Subgroups — #18086350

Order 4864.

522 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×#11926744	C₂	1	1	yes	maximal, characteristic
2	#14564572	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564440	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926294	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926287	C₂	1	1	yes	maximal, characteristic
6	#14561518	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₉×#1803	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64527	—	2	1	no	—
9	C₂×#10597320	C₂²	1	1	yes	characteristic
10	#11926744	—	2	2	no	—
11	#11926744	—	2	2	no	—
12	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×#10597266	—	2	1	no	—
15	C₂×#10597266	—	2	1	no	—
16	C₂×#10597266	—	2	1	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	#11926299	—	2	1	no	—
19	#11926299	—	2	1	no	—
20	#11926294	—	2	2	no	—
21	#11926287	—	2	2	no	—
22	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₉×#103	—	2	1	no	—
25	C₁₉×#384	C₂²	1	1	yes	characteristic
26	C₁₉×#340	—	2	1	no	—
27	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	—	2	1	no	—
30	C₂²×D₇₆	—	2	1	no	—
31	C₂²×C₈×C₁₉	—	2	1	no	—
32	C₄×Q₈×C₁₉	—	2	1	no	—
33	C₄×Q₈×C₁₉	—	2	1	no	—
34	C₄×Q₈×C₁₉	—	2	1	no	—
35	C₄×Q₈×C₁₉	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
39	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
40	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₉	—	2	1	no	—
42	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
43	C₂×#64527	—	2	4	no	—
44	C₂×#64527	—	4	2	no	—
45	C₂×#64527	—	4	2	no	—
46	C₂²×C₁₉⋊C₈	—	2	1	no	—
47	C₂²×C₁₉⋊C₈	—	2	1	no	—
48	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
49	C₂²×C₁₉⋊C₈	D₄	1	1	yes	characteristic
50	#10597320	—	2	1	no	—
51	#10597320	—	2	1	no	—
52	#10597320	—	2	1	no	—
53	#10597320	D₄	1	2	yes	—
54	C₁₉×C₄⋊C₈	—	2	1	no	—
55	C₁₉×C₄⋊C₈	—	2	1	no	—
56	C₁₉×#103	—	4	2	no	—
57	#10597266	—	2	4	no	—
58	#10597266	—	4	2	no	—
59	#10597266	—	4	2	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)	D₄	1	2	yes	—
64	C₄×C₁₉⋊C₈	—	2	1	no	—
65	C₄×C₁₉⋊C₈	—	2	1	no	—
66	C₂³×D₁₉	—	4	1	no	—
67	C₂×Q₈×C₁₉	—	2	1	no	—
68	C₂×Q₈×C₁₉	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	1	no	—
70	C₂×Q₈×C₁₉	—	2	1	no	—
71	C₂×Q₈×C₁₉	—	2	1	no	—
72	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	—
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	—	4	1	no	—
76	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
79	C₂×D₇₆	—	2	2	no	—
80	C₂×D₇₆	—	2	2	no	—
81	C₂×D₇₆	—	2	2	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	C₂×D₇₆	—	4	1	no	—
90	C₂×D₇₆	—	4	1	no	—
91	C₂×D₇₆	—	4	1	no	—
92	C₂×D₇₆	—	4	1	no	—
93	C₂×D₇₆	—	8	1	no	—
94	C₂×D₇₆	—	8	1	no	—
95	C₂×C₈×C₁₉	—	4	1	no	—
96	C₂×C₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	—	4	1	no	—
98	C₄⋊C₄×C₁₉	—	2	1	no	—
99	C₄⋊C₄×C₁₉	—	2	1	no	—
100	C₄⋊C₄×C₁₉	—	4	1	no	—
101	C₄⋊C₄×C₁₉	—	4	1	no	—
102	C₄⋊C₄×C₁₉	—	4	1	no	—
103	C₄⋊C₄×C₁₉	—	4	1	no	—
104	C₄⋊C₄×C₁₉	—	4	1	no	—
105	C₄⋊C₄×C₁₉	—	4	1	no	—
106	C₄⋊C₄×C₁₉	—	8	1	no	—
107	C₄²×C₁₉	—	4	1	no	—
108	C₄²×C₁₉	—	4	1	no	—
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	#41	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	#64527	—	4	8	no	—
114	C₂×C₁₉⋊C₈	—	2	1	no	—
115	C₂×C₁₉⋊C₈	—	2	1	no	—
116	C₂×C₁₉⋊C₈	—	2	2	no	—
117	C₂×C₁₉⋊C₈	—	2	1	no	—
118	C₂×C₁₉⋊C₈	—	2	1	no	—
119	C₂×C₁₉⋊C₈	—	2	1	no	—
120	C₂×C₁₉⋊C₈	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	4	1	no	—
122	C₂×C₁₉⋊C₈	—	4	1	no	—
123	C₂×C₁₉⋊C₈	—	4	1	no	—
124	C₂×C₁₉⋊C₈	—	4	1	no	—
125	C₂×C₁₉⋊C₈	SD₁₆	1	2	yes	complemented
126	#10475	—	19	1	no	maximal, Sylow
127	C₂³×C₁₉	#121	1	1	yes	characteristic
128	C₂²×D₁₉	—	4	2	no	—
129	C₂²×D₁₉	—	8	1	no	—
130	C₂²×D₁₉	—	8	1	no	—
131	C₂²×D₁₉	—	8	1	no	—
132	C₂²×D₁₉	—	8	1	no	—
133	C₂²×D₁₉	—	8	1	no	—
134	C₂²×D₁₉	—	8	1	no	—
135	Q₈×C₁₉	—	2	2	no	—
136	Q₈×C₁₉	—	2	2	no	—
137	Q₈×C₁₉	—	4	1	no	—
138	Q₈×C₁₉	—	4	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	2	no	—
142	C₂×C₄×C₁₉	—	4	1	no	—
143	C₂×C₄×C₁₉	—	4	1	no	—
144	C₂×C₄×C₁₉	—	4	1	no	—
145	C₂×C₄×C₁₉	—	4	1	no	—
146	C₂×C₄×C₁₉	—	4	1	no	—
147	C₂×C₄×C₁₉	—	8	1	no	—
148	C₂×C₄×C₁₉	—	8	1	no	—
149	C₂×C₄×C₁₉	—	8	1	no	—
150	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
151	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
152	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
153	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
154	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
155	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
156	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
157	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
160	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
162	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
164	D₇₆	—	4	2	no	—
165	D₇₆	—	4	2	no	—
166	D₇₆	—	4	2	no	—
167	D₇₆	—	4	2	no	—
168	D₇₆	—	8	2	no	—
169	D₇₆	—	8	2	no	—
170	D₇₆	—	8	1	no	—
171	D₇₆	—	8	1	no	—
172	D₇₆	—	8	1	no	—
173	D₇₆	—	8	1	no	—
174	C₈×C₁₉	—	8	1	no	—
175	C₁₉⋊C₈	—	2	2	no	—
176	C₁₉⋊C₈	—	4	2	no	—
177	C₁₉⋊C₈	—	4	1	no	—
178	C₁₉⋊C₈	—	8	1	no	—
179	C₂×#460	—	19	1	no	—
180	#1984	—	19	1	no	—
181	#1957	—	19	1	no	—
182	#1803	D₁₉	1	1	yes	characteristic, complemented
183	C₂×#334	—	19	1	no	—
184	C₂×#331	—	19	1	no	—
185	#1296	—	19	1	no	—
186	C₂²×C₁₉	#394	1	1	yes	characteristic
187	C₂²×C₁₉	#460	1	1	yes	characteristic
188	C₂²×C₁₉	#464	1	1	yes	characteristic
189	C₂²×C₁₉	#465	1	1	yes	characteristic
190	C₂²×C₁₉	#469	1	1	yes	characteristic
191	C₂²×C₁₉	#471	1	1	yes	characteristic
192	C₂²×C₁₉	#472	1	1	yes	characteristic
193	C₂×D₁₉	—	8	2	no	—
194	C₂×D₁₉	—	8	2	no	—
195	C₂×D₁₉	—	8	2	no	—
196	C₂×D₁₉	—	16	1	no	—
197	C₂×D₁₉	—	16	1	no	—
198	C₂×D₁₉	—	16	1	no	—
199	C₂×D₁₉	—	16	1	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	2	no	—
203	C₄×C₁₉	—	8	1	no	—
204	C₄×C₁₉	—	16	1	no	—
205	C₄×C₁₉	#449	1	1	yes	characteristic
206	C₄×C₁₉	#450	1	1	yes	characteristic
207	C₄×C₁₉	#461	1	1	yes	characteristic
208	C₄×C₁₉	#463	1	1	yes	characteristic
209	C₄×C₁₉	#465	1	1	yes	characteristic
210	C₄×C₁₉	#468	1	1	yes	characteristic
211	C₄×C₁₉	#481	1	1	yes	characteristic
212	C₄×C₁₉	#482	1	1	yes	characteristic
213	C₂²×SD₁₆	—	38	1	no	—
214	C₂×#127	—	19	1	no	—
215	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
216	#460	—	38	2	no	—
217	#460	—	38	2	no	—
218	C₂×C₄⋊C₈	—	19	1	no	—
219	C₂×C₄⋊C₈	—	19	1	no	—
220	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
221	C₂×#103	—	2	1	no	—
222	C₂×#102	—	38	1	no	—
223	C₂×#102	—	38	1	no	—
224	C₂×#102	—	38	1	no	—
225	C₂×C₄×C₈	—	19	1	no	—
226	#384	C₂×D₁₉	1	1	yes	characteristic
227	#340	—	2	1	no	—
228	#336	—	38	1	no	—
229	#336	—	38	1	no	—
230	#334	—	38	2	no	—
231	#331	—	38	2	no	—
232	C₂×C₁₉	#1666	1	1	yes	characteristic
233	C₂×C₁₉	#1678	1	1	yes	characteristic
234	C₂×C₁₉	#1688	1	1	yes	characteristic
235	C₂×C₁₉	#1702	1	1	yes	characteristic
236	C₂×C₁₉	#2034	1	1	yes	characteristic
237	C₂×C₁₉	#2051	1	1	yes	characteristic
238	C₂×C₁₉	#2055	1	1	yes	characteristic
239	D₁₉	—	16	2	no	—
240	C₂²×Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
241	C₂²×D₄	—	38	1	no	—
242	C₂²×D₄	—	38	1	no	—
243	C₂²×D₄	—	38	1	no	—
244	C₂×SD₁₆	—	38	4	no	—
245	C₂×SD₁₆	—	76	2	no	—
246	C₂×SD₁₆	—	76	2	no	—
247	C₂²×C₈	—	2	1	no	—
248	C₂²×C₈	—	19	1	no	—
249	C₂²×C₈	—	19	1	no	—
250	C₂²×C₈	—	38	1	no	—
251	C₂²×C₈	—	38	1	no	—
252	#127	—	19	2	no	—
253	#127	—	38	1	no	—
254	#127	—	38	1	no	—
255	#127	—	38	1	no	—
256	C₄×Q₈	—	2	1	no	—
257	C₄×Q₈	—	2	1	no	—
258	C₄×Q₈	—	2	1	no	—
259	C₄×Q₈	—	2	1	no	—
260	C₂×C₄⋊C₄	—	2	1	no	—
261	C₂×C₄⋊C₄	—	2	1	no	—
262	C₂×C₄⋊C₄	—	2	1	no	—
263	C₂×C₄⋊C₄	—	2	1	no	—
264	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
265	C₂×C₄²	—	2	1	no	—
266	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
267	C₄⋊C₈	—	2	1	no	—
268	C₄⋊C₈	—	2	1	no	—
269	C₄⋊C₈	—	19	2	no	—
270	C₄⋊C₈	—	38	1	no	—
271	C₄⋊C₈	—	38	1	no	—
272	C₄⋊C₈	—	38	1	no	—
273	#103	—	4	2	no	—
274	#102	—	38	4	no	—
275	#102	—	76	2	no	—
276	#102	—	76	2	no	—
277	C₄×C₈	—	38	1	no	—
278	C₄×C₈	—	38	1	no	—
279	C₁₉	#10475	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	—	76	1	no	—
281	C₂×Q₈	—	2	1	no	—
282	C₂×Q₈	—	2	1	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	1	no	—
286	C₂×Q₈	#64527	1	2	yes	—
287	C₂×D₄	—	38	2	no	—
288	C₂×D₄	—	38	2	no	—
289	C₂×D₄	—	38	2	no	—
290	C₂×D₄	—	76	1	no	—
291	C₂×D₄	—	76	1	no	—
292	C₂×D₄	—	76	1	no	—
293	C₂×D₄	—	76	1	no	—
294	C₂×D₄	—	76	1	no	—
295	C₂×D₄	—	76	1	no	—
296	C₂×D₄	—	76	1	no	—
297	C₂×D₄	—	76	1	no	—
298	C₂×D₄	—	76	1	no	—
299	C₂×D₄	—	76	1	no	—
300	C₂×D₄	—	76	1	no	—
301	C₂×D₄	—	152	1	no	—
302	C₂×D₄	—	152	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	#64543	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
309	SD₁₆	—	76	8	no	—
310	C₂×C₈	—	4	1	no	—
311	C₂×C₈	—	4	1	no	—
312	C₂×C₈	—	4	1	no	—
313	C₂×C₈	—	19	2	no	—
314	C₂×C₈	—	38	1	no	—
315	C₂×C₈	—	38	1	no	—
316	C₂×C₈	—	38	2	no	—
317	C₂×C₈	—	38	1	no	—
318	C₂×C₈	—	38	1	no	—
319	C₂×C₈	—	38	1	no	—
320	C₂×C₈	—	76	1	no	—
321	C₂×C₈	—	76	1	no	—
322	C₂×C₈	—	76	1	no	—
323	C₂×C₈	—	76	1	no	—
324	C₂×C₈	—	76	1	no	—
325	C₄⋊C₄	—	2	1	no	—
326	C₄⋊C₄	—	2	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄⋊C₄	—	4	1	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	8	1	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	#64541	1	1	yes	characteristic
337	C₄²	#64541	1	1	yes	characteristic
338	C₄²	D₄×D₁₉	1	1	yes	characteristic
339	C₄²	D₄×D₁₉	1	1	yes	characteristic
340	C₂³	—	76	2	no	—
341	C₂³	—	152	1	no	—
342	C₂³	—	152	1	no	—
343	C₂³	—	152	1	no	—
344	C₂³	—	152	1	no	—
345	C₂³	—	152	1	no	—
346	C₂³	—	152	1	no	—
347	C₂³	#10597385	1	1	yes	characteristic
348	Q₈	—	2	2	no	—
349	Q₈	—	2	2	no	—
350	Q₈	—	4	1	no	—
351	Q₈	—	4	1	no	—
352	D₄	—	76	2	no	—
353	D₄	—	76	2	no	—
354	D₄	—	76	2	no	—
355	D₄	—	76	2	no	—
356	D₄	—	152	2	no	—
357	D₄	—	152	2	no	—
358	D₄	—	152	1	no	—
359	D₄	—	152	1	no	—
360	D₄	—	152	1	no	—
361	D₄	—	152	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	1	no	—
366	C₂×C₄	—	4	1	no	—
367	C₂×C₄	—	4	1	no	—
368	C₂×C₄	—	4	1	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	8	1	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	#10597329	1	1	yes	characteristic
374	C₂×C₄	#10597330	1	1	yes	characteristic
375	C₂×C₄	#10597330	1	1	yes	characteristic
376	C₂×C₄	#10597331	1	1	yes	characteristic
377	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
378	C₂×C₄	#10597360	1	1	yes	characteristic
379	C₂×C₄	#10597364	1	1	yes	characteristic
380	C₂×C₄	#10597365	1	1	yes	characteristic
381	C₂×C₄	#10597375	1	1	yes	characteristic
382	C₂×C₄	#10597378	1	1	yes	characteristic
383	C₂×C₄	#10597383	1	1	yes	characteristic
384	C₂×C₄	C₂×#64527	1	1	yes	characteristic
385	C₂×C₄	#10597395	1	1	yes	characteristic
386	C₂×C₄	#10597396	1	1	yes	characteristic
387	C₈	—	8	1	no	—
388	C₈	—	38	2	no	—
389	C₈	—	76	1	no	—
390	C₈	—	76	2	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	304	1	no	—
393	C₂²	—	304	1	no	—
394	C₂²	—	304	1	no	—
395	C₂²	—	304	1	no	—
396	C₂²	—	152	2	no	—
397	C₂²	—	152	2	no	—
398	C₂²	—	152	2	no	—
399	C₂²	#11926459	1	1	yes	characteristic
400	C₂²	#11926742	1	1	yes	characteristic
401	C₂²	#11926768	1	1	yes	characteristic
402	C₂²	#11926775	1	1	yes	characteristic
403	C₂²	#11926795	1	1	yes	characteristic
404	C₂²	#11926809	1	1	yes	characteristic
405	C₂²	#11926812	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	8	1	no	—
410	C₄	—	16	1	no	—
411	C₄	#11926687	1	1	yes	characteristic
412	C₄	#11926694	1	1	yes	characteristic
413	C₄	#11926748	1	1	yes	characteristic
414	C₄	#11926762	1	1	yes	characteristic
415	C₄	#11926776	1	1	yes	characteristic
416	C₄	#11926793	1	1	yes	characteristic
417	C₄	#11926862	1	1	yes	characteristic
418	C₄	#11926868	1	1	yes	characteristic
419	C₂	—	304	2	no	—
420	C₂	#14562985	1	1	yes	characteristic
421	C₂	#14563053	1	1	yes	characteristic
422	C₂	#14563117	1	1	yes	characteristic
423	C₂	#14563205	1	1	yes	characteristic
424	C₂	#14564824	1	1	yes	characteristic
425	C₂	#14564925	1	1	yes	characteristic
426	C₂	#14564949	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1803	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂×#10597320	C₂²
hypercenter	#1803	D₁₉
hypocenter	C₁₉	#10475
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1803

Complements

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

N	H ≅ G/N	type
2. #14564572	C₂	semidirect
4. C₂×#11926294	C₂	semidirect
6. #14561518	C₂	semidirect
7. C₁₉×#1803	C₂	semidirect
125. C₂×C₁₉⋊C₈	SD₁₆	semidirect
182. #1803	D₁₉	semidirect
279. C₁₉	#10475	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926744	2
#14564572	2
#14564440	2
C₂×#11926294	2
C₂×#11926287	2
#14561518	2
C₁₉×#1803	2
#10475	19