Subgroups — #14575129

Order 2432.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 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	C₂×SD₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927202	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927179	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926787	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926777	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926756	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926741	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926693	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926686	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926681	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926676	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926646	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926617	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#496	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
18	C₂×D₄×D₁₉	—	2	1	no	—
19	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
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, complemented
24	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₁₉×#127	C₂²	1	1	yes	characteristic
26	C₁₉×#124	C₂²	1	1	yes	characteristic, complemented
27	#10597392	C₂²	1	1	yes	characteristic, complemented
28	C₂×#64527	C₂²	1	1	yes	characteristic
29	#10597384	—	2	1	no	—
30	#10597384	C₂²	1	1	yes	characteristic
31	#10597384	C₂²	1	1	yes	characteristic
32	#10597384	C₂²	1	1	yes	characteristic, complemented
33	#10597383	—	2	1	no	—
34	#10597383	—	2	1	no	—
35	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
36	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
37	C₂×#64525	C₂²	1	1	yes	characteristic
38	SD₁₆×D₁₉	—	2	4	no	—
39	#10597357	—	2	4	no	—
40	C₂×#64516	C₂²	1	1	yes	characteristic
41	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
43	#10597331	—	2	1	no	—
44	#10597330	—	2	1	no	—
45	(C₂²⋊D₁₉)⋊C₄	—	2	1	no	—
46	#10597324	—	2	1	no	—
47	C₄×D₇₆	C₂²	1	1	yes	characteristic
48	C₄×D₇₆	C₂²	1	1	yes	characteristic
49	C₄×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
50	C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
51	#10597292	C₂²	1	1	yes	characteristic, complemented
52	#10597289	C₂²	1	1	yes	characteristic, complemented
53	#10597289	C₂²	1	1	yes	characteristic, complemented
54	#10597289	C₂²	1	1	yes	characteristic, complemented
55	#10597278	C₂²	1	1	yes	characteristic
56	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	#10597275	C₂²	1	1	yes	characteristic, complemented
59	#10597273	C₂²	1	1	yes	characteristic, complemented
60	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉	—	2	1	no	—
62	C₂³×D₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₁₉	—	2	1	no	—
65	C₂×D₄×C₁₉	—	2	1	no	—
66	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊D₁₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₉	—	2	1	no	—
75	C₂²×Dic₁₉	—	2	1	no	—
76	Q₈×D₁₉	—	2	2	no	—
77	Q₈×D₁₉	—	4	1	no	—
78	#64543	—	2	2	no	—
79	#64543	—	4	1	no	—
80	D₄×D₁₉	—	2	2	no	—
81	D₄×D₁₉	—	2	2	no	—
82	D₄×D₁₉	—	4	1	no	—
83	D₄×D₁₉	—	4	1	no	—
84	D₄×D₁₉	—	4	4	no	—
85	C₂×D₇₆	D₄	1	1	yes	characteristic
86	C₂×D₇₆	C₂³	1	1	yes	characteristic
87	C₂×C₄×D₁₉	—	2	1	no	—
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
90	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
91	C₂×Dic₃₈	—	2	1	no	—
92	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
93	SD₁₆×C₁₉	—	2	2	no	—
94	SD₁₆×C₁₉	—	4	1	no	—
95	D₈×C₁₉	—	2	2	no	—
96	D₈×C₁₉	—	4	1	no	—
97	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂²⋊C₄×C₁₉	—	2	1	no	—
101	C₄²×C₁₉	C₂³	1	1	yes	characteristic
102	C₂²⋊Dic₁₉	—	2	1	no	—
103	C₂²⋊Dic₁₉	—	2	1	no	—
104	C₂²⋊Dic₁₉	—	2	1	no	—
105	#64527	—	2	2	no	—
106	#64526	—	2	2	no	—
107	#64526	—	2	2	no	—
108	#64525	—	2	2	no	—
109	(C₂×D₁₉)⋊C₄	—	2	1	no	—
110	(C₂×D₁₉)⋊C₄	—	2	1	no	—
111	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
112	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
113	C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
114	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
115	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
116	Dic₁₉⋊C₄	—	2	1	no	—
117	Dic₁₉⋊C₄	—	2	1	no	—
118	C₄×Dic₁₉	—	2	1	no	—
119	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
121	#64516	D₄	1	4	yes	complemented
122	#64515	—	2	2	no	—
123	C₈×D₁₉	—	2	2	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂²×D₁₉	—	2	1	no	—
128	C₂²×D₁₉	—	4	2	no	—
129	C₂²×D₁₉	—	4	2	no	—
130	C₂²×D₁₉	—	4	2	no	—
131	C₂²×D₁₉	—	4	2	no	—
132	C₂²×D₁₉	—	8	1	no	—
133	C₂²×D₁₉	—	8	1	no	—
134	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₁₉	—	2	1	no	—
137	Q₈×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	—	2	1	no	—
142	D₄×C₁₉	—	2	1	no	—
143	D₄×C₁₉	—	2	1	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	8	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
150	C₂²⋊D₁₉	—	4	2	no	—
151	C₂²⋊D₁₉	—	4	2	no	—
152	C₂²⋊D₁₉	—	4	2	no	—
153	C₂²⋊D₁₉	—	4	2	no	—
154	C₂²⋊D₁₉	—	4	2	no	—
155	C₂²⋊D₁₉	—	4	2	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	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
162	D₇₆	—	2	2	no	—
163	D₇₆	—	2	1	no	—
164	D₇₆	C₂×D₄	1	2	yes	—
165	C₄×D₁₉	—	2	1	no	—
166	C₄×D₁₉	—	2	1	no	—
167	C₄×D₁₉	—	2	1	no	—
168	C₄×D₁₉	—	2	1	no	—
169	C₄×D₁₉	—	4	2	no	—
170	C₄×D₁₉	—	4	2	no	—
171	Dic₃₈	—	2	1	no	—
172	Dic₃₈	—	4	2	no	—
173	Dic₃₈	C₂×D₄	1	2	yes	complemented
174	C₈×C₁₉	—	2	1	no	—
175	C₈×C₁₉	C₂×D₄	1	2	yes	complemented
176	C₁₉⋊C₈	—	2	1	no	—
177	C₁₉⋊C₈	—	2	1	no	—
178	#3265	—	19	1	no	maximal, Sylow
179	C₂²×C₁₉	—	4	1	no	—
180	C₂²×C₁₉	—	4	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	C₂²×D₄	1	1	yes	characteristic
189	C₂×D₁₉	—	2	1	no	—
190	C₂×D₁₉	—	2	1	no	—
191	C₂×D₁₉	—	2	1	no	—
192	C₂×D₁₉	—	2	2	no	—
193	C₂×D₁₉	—	2	1	no	—
194	C₂×D₁₉	—	2	1	no	—
195	C₂×D₁₉	—	4	1	no	—
196	C₂×D₁₉	—	4	1	no	—
197	C₂×D₁₉	—	8	4	no	—
198	C₂×D₁₉	—	8	4	no	—
199	C₂×D₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	2	1	no	—
202	C₄×C₁₉	—	4	1	no	—
203	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
204	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
205	Dic₁₉	—	2	2	no	—
206	Dic₁₉	—	2	1	no	—
207	Dic₁₉	—	2	1	no	—
208	Dic₁₉	—	4	1	no	—
209	Dic₁₉	—	4	1	no	—
210	C₂×AGL(1,ℤ/8)	—	19	1	no	—
211	C₂²×SD₁₆	—	19	1	no	—
212	#548	—	19	1	no	—
213	D₄²	—	19	1	no	—
214	#496	D₁₉	1	1	yes	characteristic, complemented
215	#468	—	19	1	no	—
216	#466	—	19	1	no	—
217	#463	—	19	1	no	—
218	#460	—	19	1	no	—
219	#450	—	19	1	no	—
220	#449	—	19	1	no	—
221	#448	—	19	1	no	—
222	#447	—	19	1	no	—
223	#440	—	19	1	no	—
224	#435	—	19	1	no	—
225	C₂×C₁₉	—	8	1	no	—
226	C₂×C₁₉	—	8	1	no	—
227	C₂×C₁₉	—	8	1	no	—
228	C₂×C₁₉	D₄²	1	1	yes	characteristic
229	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
230	C₂×C₁₉	#577	1	1	yes	characteristic
231	D₁₉	—	2	2	no	—
232	D₁₉	—	4	1	no	—
233	D₁₉	—	4	2	no	—
234	C₂×#41	—	19	1	no	—
235	C₂²×Q₈	—	19	1	no	—
236	C₂²×D₄	—	19	1	no	—
237	C₂²×D₄	—	19	1	no	—
238	C₂²×D₄	—	38	1	no	—
239	AGL(1,ℤ/8)	—	38	4	no	—
240	C₂×SD₁₆	—	19	1	no	—
241	C₂×SD₁₆	—	19	1	no	—
242	C₂×SD₁₆	—	19	1	no	—
243	C₂×SD₁₆	—	19	1	no	—
244	C₂×SD₁₆	—	38	4	no	—
245	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
246	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
247	C₂×D₈	—	19	1	no	—
248	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
249	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
250	C₂×M₁₆	—	19	1	no	—
251	C₂²×C₈	—	19	1	no	—
252	#127	C₂×D₁₉	1	1	yes	characteristic
253	#124	—	38	1	no	—
254	#124	C₂×D₁₉	1	1	yes	characteristic, complemented
255	C₂²⋊Q₈	—	19	1	no	—
256	C₂²⋊Q₈	—	38	1	no	—
257	#121	—	19	1	no	—
258	#121	—	19	1	no	—
259	#121	—	19	1	no	—
260	#121	—	38	1	no	—
261	#121	—	38	1	no	—
262	#120	—	38	1	no	—
263	#120	—	38	1	no	—
264	C₄×Q₈	—	19	1	no	—
265	C₄×D₄	—	19	1	no	—
266	C₄×D₄	—	19	1	no	—
267	C₄×D₄	—	38	1	no	—
268	#107	—	19	1	no	—
269	C₄⋊C₈	—	19	1	no	—
270	#103	—	19	1	no	—
271	#103	—	19	1	no	—
272	#102	—	19	1	no	—
273	#102	—	19	1	no	—
274	#102	—	19	1	no	—
275	#102	—	19	1	no	—
276	C₂²⋊C₈	—	19	1	no	—
277	C₂²⋊C₈	—	19	1	no	—
278	#97	C₂×D₁₉	1	1	yes	characteristic, complemented
279	C₁₉	#3265	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	—	38	1	no	—
281	C₂⁴	—	38	1	no	—
282	#41	—	38	2	no	—
283	#41	—	76	1	no	—
284	C₂×Q₈	—	19	1	no	—
285	C₂×Q₈	—	38	1	no	—
286	C₂×Q₈	—	38	2	no	—
287	C₂×Q₈	—	76	1	no	—
288	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	19	1	no	—
292	C₂×D₄	—	19	1	no	—
293	C₂×D₄	—	38	1	no	—
294	C₂×D₄	—	38	1	no	—
295	C₂×D₄	—	38	2	no	—
296	C₂×D₄	—	38	2	no	—
297	C₂×D₄	—	38	1	no	—
298	C₂×D₄	—	38	1	no	—
299	C₂×D₄	—	38	1	no	—
300	C₂×D₄	—	38	1	no	—
301	C₂×D₄	—	76	1	no	—
302	C₂×D₄	—	76	1	no	—
303	C₂×D₄	—	76	4	no	—
304	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
305	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
307	C₂²×C₄	—	19	1	no	—
308	C₂²×C₄	—	19	1	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	—	38	1	no	—
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	4	1	no	—
314	SD₁₆	—	19	4	no	—
315	SD₁₆	—	38	2	no	—
316	SD₁₆	—	38	2	no	—
317	SD₁₆	—	38	2	no	—
318	D₈	—	2	2	no	—
319	D₈	—	4	1	no	—
320	D₈	—	38	2	no	—
321	M₁₆	—	38	2	no	—
322	C₂×C₈	—	19	1	no	—
323	C₂×C₈	—	19	1	no	—
324	C₂×C₈	—	38	2	no	—
325	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
327	C₄⋊C₄	—	19	1	no	—
328	C₄⋊C₄	—	19	1	no	—
329	C₄⋊C₄	—	19	1	no	—
330	C₄⋊C₄	—	38	1	no	—
331	C₄⋊C₄	—	38	1	no	—
332	C₂²⋊C₄	—	2	1	no	—
333	C₂²⋊C₄	—	2	1	no	—
334	C₂²⋊C₄	—	19	1	no	—
335	C₂²⋊C₄	—	19	1	no	—
336	C₂²⋊C₄	—	38	1	no	—
337	C₂²⋊C₄	—	38	1	no	—
338	C₂²⋊C₄	—	38	1	no	—
339	C₂²⋊C₄	—	38	1	no	—
340	C₂²⋊C₄	—	38	1	no	—
341	C₄²	—	38	1	no	—
342	C₄²	C₂²×D₁₉	1	1	yes	characteristic
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	2	1	no	—
346	C₂³	—	19	1	no	—
347	C₂³	—	19	1	no	—
348	C₂³	—	38	1	no	—
349	C₂³	—	76	2	no	—
350	C₂³	—	76	2	no	—
351	C₂³	—	76	2	no	—
352	C₂³	—	76	2	no	—
353	C₂³	—	152	1	no	—
354	C₂³	—	152	1	no	—
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	19	2	no	—
358	Q₈	—	38	1	no	—
359	Q₈	—	76	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	2	1	no	—
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	4	2	no	—
367	D₄	—	8	1	no	—
368	D₄	—	19	2	no	—
369	D₄	—	38	2	no	—
370	D₄	—	38	1	no	—
371	D₄	—	76	2	no	—
372	D₄	—	76	2	no	—
373	D₄	—	76	2	no	—
374	D₄	—	76	2	no	—
375	D₄	—	76	2	no	—
376	D₄	—	76	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	19	1	no	—
379	C₂×C₄	—	19	1	no	—
380	C₂×C₄	—	38	1	no	—
381	C₂×C₄	—	38	1	no	—
382	C₂×C₄	—	38	1	no	—
383	C₂×C₄	—	38	1	no	—
384	C₂×C₄	—	38	1	no	—
385	C₂×C₄	—	38	1	no	—
386	C₂×C₄	—	38	1	no	—
387	C₂×C₄	—	76	2	no	—
388	C₂×C₄	—	76	2	no	—
389	C₂×C₄	—	76	2	no	—
390	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
391	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	38	1	no	—
395	C₈	—	38	1	no	—
396	C₈	D₄×D₁₉	1	2	yes	complemented
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	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	19	2	no	—
407	C₂²	—	38	1	no	—
408	C₂²	—	38	1	no	—
409	C₂²	—	38	1	no	—
410	C₂²	—	38	1	no	—
411	C₂²	—	38	1	no	—
412	C₂²	—	38	2	no	—
413	C₂²	—	76	1	no	—
414	C₂²	—	76	1	no	—
415	C₂²	—	152	4	no	—
416	C₂²	—	152	4	no	—
417	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	38	1	no	—
422	C₄	—	38	1	no	—
423	C₄	—	38	2	no	—
424	C₄	—	76	1	no	—
425	C₄	—	76	1	no	—
426	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
427	C₄	#10597430	1	1	yes	characteristic
428	C₂	—	8	1	no	—
429	C₂	—	8	1	no	—
430	C₂	—	8	1	no	—
431	C₂	—	38	2	no	—
432	C₂	—	76	1	no	—
433	C₂	—	76	2	no	—
434	C₂	#11927179	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
436	C₂	#11927354	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₁₉×#496	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#496	D₁₉
hypocenter	C₁₉	#3265
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

Complements

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

N	H ≅ G/N	type
1. C₂×#10597357	C₂	semidirect
2. C₂×SD₁₆×D₁₉	C₂	semidirect
3. #11927202	C₂	semidirect
4. #11927179	C₂	semidirect
5. #11926787	C₂	semidirect
6. #11926777	C₂	semidirect
7. #11926756	C₂	semidirect
8. #11926741	C₂	semidirect
9. #11926693	C₂	semidirect
10. #11926686	C₂	semidirect
11. #11926681	C₂	semidirect
12. #11926676	C₂	semidirect
13. #11926646	C₂	semidirect
14. #11926617	C₂	semidirect
15. C₁₉×#496	C₂	semidirect
16. C₂×Q₈×D₁₉	C₂²	semidirect
17. C₂×#64543	C₂²	semidirect
21. C₂×SD₁₆×C₁₉	C₂²	semidirect
22. C₂×SD₁₆×C₁₉	C₂²	semidirect
23. C₂×D₈×C₁₉	C₂²	semidirect
24. C₂×D₈×C₁₉	C₂²	semidirect
26. C₁₉×#124	C₂²	semidirect
27. #10597392	C₂²	semidirect
32. #10597384	C₂²	semidirect
35. C₂×#64526	C₂²	semidirect
36. C₂×#64526	C₂²	semidirect
41. C₂×#64515	C₂²	semidirect
42. C₂×C₈×D₁₉	C₂²	semidirect
49. C₄×Dic₃₈	C₂²	semidirect
50. C₁₉×#97	C₂²	semidirect
51. #10597292	C₂²	semidirect
52. #10597289	C₂²	semidirect
53. #10597289	C₂²	semidirect
54. #10597289	C₂²	semidirect
56. (C₂×D₁₉)⋊C₈	C₂²	semidirect
57. (C₂×D₁₉)⋊C₈	C₂²	semidirect
58. #10597275	C₂²	semidirect
59. #10597273	C₂²	semidirect
60. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
121. #64516	D₄	semidirect
173. Dic₃₈	C₂×D₄	semidirect
175. C₈×C₁₉	C₂×D₄	semidirect
199. C₂×D₁₉	AGL(1,ℤ/8)	semidirect
214. #496	D₁₉	semidirect
245. C₂×SD₁₆	C₂×D₁₉	semidirect
246. C₂×SD₁₆	C₂×D₁₉	semidirect
248. C₂×D₈	C₂×D₁₉	semidirect
249. C₂×D₈	C₂×D₁₉	semidirect
254. #124	C₂×D₁₉	semidirect
278. #97	C₂×D₁₉	semidirect
279. C₁₉	#3265	semidirect
396. C₈	D₄×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
C₂×SD₁₆×D₁₉	2
#11927202	2
#11927179	2
#11926787	2
#11926777	2
#11926756	2
#11926741	2
#11926693	2
#11926686	2
#11926681	2
#11926676	2
#11926646	2
#11926617	2
C₁₉×#496	2
#3265	19