Subgroups — #14575240

Order 2432.

520 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×#10597357	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927182	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926925	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926790	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926787	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926761	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926757	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926706	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926703	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926678	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926676	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926620	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
18	C₂×#64543	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
21	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	#10597399	—	2	1	no	—
27	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
28	#10597393	C₂²	1	1	yes	characteristic, complemented
29	#10597392	C₂²	1	1	yes	characteristic, complemented
30	C₂×#64528	C₂²	1	1	yes	characteristic, complemented
31	#10597385	—	2	1	no	—
32	#10597385	—	2	1	no	—
33	#10597384	C₂²	1	1	yes	characteristic
34	#10597383	—	2	1	no	—
35	#10597382	C₂²	1	1	yes	characteristic, complemented
36	#10597381	—	2	1	no	—
37	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
38	D₄×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
39	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
40	C₂×#64525	C₂²	1	1	yes	characteristic
41	C₂×#64525	C₂²	1	1	yes	characteristic
42	#10597376	C₂²	1	1	yes	characteristic
43	#10597375	—	2	1	no	—
44	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
45	C₂×(C₂×D₁₉)⋊C₄	—	2	1	no	—
46	#10597370	C₂²	1	1	yes	characteristic, complemented
47	#10597357	—	2	4	no	—
48	C₂×#64516	C₂²	1	1	yes	characteristic, complemented
49	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
50	#10597292	C₂²	1	1	yes	characteristic, complemented
51	#10597289	C₂²	1	1	yes	characteristic, complemented
52	#10597289	C₂²	1	1	yes	characteristic, complemented
53	#10597289	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#10597278	C₂²	1	1	yes	characteristic, complemented
56	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	#10597275	C₂²	1	1	yes	characteristic, complemented
58	#10597273	C₂²	1	1	yes	characteristic, complemented
59	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₁₉	—	2	1	no	—
62	C₂³×D₁₉	—	2	1	no	—
63	#41×C₁₉	—	2	2	no	—
64	#41×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₉	—	2	1	no	—
76	C₂×C₂²⋊D₁₉	—	2	1	no	—
77	C₂×C₂²⋊D₁₉	—	2	1	no	—
78	C₂×C₂²⋊D₁₉	—	2	1	no	—
79	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
80	C₂²×Dic₁₉	—	2	1	no	—
81	C₂²×Dic₁₉	—	2	1	no	—
82	C₂²×Dic₁₉	—	2	1	no	—
83	#64543	—	2	2	no	—
84	#64543	—	4	1	no	—
85	D₄×D₁₉	—	2	2	no	—
86	D₄×D₁₉	—	4	1	no	—
87	C₂×D₇₆	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
89	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
90	SD₁₆×C₁₉	—	2	2	no	—
91	SD₁₆×C₁₉	—	2	2	no	—
92	D₈×C₁₉	—	2	2	no	—
93	D₈×C₁₉	D₄	1	4	yes	complemented
94	M₁₆×C₁₉	—	2	2	no	—
95	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₂²⋊Dic₁₉	—	2	1	no	—
98	C₂²⋊Dic₁₉	—	2	1	no	—
99	C₂²⋊Dic₁₉	—	2	1	no	—
100	C₂²⋊Dic₁₉	—	2	1	no	—
101	C₂²⋊Dic₁₉	—	2	1	no	—
102	C₂²⋊Dic₁₉	—	2	1	no	—
103	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
104	#64528	—	4	1	no	—
105	#64526	—	2	2	no	—
106	#64525	—	2	2	no	—
107	#64525	—	4	1	no	—
108	(C₂×D₁₉)⋊C₄	—	2	1	no	—
109	(C₂×D₁₉)⋊C₄	—	2	1	no	—
110	(C₂×D₁₉)⋊C₄	—	2	1	no	—
111	(C₂×D₁₉)⋊C₄	—	2	1	no	—
112	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
113	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
114	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
115	Dic₁₉⋊C₄	—	2	1	no	—
116	Dic₁₉⋊C₄	—	2	1	no	—
117	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
118	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
119	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
121	#64516	—	2	2	no	—
122	#64515	—	2	2	no	—
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	4	2	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	8	1	no	—
129	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₁₉	—	2	1	no	—
131	C₂²×D₁₉	—	4	2	no	—
132	C₂²×D₁₉	—	4	2	no	—
133	C₂²×D₁₉	—	8	1	no	—
134	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
135	Q₈×C₁₉	—	2	1	no	—
136	Q₈×C₁₉	—	2	1	no	—
137	D₄×C₁₉	—	2	1	no	—
138	D₄×C₁₉	—	2	1	no	—
139	D₄×C₁₉	—	2	1	no	—
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	4	2	no	—
142	D₄×C₁₉	—	4	2	no	—
143	D₄×C₁₉	C₂×D₄	1	2	yes	—
144	D₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	4	2	no	—
149	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
150	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
151	C₂²⋊D₁₉	—	4	1	no	—
152	C₂²⋊D₁₉	—	4	2	no	—
153	C₂²⋊D₁₉	—	4	2	no	—
154	C₂²⋊D₁₉	—	8	1	no	—
155	C₂²⋊D₁₉	—	8	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	2	1	no	—
159	C₂×Dic₁₉	—	4	2	no	—
160	C₂×Dic₁₉	—	8	1	no	—
161	C₂×Dic₁₉	—	8	1	no	—
162	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
165	D₇₆	—	2	1	no	—
166	D₇₆	—	2	1	no	—
167	C₄×D₁₉	—	2	1	no	—
168	C₄×D₁₉	—	2	1	no	—
169	Dic₃₈	—	2	1	no	—
170	Dic₃₈	—	2	1	no	—
171	C₈×C₁₉	—	2	1	no	—
172	C₈×C₁₉	C₂×D₄	1	2	yes	—
173	C₁₉⋊C₈	—	2	1	no	—
174	C₁₉⋊C₈	—	2	1	no	—
175	#3273	—	19	1	no	maximal, Sylow
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	4	1	no	—
182	C₂²×C₁₉	—	4	1	no	—
183	C₂²×C₁₉	—	4	1	no	—
184	C₂²×C₁₉	—	4	1	no	—
185	C₂²×C₁₉	—	4	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	8	4	no	—
189	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₂×D₁₉	—	2	1	no	—
191	C₂×D₁₉	—	2	1	no	—
192	C₂×D₁₉	—	2	1	no	—
193	C₂×D₁₉	—	4	1	no	—
194	C₂×D₁₉	—	4	1	no	—
195	C₂×D₁₉	—	4	1	no	—
196	C₂×D₁₉	—	8	4	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
201	Dic₁₉	—	2	1	no	—
202	Dic₁₉	—	2	1	no	—
203	Dic₁₉	—	2	1	no	—
204	Dic₁₉	—	4	1	no	—
205	Dic₁₉	—	4	1	no	—
206	Dic₁₉	—	4	1	no	—
207	C₂×AGL(1,ℤ/8)	—	19	1	no	—
208	C₂×AGL(1,ℤ/8)	D₁₉	1	1	yes	characteristic, complemented
209	#546	—	19	1	no	—
210	#546	—	19	1	no	—
211	#495	—	19	1	no	—
212	#468	—	19	1	no	—
213	#468	—	19	1	no	—
214	#463	—	19	1	no	—
215	#463	—	19	1	no	—
216	#452	—	19	1	no	—
217	#452	—	19	1	no	—
218	#447	—	19	1	no	—
219	#447	—	19	1	no	—
220	C₄×D₈	—	19	1	no	—
221	#436	—	19	1	no	—
222	C₂×C₁₉	—	4	2	no	—
223	C₂×C₁₉	—	4	1	no	—
224	C₂×C₁₉	—	4	2	no	—
225	C₂×C₁₉	—	8	1	no	—
226	C₂×C₁₉	D₄²	1	1	yes	characteristic
227	C₂×C₁₉	#575	1	1	yes	characteristic
228	C₂×C₁₉	#576	1	1	yes	characteristic
229	D₁₉	—	4	1	no	—
230	D₁₉	—	8	1	no	—
231	C₂×#41	—	19	1	no	—
232	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
233	C₂²×D₄	—	19	1	no	—
234	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
235	AGL(1,ℤ/8)	—	2	4	no	—
236	AGL(1,ℤ/8)	—	38	4	no	—
237	C₂×Q₁₆	—	19	1	no	—
238	C₂×SD₁₆	—	19	1	no	—
239	C₂×SD₁₆	—	19	1	no	—
240	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
241	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
242	C₂×D₈	—	19	1	no	—
243	C₂×D₈	—	19	1	no	—
244	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
245	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
246	C₂×M₁₆	—	19	1	no	—
247	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
248	#124	—	19	1	no	—
249	#124	—	19	1	no	—
250	#123	—	38	1	no	—
251	#123	—	38	1	no	—
252	C₂²⋊Q₈	—	19	1	no	—
253	C₂²⋊Q₈	—	19	1	no	—
254	#121	—	19	1	no	—
255	#121	—	19	1	no	—
256	#121	—	38	1	no	—
257	#121	—	38	1	no	—
258	#120	—	38	1	no	—
259	#120	—	38	1	no	—
260	C₄×D₄	—	19	1	no	—
261	C₄×D₄	—	19	1	no	—
262	C₄×D₄	—	19	1	no	—
263	C₂×C₂²⋊C₄	—	38	1	no	—
264	C₂×C₂²⋊C₄	—	38	1	no	—
265	#107	—	19	1	no	—
266	C₄⋊C₈	—	19	1	no	—
267	#103	—	19	1	no	—
268	#103	—	19	1	no	—
269	#102	—	19	1	no	—
270	#102	—	19	1	no	—
271	#102	—	19	1	no	—
272	#102	—	19	1	no	—
273	C₂²⋊C₈	—	19	1	no	—
274	C₂²⋊C₈	—	19	1	no	—
275	C₄×C₈	—	19	1	no	—
276	C₁₉	#3273	1	1	yes	characteristic, complemented, Sylow
277	C₂⁴	—	2	1	no	—
278	C₂⁴	—	38	1	no	—
279	#41	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	38	2	no	—
282	#41	—	76	1	no	—
283	C₂×Q₈	—	19	1	no	—
284	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	19	1	no	—
290	C₂×D₄	—	19	1	no	—
291	C₂×D₄	—	38	1	no	—
292	C₂×D₄	—	38	2	no	—
293	C₂×D₄	—	38	1	no	—
294	C₂×D₄	—	38	1	no	—
295	C₂×D₄	—	38	1	no	—
296	C₂×D₄	—	76	1	no	—
297	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
298	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	19	1	no	—
302	C₂²×C₄	—	38	1	no	—
303	C₂²×C₄	—	38	1	no	—
304	C₂²×C₄	—	38	1	no	—
305	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
306	Q₁₆	—	76	1	no	—
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	38	2	no	—
310	SD₁₆	—	38	2	no	—
311	D₈	—	2	2	no	—
312	D₈	—	38	2	no	—
313	D₈	—	76	1	no	—
314	D₈	C₂²⋊D₁₉	1	4	yes	complemented
315	M₁₆	—	2	2	no	—
316	M₁₆	—	38	2	no	—
317	C₂×C₈	—	19	1	no	—
318	C₂×C₈	—	19	1	no	—
319	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
320	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
321	C₄⋊C₄	—	19	1	no	—
322	C₄⋊C₄	—	19	1	no	—
323	C₄⋊C₄	—	19	1	no	—
324	C₄⋊C₄	—	38	1	no	—
325	C₄⋊C₄	—	38	1	no	—
326	C₂²⋊C₄	—	19	1	no	—
327	C₂²⋊C₄	—	19	1	no	—
328	C₂²⋊C₄	—	38	1	no	—
329	C₂²⋊C₄	—	38	1	no	—
330	C₂²⋊C₄	—	38	1	no	—
331	C₂²⋊C₄	—	38	1	no	—
332	C₂²⋊C₄	—	38	1	no	—
333	C₂²⋊C₄	—	38	1	no	—
334	C₂²⋊C₄	—	38	1	no	—
335	C₂²⋊C₄	—	38	1	no	—
336	C₂²⋊C₄	—	38	1	no	—
337	C₂²⋊C₄	—	38	1	no	—
338	C₄²	—	19	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	8	1	no	—
345	C₂³	—	19	1	no	—
346	C₂³	—	38	1	no	—
347	C₂³	—	76	2	no	—
348	C₂³	—	76	2	no	—
349	C₂³	—	152	1	no	—
350	C₂³	D₄×D₁₉	1	1	yes	characteristic
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	38	1	no	—
354	Q₈	—	38	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	2	1	no	—
357	D₄	—	2	1	no	—
358	D₄	—	2	1	no	—
359	D₄	—	4	2	no	—
360	D₄	—	4	2	no	—
361	D₄	—	38	1	no	—
362	D₄	—	38	1	no	—
363	D₄	—	76	1	no	—
364	D₄	—	76	2	no	—
365	D₄	—	76	2	no	—
366	D₄	—	152	1	no	—
367	D₄	—	152	1	no	—
368	D₄	C₂×C₂²⋊D₁₉	1	2	yes	—
369	D₄	C₂×C₂²⋊D₁₉	1	2	yes	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	19	1	no	—
375	C₂×C₄	—	19	1	no	—
376	C₂×C₄	—	19	1	no	—
377	C₂×C₄	—	38	1	no	—
378	C₂×C₄	—	38	1	no	—
379	C₂×C₄	—	38	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	38	1	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	—	152	1	no	—
384	C₂×C₄	—	152	1	no	—
385	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
386	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
387	C₈	—	2	1	no	—
388	C₈	—	38	1	no	—
389	C₈	—	38	1	no	—
390	C₈	C₂×C₂²⋊D₁₉	1	2	yes	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	8	4	no	—
404	C₂²	—	38	1	no	—
405	C₂²	—	38	1	no	—
406	C₂²	—	38	1	no	—
407	C₂²	—	76	1	no	—
408	C₂²	—	76	1	no	—
409	C₂²	—	76	1	no	—
410	C₂²	—	152	4	no	—
411	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	4	1	no	—
414	C₄	—	38	1	no	—
415	C₄	—	38	1	no	—
416	C₄	—	38	1	no	—
417	C₄	—	76	1	no	—
418	C₄	—	76	1	no	—
419	C₄	—	76	1	no	—
420	C₄	#10597430	1	1	yes	characteristic
421	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
422	C₂	—	4	1	no	—
423	C₂	—	4	2	no	—
424	C₂	—	4	2	no	—
425	C₂	—	8	1	no	—
426	C₂	—	76	1	no	—
427	C₂	—	152	1	no	—
428	C₂	D₄×C₂²⋊D₁₉	1	1	yes	characteristic
429	C₂	#11927340	1	1	yes	characteristic
430	C₂	#11927348	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×AGL(1,ℤ/8)	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₉
hypocenter	C₁₉	#3273
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#10597357	C₂	semidirect
2. #11927188	C₂	semidirect
3. #11927182	C₂	semidirect
4. #11926925	C₂	semidirect
5. #11926790	C₂	semidirect
6. #11926787	C₂	semidirect
7. #11926761	C₂	semidirect
8. #11926757	C₂	semidirect
9. #11926706	C₂	semidirect
10. #11926703	C₂	semidirect
11. #11926678	C₂	semidirect
12. #11926676	C₂	semidirect
13. D₈×Dic₁₉	C₂	semidirect
14. #11926620	C₂	semidirect
15. C₂×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
17. C₂²×D₄×C₁₉	C₂²	semidirect
19. C₂×D₄×D₁₉	C₂²	semidirect
21. C₂×SD₁₆×C₁₉	C₂²	semidirect
22. C₂×SD₁₆×C₁₉	C₂²	semidirect
25. C₂×M₁₆×C₁₉	C₂²	semidirect
28. #10597393	C₂²	semidirect
29. #10597392	C₂²	semidirect
30. C₂×#64528	C₂²	semidirect
35. #10597382	C₂²	semidirect
37. D₄×Dic₁₉	C₂²	semidirect
38. D₄×Dic₁₉	C₂²	semidirect
39. C₂×#64526	C₂²	semidirect
46. #10597370	C₂²	semidirect
48. C₂×#64516	C₂²	semidirect
49. C₂×#64515	C₂²	semidirect
50. #10597292	C₂²	semidirect
51. #10597289	C₂²	semidirect
52. #10597289	C₂²	semidirect
53. #10597289	C₂²	semidirect
54. C₂²⋊(C₁₉⋊C₈)	C₂²	semidirect
55. #10597278	C₂²	semidirect
56. (C₂×D₁₉)⋊C₈	C₂²	semidirect
57. #10597275	C₂²	semidirect
58. #10597273	C₂²	semidirect
59. Dic₁₉⋊C₈	C₂²	semidirect
60. C₈×Dic₁₉	C₂²	semidirect
93. D₈×C₁₉	D₄	semidirect
208. C₂×AGL(1,ℤ/8)	D₁₉	semidirect
234. C₂²×D₄	C₂×D₁₉	semidirect
240. C₂×SD₁₆	C₂×D₁₉	semidirect
241. C₂×SD₁₆	C₂×D₁₉	semidirect
247. C₂×M₁₆	C₂×D₁₉	semidirect
276. C₁₉	#3273	semidirect
314. D₈	C₂²⋊D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597357	2
#11927188	2
#11927182	2
#11926925	2
#11926790	2
#11926787	2
#11926761	2
#11926757	2
#11926706	2
#11926703	2
#11926678	2
#11926676	2
D₈×Dic₁₉	2
#11926620	2
C₂×C₁₉×AGL(1,ℤ/8)	2
#3273	19