Subgroups — C₁₉×#32694 #18038653

Order 4864.

662 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2567	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2546	C₂	1	1	yes	maximal, characteristic
3	C₁₉×#2088	C₂	1	2	yes	maximal
4	C₁₉×#2058	C₂	1	2	yes	maximal
5	C₁₉×#2058	C₂	1	2	yes	maximal
6	C₁₉×#1985	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1943	C₂	1	2	yes	maximal
8	C₁₉×#1921	C₂	1	2	yes	maximal
9	C₁₉×#1918	C₂	1	2	yes	maximal
10	C₂×C₁₉×C₄⋊Q₈	—	2	1	no	—
11	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×#107	C₂²	1	2	yes	—
15	C₂×C₁₉×#106	C₂²	1	2	yes	—
16	C₂×C₁₉×#106	C₂²	1	2	yes	—
17	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×C₁₉×#97	C₂²	1	1	yes	characteristic
19	C₁₉×#398	—	2	1	no	—
20	C₁₉×#398	—	2	1	no	—
21	C₁₉×#395	—	2	1	no	—
22	C₁₉×#395	—	2	1	no	—
23	C₁₉×#391	—	2	1	no	—
24	C₁₉×#391	—	2	1	no	—
25	C₁₉×#389	C₂²	1	2	yes	—
26	C₁₉×#389	C₂²	1	2	yes	—
27	C₁₉×#389	C₂²	1	2	yes	—
28	C₁₉×#389	C₂²	1	2	yes	—
29	C₁₉×#384	—	2	1	no	—
30	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
32	C₁₉×#340	C₂²	1	2	yes	—
33	C₁₉×#340	C₂²	1	2	yes	—
34	C₁₉×#340	C₂²	1	2	yes	—
35	C₁₉×#340	C₂²	1	2	yes	—
36	C₁₉×#340	C₂²	1	2	yes	—
37	C₁₉×#336	C₂²	1	2	yes	—
38	C₁₉×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₁₉	—	2	1	no	—
40	C₂²×Q₈×C₁₉	—	2	1	no	—
41	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
43	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
44	C₁₉×C₄⋊Q₈	—	4	1	no	—
45	C₁₉×C₄⋊Q₈	—	4	1	no	—
46	C₁₉×C₄⋊Q₈	—	4	1	no	—
47	C₁₉×C₄⋊Q₈	—	4	1	no	—
48	C₁₉×C₄⋊Q₈	—	4	4	no	—
49	C₄×Q₈×C₁₉	—	4	1	no	—
50	C₄×Q₈×C₁₉	—	4	1	no	—
51	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
52	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
53	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
54	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
55	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
56	C₂×C₄⋊C₄×C₁₉	—	2	2	no	—
57	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
60	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
64	C₂×C₄²×C₁₉	—	2	1	no	—
65	C₂×C₄²×C₁₉	—	2	1	no	—
66	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
69	C₁₉×#107	Q₈	1	8	yes	complemented
70	C₁₉×#106	—	4	2	no	—
71	C₁₉×#106	—	4	2	no	—
72	C₁₉×C₄⋊C₈	—	4	1	no	—
73	C₁₉×#97	—	4	1	no	—
74	C₁₉×#95	—	2	1	no	—
75	C₁₉×#95	—	2	1	no	—
76	C₁₉×#95	—	2	2	no	—
77	C₁₉×#95	—	2	2	no	—
78	C₁₉×#95	—	2	2	no	—
79	C₁₉×#95	—	2	2	no	—
80	C₂×Q₈×C₁₉	—	2	2	no	—
81	C₂×Q₈×C₁₉	—	2	2	no	—
82	C₂×Q₈×C₁₉	—	4	1	no	—
83	C₂×Q₈×C₁₉	—	4	2	no	—
84	C₂×Q₈×C₁₉	—	4	2	no	—
85	C₂×Q₈×C₁₉	—	4	2	no	—
86	C₂×Q₈×C₁₉	—	4	2	no	—
87	C₂×Q₈×C₁₉	—	8	2	no	—
88	C₂²×C₄×C₁₉	—	2	2	no	—
89	C₂²×C₄×C₁₉	—	2	2	no	—
90	C₂²×C₄×C₁₉	—	2	2	no	—
91	C₂²×C₄×C₁₉	—	2	2	no	—
92	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
99	C₂×C₈×C₁₉	—	2	2	no	—
100	C₂×C₈×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	—	2	2	no	—
102	C₂×C₈×C₁₉	—	2	4	no	—
103	C₂×C₈×C₁₉	C₂×Q₈	1	4	yes	—
104	C₄⋊C₄×C₁₉	—	2	2	no	—
105	C₄⋊C₄×C₁₉	—	2	2	no	—
106	C₄⋊C₄×C₁₉	—	2	2	no	—
107	C₄⋊C₄×C₁₉	—	2	2	no	—
108	C₄⋊C₄×C₁₉	—	2	2	no	—
109	C₄⋊C₄×C₁₉	—	2	2	no	—
110	C₄⋊C₄×C₁₉	—	4	1	no	—
111	C₄⋊C₄×C₁₉	—	4	1	no	—
112	C₄⋊C₄×C₁₉	—	4	1	no	—
113	C₄⋊C₄×C₁₉	—	4	2	no	—
114	C₄⋊C₄×C₁₉	—	4	2	no	—
115	C₄⋊C₄×C₁₉	—	4	4	no	—
116	C₄⋊C₄×C₁₉	—	4	4	no	—
117	C₄⋊C₄×C₁₉	—	8	2	no	—
118	C₄⋊C₄×C₁₉	—	8	2	no	—
119	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
120	C₄⋊C₄×C₁₉	C₂×Q₈	1	4	yes	—
121	C₄²×C₁₉	—	2	1	no	—
122	C₄²×C₁₉	—	2	1	no	—
123	C₄²×C₁₉	—	2	1	no	—
124	C₄²×C₁₉	—	2	1	no	—
125	C₄²×C₁₉	—	2	1	no	—
126	C₄²×C₁₉	—	2	1	no	—
127	C₄²×C₁₉	—	4	2	no	—
128	C₄²×C₁₉	—	4	2	no	—
129	#32694	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
130	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
131	Q₈×C₁₉	—	4	4	no	—
132	Q₈×C₁₉	—	8	4	no	—
133	Q₈×C₁₉	—	8	4	no	—
134	C₂×C₄×C₁₉	—	2	1	no	—
135	C₂×C₄×C₁₉	—	2	1	no	—
136	C₂×C₄×C₁₉	—	2	1	no	—
137	C₂×C₄×C₁₉	—	2	1	no	—
138	C₂×C₄×C₁₉	—	2	1	no	—
139	C₂×C₄×C₁₉	—	2	1	no	—
140	C₂×C₄×C₁₉	—	2	1	no	—
141	C₂×C₄×C₁₉	—	2	1	no	—
142	C₂×C₄×C₁₉	—	2	4	no	—
143	C₂×C₄×C₁₉	—	2	4	no	—
144	C₂×C₄×C₁₉	—	2	1	no	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	2	no	—
147	C₂×C₄×C₁₉	—	2	2	no	—
148	C₂×C₄×C₁₉	—	2	2	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	—	4	2	no	—
152	C₂×C₄×C₁₉	—	4	2	no	—
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	2	no	—
155	C₂×C₄×C₁₉	—	4	2	no	—
156	C₂×C₄×C₁₉	—	4	2	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
160	C₂×C₄×C₁₉	#137	1	2	yes	—
161	C₂×C₄×C₁₉	C₂²×Q₈	1	2	yes	—
162	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
163	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
164	C₂×C₄×C₁₉	2₋¹⁺⁴	1	2	yes	—
165	C₈×C₁₉	—	2	4	no	—
166	C₈×C₁₉	—	4	2	no	—
167	#2567	C₂×C₁₉	1	1	yes	characteristic
168	#2546	C₂×C₁₉	1	1	yes	characteristic
169	#2088	C₂×C₁₉	1	2	yes	—
170	#2058	C₂×C₁₉	1	2	yes	—
171	#2058	C₂×C₁₉	1	2	yes	—
172	#1985	C₂×C₁₉	1	1	yes	characteristic
173	#1943	C₂×C₁₉	1	2	yes	—
174	#1921	C₂×C₁₉	1	2	yes	—
175	#1918	C₂×C₁₉	1	2	yes	—
176	C₂²×C₁₉	#534	1	1	yes	characteristic
177	C₂²×C₁₉	D₄×Q₈	1	2	yes	—
178	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
179	C₂²×C₁₉	C₂×#137	1	1	yes	characteristic
180	C₂²×C₁₉	#577	1	2	yes	—
181	C₄×C₁₉	—	2	2	no	—
182	C₄×C₁₉	—	2	2	no	—
183	C₄×C₁₉	—	4	4	no	—
184	C₄×C₁₉	—	4	4	no	—
185	C₄×C₁₉	—	4	1	no	—
186	C₄×C₁₉	—	4	1	no	—
187	C₄×C₁₉	—	4	1	no	—
188	C₄×C₁₉	—	4	1	no	—
189	C₄×C₁₉	—	8	2	no	—
190	C₄×C₁₉	—	8	2	no	—
191	C₄×C₁₉	#544	1	2	yes	—
192	C₄×C₁₉	Q₈²	1	1	yes	characteristic
193	C₄×C₁₉	#563	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	—	2	1	no	—
195	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
196	C₂×C₄⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
197	C₂×C₄×Q₈	C₂²×C₁₉	1	1	yes	characteristic
198	C₂×#107	C₂²×C₁₉	1	2	yes	—
199	C₂×#106	C₂²×C₁₉	1	2	yes	—
200	C₂×#106	C₂²×C₁₉	1	2	yes	—
201	C₂×C₄⋊C₈	C₂²×C₁₉	1	1	yes	characteristic
202	C₂×#97	C₂²×C₁₉	1	1	yes	characteristic
203	#398	—	2	1	no	—
204	#398	—	2	1	no	—
205	#395	—	2	1	no	—
206	#395	—	2	1	no	—
207	#391	—	2	1	no	—
208	#391	—	2	1	no	—
209	#389	C₂²×C₁₉	1	2	yes	—
210	#389	C₂²×C₁₉	1	2	yes	—
211	#389	C₂²×C₁₉	1	2	yes	—
212	#389	C₂²×C₁₉	1	2	yes	—
213	#384	—	2	1	no	—
214	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂²×C₁₉	1	1	yes	characteristic
216	#340	C₂²×C₁₉	1	2	yes	—
217	#340	C₂²×C₁₉	1	2	yes	—
218	#340	C₂²×C₁₉	1	2	yes	—
219	#340	C₂²×C₁₉	1	2	yes	—
220	#340	C₂²×C₁₉	1	2	yes	—
221	#336	C₂²×C₁₉	1	2	yes	—
222	#336	C₂²×C₁₉	1	2	yes	—
223	C₂×C₁₉	#2734	1	1	yes	characteristic
224	C₂×C₁₉	#3193	1	1	yes	characteristic
225	C₂×C₁₉	#3200	1	1	yes	characteristic
226	C₂×C₁₉	#3384	1	2	yes	—
227	C₂×C₁₉	#3387	1	2	yes	—
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	D₄×C₁₉	1	1	yes	characteristic
231	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
232	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
233	C₄⋊Q₈	—	4	1	no	—
234	C₄⋊Q₈	—	4	1	no	—
235	C₄⋊Q₈	—	4	1	no	—
236	C₄⋊Q₈	—	4	1	no	—
237	C₄⋊Q₈	—	4	4	no	—
238	C₄×Q₈	—	4	1	no	—
239	C₄×Q₈	—	4	1	no	—
240	C₂×C₄⋊C₄	—	2	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
247	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
248	C₂×C₄⋊C₄	D₄×C₁₉	1	1	yes	characteristic
249	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
250	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
253	C₂×C₄²	—	2	1	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
256	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
258	#107	Q₈×C₁₉	1	8	yes	complemented
259	#106	—	4	2	no	—
260	#106	—	4	2	no	—
261	C₄⋊C₈	—	4	1	no	—
262	#97	—	4	1	no	—
263	#95	—	2	1	no	—
264	#95	—	2	1	no	—
265	#95	—	2	2	no	—
266	#95	—	2	2	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	C₁₉	#32694	1	1	yes	characteristic, direct product factor, Sylow
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	4	1	no	—
273	C₂×Q₈	—	4	2	no	—
274	C₂×Q₈	—	4	2	no	—
275	C₂×Q₈	—	4	2	no	—
276	C₂×Q₈	—	4	2	no	—
277	C₂×Q₈	—	8	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
284	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
287	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
288	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	C₂×Q₈×C₁₉	1	4	yes	—
294	C₄⋊C₄	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	4	1	no	—
301	C₄⋊C₄	—	4	1	no	—
302	C₄⋊C₄	—	4	1	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	4	2	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	4	4	no	—
307	C₄⋊C₄	—	8	2	no	—
308	C₄⋊C₄	—	8	2	no	—
309	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
310	C₄⋊C₄	C₂×Q₈×C₁₉	1	4	yes	—
311	C₄²	—	2	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	2	1	no	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	2	1	no	—
317	C₄²	—	4	2	no	—
318	C₄²	—	4	2	no	—
319	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
320	Q₈	—	4	4	no	—
321	Q₈	—	8	4	no	—
322	Q₈	—	8	4	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
349	C₂×C₄	C₁₉×#137	1	2	yes	—
350	C₂×C₄	C₂²×Q₈×C₁₉	1	2	yes	—
351	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
352	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
353	C₂×C₄	C₁₉×2₋¹⁺⁴	1	2	yes	—
354	C₈	—	2	4	no	—
355	C₈	—	4	2	no	—
356	C₂²	C₁₉×#534	1	1	yes	characteristic
357	C₂²	D₄×Q₈×C₁₉	1	2	yes	—
358	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
359	C₂²	C₂×C₁₉×#137	1	1	yes	characteristic
360	C₂²	C₁₉×#577	1	2	yes	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	1	no	—
364	C₄	—	4	1	no	—
365	C₄	—	4	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	4	no	—
368	C₄	—	4	4	no	—
369	C₄	—	8	2	no	—
370	C₄	—	8	2	no	—
371	C₄	C₁₉×#544	1	2	yes	—
372	C₄	Q₈²×C₁₉	1	1	yes	characteristic
373	C₄	C₁₉×#563	1	1	yes	characteristic
374	C₂	C₁₉×#2734	1	1	yes	characteristic
375	C₂	C₁₉×#3193	1	1	yes	characteristic
376	C₂	C₁₉×#3200	1	1	yes	characteristic
377	C₂	C₁₉×#3384	1	2	yes	—
378	C₂	C₁₉×#3387	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂×C₄×Q₈×C₁₉ ◁ G

Complements

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

N	H ≅ G/N	type
69. C₁₉×#107	Q₈	semidirect
129. #32694	C₁₉	direct (N × H)
258. #107	Q₈×C₁₉	semidirect
269. C₁₉	#32694	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₉×#2567	2
C₁₉×#2546	2
C₁₉×#2088	2
C₁₉×#2058	2
C₁₉×#1985	2
C₁₉×#1943	2
C₁₉×#1921	2
C₁₉×#1918	2
#32694	19

Subgroups — C19×#32694 #18038653

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32694 #18038653