Subgroups — #14575169

Order 2432.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597362	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927213	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927188	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926932	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926790	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926777	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926764	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926737	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926706	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926688	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926686	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926678	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926645	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926613	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
18	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
19	C₂×#64543	C₂²	1	1	yes	characteristic
20	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
21	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
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
26	#10597399	—	2	1	no	—
27	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
28	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#64528	C₂²	1	1	yes	characteristic, complemented
30	#10597386	—	2	1	no	—
31	#10597386	C₂²	1	1	yes	characteristic, complemented
32	#10597385	—	2	1	no	—
33	#10597384	—	2	1	no	—
34	#10597384	C₂²	1	1	yes	characteristic
35	#10597384	C₂²	1	1	yes	characteristic, complemented
36	#10597382	C₂²	1	1	yes	characteristic
37	#10597381	—	2	1	no	—
38	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
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	—	2	1	no	—
43	#10597376	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₁₉	—	2	1	no	—
45	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
46	#10597370	C₂²	1	1	yes	characteristic
47	#10597362	—	2	4	no	—
48	C₂×#64516	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
50	#10597292	C₂²	1	1	yes	characteristic, complemented
51	#10597289	C₂²	1	1	yes	characteristic
52	#10597289	C₂²	1	1	yes	characteristic
53	#10597289	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
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	#10597272	C₂²	1	1	yes	characteristic, complemented
60	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₁₉	—	2	1	no	—
62	#41×C₁₉	—	2	2	no	—
63	#41×C₁₉	—	4	1	no	—
64	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×D₄×C₁₉	—	2	2	no	—
66	C₂×D₄×C₁₉	—	2	1	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	4	1	no	—
69	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂²×C₄×C₁₉	—	2	1	no	—
73	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊D₁₉	—	2	1	no	—
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	—	2	1	no	—
80	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
81	C₂²×Dic₁₉	—	2	1	no	—
82	C₂²×Dic₁₉	—	2	1	no	—
83	#64545	—	2	2	no	—
84	#64545	—	4	1	no	—
85	#64543	—	2	2	no	—
86	#64543	—	4	1	no	—
87	C₂×D₇₆	—	2	1	no	—
88	C₂×D₇₆	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₁₉	—	2	1	no	—
90	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
91	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
92	SD₁₆×C₁₉	—	2	2	no	—
93	SD₁₆×C₁₉	D₄	1	4	yes	complemented
94	D₈×C₁₉	—	2	2	no	—
95	D₈×C₁₉	—	2	2	no	—
96	M₁₆×C₁₉	—	2	2	no	—
97	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
98	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
104	C₂²⋊Dic₁₉	—	2	1	no	—
105	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
106	#64528	—	2	2	no	—
107	#64526	—	4	1	no	—
108	#64525	—	2	2	no	—
109	#64525	—	4	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	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
115	Dic₁₉⋊C₄	—	2	1	no	—
116	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
117	C₄×Dic₁₉	—	2	1	no	—
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	C₈×D₁₉	—	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	C₂×D₄	1	1	yes	characteristic
132	Q₈×C₁₉	—	2	1	no	—
133	Q₈×C₁₉	C₂×D₄	1	2	yes	—
134	D₄×C₁₉	—	2	1	no	—
135	D₄×C₁₉	—	2	1	no	—
136	D₄×C₁₉	—	2	1	no	—
137	D₄×C₁₉	—	2	1	no	—
138	D₄×C₁₉	—	2	1	no	—
139	D₄×C₁₉	—	4	2	no	—
140	D₄×C₁₉	—	4	2	no	—
141	D₄×C₁₉	C₂×D₄	1	2	yes	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	4	2	no	—
146	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
148	C₂²⋊D₁₉	—	4	1	no	—
149	C₂²⋊D₁₉	—	4	2	no	—
150	C₂²⋊D₁₉	—	4	2	no	—
151	C₂²⋊D₁₉	—	8	1	no	—
152	C₂²⋊D₁₉	—	8	1	no	—
153	C₂²⋊D₁₉	—	8	1	no	—
154	C₂²⋊D₁₉	—	8	1	no	—
155	C₂×Dic₁₉	—	2	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	4	2	no	—
159	C₂×Dic₁₉	—	8	1	no	—
160	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
161	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
162	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
163	D₇₆	—	2	1	no	—
164	D₇₆	—	2	1	no	—
165	D₇₆	—	4	2	no	—
166	C₄×D₁₉	—	2	1	no	—
167	C₄×D₁₉	—	2	1	no	—
168	C₄×D₁₉	—	4	2	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	#3268	—	19	1	no	maximal, Sylow
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	1	no	—
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	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	—	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	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
199	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
200	Dic₁₉	—	2	1	no	—
201	Dic₁₉	—	2	1	no	—
202	Dic₁₉	—	2	1	no	—
203	Dic₁₉	—	4	1	no	—
204	Dic₁₉	—	4	1	no	—
205	Dic₁₉	—	4	1	no	—
206	C₂×AGL(1,ℤ/8)	D₁₉	1	1	yes	characteristic, complemented
207	C₂×#135	—	19	1	no	—
208	#550	—	19	1	no	—
209	#546	—	19	1	no	—
210	#496	—	19	1	no	—
211	#468	—	19	1	no	—
212	#466	—	19	1	no	—
213	#464	—	19	1	no	—
214	#459	—	19	1	no	—
215	#452	—	19	1	no	—
216	#449	—	19	1	no	—
217	#449	—	19	1	no	—
218	#447	—	19	1	no	—
219	#440	—	19	1	no	—
220	#435	—	19	1	no	—
221	C₂×C₁₉	—	4	1	no	—
222	C₂×C₁₉	—	4	2	no	—
223	C₂×C₁₉	—	8	1	no	—
224	C₂×C₁₉	—	8	1	no	—
225	C₂×C₁₉	D₄²	1	1	yes	characteristic
226	C₂×C₁₉	#575	1	1	yes	characteristic
227	C₂×C₁₉	#576	1	1	yes	characteristic
228	D₁₉	—	4	1	no	—
229	D₁₉	—	8	1	no	—
230	C₂×#41	—	19	1	no	—
231	C₂×#41	—	19	1	no	—
232	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
233	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
234	AGL(1,ℤ/8)	—	2	4	no	—
235	#135	—	38	4	no	—
236	C₂×Q₁₆	—	19	1	no	—
237	C₂×SD₁₆	—	19	1	no	—
238	C₂×SD₁₆	—	19	1	no	—
239	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
240	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
241	C₂×D₈	—	19	1	no	—
242	C₂×D₈	—	19	1	no	—
243	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
244	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
245	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic
246	C₂²×C₈	—	19	1	no	—
247	#127	—	19	1	no	—
248	#127	—	38	1	no	—
249	#124	—	19	1	no	—
250	#123	—	38	1	no	—
251	C₂²⋊Q₈	—	19	1	no	—
252	#121	—	19	1	no	—
253	#121	—	19	1	no	—
254	#121	—	19	1	no	—
255	#121	—	38	1	no	—
256	#121	—	38	1	no	—
257	#121	—	38	1	no	—
258	#120	—	38	1	no	—
259	C₄×Q₈	—	19	1	no	—
260	C₄×D₄	—	19	1	no	—
261	C₄×D₄	—	19	1	no	—
262	C₄×D₄	—	38	1	no	—
263	C₂×C₂²⋊C₄	—	38	1	no	—
264	#107	—	19	1	no	—
265	C₄⋊C₈	—	19	1	no	—
266	#103	—	19	1	no	—
267	#103	—	19	1	no	—
268	#102	—	19	1	no	—
269	#102	—	19	1	no	—
270	#102	—	19	1	no	—
271	#102	—	19	1	no	—
272	C₂²⋊C₈	—	19	1	no	—
273	C₂²⋊C₈	—	19	1	no	—
274	#97	—	19	1	no	—
275	C₁₉	#3268	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	—	2	1	no	—
277	#41	—	2	2	no	—
278	#41	—	4	1	no	—
279	#41	—	38	2	no	—
280	#41	—	38	2	no	—
281	#41	—	76	1	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	1	no	—
293	C₂×D₄	—	38	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	C₂²×D₁₉	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	19	1	no	—
303	C₂²×C₄	—	38	1	no	—
304	C₂²×C₄	—	38	1	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
307	Q₁₆	—	38	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	38	2	no	—
310	SD₁₆	—	76	1	no	—
311	SD₁₆	C₂²⋊D₁₉	1	4	yes	complemented
312	D₈	—	2	2	no	—
313	D₈	—	2	2	no	—
314	D₈	—	38	2	no	—
315	D₈	—	76	1	no	—
316	M₁₆	—	2	2	no	—
317	C₂×C₈	—	19	1	no	—
318	C₂×C₈	—	19	1	no	—
319	C₂×C₈	—	38	2	no	—
320	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
321	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
322	C₄⋊C₄	—	19	1	no	—
323	C₄⋊C₄	—	19	1	no	—
324	C₄⋊C₄	—	19	1	no	—
325	C₄⋊C₄	—	38	1	no	—
326	C₄⋊C₄	—	38	1	no	—
327	C₂²⋊C₄	—	19	1	no	—
328	C₂²⋊C₄	—	19	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	C₄²	—	19	1	no	—
337	C₄²	—	38	1	no	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	4	2	no	—
342	C₂³	—	4	2	no	—
343	C₂³	—	8	1	no	—
344	C₂³	—	19	1	no	—
345	C₂³	—	38	1	no	—
346	C₂³	D₄×D₁₉	1	1	yes	characteristic
347	Q₈	—	2	1	no	—
348	Q₈	—	38	1	no	—
349	Q₈	—	38	1	no	—
350	Q₈	C₂×C₂²⋊D₁₉	1	2	yes	—
351	D₄	—	2	1	no	—
352	D₄	—	2	1	no	—
353	D₄	—	2	1	no	—
354	D₄	—	2	1	no	—
355	D₄	—	2	1	no	—
356	D₄	—	4	2	no	—
357	D₄	—	4	2	no	—
358	D₄	—	38	1	no	—
359	D₄	—	38	1	no	—
360	D₄	—	76	2	no	—
361	D₄	—	76	1	no	—
362	D₄	—	76	2	no	—
363	D₄	—	76	2	no	—
364	D₄	—	152	1	no	—
365	D₄	—	152	1	no	—
366	D₄	—	152	1	no	—
367	D₄	—	152	1	no	—
368	D₄	C₂×C₂²⋊D₁₉	1	2	yes	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	19	1	no	—
374	C₂×C₄	—	19	1	no	—
375	C₂×C₄	—	19	1	no	—
376	C₂×C₄	—	38	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	—	76	2	no	—
382	C₂×C₄	—	76	2	no	—
383	C₂×C₄	—	152	1	no	—
384	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
385	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
386	C₈	—	2	1	no	—
387	C₈	—	38	1	no	—
388	C₈	—	38	1	no	—
389	C₈	C₂×C₂²⋊D₁₉	1	2	yes	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	4	1	no	—
395	C₂²	—	4	1	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	—	8	4	no	—
403	C₂²	—	38	1	no	—
404	C₂²	—	38	1	no	—
405	C₂²	—	38	1	no	—
406	C₂²	—	76	1	no	—
407	C₂²	—	76	1	no	—
408	C₂²	—	76	1	no	—
409	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	38	1	no	—
413	C₄	—	38	1	no	—
414	C₄	—	38	1	no	—
415	C₄	—	76	1	no	—
416	C₄	—	76	1	no	—
417	C₄	—	76	1	no	—
418	C₄	#10597430	1	1	yes	characteristic
419	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
420	C₂	—	4	1	no	—
421	C₂	—	4	2	no	—
422	C₂	—	8	1	no	—
423	C₂	—	8	1	no	—
424	C₂	—	76	1	no	—
425	C₂	—	152	1	no	—
426	C₂	D₄×C₂²⋊D₁₉	1	1	yes	characteristic
427	C₂	#11927340	1	1	yes	characteristic
428	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	#3268
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×#10597362	C₂	semidirect
2. #11927213	C₂	semidirect
3. #11927188	C₂	semidirect
4. #11926932	C₂	semidirect
5. #11926790	C₂	semidirect
6. #11926777	C₂	semidirect
7. #11926764	C₂	semidirect
8. #11926737	C₂	semidirect
9. #11926706	C₂	semidirect
10. #11926688	C₂	semidirect
11. #11926686	C₂	semidirect
12. #11926678	C₂	semidirect
13. #11926645	C₂	semidirect
14. #11926613	C₂	semidirect
15. C₂×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
18. C₂×#64545	C₂²	semidirect
28. Q₈×Dic₁₉	C₂²	semidirect
29. C₂×#64528	C₂²	semidirect
31. #10597386	C₂²	semidirect
35. #10597384	C₂²	semidirect
39. C₂×#64526	C₂²	semidirect
48. C₂×#64516	C₂²	semidirect
49. C₂×C₈×D₁₉	C₂²	semidirect
50. #10597292	C₂²	semidirect
53. #10597289	C₂²	semidirect
55. #10597278	C₂²	semidirect
56. (C₂×D₁₉)⋊C₈	C₂²	semidirect
57. #10597275	C₂²	semidirect
58. #10597273	C₂²	semidirect
59. #10597272	C₂²	semidirect
60. Dic₁₉⋊C₈	C₂²	semidirect
93. SD₁₆×C₁₉	D₄	semidirect
206. C₂×AGL(1,ℤ/8)	D₁₉	semidirect
275. C₁₉	#3268	semidirect
311. SD₁₆	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×#10597362	2
#11927213	2
#11927188	2
#11926932	2
#11926790	2
#11926777	2
#11926764	2
#11926737	2
#11926706	2
#11926688	2
#11926686	2
#11926678	2
#11926645	2
#11926613	2
C₂×C₁₉×AGL(1,ℤ/8)	2
#3268	19