Subgroups — #14575233

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×#10597360	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597378	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927196	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926915	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926792	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926789	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926747	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926738	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926696	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926691	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926688	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926624	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926619	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#450	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊D₁₉	—	2	1	no	—
18	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
20	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
21	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
23	C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	#10597399	—	2	1	no	—
25	#10597390	C₂²	1	1	yes	characteristic, complemented
26	C₂×#64527	C₂²	1	1	yes	characteristic, complemented
27	#10597386	C₂²	1	1	yes	characteristic
28	#10597385	—	2	1	no	—
29	#10597384	C₂²	1	1	yes	characteristic
30	#10597383	—	2	1	no	—
31	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
32	C₂×#64526	C₂²	1	1	yes	characteristic
33	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
34	#10597378	—	2	4	no	—
35	C₂×#64525	C₂²	1	1	yes	characteristic
36	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
37	#10597376	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
39	C₂×#64520	C₂²	1	1	yes	characteristic, complemented
40	#10597360	—	2	4	no	—
41	C₂×D₁₅₂	C₂²	1	1	yes	characteristic, complemented
42	C₂×#64516	C₂²	1	1	yes	characteristic, complemented
43	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
44	#10597343	C₂²	1	1	yes	characteristic, complemented
45	#10597340	—	2	1	no	—
46	#10597339	C₂²	1	1	yes	characteristic, complemented
47	C₄⋊C₄×D₁₉	—	2	1	no	—
48	#10597330	—	2	1	no	—
49	#10597329	—	2	1	no	—
50	C₁₉×#102	C₂²	1	1	yes	characteristic
51	C₁₉×#102	C₂²	1	1	yes	characteristic, complemented
52	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
53	#10597292	C₂²	1	1	yes	characteristic, complemented
54	#10597278	C₂²	1	1	yes	characteristic, complemented
55	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
56	#10597273	C₂²	1	1	yes	characteristic, complemented
57	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	C₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
59	#10597266	C₂²	1	1	yes	characteristic, complemented
60	#10597264	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₁₉	—	2	1	no	—
62	C₂³×D₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₁₉	—	2	2	no	—
65	C₂×D₄×C₁₉	—	2	1	no	—
66	C₂×D₄×C₁₉	—	4	1	no	—
67	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₁₉	—	2	1	no	—
76	C₂×C₂²⋊D₁₉	—	4	4	no	—
77	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
78	C₂²×Dic₁₉	—	2	1	no	—
79	#64545	—	2	2	no	—
80	#64545	—	4	1	no	—
81	D₄×D₁₉	—	2	2	no	—
82	D₄×D₁₉	—	4	1	no	—
83	#64541	—	2	2	no	—
84	#64541	—	4	1	no	—
85	C₂×D₇₆	—	2	1	no	—
86	C₂×D₇₆	C₂³	1	1	yes	characteristic
87	C₂×D₇₆	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	—	2	1	no	—
91	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
92	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
93	SD₁₆×C₁₉	—	2	2	no	—
94	SD₁₆×C₁₉	—	4	1	no	—
95	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
96	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
97	C₄⋊C₄×C₁₉	—	2	1	no	—
98	C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₄×C₁₉	—	2	1	no	—
100	C₂²⋊Dic₁₉	—	2	1	no	—
101	C₂²⋊Dic₁₉	—	2	1	no	—
102	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
103	#64527	—	2	2	no	—
104	#64526	—	2	2	no	—
105	#64526	—	2	2	no	—
106	#64525	—	2	2	no	—
107	#64525	D₄	1	4	yes	complemented
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	D₄	1	1	yes	characteristic
112	C₄⋊Dic₁₉	—	2	1	no	—
113	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
114	Dic₁₉⋊C₄	—	2	1	no	—
115	Dic₁₉⋊C₄	—	2	1	no	—
116	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
117	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
118	#64520	—	2	2	no	—
119	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
120	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
121	D₁₅₂	—	2	2	no	—
122	#64516	—	4	1	no	—
123	#64515	—	2	2	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	—	2	1	no	—
132	C₂²×D₁₉	—	4	2	no	—
133	C₂²×D₁₉	—	4	2	no	—
134	C₂²×D₁₉	—	8	1	no	—
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	—	4	2	no	—
142	D₄×C₁₉	C₂×D₄	1	2	yes	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₂²⋊D₁₉	—	2	2	no	—
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	—	8	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	4	2	no	—
159	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
160	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
162	D₇₆	—	2	1	no	—
163	D₇₆	—	2	1	no	—
164	D₇₆	—	2	1	no	—
165	D₇₆	—	4	2	no	—
166	D₇₆	C₂×D₄	1	2	yes	complemented
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	C₄×D₁₉	—	4	2	no	—
172	Dic₃₈	—	2	1	no	—
173	Dic₃₈	—	2	1	no	—
174	C₈×C₁₉	—	2	1	no	—
175	C₈×C₁₉	—	2	1	no	—
176	C₁₉⋊C₈	—	2	1	no	—
177	C₁₉⋊C₈	C₂×D₄	1	2	yes	complemented
178	#3272	—	19	1	no	maximal, Sylow
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	2	no	—
181	C₂²×C₁₉	—	2	1	no	—
182	C₂²×C₁₉	—	2	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	2	no	—
192	C₂×D₁₉	—	2	1	no	—
193	C₂×D₁₉	—	2	1	no	—
194	C₂×D₁₉	—	4	1	no	—
195	C₂×D₁₉	—	4	1	no	—
196	C₂×D₁₉	—	4	1	no	—
197	C₂×D₁₉	—	4	1	no	—
198	C₂×D₁₉	—	4	1	no	—
199	C₂×D₁₉	—	8	4	no	—
200	C₄×C₁₉	—	2	1	no	—
201	C₄×C₁₉	—	4	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	1	no	—
206	Dic₁₉	—	2	1	no	—
207	Dic₁₉	—	4	1	no	—
208	Dic₁₉	—	4	1	no	—
209	Dic₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
210	C₂×AGL(1,ℤ/8)	—	19	1	no	—
211	C₂×AGL(1,ℤ/8)	—	19	1	no	—
212	#547	—	19	1	no	—
213	D₄²	—	19	1	no	—
214	#492	—	19	1	no	—
215	#468	—	19	1	no	—
216	#468	—	19	1	no	—
217	#461	—	19	1	no	—
218	#459	—	19	1	no	—
219	#450	—	19	1	no	—
220	#450	D₁₉	1	1	yes	characteristic, complemented
221	#449	—	19	1	no	—
222	#449	—	19	1	no	—
223	C₄×D₈	—	19	1	no	—
224	#436	—	19	1	no	—
225	C₂×C₁₉	—	4	2	no	—
226	C₂×C₁₉	—	4	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	—	4	1	no	—
232	D₁₉	—	4	2	no	—
233	D₁₉	—	8	1	no	—
234	C₂×#41	—	19	1	no	—
235	C₂×#41	—	19	1	no	—
236	C₂²×D₄	—	19	1	no	—
237	C₂²×D₄	—	38	1	no	—
238	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
239	AGL(1,ℤ/8)	—	38	4	no	—
240	AGL(1,ℤ/8)	—	38	4	no	—
241	C₂×SD₁₆	—	19	1	no	—
242	C₂×SD₁₆	—	19	1	no	—
243	C₂×SD₁₆	—	19	1	no	—
244	C₂×SD₁₆	—	19	1	no	—
245	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
246	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
247	C₂×D₈	—	19	1	no	—
248	C₂×D₈	—	19	1	no	—
249	C₂×D₈	—	19	1	no	—
250	C₂×M₁₆	—	19	1	no	—
251	C₂×M₁₆	—	19	1	no	—
252	C₄⋊Q₈	—	19	1	no	—
253	#127	—	19	1	no	—
254	#123	—	38	1	no	—
255	#123	—	38	1	no	—
256	C₂²⋊Q₈	—	19	1	no	—
257	C₂²⋊Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
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×D₄	—	19	1	no	—
265	C₄×D₄	—	19	1	no	—
266	C₄×D₄	—	19	1	no	—
267	C₂×C₄⋊C₄	—	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	C₂×D₁₉	1	1	yes	characteristic
275	#102	C₂×D₁₉	1	1	yes	characteristic, complemented
276	C₂²⋊C₈	—	19	1	no	—
277	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
278	C₄×C₈	—	19	1	no	—
279	C₁₉	#3272	1	1	yes	characteristic, complemented, Sylow
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	38	1	no	—
282	#41	—	38	2	no	—
283	#41	—	38	2	no	—
284	#41	—	76	1	no	—
285	#41	—	76	1	no	—
286	C₂×Q₈	—	19	1	no	—
287	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	4	1	no	—
291	C₂×D₄	—	19	1	no	—
292	C₂×D₄	—	19	1	no	—
293	C₂×D₄	—	19	1	no	—
294	C₂×D₄	—	38	1	no	—
295	C₂×D₄	—	38	1	no	—
296	C₂×D₄	—	38	1	no	—
297	C₂×D₄	—	38	1	no	—
298	C₂×D₄	—	38	2	no	—
299	C₂×D₄	—	38	1	no	—
300	C₂×D₄	—	38	1	no	—
301	C₂×D₄	—	38	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	C₂²×C₄	—	19	1	no	—
307	C₂²×C₄	—	38	1	no	—
308	C₂²×C₄	—	38	1	no	—
309	C₂²×C₄	—	38	1	no	—
310	C₂²×C₄	—	38	1	no	—
311	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	4	1	no	—
314	SD₁₆	—	38	2	no	—
315	SD₁₆	—	38	2	no	—
316	SD₁₆	—	38	2	no	—
317	SD₁₆	—	76	1	no	—
318	D₈	—	19	4	no	—
319	D₈	—	38	2	no	—
320	D₈	—	38	2	no	—
321	M₁₆	—	38	2	no	—
322	M₁₆	—	38	2	no	—
323	C₂×C₈	—	19	1	no	—
324	C₂×C₈	—	19	1	no	—
325	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
327	C₄⋊C₄	—	2	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	C₄⋊C₄	—	38	1	no	—
333	C₄⋊C₄	C₂²×D₁₉	1	1	yes	characteristic
334	C₂²⋊C₄	—	2	1	no	—
335	C₂²⋊C₄	—	19	1	no	—
336	C₂²⋊C₄	—	19	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	C₂²⋊C₄	—	38	1	no	—
342	C₄²	—	19	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	19	1	no	—
349	C₂³	—	38	1	no	—
350	C₂³	—	38	1	no	—
351	C₂³	—	76	2	no	—
352	C₂³	—	76	2	no	—
353	C₂³	—	152	1	no	—
354	C₂³	D₄×D₁₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	38	1	no	—
358	Q₈	—	38	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	4	2	no	—
363	D₄	—	19	2	no	—
364	D₄	—	38	2	no	—
365	D₄	—	38	1	no	—
366	D₄	—	38	1	no	—
367	D₄	—	38	1	no	—
368	D₄	—	76	2	no	—
369	D₄	—	76	2	no	—
370	D₄	—	76	2	no	—
371	D₄	—	76	2	no	—
372	D₄	—	76	2	no	—
373	D₄	—	76	2	no	—
374	D₄	—	152	1	no	—
375	D₄	D₄×D₁₉	1	2	yes	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	19	1	no	—
381	C₂×C₄	—	19	1	no	—
382	C₂×C₄	—	19	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	—	76	2	no	—
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	—	2	1	no	—
395	C₈	—	19	2	no	—
396	C₈	—	38	1	no	—
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	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	—	8	4	no	—
407	C₂²	—	38	1	no	—
408	C₂²	—	38	1	no	—
409	C₂²	—	38	1	no	—
410	C₂²	—	38	2	no	—
411	C₂²	—	76	1	no	—
412	C₂²	—	76	1	no	—
413	C₂²	—	76	1	no	—
414	C₂²	—	76	1	no	—
415	C₂²	—	76	1	no	—
416	C₂²	—	152	4	no	—
417	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	4	1	no	—
420	C₄	—	4	1	no	—
421	C₄	—	19	2	no	—
422	C₄	—	38	1	no	—
423	C₄	—	38	1	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	—	4	1	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	76	1	no	—
432	C₂	—	76	2	no	—
433	C₂	—	152	1	no	—
434	C₂	#11927176	1	1	yes	characteristic
435	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
436	C₂	#11927350	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×#450	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	#450	D₁₉
hypocenter	C₁₉	#3272
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #450

Complements

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

N	H ≅ G/N	type
1. C₂×#10597360	C₂	semidirect
2. C₂×#10597378	C₂	semidirect
3. #11927196	C₂	semidirect
4. D₄×C₂²⋊D₁₉	C₂	semidirect
5. #11926915	C₂	semidirect
6. #11926792	C₂	semidirect
7. #11926789	C₂	semidirect
8. #11926747	C₂	semidirect
9. #11926738	C₂	semidirect
10. #11926696	C₂	semidirect
11. #11926691	C₂	semidirect
12. #11926688	C₂	semidirect
13. #11926624	C₂	semidirect
14. #11926619	C₂	semidirect
15. C₁₉×#450	C₂	semidirect
18. C₂×#64545	C₂²	semidirect
20. C₂×#64541	C₂²	semidirect
22. C₂×SD₁₆×C₁₉	C₂²	semidirect
23. C₁₉×C₂²⋊Q₈	C₂²	semidirect
25. #10597390	C₂²	semidirect
26. C₂×#64527	C₂²	semidirect
33. C₂×#64526	C₂²	semidirect
36. C₂×#64525	C₂²	semidirect
39. C₂×#64520	C₂²	semidirect
41. C₂×D₁₅₂	C₂²	semidirect
42. C₂×#64516	C₂²	semidirect
43. C₂×#64515	C₂²	semidirect
44. #10597343	C₂²	semidirect
46. #10597339	C₂²	semidirect
51. C₁₉×#102	C₂²	semidirect
52. C₁₉×C₂²⋊C₈	C₂²	semidirect
53. #10597292	C₂²	semidirect
54. #10597278	C₂²	semidirect
55. (C₂×D₁₉)⋊C₈	C₂²	semidirect
56. #10597273	C₂²	semidirect
57. Dic₁₉⋊C₈	C₂²	semidirect
58. C₈×Dic₁₉	C₂²	semidirect
59. #10597266	C₂²	semidirect
60. #10597264	C₂²	semidirect
107. #64525	D₄	semidirect
166. D₇₆	C₂×D₄	semidirect
177. C₁₉⋊C₈	C₂×D₄	semidirect
209. Dic₁₉	AGL(1,ℤ/8)	semidirect
220. #450	D₁₉	semidirect
246. C₂×SD₁₆	C₂×D₁₉	semidirect
257. C₂²⋊Q₈	C₂×D₁₉	semidirect
275. #102	C₂×D₁₉	semidirect
277. C₂²⋊C₈	C₂×D₁₉	semidirect
279. C₁₉	#3272	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597360	2
C₂×#10597378	2
#11927196	2
D₄×C₂²⋊D₁₉	2
#11926915	2
#11926792	2
#11926789	2
#11926747	2
#11926738	2
#11926696	2
#11926691	2
#11926688	2
#11926624	2
#11926619	2
C₁₉×#450	2
#3272	19