Subgroups — #18078476

Order 4864.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566545	C₂	1	1	yes	maximal, characteristic, complemented
2	#14562195	C₂	1	1	yes	maximal, characteristic, complemented
3	#14562130	C₂	1	1	yes	maximal, characteristic, complemented
4	#14562026	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561536	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561495	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#3036	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₁₉	—	2	1	no	—
9	#11926597	C₂²	1	1	yes	characteristic
10	#11926597	C₂²	1	1	yes	characteristic
11	#11926443	—	2	1	no	—
12	#11926419	—	2	2	no	—
13	#11926410	C₂²	1	1	yes	characteristic
14	#11926404	—	2	1	no	—
15	C₄×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
16	C₂×C₁₉⋊#95	—	2	1	no	—
17	#11926278	—	2	1	no	—
18	#11926278	—	2	1	no	—
19	#11926278	—	2	2	no	—
20	D₄⋊(C₁₉⋊C₈)	—	2	2	no	—
21	C₂×C₁₉×AGL(1,ℤ/8)	—	2	1	no	—
22	C₁₉×#532	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₁₉×#463	—	2	2	no	—
25	C₁₉×#461	C₄	1	2	yes	complemented
26	C₁₉×#459	C₄	1	2	yes	complemented
27	C₁₉×#423	C₂²	1	1	yes	characteristic
28	C₁₉×#417	—	2	1	no	—
29	C₂×#41×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
31	C₂³×C₄×C₁₉	—	2	1	no	—
32	C₂³×Dic₁₉	—	2	2	no	—
33	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
34	C₁₉×AGL(1,ℤ/8)	—	4	2	no	—
35	C₂×SD₁₆×C₁₉	—	2	2	no	—
36	C₂×D₈×C₁₉	—	2	2	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic, complemented
39	C₁₉×#127	C₂×C₄	1	1	yes	characteristic, complemented
40	C₁₉×#124	—	2	1	no	—
41	C₁₉×#121	—	2	1	no	—
42	C₁₉×#121	—	2	1	no	—
43	C₄×D₄×C₁₉	—	2	1	no	—
44	C₄×D₄×C₁₉	—	2	1	no	—
45	C₄×D₄×C₁₉	—	2	1	no	—
46	C₄×D₄×C₁₉	—	2	1	no	—
47	C₄×D₄×C₁₉	C₂×C₄	1	2	yes	—
48	C₄×D₄×C₁₉	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×C₂²⋊Dic₁₉	—	2	2	no	—
53	D₄×Dic₁₉	—	4	2	no	—
54	D₄×Dic₁₉	—	4	2	no	—
55	C₂×C₄⋊Dic₁₉	—	2	1	no	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	2	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	complemented
61	C₁₉×#103	—	2	2	no	—
62	C₁₉×#102	—	2	2	no	—
63	C₁₉⋊#95	—	2	2	no	—
64	C₁₉⋊#95	—	2	1	no	—
65	C₁₉⋊#95	D₄	1	1	yes	characteristic
66	C₁₉⋊#95	D₄	1	1	yes	characteristic
67	C₁₉⋊#95	D₄	1	2	yes	—
68	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₂²⋊(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	C₄×C₁₉⋊C₈	—	2	1	no	—
74	C₂⁴×C₁₉	—	2	1	no	—
75	#41×C₁₉	—	4	1	no	—
76	#41×C₁₉	—	4	1	no	—
77	#41×C₁₉	—	4	1	no	—
78	#41×C₁₉	—	4	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	2	1	no	—
83	C₂×D₄×C₁₉	—	2	1	no	—
84	C₂×D₄×C₁₉	—	2	1	no	—
85	C₂×D₄×C₁₉	—	2	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
88	C₂×D₄×C₁₉	D₈	1	2	yes	—
89	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
90	C₂²×C₄×C₁₉	—	2	1	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	—	2	2	no	—
93	C₂²×C₄×C₁₉	—	4	1	no	—
94	C₂²×C₄×C₁₉	—	8	2	no	—
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₁₉	—	2	1	no	—
99	C₂²×Dic₁₉	—	2	1	no	—
100	C₂²×Dic₁₉	—	2	2	no	—
101	C₂²×Dic₁₉	—	4	4	no	—
102	C₂²×Dic₁₉	—	4	4	no	—
103	C₂²×Dic₁₉	—	8	2	no	—
104	SD₁₆×C₁₉	—	4	4	no	—
105	D₈×C₁₉	—	4	4	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	1	no	—
112	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	2	yes	—
113	C₂²⋊C₄×C₁₉	—	2	2	no	—
114	C₂²⋊C₄×C₁₉	—	2	2	no	—
115	C₂²⋊C₄×C₁₉	—	4	1	no	—
116	C₂²⋊C₄×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₁₉	#41	1	1	yes	characteristic
120	C₄²×C₁₉	#41	1	1	yes	characteristic
121	C₂²⋊Dic₁₉	—	4	4	no	—
122	C₄⋊Dic₁₉	—	4	2	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄⋊Dic₁₉	—	4	1	no	—
125	C₄⋊Dic₁₉	—	8	2	no	—
126	C₄×Dic₁₉	—	4	1	no	—
127	C₄×Dic₁₉	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	1	no	—
129	C₂×C₁₉⋊C₈	—	4	1	no	—
130	#9179	—	19	1	no	maximal, Sylow
131	C₂³×C₁₉	—	2	2	no	—
132	C₂³×C₁₉	—	2	2	no	—
133	C₂³×C₁₉	—	2	2	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	4	1	no	—
137	C₂³×C₁₉	#120	1	1	yes	characteristic
138	Q₈×C₁₉	—	4	1	no	—
139	Q₈×C₁₉	—	4	1	no	—
140	D₄×C₁₉	—	2	2	no	—
141	D₄×C₁₉	—	2	2	no	—
142	D₄×C₁₉	—	2	2	no	—
143	D₄×C₁₉	—	4	1	no	—
144	D₄×C₁₉	—	4	1	no	—
145	D₄×C₁₉	—	8	1	no	—
146	D₄×C₁₉	—	8	1	no	—
147	D₄×C₁₉	—	8	1	no	—
148	D₄×C₁₉	—	8	1	no	—
149	D₄×C₁₉	#102	1	4	yes	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	4	1	no	—
152	C₂×C₄×C₁₉	—	4	1	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	1	no	—
155	C₂×C₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	8	2	no	—
157	C₂×C₄×C₁₉	—	8	1	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#123	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	2	no	—
170	C₂×Dic₁₉	—	4	1	no	—
171	C₂×Dic₁₉	—	4	1	no	—
172	C₂×Dic₁₉	—	4	1	no	—
173	C₂×Dic₁₉	—	4	1	no	—
174	C₂×Dic₁₉	—	4	2	no	—
175	C₂×Dic₁₉	—	4	2	no	—
176	C₂×Dic₁₉	—	4	1	no	—
177	C₂×Dic₁₉	—	4	2	no	—
178	C₂×Dic₁₉	—	8	8	no	—
179	C₈×C₁₉	—	4	2	no	—
180	C₁₉⋊C₈	—	8	1	no	—
181	C₁₉⋊C₈	—	8	1	no	—
182	#3036	D₁₉	1	1	yes	characteristic
183	#2349	—	19	1	no	—
184	#1517	—	19	1	no	—
185	#1502	—	19	1	no	—
186	#1478	—	19	1	no	—
187	#1303	—	19	1	no	—
188	#1286	—	19	1	no	—
189	C₂²×C₁₉	—	2	1	no	—
190	C₂²×C₁₉	—	2	1	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	—	4	4	no	—
193	C₂²×C₁₉	—	4	4	no	—
194	C₂²×C₁₉	—	4	2	no	—
195	C₂²×C₁₉	—	4	2	no	—
196	C₂²×C₁₉	—	8	1	no	—
197	C₂²×C₁₉	—	8	1	no	—
198	C₂²×C₁₉	—	8	1	no	—
199	C₂²×C₁₉	#386	1	1	yes	characteristic
200	C₂²×C₁₉	#447	1	1	yes	characteristic
201	C₂²×C₁₉	#448	1	1	yes	characteristic
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	2	1	no	—
205	C₄×C₁₉	—	2	1	no	—
206	C₄×C₁₉	—	4	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	C₂×#102	1	1	yes	characteristic
209	C₄×C₁₉	#417	1	1	yes	characteristic
210	C₄×C₁₉	#480	1	1	yes	characteristic
211	C₄×C₁₉	#481	1	1	yes	characteristic
212	Dic₁₉	—	4	2	no	—
213	Dic₁₉	—	8	1	no	—
214	Dic₁₉	—	8	2	no	—
215	C₂×AGL(1,ℤ/8)	—	2	1	no	—
216	#532	C₂×D₁₉	1	1	yes	characteristic
217	C₂×C₄×D₄	—	38	1	no	—
218	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
219	#463	—	2	2	no	—
220	#461	Dic₁₉	1	2	yes	complemented
221	#459	Dic₁₉	1	2	yes	complemented
222	#431	—	19	1	no	—
223	#431	—	19	1	no	—
224	#423	C₂×D₁₉	1	1	yes	characteristic
225	#417	—	2	1	no	—
226	#389	—	38	1	no	—
227	#385	—	38	2	no	—
228	#382	—	19	1	no	—
229	#380	—	38	1	no	—
230	C₄×C₄⋊C₄	—	19	1	no	—
231	C₂×#95	—	38	1	no	—
232	#327	—	38	1	no	—
233	#327	—	38	1	no	—
234	#327	—	38	2	no	—
235	D₄⋊C₈	—	38	2	no	—
236	C₂×C₁₉	—	2	1	no	—
237	C₂×C₁₉	—	2	1	no	—
238	C₂×C₁₉	—	4	4	no	—
239	C₂×C₁₉	—	16	1	no	—
240	C₂×C₁₉	#1874	1	1	yes	characteristic
241	C₂×C₁₉	#1904	1	1	yes	characteristic
242	C₂×C₁₉	#1906	1	1	yes	characteristic
243	C₂×#41	—	2	1	no	—
244	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	—	38	2	no	—
247	AGL(1,ℤ/8)	—	4	2	no	—
248	AGL(1,ℤ/8)	—	4	2	no	—
249	C₂×SD₁₆	—	2	2	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×M₁₆	—	2	1	no	—
252	C₄⋊Q₈	C₂×Dic₁₉	1	1	yes	characteristic, complemented
253	#127	C₂×Dic₁₉	1	1	yes	characteristic, complemented
254	#124	—	2	1	no	—
255	#121	—	2	1	no	—
256	#121	—	2	1	no	—
257	C₄×D₄	—	2	1	no	—
258	C₄×D₄	—	2	1	no	—
259	C₄×D₄	—	2	1	no	—
260	C₄×D₄	—	2	1	no	—
261	C₄×D₄	—	76	2	no	—
262	C₄×D₄	—	76	2	no	—
263	C₄×D₄	C₂×Dic₁₉	1	2	yes	—
264	C₄×D₄	C₂²⋊D₁₉	1	2	yes	—
265	C₂×C₄⋊C₄	—	38	1	no	—
266	C₂×C₄⋊C₄	—	38	1	no	—
267	C₂×C₄⋊C₄	—	38	2	no	—
268	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₂²⋊C₄	—	38	2	no	—
271	C₂×C₄²	—	38	1	no	—
272	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	C₂×Dic₁₉	1	2	yes	complemented
277	#103	—	2	2	no	—
278	#102	—	2	2	no	—
279	C₂²⋊C₈	—	38	1	no	—
280	C₂²⋊C₈	—	38	1	no	—
281	C₄×C₈	—	38	1	no	—
282	C₄×C₈	—	38	1	no	—
283	#95	—	19	1	no	—
284	#95	—	19	1	no	—
285	#95	—	19	2	no	—
286	#95	—	38	2	no	—
287	#95	—	38	1	no	—
288	C₁₉	#9179	1	1	yes	characteristic, complemented, Sylow
289	C₂⁴	—	2	1	no	—
290	#41	—	4	1	no	—
291	#41	—	4	1	no	—
292	#41	—	4	1	no	—
293	#41	—	4	1	no	—
294	C₂×Q₈	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	2	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	#64525	1	2	yes	—
303	C₂×D₄	#64526	1	2	yes	—
304	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	4	1	no	—
309	C₂²×C₄	—	8	2	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	—	38	2	no	—
312	C₂²×C₄	—	38	1	no	—
313	C₂²×C₄	—	76	4	no	—
314	C₂²×C₄	—	76	4	no	—
315	C₂²×C₄	—	152	2	no	—
316	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
317	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
318	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
319	SD₁₆	—	4	4	no	—
320	D₈	—	4	4	no	—
321	M₁₆	—	4	1	no	—
322	M₁₆	—	4	1	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	76	1	no	—
325	C₂×C₈	—	76	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	76	2	no	—
330	C₄⋊C₄	—	76	1	no	—
331	C₄⋊C₄	—	76	1	no	—
332	C₄⋊C₄	—	152	2	no	—
333	C₄⋊C₄	C₂²⋊Dic₁₉	1	2	yes	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₂²⋊C₄	—	76	4	no	—
339	C₄²	—	76	1	no	—
340	C₄²	—	76	1	no	—
341	C₄²	#64543	1	1	yes	characteristic
342	C₄²	#64543	1	1	yes	characteristic
343	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
344	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	#10597383	1	1	yes	characteristic
352	Q₈	—	4	1	no	—
353	Q₈	—	4	1	no	—
354	D₄	—	2	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	1	no	—
358	D₄	—	4	1	no	—
359	D₄	—	8	1	no	—
360	D₄	—	8	1	no	—
361	D₄	—	8	1	no	—
362	D₄	—	8	1	no	—
363	D₄	#10597289	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	8	2	no	—
370	C₂×C₄	—	8	2	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	38	2	no	—
374	C₂×C₄	—	76	1	no	—
375	C₂×C₄	—	76	1	no	—
376	C₂×C₄	—	76	1	no	—
377	C₂×C₄	—	76	1	no	—
378	C₂×C₄	—	76	2	no	—
379	C₂×C₄	—	76	2	no	—
380	C₂×C₄	—	76	1	no	—
381	C₂×C₄	—	76	2	no	—
382	C₂×C₄	—	152	8	no	—
383	C₂×C₄	C₂×#64525	1	1	yes	characteristic
384	C₂×C₄	C₂×#64526	1	1	yes	characteristic
385	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
386	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
387	C₂×C₄	#10597381	1	1	yes	characteristic
388	C₂×C₄	#10597385	1	1	yes	characteristic
389	C₂×C₄	#10597385	1	1	yes	characteristic
390	C₂×C₄	#10597395	1	1	yes	characteristic
391	C₂×C₄	#10597397	1	1	yes	characteristic
392	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	—	152	1	no	—
395	C₈	—	152	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	4	no	—
399	C₂²	—	4	4	no	—
400	C₂²	—	4	4	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	8	1	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	#11926424	1	1	yes	characteristic
407	C₂²	#11926677	1	1	yes	characteristic
408	C₂²	#11926682	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	8	1	no	—
415	C₄	—	76	2	no	—
416	C₄	—	152	2	no	—
417	C₄	—	152	1	no	—
418	C₄	C₂×#10597289	1	1	yes	characteristic
419	C₄	#11926545	1	1	yes	characteristic
420	C₄	#11926855	1	1	yes	characteristic
421	C₄	#11926860	1	1	yes	characteristic
422	C₂	—	2	1	no	—
423	C₂	—	2	1	no	—
424	C₂	—	4	4	no	—
425	C₂	—	16	1	no	—
426	C₂	#14563953	1	1	yes	characteristic
427	C₂	#14564124	1	1	yes	characteristic
428	C₂	#14564138	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#11926424
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₁₉×#3036	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3036	D₁₉
hypocenter	C₁₉	#9179
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3036

Complements

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

N	H ≅ G/N	type
1. #14566545	C₂	semidirect
2. #14562195	C₂	semidirect
3. #14562130	C₂	semidirect
4. #14562026	C₂	semidirect
5. #14561536	C₂	semidirect
6. #14561495	C₂	semidirect
25. C₁₉×#461	C₄	semidirect
26. C₁₉×#459	C₄	semidirect
38. C₁₉×C₄⋊Q₈	C₂×C₄	semidirect
39. C₁₉×#127	C₂×C₄	semidirect
60. C₁₉×C₄⋊C₈	C₂×C₄	semidirect
220. #461	Dic₁₉	semidirect
221. #459	Dic₁₉	semidirect
252. C₄⋊Q₈	C₂×Dic₁₉	semidirect
253. #127	C₂×Dic₁₉	semidirect
276. C₄⋊C₈	C₂×Dic₁₉	semidirect
288. C₁₉	#9179	semidirect

Maximal subgroups

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

subgroup	index
#14566545	2
#14562195	2
#14562130	2
#14562026	2
#14561536	2
#14561495	2
C₁₉×#3036	2
#9179	19