Dic₁₉	C₄⋊C₄	1	2	yes	—
120	Dic₁₉⋊C₄	—	4	2	no	—
121	Dic₁₉⋊C₄	—	4	2	no	—
122	C₄×Dic₁₉	—	2	1	no	—
123	C₄×Dic₁₉	—	2	1	no	—
124	C₄×Dic₁₉	—	2	1	no	—
125	C₄×Dic₁₉	—	2	1	no	—
126	C₄×Dic₁₉	—	2	1	no	—
127	C₄×Dic₁₉	—	2	1	no	—
128	C₄×Dic₁₉	—	2	2	no	—
129	C₄×Dic₁₉	—	4	1	no	—
130	C₄×Dic₁₉	D₈	1	2	yes	—
131	C₄×Dic₁₉	SD₁₆	1	2	yes	—
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	C₂×C₁₉⋊C₈	—	4	1	no	—
138	#8567	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
140	C₂²×D₁₉	—	2	2	no	—
141	C₂²×D₁₉	—	4	1	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	C₂²×D₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	4	1	no	—
150	C₂×C₄×C₁₉	—	4	1	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	1	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#131	1	1	yes	characteristic
165	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
169	C₂×Dic₁₉	—	2	1	no	—
170	C₂×Dic₁₉	—	2	1	no	—
171	C₂×Dic₁₉	—	2	1	no	—
172	C₂×Dic₁₉	—	2	1	no	—
173	C₂×Dic₁₉	—	2	1	no	—
174	C₂×Dic₁₉	—	2	1	no	—
175	C₂×Dic₁₉	—	2	2	no	—
176	C₂×Dic₁₉	—	2	1	no	—
177	C₂×Dic₁₉	—	2	1	no	—
178	C₂×Dic₁₉	—	2	1	no	—
179	C₂×Dic₁₉	—	4	1	no	—
180	C₂×Dic₁₉	—	4	1	no	—
181	C₂×Dic₁₉	#102	1	2	yes	—
182	C₂×Dic₁₉	#102	1	2	yes	—
183	C₂×Dic₁₉	#104	1	2	yes	—
184	D₇₆	—	2	2	no	—
185	D₇₆	—	2	2	no	—
186	D₇₆	—	4	1	no	—
187	D₇₆	—	4	1	no	—
188	C₄×D₁₉	—	4	2	no	—
189	C₄×D₁₉	—	4	2	no	—
190	C₄×D₁₉	—	4	2	no	—
191	C₄×D₁₉	—	4	2	no	—
192	C₈×C₁₉	—	4	2	no	—
193	C₈×C₁₉	—	8	1	no	—
194	C₁₉⋊C₈	—	4	2	no	—
195	C₁₉⋊C₈	—	8	1	no	—
196	#2293	—	19	1	no	—
197	#1842	—	19	1	no	—
198	C₄×C₄⋊C₈	—	19	1	no	—
199	C₂×D₄⋊C₈	—	19	1	no	—
200	C₂×D₄⋊C₈	—	19	1	no	—
201	#1279	—	19	1	no	—
202	#1279	D₁₉	1	1	yes	characteristic, complemented
203	C₂²×C₁₉	#380	1	1	yes	characteristic
204	C₂²×C₁₉	#408	1	1	yes	characteristic
205	C₂²×C₁₉	#408	1	1	yes	characteristic
206	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
207	C₂²×C₁₉	#417	1	1	yes	characteristic
208	C₂²×C₁₉	C₂×#104	1	1	yes	characteristic
209	C₂²×C₁₉	#421	1	1	yes	characteristic
210	C₂×D₁₉	—	4	2	no	—
211	C₂×D₁₉	—	4	2	no	—
212	C₂×D₁₉	—	4	2	no	—
213	C₂×D₁₉	—	8	1	no	—
214	C₂×D₁₉	—	8	1	no	—
215	C₂×D₁₉	—	8	1	no	—
216	C₂×D₁₉	—	8	1	no	—
217	C₄×C₁₉	—	2	1	no	—
218	C₄×C₁₉	—	2	1	no	—
219	C₄×C₁₉	—	8	1	no	—
220	C₄×C₁₉	—	8	1	no	—
221	C₄×C₁₉	#424	1	1	yes	characteristic
222	C₄×C₁₉	#424	1	1	yes	characteristic
223	C₄×C₁₉	#433	1	1	yes	characteristic
224	C₄×C₁₉	#433	1	1	yes	characteristic
225	C₄×C₁₉	#459	1	1	yes	characteristic
226	C₄×C₁₉	#461	1	1	yes	characteristic
227	C₄×C₁₉	#474	1	1	yes	characteristic
228	C₄×C₁₉	#476	1	1	yes	characteristic
229	Dic₁₉	—	2	2	no	—
230	Dic₁₉	—	2	2	no	—
231	Dic₁₉	—	2	2	no	—
232	Dic₁₉	—	4	2	no	—
233	Dic₁₉	—	4	1	no	—
234	C₂×C₄×D₄	—	19	1	no	—
235	C₂×#117	—	38	1	no	—
236	C₂×C₄⋊C₈	—	19	1	no	—
237	C₂×C₄⋊C₈	—	38	1	no	—
238	C₂×C₄⋊C₈	—	38	1	no	—
239	C₂×C₄⋊C₈	—	38	1	no	—
240	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
241	C₂×C₄×C₈	—	19	1	no	—
242	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
243	#390	—	19	1	no	—
244	#390	—	19	1	no	—
245	#389	—	19	1	no	—
246	#389	—	19	1	no	—
247	#388	—	38	1	no	—
248	#388	—	38	1	no	—
249	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
250	C₄×C₂²⋊C₄	—	38	1	no	—
251	C₄³	—	19	1	no	—
252	#336	—	38	1	no	—
253	D₄⋊C₈	—	38	2	no	—
254	D₄⋊C₈	—	38	2	no	—
255	C₂×C₁₉	#1480	1	1	yes	characteristic
256	C₂×C₁₉	#1483	1	1	yes	characteristic
257	C₂×C₁₉	#1492	1	1	yes	characteristic
258	C₂×C₁₉	#1495	1	1	yes	characteristic
259	C₂×C₁₉	#1798	1	1	yes	characteristic
260	C₂×C₁₉	#1802	1	1	yes	characteristic
261	C₂×C₁₉	#1806	1	1	yes	characteristic
262	D₁₉	—	8	2	no	—
263	C₂²×D₄	—	19	1	no	—
264	C₂³×C₄	—	38	1	no	—
265	C₂²×C₈	—	2	1	no	—
266	C₂²×C₈	—	2	1	no	—
267	C₂²×C₈	—	38	1	no	—
268	C₂²×C₈	—	38	1	no	—
269	C₄×D₄	—	19	2	no	—
270	C₄×D₄	—	19	2	no	—
271	C₄×D₄	—	38	1	no	—
272	C₄×D₄	—	38	1	no	—
273	#117	—	76	2	no	—
274	#117	—	76	2	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	C₄×D₁₉	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	—	38	1	no	—
281	C₂×C₂²⋊C₄	—	38	1	no	—
282	C₂×C₂²⋊C₄	—	38	1	no	—
283	C₂×C₂²⋊C₄	—	38	1	no	—
284	C₂×C₂²⋊C₄	—	38	1	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	19	1	no	—
287	C₂×C₄²	—	19	1	no	—
288	C₂×C₄²	—	19	1	no	—
289	C₂×C₄²	—	19	1	no	—
290	C₂×C₄²	—	19	1	no	—
291	C₂×C₄²	—	19	1	no	—
292	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	2	1	no	—
295	C₄⋊C₈	—	38	4	no	—
296	C₄⋊C₈	—	38	1	no	—
297	C₄⋊C₈	—	38	1	no	—
298	C₄⋊C₈	—	76	2	no	—
299	C₄⋊C₈	—	76	2	no	—
300	C₄×C₈	—	2	1	no	—
301	C₄×C₈	—	2	1	no	—
302	C₄×C₈	—	38	1	no	—
303	C₄×C₈	—	38	1	no	—
304	#95	—	2	1	no	—
305	#95	—	38	1	no	—
306	#95	—	38	1	no	—
307	C₁₉	#8567	1	1	yes	characteristic, complemented, Sylow
308	C₂⁴	—	38	1	no	—
309	C₂×D₄	—	19	2	no	—
310	C₂×D₄	—	38	1	no	—
311	C₂×D₄	—	38	1	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	—	19	1	no	—
318	C₂²×C₄	—	19	1	no	—
319	C₂²×C₄	—	19	1	no	—
320	C₂²×C₄	—	19	1	no	—
321	C₂²×C₄	—	38	1	no	—
322	C₂²×C₄	—	38	2	no	—
323	C₂²×C₄	—	38	2	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	C₂×C₄×D₁₉	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	4	1	no	—
333	C₂×C₈	—	4	1	no	—
334	C₂×C₈	—	4	1	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	4	1	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	C₂×C₈	—	76	1	no	—
343	C₄⋊C₄	—	2	1	no	—
344	C₄⋊C₄	—	2	1	no	—
345	C₄⋊C₄	—	2	1	no	—
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	19	2	no	—
348	C₄⋊C₄	—	38	1	no	—
349	C₄⋊C₄	—	76	2	no	—
350	C₄⋊C₄	—	76	2	no	—
351	C₂²⋊C₄	—	38	2	no	—
352	C₂²⋊C₄	—	38	2	no	—
353	C₂²⋊C₄	—	76	2	no	—
354	C₂²⋊C₄	—	76	2	no	—
355	C₂²⋊C₄	—	76	2	no	—
356	C₂²⋊C₄	—	76	2	no	—
357	C₄²	—	4	1	no	—
358	C₄²	—	4	1	no	—
359	C₄²	—	19	2	no	—
360	C₄²	—	19	2	no	—
361	C₄²	—	38	2	no	—
362	C₄²	—	38	1	no	—
363	C₄²	—	38	1	no	—
364	C₄²	—	38	1	no	—
365	C₄²	—	38	1	no	—
366	C₄²	—	38	1	no	—
367	C₄²	—	38	1	no	—
368	C₄²	—	76	1	no	—
369	C₄²	#64541	1	1	yes	characteristic
370	C₄²	#64541	1	1	yes	characteristic
371	C₄²	D₄×D₁₉	1	1	yes	characteristic
372	C₄²	Q₈×D₁₉	1	1	yes	characteristic
373	C₂³	—	38	2	no	—
374	C₂³	—	76	1	no	—
375	C₂³	—	76	1	no	—
376	C₂³	—	76	1	no	—
377	C₂³	—	76	1	no	—
378	C₂³	—	76	1	no	—
379	C₂³	—	76	1	no	—
380	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
381	D₄	—	38	2	no	—
382	D₄	—	38	2	no	—
383	D₄	—	76	1	no	—
384	D₄	—	76	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	4	1	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	19	2	no	—
394	C₂×C₄	—	19	2	no	—
395	C₂×C₄	—	19	2	no	—
396	C₂×C₄	—	38	1	no	—
397	C₂×C₄	—	38	1	no	—
398	C₂×C₄	—	38	1	no	—
399	C₂×C₄	—	38	1	no	—
400	C₂×C₄	—	38	1	no	—
401	C₂×C₄	—	38	1	no	—
402	C₂×C₄	—	38	1	no	—
403	C₂×C₄	—	38	1	no	—
404	C₂×C₄	—	38	2	no	—
405	C₂×C₄	—	38	1	no	—
406	C₂×C₄	—	76	1	no	—
407	C₂×C₄	—	76	1	no	—
408	C₂×C₄	—	76	2	no	—
409	C₂×C₄	—	76	2	no	—
410	C₂×C₄	—	76	2	no	—
411	C₂×C₄	—	76	2	no	—
412	C₂×C₄	#10597318	1	1	yes	characteristic
413	C₂×C₄	#10597330	1	1	yes	characteristic
414	C₂×C₄	#10597330	1	1	yes	characteristic
415	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
416	C₂×C₄	#10597342	1	1	yes	characteristic
417	C₂×C₄	#10597342	1	1	yes	characteristic
418	C₂×C₄	#10597347	1	1	yes	characteristic
419	C₂×C₄	#10597347	1	1	yes	characteristic
420	C₂×C₄	#10597353	1	1	yes	characteristic
421	C₂×C₄	#10597353	1	1	yes	characteristic
422	C₂×C₄	D₈×D₁₉	1	1	yes	characteristic
423	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
424	C₂×C₄	#10597360	1	1	yes	characteristic
425	C₂×C₄	#10597364	1	1	yes	characteristic
426	C₈	—	4	2	no	—
427	C₈	—	8	1	no	—
428	C₈	—	76	2	no	—
429	C₈	—	152	1	no	—
430	C₂²	—	76	2	no	—
431	C₂²	—	76	2	no	—
432	C₂²	—	76	2	no	—
433	C₂²	—	152	1	no	—
434	C₂²	—	152	1	no	—
435	C₂²	—	152	1	no	—
436	C₂²	—	152	1	no	—
437	C₂²	#11926403	1	1	yes	characteristic
438	C₂²	#11926509	1	1	yes	characteristic
439	C₂²	#11926509	1	1	yes	characteristic
440	C₂²	#102×D₁₉	1	1	yes	characteristic
441	C₂²	#11926544	1	1	yes	characteristic
442	C₂²	#104×D₁₉	1	1	yes	characteristic
443	C₂²	#11926559	1	1	yes	characteristic
444	C₄	—	2	1	no	—
445	C₄	—	2	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	38	2	no	—
449	C₄	—	38	2	no	—
450	C₄	—	38	2	no	—
451	C₄	—	76	2	no	—
452	C₄	—	76	1	no	—
453	C₄	#11926569	1	1	yes	characteristic
454	C₄	#11926569	1	1	yes	characteristic
455	C₄	#11926603	1	1	yes	characteristic
456	C₄	#11926606	1	1	yes	characteristic
457	C₄	#11926738	1	1	yes	characteristic
458	C₄	#11926748	1	1	yes	characteristic
459	C₄	#11926823	1	1	yes	characteristic
460	C₄	#11926833	1	1	yes	characteristic
461	C₂	—	152	2	no	—
462	C₂	#14562032	1	1	yes	characteristic
463	C₂	#14562047	1	1	yes	characteristic
464	C₂	#14562084	1	1	yes	characteristic
465	C₂	#14562099	1	1	yes	characteristic
466	C₂	#14563618	1	1	yes	characteristic
467	C₂	#14563634	1	1	yes	characteristic
468	C₂	#14563654	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	C₂²×D₇₆	C₂×C₄
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1279	D₁₉
hypocenter	C₁₉	#8567
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
2. #14563786	C₂	semidirect
3. C₄×Dic₁₉⋊C₈	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#1279	C₂	semidirect
202. #1279	D₁₉	semidirect
307. C₁₉	#8567	semidirect

Maximal subgroups

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

subgroup	index
#14566096	2
#14563786	2
C₄×Dic₁₉⋊C₈	2
C₂×#11926273	2
C₂×#11926271	2
#14561476	2
C₁₉×#1279	2
#8567	19