Subgroups — #18085312

Order 4864.

802 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926916	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#11926890	C₂	1	1	yes	maximal, characteristic, complemented
3	#14564596	C₂	1	1	yes	maximal, characteristic, complemented
4	#14564442	C₂	1	1	yes	maximal, characteristic, complemented
5	#14564442	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₉⋊#1273	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×#493	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64526	—	2	2	no	—
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	#11926916	—	2	2	no	—
11	#11926916	—	2	2	no	—
12	#11926890	—	2	2	no	—
13	#11926890	—	2	2	no	—
14	C₂×#10597289	—	2	2	no	—
15	C₂×#10597289	—	2	2	no	—
16	C₂×#10597289	—	2	2	no	—
17	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
19	#11926414	C₂²	1	1	yes	characteristic
20	#11926307	—	2	2	no	—
21	C₂²×D₈×C₁₉	—	2	2	no	—
22	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
24	C₁₉×#493	—	2	2	no	—
25	C₁₉×#493	—	2	2	no	—
26	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₁₉	—	2	1	no	—
28	C₂²×D₄×C₁₉	—	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	—	2	1	no	—
33	C₂²×Dic₃₈	—	2	1	no	—
34	C₂×D₈×C₁₉	—	2	8	no	—
35	C₂×D₈×C₁₉	—	4	4	no	—
36	C₂×D₈×C₁₉	—	4	4	no	—
37	C₂²×C₈×C₁₉	D₄	1	2	yes	—
38	C₁₉×#127	—	2	1	no	—
39	C₁₉×#127	—	2	1	no	—
40	C₁₉×#127	—	2	1	no	—
41	C₁₉×#127	—	2	1	no	—
42	C₁₉×#127	—	2	1	no	—
43	C₁₉×#127	—	2	1	no	—
44	C₁₉×#127	D₄	1	2	yes	—
45	C₁₉×#127	D₄	1	2	yes	—
46	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
47	C₂×#64526	—	2	8	no	—
48	C₂×#64526	—	4	4	no	—
49	C₂×#64526	—	4	4	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄⋊Dic₁₉	—	2	1	no	—
55	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
56	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
57	#10597315	—	2	1	no	—
58	#10597315	—	2	1	no	—
59	#10597315	—	2	1	no	—
60	#10597315	D₄	1	2	yes	—
61	C₄×C₈×C₁₉	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	#10597289	—	2	8	no	—
64	#10597289	—	4	4	no	—
65	#10597289	—	4	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	—	2	1	no	—
70	C₂⁴×C₁₉	—	4	1	no	—
71	C₂⁴×C₁₉	—	4	1	no	—
72	C₂×D₄×C₁₉	—	2	2	no	—
73	C₂×D₄×C₁₉	—	2	2	no	—
74	C₂×D₄×C₁₉	—	2	2	no	—
75	C₂×D₄×C₁₉	—	2	2	no	—
76	C₂×D₄×C₁₉	—	2	2	no	—
77	C₂×D₄×C₁₉	—	2	2	no	—
78	C₂×D₄×C₁₉	—	4	1	no	—
79	C₂×D₄×C₁₉	—	4	1	no	—
80	C₂×D₄×C₁₉	—	4	1	no	—
81	C₂×D₄×C₁₉	—	4	1	no	—
82	C₂×D₄×C₁₉	—	4	1	no	—
83	C₂×D₄×C₁₉	—	4	1	no	—
84	C₂×D₄×C₁₉	—	4	2	no	—
85	C₂×D₄×C₁₉	—	4	2	no	—
86	C₂×D₄×C₁₉	—	4	2	no	—
87	C₂×D₄×C₁₉	—	4	2	no	—
88	C₂×D₄×C₁₉	—	4	2	no	—
89	C₂×D₄×C₁₉	—	4	2	no	—
90	C₂×D₄×C₁₉	—	4	2	no	—
91	C₂×D₄×C₁₉	—	4	2	no	—
92	C₂×D₄×C₁₉	—	4	2	no	—
93	C₂×D₄×C₁₉	—	4	2	no	—
94	C₂×D₄×C₁₉	—	4	2	no	—
95	C₂×D₄×C₁₉	—	4	2	no	—
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₁₉	—	4	1	no	—
100	C₂²×Dic₁₉	—	4	1	no	—
101	C₂×Dic₃₈	—	2	2	no	—
102	C₂×Dic₃₈	—	4	2	no	—
103	C₂×Dic₃₈	—	4	2	no	—
104	C₂×Dic₃₈	—	4	1	no	—
105	D₈×C₁₉	—	4	16	no	—
106	C₂×C₈×C₁₉	—	2	2	no	—
107	C₂×C₈×C₁₉	—	2	2	no	—
108	C₂×C₈×C₁₉	SD₁₆	1	4	yes	complemented
109	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
110	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
111	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₄²×C₁₉	#41	1	1	yes	characteristic
113	#64526	—	4	16	no	—
114	C₄⋊Dic₁₉	—	2	2	no	—
115	C₄⋊Dic₁₉	—	2	2	no	—
116	C₄⋊Dic₁₉	—	4	1	no	—
117	C₄⋊Dic₁₉	—	4	1	no	—
118	C₄⋊Dic₁₉	—	4	2	no	—
119	C₄⋊Dic₁₉	—	4	2	no	—
120	C₄⋊Dic₁₉	—	4	2	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	—	2	2	no	—
126	C₂×C₁₉⋊C₈	D₈	1	4	yes	complemented
127	#10305	—	19	1	no	maximal, Sylow
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	4	2	no	—
130	C₂³×C₁₉	—	8	1	no	—
131	C₂³×C₁₉	—	8	1	no	—
132	C₂³×C₁₉	—	8	1	no	—
133	C₂³×C₁₉	—	8	1	no	—
134	C₂³×C₁₉	—	8	1	no	—
135	C₂³×C₁₉	—	8	1	no	—
136	C₂³×C₁₉	—	8	1	no	—
137	C₂³×C₁₉	—	8	1	no	—
138	C₂³×C₁₉	—	8	1	no	—
139	C₂³×C₁₉	—	8	1	no	—
140	C₂³×C₁₉	—	8	1	no	—
141	C₂³×C₁₉	—	8	1	no	—
142	C₂³×C₁₉	#127	1	1	yes	characteristic
143	D₄×C₁₉	—	4	4	no	—
144	D₄×C₁₉	—	4	4	no	—
145	D₄×C₁₉	—	4	4	no	—
146	D₄×C₁₉	—	4	4	no	—
147	D₄×C₁₉	—	4	4	no	—
148	D₄×C₁₉	—	4	4	no	—
149	D₄×C₁₉	—	8	2	no	—
150	D₄×C₁₉	—	8	2	no	—
151	D₄×C₁₉	—	8	2	no	—
152	D₄×C₁₉	—	8	2	no	—
153	D₄×C₁₉	—	8	2	no	—
154	D₄×C₁₉	—	8	2	no	—
155	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
156	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
157	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
160	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂×D₈	1	2	yes	—
162	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
163	C₂×C₄×C₁₉	#135	1	2	yes	—
164	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
167	C₂×Dic₁₉	—	4	2	no	—
168	C₂×Dic₁₉	—	8	1	no	—
169	C₂×Dic₁₉	—	8	1	no	—
170	C₂×Dic₁₉	—	8	1	no	—
171	C₂×Dic₁₉	—	8	1	no	—
172	C₂×Dic₁₉	—	8	1	no	—
173	Dic₃₈	—	4	4	no	—
174	Dic₃₈	—	8	2	no	—
175	C₈×C₁₉	—	2	4	no	—
176	C₁₉⋊C₈	—	2	4	no	—
177	C₁₉⋊C₈	—	4	2	no	—
178	C₂×#493	D₁₉	1	1	yes	characteristic
179	C₂×#492	—	19	1	no	—
180	C₂×#486	—	19	1	no	—
181	#1990	—	19	1	no	—
182	#1957	—	19	1	no	—
183	#1957	—	19	1	no	—
184	#1273	—	19	1	no	—
185	C₂²×C₁₉	—	8	2	no	—
186	C₂²×C₁₉	—	8	2	no	—
187	C₂²×C₁₉	—	8	2	no	—
188	C₂²×C₁₉	—	8	2	no	—
189	C₂²×C₁₉	—	8	2	no	—
190	C₂²×C₁₉	—	8	2	no	—
191	C₂²×C₁₉	—	16	1	no	—
192	C₂²×C₁₉	—	16	1	no	—
193	C₂²×C₁₉	—	16	1	no	—
194	C₂²×C₁₉	—	16	1	no	—
195	C₂²×C₁₉	—	16	1	no	—
196	C₂²×C₁₉	—	16	1	no	—
197	C₂²×C₁₉	—	16	1	no	—
198	C₂²×C₁₉	—	16	1	no	—
199	C₂²×C₁₉	#392	1	1	yes	characteristic
200	C₂²×C₁₉	#492	1	1	yes	characteristic
201	C₂²×C₁₉	#493	1	1	yes	characteristic
202	C₂²×C₁₉	#495	1	1	yes	characteristic
203	C₂²×C₁₉	#496	1	1	yes	characteristic
204	C₂²×C₁₉	#496	1	1	yes	characteristic
205	C₂²×C₁₉	#496	1	1	yes	characteristic
206	C₄×C₁₉	#447	1	2	yes	—
207	C₄×C₁₉	#449	1	2	yes	—
208	C₄×C₁₉	#450	1	2	yes	—
209	C₄×C₁₉	#459	1	2	yes	—
210	C₄×C₁₉	#460	1	2	yes	—
211	C₄×C₁₉	#463	1	2	yes	—
212	Dic₁₉	—	8	2	no	—
213	Dic₁₉	—	16	1	no	—
214	C₂²×SD₁₆	—	38	2	no	—
215	C₂²×D₈	—	2	2	no	—
216	C₂×C₄⋊Q₈	—	19	1	no	—
217	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
218	C₂×#127	C₂×D₁₉	1	1	yes	characteristic
219	#493	—	2	2	no	—
220	#493	—	2	2	no	—
221	#492	—	38	2	no	—
222	#492	—	38	2	no	—
223	#486	—	38	2	no	—
224	#486	—	38	2	no	—
225	C₂×#102	—	38	2	no	—
226	C₂×#102	—	38	2	no	—
227	C₂×#102	—	38	2	no	—
228	C₂×C₄×C₈	—	19	1	no	—
229	C₂×C₄×C₈	—	19	1	no	—
230	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
231	#384	—	19	1	no	—
232	#340	—	38	2	no	—
233	C₂×C₁₉	—	16	2	no	—
234	C₂×C₁₉	—	16	2	no	—
235	C₂×C₁₉	#1706	1	1	yes	characteristic
236	C₂×C₁₉	#1715	1	1	yes	characteristic
237	C₂×C₁₉	#1717	1	1	yes	characteristic
238	C₂×C₁₉	#1721	1	1	yes	characteristic
239	C₂×C₁₉	#2011	1	1	yes	characteristic
240	C₂×C₁₉	#2012	1	1	yes	characteristic
241	C₂×C₁₉	#2014	1	1	yes	characteristic
242	C₂²×Q₈	—	38	1	no	—
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂²×D₄	—	2	1	no	—
249	C₂×SD₁₆	—	38	8	no	—
250	C₂×SD₁₆	—	76	4	no	—
251	C₂×SD₁₆	—	76	4	no	—
252	C₂×D₈	—	2	8	no	—
253	C₂×D₈	—	4	4	no	—
254	C₂×D₈	—	4	4	no	—
255	C₂²×C₈	—	19	2	no	—
256	C₂²×C₈	—	19	2	no	—
257	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
258	C₄⋊Q₈	—	19	2	no	—
259	C₄⋊Q₈	—	38	1	no	—
260	C₄⋊Q₈	—	38	1	no	—
261	C₄⋊Q₈	—	38	1	no	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	—	2	1	no	—
266	#127	—	2	1	no	—
267	#127	—	2	1	no	—
268	#127	C₂²⋊D₁₉	1	2	yes	—
269	#127	C₂²⋊D₁₉	1	2	yes	—
270	C₂×C₄⋊C₄	—	38	1	no	—
271	C₂×C₄⋊C₄	—	38	1	no	—
272	C₂×C₄⋊C₄	—	38	1	no	—
273	C₂×C₄⋊C₄	—	38	1	no	—
274	C₂×C₄⋊C₄	—	38	1	no	—
275	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
276	#102	—	38	8	no	—
277	#102	—	76	4	no	—
278	#102	—	76	4	no	—
279	C₄×C₈	—	2	1	no	—
280	C₄×C₈	—	2	1	no	—
281	C₄×C₈	—	38	1	no	—
282	C₄×C₈	—	38	1	no	—
283	C₄×C₈	—	38	1	no	—
284	C₄×C₈	—	38	1	no	—
285	C₁₉	#10305	1	1	yes	characteristic, complemented, Sylow
286	C₂⁴	—	4	1	no	—
287	C₂⁴	—	4	1	no	—
288	C₂×Q₈	—	38	2	no	—
289	C₂×Q₈	—	76	1	no	—
290	C₂×Q₈	—	76	2	no	—
291	C₂×Q₈	—	76	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	2	no	—
298	C₂×D₄	—	4	2	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	1	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	—	4	2	no	—
309	C₂×D₄	—	4	2	no	—
310	C₂×D₄	—	4	2	no	—
311	C₂×D₄	—	4	2	no	—
312	C₂×D₄	—	4	2	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂×D₄	—	4	2	no	—
315	C₂×D₄	—	4	2	no	—
316	C₂²×C₄	—	76	1	no	—
317	C₂²×C₄	—	76	1	no	—
318	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
319	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
320	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
321	SD₁₆	—	76	16	no	—
322	D₈	—	4	16	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	19	4	no	—
326	C₂×C₈	—	38	2	no	—
327	C₂×C₈	—	38	2	no	—
328	C₂×C₈	—	38	2	no	—
329	C₂×C₈	—	38	2	no	—
330	C₂×C₈	—	38	2	no	—
331	C₂×C₈	#64526	1	4	yes	complemented
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	C₄⋊C₄	—	76	2	no	—
337	C₄⋊C₄	—	76	2	no	—
338	C₄⋊C₄	—	76	2	no	—
339	C₄²	D₄×D₁₉	1	1	yes	characteristic
340	C₄²	#64543	1	1	yes	characteristic
341	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
342	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	1	no	—
346	C₂³	—	8	1	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	8	1	no	—
351	C₂³	—	8	1	no	—
352	C₂³	—	8	1	no	—
353	C₂³	—	8	1	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	8	1	no	—
356	C₂³	—	8	1	no	—
357	C₂³	#10597386	1	1	yes	characteristic
358	Q₈	—	76	4	no	—
359	Q₈	—	152	2	no	—
360	D₄	—	4	4	no	—
361	D₄	—	4	4	no	—
362	D₄	—	4	4	no	—
363	D₄	—	4	4	no	—
364	D₄	—	4	4	no	—
365	D₄	—	4	4	no	—
366	D₄	—	8	2	no	—
367	D₄	—	8	2	no	—
368	D₄	—	8	2	no	—
369	D₄	—	8	2	no	—
370	D₄	—	8	2	no	—
371	D₄	—	8	2	no	—
372	C₂×C₄	—	76	2	no	—
373	C₂×C₄	—	152	1	no	—
374	C₂×C₄	—	152	1	no	—
375	C₂×C₄	—	152	1	no	—
376	C₂×C₄	—	152	1	no	—
377	C₂×C₄	—	152	1	no	—
378	C₂×C₄	D₈×D₁₉	1	2	yes	—
379	C₂×C₄	#10597357	1	2	yes	—
380	C₂×C₄	#10597357	1	2	yes	—
381	C₂×C₄	#10597358	1	2	yes	—
382	C₂×C₄	#10597378	1	2	yes	—
383	C₂×C₄	C₂×#64526	1	2	yes	—
384	C₂×C₄	#10597383	1	1	yes	characteristic
385	C₂×C₄	#10597383	1	1	yes	characteristic
386	C₂×C₄	#10597384	1	1	yes	characteristic
387	C₂×C₄	#10597385	1	1	yes	characteristic
388	C₂×C₄	#10597385	1	1	yes	characteristic
389	C₂×C₄	#10597399	1	1	yes	characteristic
390	C₈	—	2	4	no	—
391	C₈	—	38	4	no	—
392	C₈	—	76	2	no	—
393	C₂²	—	8	2	no	—
394	C₂²	—	8	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	2	no	—
398	C₂²	—	8	2	no	—
399	C₂²	—	16	1	no	—
400	C₂²	—	16	1	no	—
401	C₂²	—	16	1	no	—
402	C₂²	—	16	1	no	—
403	C₂²	—	16	1	no	—
404	C₂²	—	16	1	no	—
405	C₂²	—	16	1	no	—
406	C₂²	—	16	1	no	—
407	C₂²	#11926452	1	1	yes	characteristic
408	C₂²	#11926916	1	1	yes	characteristic
409	C₂²	#11926919	1	1	yes	characteristic
410	C₂²	#11926927	1	1	yes	characteristic
411	C₂²	#11926931	1	1	yes	characteristic
412	C₂²	#11926932	1	1	yes	characteristic
413	C₂²	#11926932	1	1	yes	characteristic
414	C₄	—	304	1	no	—
415	C₄	—	152	2	no	—
416	C₄	#11926676	1	2	yes	—
417	C₄	#11926686	1	2	yes	—
418	C₄	#11926695	1	2	yes	—
419	C₄	#11926737	1	2	yes	—
420	C₄	#11926741	1	2	yes	—
421	C₄	#11926757	1	2	yes	—
422	C₂	—	16	2	no	—
423	C₂	—	16	2	no	—
424	C₂	#14563224	1	1	yes	characteristic
425	C₂	#14563261	1	1	yes	characteristic
426	C₂	#14563273	1	1	yes	characteristic
427	C₂	#14563300	1	1	yes	characteristic
428	C₂	#14564704	1	1	yes	characteristic
429	C₂	#14564710	1	1	yes	characteristic
430	C₂	#14564723	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597386
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting, prime radical	C₂×C₁₉×#493	C₂
socle	C₂³×C₁₉	#127
hypercenter	C₂×#493	D₁₉
hypocenter	C₁₉	#10305
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#493

Complements

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

N	H ≅ G/N	type
1. C₂×#11926916	C₂	semidirect
2. C₂×#11926890	C₂	semidirect
3. #14564596	C₂	semidirect
4. #14564442	C₂	semidirect
5. #14564442	C₂	semidirect
6. C₁₉⋊#1273	C₂	semidirect
108. C₂×C₈×C₁₉	SD₁₆	semidirect
126. C₂×C₁₉⋊C₈	D₈	semidirect
285. C₁₉	#10305	semidirect
331. C₂×C₈	#64526	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926916	2
C₂×#11926890	2
#14564596	2
#14564442	2
C₁₉⋊#1273	2
C₂×C₁₉×#493	2
#10305	19