Subgroups — #18083630

Order 4864.

670 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926892	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926744	C₂	1	1	yes	maximal, characteristic
3	#14564562	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926290	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×Q₈⋊(C₁₉⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926892	—	2	2	no	—
11	#11926892	—	2	2	no	—
12	#11926744	—	2	2	no	—
13	#11926744	—	2	2	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#10597266	—	2	1	no	—
17	C₂×#10597266	—	2	2	no	—
18	C₂×#10597266	—	2	2	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926290	—	2	2	no	—
21	Q₈⋊(C₁₉⋊C₈)	—	2	2	no	—
22	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
23	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#398	—	2	2	no	—
26	C₁₉×#391	—	2	1	no	—
27	C₁₉×#389	—	2	2	no	—
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Q₈×C₁₉	—	2	1	no	—
30	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
31	C₂²×D₇₆	—	2	1	no	—
32	C₂²×D₇₆	—	2	1	no	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₁₉×C₄⋊Q₈	—	2	1	no	—
37	C₁₉×C₄⋊Q₈	—	2	1	no	—
38	C₁₉×C₄⋊Q₈	—	4	2	no	—
39	C₁₉×C₄⋊Q₈	—	4	2	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₄×Q₈×C₁₉	—	2	1	no	—
43	C₄×Q₈×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	4	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
50	C₂×C₄²×C₁₉	—	2	1	no	—
51	C₂×C₄²×C₁₉	—	2	1	no	—
52	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
53	C₂×#64527	—	2	4	no	—
54	C₂×#64527	—	4	2	no	—
55	C₂×#64527	—	4	2	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	C₂²×C₁₉⋊C₈	—	2	1	no	—
58	C₂²×C₁₉⋊C₈	—	2	1	no	—
59	#10597320	—	2	1	no	—
60	#10597320	—	2	1	no	—
61	#10597320	—	2	1	no	—
62	#10597320	D₄	1	2	yes	—
63	C₁₉×#95	—	2	4	no	—
64	C₁₉×#95	—	2	1	no	—
65	#10597266	—	2	8	no	—
66	#10597266	—	2	4	no	—
67	#10597266	—	4	4	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
71	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
72	C₄×C₁₉⋊C₈	—	2	1	no	—
73	C₄×C₁₉⋊C₈	D₄	1	2	yes	—
74	C₂³×D₁₉	—	4	1	no	—
75	C₂×Q₈×C₁₉	—	2	1	no	—
76	C₂×Q₈×C₁₉	—	2	1	no	—
77	C₂×Q₈×C₁₉	—	2	1	no	—
78	C₂×Q₈×C₁₉	—	2	1	no	—
79	C₂×Q₈×C₁₉	—	2	1	no	—
80	C₂×Q₈×C₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	—	4	1	no	—
82	C₂×Q₈×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	—	4	1	no	—
84	C₂×Q₈×C₁₉	—	4	1	no	—
85	C₂×Q₈×C₁₉	—	4	1	no	—
86	C₂×Q₈×C₁₉	D₈	1	2	yes	—
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	1	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂×D₇₆	—	2	2	no	—
95	C₂×D₇₆	—	2	2	no	—
96	C₂×D₇₆	—	2	2	no	—
97	C₂×D₇₆	—	4	4	no	—
98	C₂×D₇₆	—	4	1	no	—
99	C₂×D₇₆	—	4	2	no	—
100	C₂×D₇₆	—	4	1	no	—
101	C₂×D₇₆	—	4	1	no	—
102	C₂×D₇₆	—	4	1	no	—
103	C₂×D₇₆	—	4	2	no	—
104	C₂×D₇₆	—	4	1	no	—
105	C₂×D₇₆	—	4	1	no	—
106	C₂×D₇₆	—	4	1	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	1	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₄⋊C₄×C₁₉	—	2	2	no	—
112	C₄⋊C₄×C₁₉	—	4	8	no	—
113	C₄⋊C₄×C₁₉	—	4	1	no	—
114	C₄⋊C₄×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	SD₁₆	1	4	yes	complemented
118	C₄²×C₁₉	—	4	1	no	—
119	C₄²×C₁₉	—	4	1	no	—
120	C₄²×C₁₉	—	4	1	no	—
121	C₄²×C₁₉	—	4	1	no	—
122	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₁₉	#41	1	1	yes	characteristic
126	#64527	—	4	8	no	—
127	C₂×C₁₉⋊C₈	—	2	2	no	—
128	C₂×C₁₉⋊C₈	—	2	2	no	—
129	C₂×C₁₉⋊C₈	—	4	2	no	—
130	C₂×C₁₉⋊C₈	—	4	1	no	—
131	C₂×C₁₉⋊C₈	—	4	1	no	—
132	C₂×C₁₉⋊C₈	—	4	1	no	—
133	C₂×C₁₉⋊C₈	—	4	2	no	—
134	#10051	—	19	1	no	maximal, Sylow
135	C₂³×C₁₉	#120	1	1	yes	characteristic
136	C₂²×D₁₉	—	4	2	no	—
137	C₂²×D₁₉	—	8	1	no	—
138	C₂²×D₁₉	—	8	2	no	—
139	C₂²×D₁₉	—	8	1	no	—
140	C₂²×D₁₉	—	8	2	no	—
141	Q₈×C₁₉	—	2	2	no	—
142	Q₈×C₁₉	—	2	2	no	—
143	Q₈×C₁₉	—	4	1	no	—
144	Q₈×C₁₉	—	4	1	no	—
145	Q₈×C₁₉	—	8	1	no	—
146	Q₈×C₁₉	—	8	1	no	—
147	Q₈×C₁₉	—	8	1	no	—
148	Q₈×C₁₉	—	8	1	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	2	no	—
151	C₂×C₄×C₁₉	—	2	4	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	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	1	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	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	#127	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
169	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
170	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
171	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#137	1	2	yes	—
173	D₇₆	—	4	4	no	—
174	D₇₆	—	4	2	no	—
175	D₇₆	—	4	2	no	—
176	D₇₆	—	4	4	no	—
177	D₇₆	—	8	2	no	—
178	D₇₆	—	8	1	no	—
179	D₇₆	—	8	1	no	—
180	D₇₆	—	8	1	no	—
181	D₇₆	—	8	1	no	—
182	C₁₉⋊C₈	—	4	2	no	—
183	C₁₉⋊C₈	—	4	2	no	—
184	C₁₉⋊C₈	—	8	1	no	—
185	C₂×#486	—	19	1	no	—
186	C₂×#460	—	19	1	no	—
187	#2546	D₁₉	1	1	yes	characteristic, complemented
188	#1982	—	19	1	no	—
189	C₂×#332	—	19	1	no	—
190	C₂×Q₈⋊C₈	—	19	1	no	—
191	#1279	—	19	1	no	—
192	C₂²×C₁₉	#392	1	1	yes	characteristic
193	C₂²×C₁₉	#447	1	1	yes	characteristic
194	C₂²×C₁₉	#448	1	2	yes	—
195	C₂²×C₁₉	#449	1	1	yes	characteristic
196	C₂²×C₁₉	#454	1	2	yes	—
197	C₂×D₁₉	—	8	2	no	—
198	C₂×D₁₉	—	8	2	no	—
199	C₂×D₁₉	—	8	2	no	—
200	C₂×D₁₉	—	16	2	no	—
201	C₂×D₁₉	—	16	2	no	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	4	4	no	—
205	C₄×C₁₉	—	4	2	no	—
206	C₄×C₁₉	—	8	2	no	—
207	C₄×C₁₉	—	8	1	no	—
208	C₄×C₁₉	#447	1	1	yes	characteristic
209	C₄×C₁₉	#449	1	1	yes	characteristic
210	C₄×C₁₉	#461	1	2	yes	—
211	C₄×C₁₉	#466	1	1	yes	characteristic
212	C₄×C₁₉	#469	1	1	yes	characteristic
213	C₄×C₁₉	#492	1	1	yes	characteristic
214	C₄×C₁₉	#497	1	1	yes	characteristic
215	C₂²×SD₁₆	—	38	1	no	—
216	C₂×C₄⋊Q₈	—	2	1	no	—
217	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
218	C₂×#127	—	19	1	no	—
219	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
220	#486	—	38	2	no	—
221	#486	—	38	2	no	—
222	#460	—	38	2	no	—
223	#460	—	38	2	no	—
224	C₂×C₄⋊C₈	—	19	1	no	—
225	C₂×C₄⋊C₈	—	19	1	no	—
226	C₂×#102	—	38	2	no	—
227	C₂×#102	—	38	1	no	—
228	C₂×#102	—	38	2	no	—
229	C₂×C₄×C₈	—	19	1	no	—
230	#398	—	2	2	no	—
231	#391	—	2	1	no	—
232	#389	—	2	2	no	—
233	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
234	#332	—	38	2	no	—
235	Q₈⋊C₈	—	38	2	no	—
236	C₂×C₁₉	#1626	1	2	yes	—
237	C₂×C₁₉	#1627	1	2	yes	—
238	C₂×C₁₉	#1999	1	1	yes	characteristic
239	C₂×C₁₉	#2003	1	1	yes	characteristic
240	C₂×C₁₉	#2013	1	1	yes	characteristic
241	D₁₉	—	16	2	no	—
242	C₂²×Q₈	—	2	1	no	—
243	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
244	C₂²×D₄	—	38	1	no	—
245	C₂²×D₄	—	38	1	no	—
246	C₂²×D₄	—	38	1	no	—
247	C₂×SD₁₆	—	38	4	no	—
248	C₂×SD₁₆	—	76	2	no	—
249	C₂×SD₁₆	—	76	2	no	—
250	C₂²×C₈	—	38	1	no	—
251	C₂²×C₈	—	38	1	no	—
252	C₂²×C₈	—	38	1	no	—
253	C₄⋊Q₈	—	2	1	no	—
254	C₄⋊Q₈	—	2	1	no	—
255	C₄⋊Q₈	—	2	1	no	—
256	C₄⋊Q₈	—	2	1	no	—
257	C₄⋊Q₈	—	4	2	no	—
258	C₄⋊Q₈	—	4	2	no	—
259	#127	—	19	2	no	—
260	#127	—	38	1	no	—
261	#127	—	38	1	no	—
262	#127	—	38	1	no	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	—	2	1	no	—
265	C₄×Q₈	—	2	1	no	—
266	C₄×Q₈	—	2	1	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
272	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
273	C₂×C₄²	—	2	1	no	—
274	C₂×C₄²	—	2	1	no	—
275	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
276	C₄⋊C₈	—	19	2	no	—
277	C₄⋊C₈	—	38	1	no	—
278	C₄⋊C₈	—	38	1	no	—
279	C₄⋊C₈	—	38	1	no	—
280	#102	—	38	4	no	—
281	#102	—	38	8	no	—
282	#102	—	76	4	no	—
283	C₄×C₈	—	19	2	no	—
284	C₄×C₈	—	38	1	no	—
285	#95	—	2	4	no	—
286	#95	—	2	1	no	—
287	C₁₉	#10051	1	1	yes	characteristic, complemented, Sylow
288	C₂⁴	—	76	1	no	—
289	C₂×Q₈	—	2	1	no	—
290	C₂×Q₈	—	2	1	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	—	4	1	no	—
295	C₂×Q₈	—	4	1	no	—
296	C₂×Q₈	—	4	1	no	—
297	C₂×Q₈	—	4	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	4	1	no	—
300	C₂×Q₈	#64525	1	2	yes	—
301	C₂×D₄	—	38	2	no	—
302	C₂×D₄	—	38	2	no	—
303	C₂×D₄	—	38	2	no	—
304	C₂×D₄	—	76	4	no	—
305	C₂×D₄	—	76	1	no	—
306	C₂×D₄	—	76	1	no	—
307	C₂×D₄	—	76	1	no	—
308	C₂×D₄	—	76	1	no	—
309	C₂×D₄	—	76	1	no	—
310	C₂×D₄	—	76	2	no	—
311	C₂×D₄	—	76	2	no	—
312	C₂×D₄	—	76	1	no	—
313	C₂×D₄	—	76	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
321	SD₁₆	—	76	8	no	—
322	C₂×C₈	—	38	2	no	—
323	C₂×C₈	—	38	2	no	—
324	C₂×C₈	—	76	2	no	—
325	C₂×C₈	—	76	1	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	2	no	—
329	C₄⋊C₄	—	2	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	1	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	4	8	no	—
335	C₄⋊C₄	—	4	1	no	—
336	C₄⋊C₄	—	4	1	no	—
337	C₄⋊C₄	—	4	1	no	—
338	C₄⋊C₄	—	4	1	no	—
339	C₄⋊C₄	#64527	1	4	yes	complemented
340	C₄²	—	4	1	no	—
341	C₄²	—	4	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	4	1	no	—
344	C₄²	D₄×D₁₉	1	1	yes	characteristic
345	C₄²	D₄×D₁₉	1	1	yes	characteristic
346	C₄²	D₄×D₁₉	1	1	yes	characteristic
347	C₄²	#64543	1	1	yes	characteristic
348	C₂³	—	76	2	no	—
349	C₂³	—	152	1	no	—
350	C₂³	—	152	2	no	—
351	C₂³	—	152	1	no	—
352	C₂³	—	152	2	no	—
353	C₂³	#10597399	1	1	yes	characteristic
354	Q₈	—	2	2	no	—
355	Q₈	—	2	2	no	—
356	Q₈	—	4	1	no	—
357	Q₈	—	4	1	no	—
358	Q₈	—	8	1	no	—
359	Q₈	—	8	1	no	—
360	Q₈	—	8	1	no	—
361	Q₈	—	8	1	no	—
362	D₄	—	76	4	no	—
363	D₄	—	76	2	no	—
364	D₄	—	76	2	no	—
365	D₄	—	76	4	no	—
366	D₄	—	152	2	no	—
367	D₄	—	152	1	no	—
368	D₄	—	152	1	no	—
369	D₄	—	152	1	no	—
370	D₄	—	152	1	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	C₂×#64525	1	1	yes	characteristic
384	C₂×C₄	#10597378	1	1	yes	characteristic
385	C₂×C₄	#10597383	1	1	yes	characteristic
386	C₂×C₄	#10597383	1	1	yes	characteristic
387	C₂×C₄	#10597384	1	1	yes	characteristic
388	C₂×C₄	#10597385	1	1	yes	characteristic
389	C₂×C₄	#10597385	1	1	yes	characteristic
390	C₂×C₄	#10597386	1	1	yes	characteristic
391	C₂×C₄	C₂×#64527	1	2	yes	—
392	C₂×C₄	#10597388	1	2	yes	—
393	C₂×C₄	#10597395	1	1	yes	characteristic
394	C₂×C₄	#10597396	1	1	yes	characteristic
395	C₈	—	76	2	no	—
396	C₈	—	76	2	no	—
397	C₈	—	152	1	no	—
398	C₂²	—	304	2	no	—
399	C₂²	—	304	2	no	—
400	C₂²	—	152	2	no	—
401	C₂²	—	152	2	no	—
402	C₂²	—	152	2	no	—
403	C₂²	#11926452	1	1	yes	characteristic
404	C₂²	#11926678	1	1	yes	characteristic
405	C₂²	#11926683	1	2	yes	—
406	C₂²	#11926689	1	1	yes	characteristic
407	C₂²	#11926717	1	2	yes	—
408	C₄	—	2	1	no	—
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	4	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	1	no	—
414	C₄	#11926677	1	1	yes	characteristic
415	C₄	#11926687	1	1	yes	characteristic
416	C₄	#11926746	1	2	yes	—
417	C₄	#11926778	1	1	yes	characteristic
418	C₄	#11926795	1	1	yes	characteristic
419	C₄	#11926918	1	1	yes	characteristic
420	C₄	#11926936	1	1	yes	characteristic
421	C₂	—	304	2	no	—
422	C₂	#14562731	1	2	yes	—
423	C₂	#14562738	1	2	yes	—
424	C₂	#14564631	1	1	yes	characteristic
425	C₂	#14564655	1	1	yes	characteristic
426	C₂	#14564718	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2546	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#2546	D₁₉
hypocenter	C₁₉	#10051
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2546

Complements

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

N	H ≅ G/N	type
4. C₂×#11926290	C₂	semidirect
5. C₂×Q₈⋊(C₁₉⋊C₈)	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#2546	C₂	semidirect
117. C₄⋊C₄×C₁₉	SD₁₆	semidirect
187. #2546	D₁₉	semidirect
287. C₁₉	#10051	semidirect
339. 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×#11926892	2
C₂×#11926744	2
#14564562	2
C₂×#11926290	2
C₂×Q₈⋊(C₁₉⋊C₈)	2
#14561476	2
C₁₉×#2546	2
#10051	19