Subgroups — #18078244

Order 4864.

752 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14571980	C₂	1	1	yes	maximal, characteristic
2	#14563615	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11926287	C₂	1	2	yes	maximal, complemented
4	#14561519	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₉×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597320	C₂²	1	1	yes	characteristic
7	C₂×#10597376	—	2	1	no	—
8	C₂×#10597376	—	2	1	no	—
9	C₂×#10597376	C₄	1	2	yes	—
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
12	#11926446	—	2	1	no	—
13	#11926446	—	2	1	no	—
14	#11926446	C₄	1	2	yes	—
15	#11926414	C₂²	1	1	yes	characteristic
16	#11926299	—	2	1	no	—
17	#11926287	—	2	4	no	—
18	C₂²×M₁₆×C₁₉	—	2	1	no	—
19	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
20	C₁₉×#423	—	2	4	no	—
21	C₂×C₁₉×C₄⋊C₈	—	2	1	no	—
22	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
23	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
24	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
25	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₉	—	2	2	no	—
27	C₂²×D₇₆	—	2	1	no	—
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	C₂×C₄	1	2	yes	—
30	C₂×M₁₆×C₁₉	—	2	4	no	—
31	C₂×M₁₆×C₁₉	—	4	2	no	—
32	C₂×M₁₆×C₁₉	—	4	2	no	—
33	C₂²×C₈×C₁₉	—	2	2	no	—
34	C₂×C₄²×C₁₉	—	2	2	no	—
35	C₂×C₄²×C₁₉	—	2	2	no	—
36	C₂×C₄²×C₁₉	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
40	#10597376	—	4	4	no	—
41	#10597376	—	4	2	no	—
42	#10597376	—	4	2	no	—
43	#10597376	—	4	4	no	—
44	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
45	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
46	C₂×(C₂×D₁₉)⋊C₄	—	2	2	no	—
47	C₂×C₄⋊Dic₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
50	C₂²×C₁₉⋊C₈	—	2	2	no	—
51	#10597320	—	2	2	no	—
52	#10597320	—	2	2	no	—
53	C₁₉×C₄⋊C₈	—	2	4	no	—
54	C₁₉×C₄⋊C₈	—	2	2	no	—
55	C₁₉×C₄⋊C₈	D₄	1	4	yes	complemented
56	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
60	C₂³×D₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	1	no	—
62	C₂²×C₄×C₁₉	—	2	1	no	—
63	C₂²×C₄×C₁₉	—	2	1	no	—
64	C₂²×C₄×C₁₉	—	2	1	no	—
65	C₂²×C₄×C₁₉	—	2	2	no	—
66	C₂²×C₄×C₁₉	—	2	2	no	—
67	C₂²×C₄×C₁₉	—	2	2	no	—
68	C₂²×C₄×C₁₉	—	2	2	no	—
69	C₂²×C₄×C₁₉	—	2	1	no	—
70	C₂²×C₄×C₁₉	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	4	1	no	—
72	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	D₈	1	2	yes	—
76	C₂²×C₄×C₁₉	SD₁₆	1	2	yes	—
77	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₂²⋊D₁₉	—	4	4	no	—
81	C₂×C₂²⋊D₁₉	—	4	4	no	—
82	C₂×C₂²⋊D₁₉	—	4	4	no	—
83	C₂²×Dic₁₉	—	2	2	no	—
84	C₂×D₇₆	—	2	4	no	—
85	C₂×D₇₆	—	4	2	no	—
86	C₂×D₇₆	—	4	2	no	—
87	C₂×D₇₆	—	4	1	no	—
88	C₂×D₇₆	—	4	2	no	—
89	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	2	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	M₁₆×C₁₉	—	4	8	no	—
98	C₂×C₈×C₁₉	—	2	4	no	—
99	C₂×C₈×C₁₉	—	4	2	no	—
100	C₂×C₈×C₁₉	—	4	2	no	—
101	C₄²×C₁₉	—	2	2	no	—
102	C₄²×C₁₉	—	2	1	no	—
103	C₄²×C₁₉	—	2	2	no	—
104	C₄²×C₁₉	—	2	1	no	—
105	C₄²×C₁₉	C₂×D₄	1	2	yes	—
106	C₄²×C₁₉	#41	1	2	yes	—
107	(C₂×D₁₉)⋊C₄	—	4	4	no	—
108	(C₂×D₁₉)⋊C₄	—	4	4	no	—
109	(C₂×D₁₉)⋊C₄	—	4	4	no	—
110	C₄⋊Dic₁₉	—	4	1	no	—
111	C₄⋊Dic₁₉	—	4	1	no	—
112	C₄⋊Dic₁₉	—	4	2	no	—
113	C₄⋊Dic₁₉	—	4	2	no	—
114	C₂×C₁₉⋊C₈	—	4	2	no	—
115	C₂×C₁₉⋊C₈	—	4	2	no	—
116	C₂×C₁₉⋊C₈	—	4	2	no	—
117	#9141	—	19	1	no	maximal, Sylow
118	C₂³×C₁₉	—	2	1	no	—
119	C₂³×C₁₉	—	2	1	no	—
120	C₂³×C₁₉	—	2	1	no	—
121	C₂³×C₁₉	—	2	1	no	—
122	C₂³×C₁₉	—	2	1	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	#102	1	2	yes	—
125	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂²×D₁₉	—	4	2	no	—
127	C₂²×D₁₉	—	4	2	no	—
128	C₂²×D₁₉	—	4	2	no	—
129	C₂²×D₁₉	—	4	2	no	—
130	C₂²×D₁₉	—	4	2	no	—
131	C₂²×D₁₉	—	4	2	no	—
132	C₂²×D₁₉	—	4	2	no	—
133	C₂×C₄×C₁₉	—	2	1	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	2	no	—
140	C₂×C₄×C₁₉	—	2	2	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	2	2	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	4	4	no	—
147	C₂×C₄×C₁₉	—	4	2	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	#100	1	2	yes	—
150	C₂×C₄×C₁₉	#102	1	2	yes	—
151	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#121	1	2	yes	—
154	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×SD₁₆	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	2	yes	—
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
161	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
162	C₂²⋊D₁₉	—	8	8	no	—
163	C₂×Dic₁₉	—	4	2	no	—
164	C₂×Dic₁₉	—	4	2	no	—
165	C₂×Dic₁₉	—	4	2	no	—
166	D₇₆	—	8	4	no	—
167	D₇₆	—	8	1	no	—
168	D₇₆	—	8	1	no	—
169	D₇₆	—	8	2	no	—
170	D₇₆	—	8	2	no	—
171	D₇₆	—	8	1	no	—
172	D₇₆	—	8	1	no	—
173	C₈×C₁₉	—	4	4	no	—
174	C₁₉⋊C₈	—	8	2	no	—
175	C₂×#423	D₁₉	1	1	yes	characteristic, complemented
176	#2856	—	19	1	no	—
177	#1797	—	19	1	no	—
178	C₂×#331	—	19	2	no	—
179	#1296	—	19	2	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	2	no	—
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	#386	1	1	yes	characteristic
188	C₂²×C₁₉	C₂×#100	1	1	yes	characteristic
189	C₂²×C₁₉	#413	1	1	yes	characteristic
190	C₂²×C₁₉	C₂×#102	1	1	yes	characteristic
191	C₂²×C₁₉	#417	1	1	yes	characteristic
192	C₂²×C₁₉	#417	1	1	yes	characteristic
193	C₂²×C₁₉	#418	1	1	yes	characteristic
194	C₂×D₁₉	—	8	2	no	—
195	C₂×D₁₉	—	8	2	no	—
196	C₂×D₁₉	—	8	2	no	—
197	C₂×D₁₉	—	8	2	no	—
198	C₂×D₁₉	—	8	2	no	—
199	C₂×D₁₉	—	8	2	no	—
200	C₂×D₁₉	—	8	2	no	—
201	C₄×C₁₉	—	2	2	no	—
202	C₄×C₁₉	—	2	2	no	—
203	C₄×C₁₉	—	2	2	no	—
204	C₄×C₁₉	—	4	1	no	—
205	C₄×C₁₉	#447	1	1	yes	characteristic
206	C₄×C₁₉	#448	1	1	yes	characteristic
207	C₄×C₁₉	#468	1	2	yes	—
208	C₄×C₁₉	#469	1	2	yes	—
209	C₄×C₁₉	#480	1	1	yes	characteristic
210	C₄×C₁₉	#481	1	1	yes	characteristic
211	Dic₁₉	—	8	2	no	—
212	C₂²×M₁₆	—	2	1	no	—
213	C₂×#127	—	19	1	no	—
214	C₂×#121	—	19	2	no	—
215	C₂×#121	—	38	1	no	—
216	C₂×#121	—	38	1	no	—
217	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
218	#423	—	2	4	no	—
219	C₂×C₄⋊C₈	—	2	1	no	—
220	C₂×C₄⋊C₈	—	19	2	no	—
221	C₂×C₄⋊C₈	C₂×D₁₉	1	2	yes	—
222	C₂×C₂²⋊C₈	—	38	1	no	—
223	#390	—	19	2	no	—
224	#390	—	38	1	no	—
225	#390	—	38	1	no	—
226	#384	—	19	1	no	—
227	#336	—	38	1	no	—
228	#331	—	38	4	no	—
229	C₂×C₁₉	—	4	2	no	—
230	C₂×C₁₉	#1545	1	1	yes	characteristic
231	C₂×C₁₉	#1547	1	1	yes	characteristic
232	C₂×C₁₉	#1557	1	1	yes	characteristic
233	C₂×C₁₉	#1560	1	1	yes	characteristic
234	C₂×C₁₉	#1874	1	1	yes	characteristic
235	C₂×C₁₉	#1895	1	1	yes	characteristic
236	C₂×C₁₉	#1900	1	1	yes	characteristic
237	D₁₉	—	16	2	no	—
238	C₂²×D₄	—	19	2	no	—
239	C₂²×D₄	—	38	2	no	—
240	C₂²×D₄	—	38	1	no	—
241	C₂²×D₄	—	38	1	no	—
242	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
243	C₂³×C₄	D₇₆	1	1	yes	characteristic
244	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂×M₁₆	—	2	4	no	—
246	C₂×M₁₆	—	4	2	no	—
247	C₂×M₁₆	—	4	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	38	2	no	—
250	#127	—	38	2	no	—
251	#127	—	38	2	no	—
252	#121	—	76	4	no	—
253	#121	—	76	2	no	—
254	#121	—	76	2	no	—
255	#121	—	76	4	no	—
256	C₂×C₄⋊C₄	—	19	2	no	—
257	C₂×C₄⋊C₄	—	38	1	no	—
258	C₂×C₄⋊C₄	—	38	1	no	—
259	C₂×C₂²⋊C₄	—	38	2	no	—
260	C₂×C₂²⋊C₄	—	38	2	no	—
261	C₂×C₂²⋊C₄	—	38	2	no	—
262	C₂×C₄²	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₄×D₁₉	1	1	yes	characteristic
265	C₂×C₄²	D₇₆	1	1	yes	characteristic
266	C₂×C₄²	C₂²⋊D₁₉	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
268	C₄⋊C₈	—	2	4	no	—
269	C₄⋊C₈	—	2	2	no	—
270	C₄⋊C₈	—	38	2	no	—
271	C₄⋊C₈	—	38	2	no	—
272	C₄⋊C₈	C₂²⋊D₁₉	1	4	yes	complemented
273	C₂²⋊C₈	—	76	2	no	—
274	C₁₉	#9141	1	1	yes	characteristic, complemented, Sylow
275	C₂⁴	—	38	2	no	—
276	C₂⁴	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
277	C₂×D₄	—	38	4	no	—
278	C₂×D₄	—	76	2	no	—
279	C₂×D₄	—	76	2	no	—
280	C₂×D₄	—	76	4	no	—
281	C₂×D₄	—	76	4	no	—
282	C₂×D₄	—	76	4	no	—
283	C₂×D₄	—	76	2	no	—
284	C₂×D₄	—	76	1	no	—
285	C₂×D₄	—	76	1	no	—
286	C₂×D₄	—	76	1	no	—
287	C₂×D₄	—	76	1	no	—
288	C₂×D₄	—	76	1	no	—
289	C₂×D₄	—	76	2	no	—
290	C₂×D₄	—	76	1	no	—
291	C₂×D₄	—	76	1	no	—
292	C₂×D₄	—	76	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	38	2	no	—
305	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
306	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
307	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
308	C₂²×C₄	#64525	1	2	yes	—
309	C₂²×C₄	#64527	1	2	yes	—
310	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
313	M₁₆	—	4	8	no	—
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	4	2	no	—
316	C₂×C₈	—	4	2	no	—
317	C₂×C₈	—	76	2	no	—
318	C₂×C₈	—	76	2	no	—
319	C₂×C₈	—	76	2	no	—
320	C₄⋊C₄	—	76	2	no	—
321	C₄⋊C₄	—	76	1	no	—
322	C₄⋊C₄	—	76	1	no	—
323	C₄⋊C₄	—	76	2	no	—
324	C₂²⋊C₄	—	76	4	no	—
325	C₂²⋊C₄	—	76	4	no	—
326	C₂²⋊C₄	—	76	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	1	no	—
331	C₄²	#64541	1	2	yes	—
332	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	1	no	—
337	C₂³	—	2	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	76	2	no	—
340	C₂³	—	76	2	no	—
341	C₂³	—	76	2	no	—
342	C₂³	—	76	2	no	—
343	C₂³	—	76	2	no	—
344	C₂³	—	76	2	no	—
345	C₂³	—	76	2	no	—
346	C₂³	#10597266	1	2	yes	—
347	C₂³	C₂×(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
348	D₄	—	152	4	no	—
349	D₄	—	152	8	no	—
350	D₄	—	152	2	no	—
351	D₄	—	152	2	no	—
352	D₄	—	152	1	no	—
353	D₄	—	152	1	no	—
354	D₄	—	152	1	no	—
355	D₄	—	152	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	76	2	no	—
373	C₂×C₄	—	76	2	no	—
374	C₂×C₄	—	76	2	no	—
375	C₂×C₄	#10597266	1	2	yes	—
376	C₂×C₄	#10597280	1	2	yes	—
377	C₂×C₄	#10597354	1	2	yes	—
378	C₂×C₄	#10597354	1	1	yes	characteristic
379	C₂×C₄	#10597355	1	1	yes	characteristic
380	C₂×C₄	C₄×C₂²⋊D₁₉	1	2	yes	—
381	C₂×C₄	#10597375	1	1	yes	characteristic
382	C₂×C₄	#10597376	1	2	yes	—
383	C₂×C₄	C₂×#64525	1	1	yes	characteristic
384	C₂×C₄	#10597378	1	1	yes	characteristic
385	C₂×C₄	C₂×#64527	1	1	yes	characteristic
386	C₂×C₄	#10597388	1	1	yes	characteristic
387	C₂×C₄	#10597399	1	1	yes	characteristic
388	C₈	—	4	4	no	—
389	C₈	—	152	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	—	4	1	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	152	2	no	—
398	C₂²	—	152	2	no	—
399	C₂²	—	152	2	no	—
400	C₂²	—	152	2	no	—
401	C₂²	—	152	2	no	—
402	C₂²	—	152	2	no	—
403	C₂²	—	152	2	no	—
404	C₂²	#11926423	1	1	yes	characteristic
405	C₂²	C₂×#10597280	1	1	yes	characteristic
406	C₂²	#11926526	1	1	yes	characteristic
407	C₂²	C₂×#10597266	1	1	yes	characteristic
408	C₂²	#11926543	1	1	yes	characteristic
409	C₂²	#11926546	1	1	yes	characteristic
410	C₂²	#11926550	1	1	yes	characteristic
411	C₄	—	2	2	no	—
412	C₄	—	2	2	no	—
413	C₄	—	2	2	no	—
414	C₄	—	4	1	no	—
415	C₄	—	152	2	no	—
416	C₄	#11926678	1	1	yes	characteristic
417	C₄	#11926683	1	1	yes	characteristic
418	C₄	#11926790	1	2	yes	—
419	C₄	#11926797	1	2	yes	—
420	C₄	#11926857	1	1	yes	characteristic
421	C₄	#11926862	1	1	yes	characteristic
422	C₂	—	4	2	no	—
423	C₂	—	304	2	no	—
424	C₂	#14562304	1	1	yes	characteristic
425	C₂	#14562313	1	1	yes	characteristic
426	C₂	#14562355	1	1	yes	characteristic
427	C₂	#14562368	1	1	yes	characteristic
428	C₂	#14563952	1	1	yes	characteristic
429	C₂	#14564073	1	1	yes	characteristic
430	C₂	#14564098	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×(C₂×D₁₉)⋊C₄
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×#423	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	#14571980	C₂
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₂×#423	D₁₉
hypocenter	C₁₉	#9141
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#423

Complements

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

N	H ≅ G/N	type
2. #14563615	C₂	semidirect
3. C₂×#11926287	C₂	semidirect
4. #14561519	C₂	semidirect
5. C₂×C₁₉×#423	C₂	semidirect
55. C₁₉×C₄⋊C₈	D₄	semidirect
175. C₂×#423	D₁₉	semidirect
272. C₄⋊C₈	C₂²⋊D₁₉	semidirect
274. C₁₉	#9141	semidirect

Maximal subgroups

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

subgroup	index
#14571980	2
#14563615	2
C₂×#11926287	2
#14561519	2
C₂×C₁₉×#423	2
#9141	19