Subgroups — #18085086

Order 4864.

646 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926890	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926834	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564430	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#11926292	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#11926288	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561469	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#459	C₂	1	1	yes	maximal, characteristic
8	C₂×#10597315	C₂²	1	1	yes	characteristic
9	#11926890	—	2	2	no	—
10	#11926890	—	2	2	no	—
11	#11926834	—	2	2	no	—
12	#11926834	—	2	2	no	—
13	C₂×#10597265	—	2	1	no	—
14	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×#10597289	—	2	2	no	—
17	C₂×#10597289	—	2	1	no	—
18	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	2	no	—
19	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
20	#11926292	—	2	2	no	—
21	#11926288	—	2	2	no	—
22	C₂²×D₈×C₁₉	—	2	1	no	—
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#459	—	2	2	no	—
26	C₁₉×#459	—	2	2	no	—
27	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×#102	—	2	1	no	—
29	C₂²×D₄×C₁₉	—	2	1	no	—
30	C₂²×D₄×C₁₉	—	2	1	no	—
31	C₂²×D₄×C₁₉	—	2	1	no	—
32	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
33	C₂³×C₄×C₁₉	—	2	1	no	—
34	C₂²×Dic₃₈	—	2	1	no	—
35	C₂×D₈×C₁₉	—	2	4	no	—
36	C₂×D₈×C₁₉	—	4	2	no	—
37	C₂×D₈×C₁₉	—	4	2	no	—
38	C₂²×C₈×C₁₉	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	D₄	1	2	yes	—
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	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂²×C₁₉⋊C₈	—	2	1	no	—
53	C₂²×C₁₉⋊C₈	—	2	1	no	—
54	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
55	#10597315	—	2	1	no	—
56	#10597315	—	2	1	no	—
57	#10597315	—	2	1	no	—
58	#10597315	D₄	1	2	yes	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
61	C₁₉×#102	—	2	4	no	—
62	#10597289	—	2	4	no	—
63	#10597289	—	2	8	no	—
64	C₂²⋊(C₁₉⋊C₈)	—	4	4	no	—
65	#10597265	—	2	4	no	—
66	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
67	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
68	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
69	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₄×C₁₉⋊C₈	—	2	1	no	—
72	C₂⁴×C₁₉	—	2	1	no	—
73	C₂⁴×C₁₉	—	4	1	no	—
74	C₂×D₄×C₁₉	—	2	1	no	—
75	C₂×D₄×C₁₉	—	2	1	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	2	2	no	—
78	C₂×D₄×C₁₉	—	2	2	no	—
79	C₂×D₄×C₁₉	—	2	1	no	—
80	C₂×D₄×C₁₉	—	2	1	no	—
81	C₂×D₄×C₁₉	—	2	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	1	no	—
85	C₂×D₄×C₁₉	—	4	1	no	—
86	C₂×D₄×C₁₉	—	4	1	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	1	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	4	1	no	—
91	C₂×D₄×C₁₉	—	8	2	no	—
92	C₂×D₄×C₁₉	SD₁₆	1	2	yes	—
93	C₂²×C₄×C₁₉	—	2	1	no	—
94	C₂²×C₄×C₁₉	—	4	1	no	—
95	C₂²×C₄×C₁₉	—	4	1	no	—
96	C₂²×C₄×C₁₉	—	4	2	no	—
97	C₂²×C₄×C₁₉	—	4	2	no	—
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
101	C₂²×Dic₁₉	—	4	1	no	—
102	C₂×Dic₃₈	—	2	2	no	—
103	C₂×Dic₃₈	—	4	1	no	—
104	C₂×Dic₃₈	—	8	2	no	—
105	D₈×C₁₉	—	4	8	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	4	1	no	—
109	C₄⋊C₄×C₁₉	—	2	1	no	—
110	C₄⋊C₄×C₁₉	—	2	1	no	—
111	C₂²⋊C₄×C₁₉	—	4	1	no	—
112	C₂²⋊C₄×C₁₉	—	4	1	no	—
113	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
114	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
115	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
116	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
117	C₄⋊Dic₁₉	—	2	2	no	—
118	C₄⋊Dic₁₉	—	2	2	no	—
119	C₄⋊Dic₁₉	—	4	1	no	—
120	C₄⋊Dic₁₉	—	4	1	no	—
121	C₂×C₁₉⋊C₈	—	2	2	no	—
122	C₂×C₁₉⋊C₈	—	2	2	no	—
123	C₂×C₁₉⋊C₈	—	2	2	no	—
124	C₂×C₁₉⋊C₈	—	2	2	no	—
125	C₂×C₁₉⋊C₈	—	4	1	no	—
126	C₂×C₁₉⋊C₈	—	4	1	no	—
127	C₂×C₁₉⋊C₈	—	4	1	no	—
128	C₂×C₁₉⋊C₈	—	4	2	no	—
129	#10267	—	19	1	no	maximal, Sylow
130	C₂³×C₁₉	—	2	2	no	—
131	C₂³×C₁₉	—	4	1	no	—
132	C₂³×C₁₉	—	4	2	no	—
133	C₂³×C₁₉	—	4	1	no	—
134	C₂³×C₁₉	—	4	2	no	—
135	C₂³×C₁₉	—	4	2	no	—
136	C₂³×C₁₉	—	8	2	no	—
137	C₂³×C₁₉	—	8	1	no	—
138	C₂³×C₁₉	—	8	1	no	—
139	C₂³×C₁₉	—	8	2	no	—
140	C₂³×C₁₉	#121	1	1	yes	characteristic
141	D₄×C₁₉	—	2	2	no	—
142	D₄×C₁₉	—	2	2	no	—
143	D₄×C₁₉	—	4	1	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	—	4	1	no	—
147	D₄×C₁₉	—	4	2	no	—
148	D₄×C₁₉	—	8	2	no	—
149	D₄×C₁₉	—	8	2	no	—
150	D₄×C₁₉	—	8	1	no	—
151	D₄×C₁₉	—	8	1	no	—
152	D₄×C₁₉	—	8	1	no	—
153	D₄×C₁₉	—	8	1	no	—
154	C₂×C₄×C₁₉	—	2	2	no	—
155	C₂×C₄×C₁₉	—	4	1	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	8	2	no	—
158	C₂×C₄×C₁₉	—	8	1	no	—
159	C₂×C₄×C₁₉	—	8	1	no	—
160	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
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	#127	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#135	1	2	yes	—
169	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
170	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
171	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
172	C₂×Dic₁₉	—	4	2	no	—
173	C₂×Dic₁₉	—	8	2	no	—
174	Dic₃₈	—	8	2	no	—
175	Dic₃₈	—	8	2	no	—
176	C₈×C₁₉	—	4	2	no	—
177	C₁₉⋊C₈	—	4	2	no	—
178	C₁₉⋊C₈	—	4	2	no	—
179	C₁₉⋊C₈	—	8	1	no	—
180	C₂×#486	—	19	1	no	—
181	C₂×#476	—	19	1	no	—
182	C₂×#459	D₁₉	1	1	yes	characteristic
183	#1954	—	19	1	no	—
184	C₂×#333	—	19	1	no	—
185	C₂×#331	—	19	1	no	—
186	#1277	—	19	1	no	—
187	C₂²×C₁₉	—	4	4	no	—
188	C₂²×C₁₉	—	4	2	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	1	no	—
191	C₂²×C₁₉	—	8	1	no	—
192	C₂²×C₁₉	—	8	2	no	—
193	C₂²×C₁₉	—	8	2	no	—
194	C₂²×C₁₉	—	8	2	no	—
195	C₂²×C₁₉	—	16	2	no	—
196	C₂²×C₁₉	—	16	2	no	—
197	C₂²×C₁₉	#392	1	1	yes	characteristic
198	C₂²×C₁₉	#463	1	2	yes	—
199	C₂²×C₁₉	#465	1	1	yes	characteristic
200	C₂²×C₁₉	#468	1	1	yes	characteristic
201	C₂²×C₁₉	#472	1	2	yes	—
202	C₄×C₁₉	—	2	1	no	—
203	C₄×C₁₉	—	2	1	no	—
204	C₄×C₁₉	—	8	1	no	—
205	C₄×C₁₉	#448	1	1	yes	characteristic
206	C₄×C₁₉	#449	1	2	yes	—
207	C₄×C₁₉	#449	1	1	yes	characteristic
208	C₄×C₁₉	#450	1	1	yes	characteristic
209	C₄×C₁₉	#452	1	1	yes	characteristic
210	C₄×C₁₉	#495	1	1	yes	characteristic
211	C₄×C₁₉	#496	1	1	yes	characteristic
212	Dic₁₉	—	8	2	no	—
213	C₂²×D₈	—	2	1	no	—
214	C₂×C₄⋊Q₈	—	19	1	no	—
215	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
217	#486	—	38	2	no	—
218	#486	—	38	2	no	—
219	#476	—	38	2	no	—
220	#476	—	38	2	no	—
221	#459	—	2	2	no	—
222	#459	—	2	2	no	—
223	C₂×#106	—	38	1	no	—
224	C₂×C₄⋊C₈	—	19	1	no	—
225	C₂×C₄⋊C₈	—	19	1	no	—
226	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
227	C₂×#102	—	2	1	no	—
228	C₂×#102	—	38	2	no	—
229	C₂×#102	—	38	1	no	—
230	C₂×C₂²⋊C₈	—	38	2	no	—
231	C₂×C₄×C₈	—	19	1	no	—
232	#333	—	38	2	no	—
233	#331	—	38	2	no	—
234	C₂×C₁₉	—	8	2	no	—
235	C₂×C₁₉	—	16	2	no	—
236	C₂×C₁₉	#1677	1	2	yes	—
237	C₂×C₁₉	#1697	1	2	yes	—
238	C₂×C₁₉	#2000	1	1	yes	characteristic
239	C₂×C₁₉	#2012	1	1	yes	characteristic
240	C₂×C₁₉	#2018	1	1	yes	characteristic
241	C₂²×Q₈	—	38	1	no	—
242	C₂²×D₄	—	2	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
246	C₂³×C₄	—	2	1	no	—
247	C₂×D₈	—	2	4	no	—
248	C₂×D₈	—	4	2	no	—
249	C₂×D₈	—	4	2	no	—
250	C₂²×C₈	—	2	1	no	—
251	C₂²×C₈	—	19	2	no	—
252	C₂²×C₈	—	38	1	no	—
253	C₂²×C₈	—	38	1	no	—
254	C₄⋊Q₈	—	19	2	no	—
255	C₄⋊Q₈	—	38	1	no	—
256	C₄⋊Q₈	—	38	1	no	—
257	C₄⋊Q₈	—	38	1	no	—
258	#127	—	2	1	no	—
259	#127	—	2	1	no	—
260	#127	—	2	1	no	—
261	#127	C₂²⋊D₁₉	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	—	2	1	no	—
266	C₂×C₄⋊C₄	—	38	1	no	—
267	C₂×C₄⋊C₄	—	38	1	no	—
268	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
271	#106	—	38	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	19	2	no	—
274	C₄⋊C₈	—	38	1	no	—
275	C₄⋊C₈	—	38	1	no	—
276	C₄⋊C₈	—	38	1	no	—
277	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
278	#102	—	2	4	no	—
279	#102	—	38	4	no	—
280	#102	—	38	8	no	—
281	C₂²⋊C₈	—	76	4	no	—
282	C₄×C₈	—	38	1	no	—
283	C₄×C₈	—	38	1	no	—
284	C₁₉	#10267	1	1	yes	characteristic, complemented, Sylow
285	C₂⁴	—	2	1	no	—
286	C₂⁴	—	4	1	no	—
287	C₂×Q₈	—	38	2	no	—
288	C₂×Q₈	—	76	1	no	—
289	C₂×Q₈	—	152	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	2	1	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	1	no	—
301	C₂×D₄	—	4	1	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	2	no	—
306	C₂×D₄	—	4	2	no	—
307	C₂×D₄	—	8	2	no	—
308	C₂×D₄	#64526	1	2	yes	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	4	1	no	—
311	C₂²×C₄	—	4	1	no	—
312	C₂²×C₄	—	4	2	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	76	1	no	—
315	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
316	C₂²×C₄	#64543	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
318	D₈	—	4	8	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	4	1	no	—
321	C₂×C₈	—	4	1	no	—
322	C₂×C₈	—	38	2	no	—
323	C₂×C₈	—	38	2	no	—
324	C₂×C₈	—	38	2	no	—
325	C₂×C₈	—	38	2	no	—
326	C₂×C₈	—	76	1	no	—
327	C₂×C₈	—	76	1	no	—
328	C₂×C₈	—	76	1	no	—
329	C₂×C₈	—	76	2	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	1	no	—
332	C₄⋊C₄	—	38	2	no	—
333	C₄⋊C₄	—	38	2	no	—
334	C₄⋊C₄	—	76	1	no	—
335	C₄⋊C₄	—	76	1	no	—
336	C₂²⋊C₄	—	4	1	no	—
337	C₂²⋊C₄	—	4	1	no	—
338	C₄²	D₄×D₁₉	1	1	yes	characteristic
339	C₄²	D₄×D₁₉	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
342	C₂³	—	2	2	no	—
343	C₂³	—	4	1	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	2	no	—
350	C₂³	—	8	2	no	—
351	C₂³	—	8	1	no	—
352	C₂³	#10597385	1	1	yes	characteristic
353	Q₈	—	152	2	no	—
354	Q₈	—	152	2	no	—
355	D₄	—	2	2	no	—
356	D₄	—	2	2	no	—
357	D₄	—	4	4	no	—
358	D₄	—	4	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	8	2	no	—
363	D₄	—	8	2	no	—
364	D₄	—	8	1	no	—
365	D₄	—	8	1	no	—
366	D₄	—	8	1	no	—
367	D₄	—	8	1	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	8	1	no	—
372	C₂×C₄	—	8	1	no	—
373	C₂×C₄	—	8	2	no	—
374	C₂×C₄	—	76	2	no	—
375	C₂×C₄	—	152	2	no	—
376	C₂×C₄	#10597357	1	2	yes	—
377	C₂×C₄	#10597358	1	2	yes	—
378	C₂×C₄	#10597378	1	1	yes	characteristic
379	C₂×C₄	C₂×#64526	1	1	yes	characteristic
380	C₂×C₄	#10597383	1	1	yes	characteristic
381	C₂×C₄	#10597383	1	1	yes	characteristic
382	C₂×C₄	#10597384	1	1	yes	characteristic
383	C₂×C₄	#10597385	1	1	yes	characteristic
384	C₂×C₄	#10597386	1	1	yes	characteristic
385	C₂×C₄	#10597396	1	1	yes	characteristic
386	C₂×C₄	#10597397	1	1	yes	characteristic
387	C₂×C₄	#10597399	1	1	yes	characteristic
388	C₈	—	4	2	no	—
389	C₈	—	76	2	no	—
390	C₈	—	76	2	no	—
391	C₈	—	152	1	no	—
392	C₂²	—	4	2	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	1	no	—
396	C₂²	—	8	1	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	8	2	no	—
400	C₂²	—	16	2	no	—
401	C₂²	—	16	2	no	—
402	C₂²	#11926452	1	1	yes	characteristic
403	C₂²	#11926757	1	2	yes	—
404	C₂²	#11926771	1	1	yes	characteristic
405	C₂²	#11926788	1	1	yes	characteristic
406	C₂²	#11926812	1	2	yes	—
407	C₄	—	2	1	no	—
408	C₄	—	2	1	no	—
409	C₄	—	8	1	no	—
410	C₄	—	152	2	no	—
411	C₄	#11926682	1	1	yes	characteristic
412	C₄	#11926686	1	2	yes	—
413	C₄	#11926687	1	1	yes	characteristic
414	C₄	#11926695	1	1	yes	characteristic
415	C₄	#11926706	1	1	yes	characteristic
416	C₄	#11926927	1	1	yes	characteristic
417	C₄	#11926932	1	1	yes	characteristic
418	C₂	—	8	2	no	—
419	C₂	—	16	2	no	—
420	C₂	#14563042	1	2	yes	—
421	C₂	#14563166	1	2	yes	—
422	C₂	#14564638	1	1	yes	characteristic
423	C₂	#14564710	1	1	yes	characteristic
424	C₂	#14564741	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597385
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#459	C₂
socle	C₂³×C₁₉	#121
hypercenter	C₂×#459	D₁₉
hypocenter	C₁₉	#10267
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. C₂×#11926890	C₂	semidirect
2. C₂×#11926834	C₂	semidirect
3. #14564430	C₂	semidirect
4. C₂×#11926292	C₂	semidirect
5. C₂×#11926288	C₂	semidirect
6. #14561469	C₂	semidirect
284. C₁₉	#10267	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926890	2
C₂×#11926834	2
#14564430	2
C₂×#11926292	2
C₂×#11926288	2
#14561469	2
C₂×C₁₉×#459	2
#10267	19