Subgroups — #18085580

Order 4864.

536 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14564562	C₂	1	1	yes	maximal, characteristic
2	#14564562	C₂	1	1	yes	maximal, characteristic
3	#14564440	C₂	1	1	yes	maximal, characteristic
4	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
5	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561476	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#2552	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#10597320	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#10597266	—	2	2	no	—
12	C₂×#10597266	—	2	1	no	—
13	C₂×#10597266	—	2	1	no	—
14	C₂×#10597266	—	2	1	no	—
15	C₂×#10597266	—	2	1	no	—
16	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₉×#125	—	2	1	no	—
18	C₁₉×#398	—	2	2	no	—
19	C₁₉×#389	—	2	1	no	—
20	C₁₉×#389	—	2	1	no	—
21	C₁₉×#384	—	2	1	no	—
22	C₁₉×#384	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂²×D₇₆	—	2	1	no	—
26	C₂²×D₇₆	—	2	1	no	—
27	C₂²×D₇₆	—	2	1	no	—
28	C₁₉×#125	—	4	2	no	—
29	C₁₉×#125	—	4	2	no	—
30	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
32	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
33	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
34	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
35	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
36	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
37	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
38	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
39	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
40	C₂×C₄²×C₁₉	—	2	1	no	—
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂²×C₁₉⋊C₈	—	2	1	no	—
44	C₂²×C₁₉⋊C₈	—	2	1	no	—
45	C₂²×C₁₉⋊C₈	—	2	1	no	—
46	#10597320	—	2	1	no	—
47	#10597320	—	2	1	no	—
48	#10597320	—	2	1	no	—
49	#10597320	Q₈	1	2	yes	—
50	C₁₉×#95	—	2	2	no	—
51	C₁₉×#95	—	2	1	no	—
52	C₁₉×#95	—	2	1	no	—
53	#10597266	—	4	4	no	—
54	#10597266	—	4	2	no	—
55	#10597266	—	4	2	no	—
56	#10597266	—	4	2	no	—
57	#10597266	—	4	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
60	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
61	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
62	C₄×C₁₉⋊C₈	—	2	1	no	—
63	C₄×C₁₉⋊C₈	—	2	1	no	—
64	C₂³×D₁₉	—	4	1	no	—
65	C₂²×C₄×C₁₉	—	2	1	no	—
66	C₂²×C₄×C₁₉	—	2	1	no	—
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	—	2	2	no	—
70	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂×D₇₆	—	2	2	no	—
74	C₂×D₇₆	—	2	2	no	—
75	C₂×D₇₆	—	2	2	no	—
76	C₂×D₇₆	—	4	2	no	—
77	C₂×D₇₆	—	4	2	no	—
78	C₂×D₇₆	—	4	1	no	—
79	C₂×D₇₆	—	4	1	no	—
80	C₂×D₇₆	—	4	1	no	—
81	C₂×D₇₆	—	4	1	no	—
82	C₂×D₇₆	—	4	1	no	—
83	C₂×D₇₆	—	4	1	no	—
84	C₂×D₇₆	—	4	1	no	—
85	C₂×D₇₆	—	4	1	no	—
86	C₂×D₇₆	—	4	1	no	—
87	C₂×D₇₆	—	4	1	no	—
88	C₂×D₇₆	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	2	1	no	—
90	C₄⋊C₄×C₁₉	—	2	1	no	—
91	C₄⋊C₄×C₁₉	—	2	1	no	—
92	C₄⋊C₄×C₁₉	—	2	1	no	—
93	C₄⋊C₄×C₁₉	—	2	1	no	—
94	C₄⋊C₄×C₁₉	—	2	1	no	—
95	C₄⋊C₄×C₁₉	—	4	2	no	—
96	C₄⋊C₄×C₁₉	—	4	4	no	—
97	C₄⋊C₄×C₁₉	—	4	4	no	—
98	C₄⋊C₄×C₁₉	—	4	1	no	—
99	C₄⋊C₄×C₁₉	—	4	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	8	2	no	—
103	C₄⋊C₄×C₁₉	D₈	1	2	yes	—
104	C₄⋊C₄×C₁₉	SD₁₆	1	2	yes	—
105	C₄²×C₁₉	—	4	1	no	—
106	C₄²×C₁₉	—	4	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
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	C₄²×C₁₉	#41	1	1	yes	characteristic
113	C₂×C₁₉⋊C₈	—	2	2	no	—
114	C₂×C₁₉⋊C₈	—	4	1	no	—
115	C₂×C₁₉⋊C₈	—	4	1	no	—
116	C₂×C₁₉⋊C₈	—	4	1	no	—
117	C₂×C₁₉⋊C₈	—	4	1	no	—
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	C₂×C₁₉⋊C₈	—	4	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	#10354	—	19	1	no	maximal, Sylow
123	C₂³×C₁₉	#120	1	1	yes	characteristic
124	C₂²×D₁₉	—	4	2	no	—
125	C₂²×D₁₉	—	8	1	no	—
126	C₂²×D₁₉	—	8	1	no	—
127	C₂²×D₁₉	—	8	1	no	—
128	C₂²×D₁₉	—	8	1	no	—
129	C₂²×D₁₉	—	8	1	no	—
130	C₂²×D₁₉	—	8	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	—	2	2	no	—
134	C₂×C₄×C₁₉	—	2	2	no	—
135	C₂×C₄×C₁₉	—	4	1	no	—
136	C₂×C₄×C₁₉	—	4	1	no	—
137	C₂×C₄×C₁₉	—	4	1	no	—
138	C₂×C₄×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	4	1	no	—
140	C₂×C₄×C₁₉	—	4	1	no	—
141	C₂×C₄×C₁₉	—	4	2	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	2	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	4	1	no	—
148	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
154	C₂×C₄×C₁₉	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
158	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	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	D₇₆	—	4	4	no	—
163	D₇₆	—	4	2	no	—
164	D₇₆	—	4	2	no	—
165	D₇₆	—	4	2	no	—
166	D₇₆	—	4	2	no	—
167	D₇₆	—	8	2	no	—
168	D₇₆	—	8	1	no	—
169	D₇₆	—	8	1	no	—
170	D₇₆	—	8	1	no	—
171	D₇₆	—	8	1	no	—
172	C₁₉⋊C₈	—	4	2	no	—
173	C₁₉⋊C₈	—	8	1	no	—
174	C₁₉⋊C₈	—	8	1	no	—
175	#2552	D₁₉	1	1	yes	characteristic, complemented
176	#1982	—	19	1	no	—
177	#1982	—	19	1	no	—
178	#1957	—	19	1	no	—
179	#1296	—	19	1	no	—
180	#1279	—	19	1	no	—
181	#1279	—	19	1	no	—
182	C₂²×C₁₉	#393	1	1	yes	characteristic
183	C₂²×C₁₉	#447	1	1	yes	characteristic
184	C₂²×C₁₉	#448	1	1	yes	characteristic
185	C₂²×C₁₉	#449	1	1	yes	characteristic
186	C₂²×C₁₉	#449	1	1	yes	characteristic
187	C₂²×C₁₉	#453	1	1	yes	characteristic
188	C₂²×C₁₉	#454	1	1	yes	characteristic
189	C₂×D₁₉	—	8	2	no	—
190	C₂×D₁₉	—	8	2	no	—
191	C₂×D₁₉	—	8	2	no	—
192	C₂×D₁₉	—	16	1	no	—
193	C₂×D₁₉	—	16	1	no	—
194	C₂×D₁₉	—	16	1	no	—
195	C₂×D₁₉	—	16	1	no	—
196	C₄×C₁₉	—	2	1	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	4	2	no	—
199	C₄×C₁₉	—	4	2	no	—
200	C₄×C₁₉	—	8	1	no	—
201	C₄×C₁₉	—	8	2	no	—
202	C₄×C₁₉	—	8	1	no	—
203	C₄×C₁₉	#474	1	1	yes	characteristic
204	C₄×C₁₉	#476	1	1	yes	characteristic
205	C₄×C₁₉	#478	1	1	yes	characteristic
206	C₄×C₁₉	#478	1	1	yes	characteristic
207	C₄×C₁₉	#486	1	1	yes	characteristic
208	C₄×C₁₉	#488	1	1	yes	characteristic
209	C₄×C₁₉	#489	1	1	yes	characteristic
210	C₄×C₁₉	#490	1	1	yes	characteristic
211	C₂×#127	—	19	1	no	—
212	C₂×#125	—	2	1	no	—
213	C₂×C₄⋊C₈	—	19	1	no	—
214	C₂×C₄⋊C₈	—	19	1	no	—
215	C₂×#102	—	38	2	no	—
216	C₂×#102	—	38	1	no	—
217	C₂×#102	—	38	1	no	—
218	C₂×#102	—	38	1	no	—
219	C₂×#102	—	38	1	no	—
220	C₂×C₄×C₈	—	19	1	no	—
221	#398	—	2	2	no	—
222	#389	—	2	1	no	—
223	#389	—	2	1	no	—
224	#384	—	2	1	no	—
225	#384	C₂×D₁₉	1	1	yes	characteristic
226	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
227	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
228	C₂×C₁₉	#1621	1	1	yes	characteristic
229	C₂×C₁₉	#1622	1	1	yes	characteristic
230	C₂×C₁₉	#1625	1	1	yes	characteristic
231	C₂×C₁₉	#1626	1	1	yes	characteristic
232	C₂×C₁₉	#2023	1	1	yes	characteristic
233	C₂×C₁₉	#2025	1	1	yes	characteristic
234	C₂×C₁₉	#2027	1	1	yes	characteristic
235	D₁₉	—	16	2	no	—
236	C₂²×D₄	—	38	1	no	—
237	C₂²×D₄	—	38	1	no	—
238	C₂²×D₄	—	38	1	no	—
239	C₂²×C₈	—	38	1	no	—
240	C₂²×C₈	—	38	1	no	—
241	C₂²×C₈	—	38	1	no	—
242	#127	—	19	2	no	—
243	#127	—	38	1	no	—
244	#127	—	38	1	no	—
245	#127	—	38	1	no	—
246	#125	—	4	2	no	—
247	#125	—	4	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	—	2	1	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
254	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
256	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	—	2	1	no	—
260	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
261	C₄⋊C₈	—	38	1	no	—
262	C₄⋊C₈	—	38	1	no	—
263	C₄⋊C₈	—	38	1	no	—
264	C₄⋊C₈	—	38	1	no	—
265	#102	—	76	2	no	—
266	#102	—	76	2	no	—
267	#102	—	76	4	no	—
268	#102	—	76	2	no	—
269	#102	—	76	2	no	—
270	C₄×C₈	—	38	1	no	—
271	C₄×C₈	—	38	1	no	—
272	#95	—	2	2	no	—
273	#95	—	2	1	no	—
274	#95	—	2	1	no	—
275	C₁₉	#10354	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	—	76	1	no	—
277	C₂×D₄	—	38	2	no	—
278	C₂×D₄	—	38	2	no	—
279	C₂×D₄	—	38	2	no	—
280	C₂×D₄	—	76	2	no	—
281	C₂×D₄	—	76	2	no	—
282	C₂×D₄	—	76	1	no	—
283	C₂×D₄	—	76	1	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	1	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	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
300	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
301	C₂×C₈	—	38	2	no	—
302	C₂×C₈	—	76	1	no	—
303	C₂×C₈	—	76	1	no	—
304	C₂×C₈	—	76	1	no	—
305	C₂×C₈	—	76	1	no	—
306	C₂×C₈	—	76	1	no	—
307	C₂×C₈	—	76	1	no	—
308	C₂×C₈	—	76	1	no	—
309	C₂×C₈	—	76	1	no	—
310	C₄⋊C₄	—	2	1	no	—
311	C₄⋊C₄	—	2	1	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	1	no	—
314	C₄⋊C₄	—	2	1	no	—
315	C₄⋊C₄	—	2	1	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	4	no	—
318	C₄⋊C₄	—	4	4	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	4	1	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	8	2	no	—
324	C₄⋊C₄	#64525	1	2	yes	—
325	C₄⋊C₄	#64527	1	2	yes	—
326	C₄²	—	4	1	no	—
327	C₄²	—	4	1	no	—
328	C₄²	—	4	1	no	—
329	C₄²	—	4	1	no	—
330	C₄²	Q₈×D₁₉	1	1	yes	characteristic
331	C₄²	#64545	1	1	yes	characteristic
332	C₄²	#64545	1	1	yes	characteristic
333	C₄²	#64545	1	1	yes	characteristic
334	C₂³	—	76	2	no	—
335	C₂³	—	152	1	no	—
336	C₂³	—	152	1	no	—
337	C₂³	—	152	1	no	—
338	C₂³	—	152	1	no	—
339	C₂³	—	152	1	no	—
340	C₂³	—	152	1	no	—
341	C₂³	#10597399	1	1	yes	characteristic
342	D₄	—	76	4	no	—
343	D₄	—	76	2	no	—
344	D₄	—	76	2	no	—
345	D₄	—	76	2	no	—
346	D₄	—	76	2	no	—
347	D₄	—	152	2	no	—
348	D₄	—	152	1	no	—
349	D₄	—	152	1	no	—
350	D₄	—	152	1	no	—
351	D₄	—	152	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	1	no	—
364	C₂×C₄	—	4	1	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	C₂×#64525	1	1	yes	characteristic
370	C₂×C₄	#10597378	1	1	yes	characteristic
371	C₂×C₄	C₂×#64527	1	1	yes	characteristic
372	C₂×C₄	#10597388	1	1	yes	characteristic
373	C₂×C₄	#10597392	1	1	yes	characteristic
374	C₂×C₄	#10597392	1	1	yes	characteristic
375	C₂×C₄	#10597392	1	1	yes	characteristic
376	C₂×C₄	#10597393	1	1	yes	characteristic
377	C₂×C₄	#10597393	1	1	yes	characteristic
378	C₂×C₄	#10597393	1	1	yes	characteristic
379	C₂×C₄	#10597395	1	1	yes	characteristic
380	C₂×C₄	#10597395	1	1	yes	characteristic
381	C₂×C₄	#10597396	1	1	yes	characteristic
382	C₂×C₄	#10597396	1	1	yes	characteristic
383	C₈	—	76	2	no	—
384	C₈	—	152	1	no	—
385	C₈	—	152	1	no	—
386	C₂²	—	304	1	no	—
387	C₂²	—	304	1	no	—
388	C₂²	—	304	1	no	—
389	C₂²	—	304	1	no	—
390	C₂²	—	152	2	no	—
391	C₂²	—	152	2	no	—
392	C₂²	—	152	2	no	—
393	C₂²	#11926455	1	1	yes	characteristic
394	C₂²	#11926678	1	1	yes	characteristic
395	C₂²	#11926683	1	1	yes	characteristic
396	C₂²	#11926689	1	1	yes	characteristic
397	C₂²	#11926689	1	1	yes	characteristic
398	C₂²	#11926712	1	1	yes	characteristic
399	C₂²	#11926717	1	1	yes	characteristic
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	4	2	no	—
403	C₄	—	4	2	no	—
404	C₄	—	8	1	no	—
405	C₄	—	8	2	no	—
406	C₄	—	8	1	no	—
407	C₄	#11926821	1	1	yes	characteristic
408	C₄	#11926831	1	1	yes	characteristic
409	C₄	#11926841	1	1	yes	characteristic
410	C₄	#11926841	1	1	yes	characteristic
411	C₄	#11926892	1	1	yes	characteristic
412	C₄	#11926901	1	1	yes	characteristic
413	C₄	#11926906	1	1	yes	characteristic
414	C₄	#11926910	1	1	yes	characteristic
415	C₂	—	304	2	no	—
416	C₂	#14562700	1	1	yes	characteristic
417	C₂	#14562707	1	1	yes	characteristic
418	C₂	#14562724	1	1	yes	characteristic
419	C₂	#14562731	1	1	yes	characteristic
420	C₂	#14564768	1	1	yes	characteristic
421	C₂	#14564778	1	1	yes	characteristic
422	C₂	#14564788	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597399
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#2552	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	#2552	D₁₉
hypocenter	C₁₉	#10354
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #2552

Complements

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

N	H ≅ G/N	type
4. #14561518	C₂	semidirect
5. #14561476	C₂	semidirect
6. #14561476	C₂	semidirect
7. C₁₉×#2552	C₂	semidirect
175. #2552	D₁₉	semidirect
275. C₁₉	#10354	semidirect

Maximal subgroups

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

subgroup	index
#14564562	2
#14564440	2
#14561518	2
#14561476	2
C₁₉×#2552	2
#10354	19