Subgroups — C₂×AGL(1,ℤ/8)×D₁₉ #14578365

Order 2432.

1720 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#10597354	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#10597360	C₂	1	2	yes	maximal, complemented
5	C₂×#10597378	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10597357	C₂	1	2	yes	maximal, complemented
8	AGL(1,ℤ/8)×D₁₉	C₂	1	16	yes	maximal, direct product factor
9	C₂×SD₁₆×D₁₉	C₂	1	2	yes	maximal, complemented
10	C₂×D₈×D₁₉	C₂	1	2	yes	maximal, complemented
11	C₂×M₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂⁴×D₁₉	—	2	1	no	—
14	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic, complemented
16	C₂²×C₂²⋊D₁₉	—	2	1	no	—
17	#41×D₁₉	—	2	4	no	—
18	#41×D₁₉	C₂²	1	8	yes	complemented
19	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
20	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#64543	—	2	1	no	—
22	C₂×#64543	C₂²	1	1	yes	characteristic, complemented
23	C₂×D₄×D₁₉	—	2	1	no	—
24	C₂×D₄×D₁₉	—	2	1	no	—
25	C₂×D₄×D₁₉	—	2	1	no	—
26	C₂×D₄×D₁₉	—	2	4	no	—
27	C₂×D₄×D₁₉	C₂²	1	2	yes	—
28	C₂×D₄×D₁₉	C₂²	1	2	yes	complemented
29	C₂×D₄×D₁₉	C₂²	1	8	yes	complemented
30	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic, complemented
31	C₂×#64541	—	2	1	no	—
32	C₂×#64541	C₂²	1	1	yes	characteristic, complemented
33	C₂²×D₇₆	C₂²	1	1	yes	characteristic, complemented
34	C₂²×C₄×D₁₉	—	2	1	no	—
35	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
36	C₁₉×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
37	C₂×SD₁₆×C₁₉	C₂²	1	2	yes	complemented
38	C₂×D₈×C₁₉	C₂²	1	2	yes	complemented
39	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
40	#10597395	C₂²	1	8	yes	complemented
41	C₂×#64527	C₂²	1	2	yes	complemented
42	C₂×#64526	C₂²	1	2	yes	complemented
43	#10597378	C₂²	1	8	yes	complemented
44	C₂×#64525	C₂²	1	2	yes	complemented
45	C₂×#64525	C₂²	1	2	yes	complemented
46	C₂×#64520	C₂²	1	1	yes	characteristic, complemented
47	#10597360	C₂²	1	16	yes	complemented
48	SD₁₆×D₁₉	C₂²	1	16	yes	complemented
49	#10597357	C₂²	1	16	yes	complemented
50	D₈×D₁₉	C₂²	1	16	yes	complemented
51	#10597354	C₂²	1	8	yes	complemented
52	M₁₆×D₁₉	C₂²	1	8	yes	complemented
53	C₂×D₁₅₂	C₂²	1	2	yes	complemented
54	C₂×#64516	C₂²	1	2	yes	complemented
55	C₂×#64515	C₂²	1	2	yes	complemented
56	C₂×C₈×D₁₉	C₂²	1	2	yes	complemented
57	C₂⁴×C₁₉	—	2	1	no	—
58	C₂³×D₁₉	—	2	1	no	—
59	C₂³×D₁₉	—	2	1	no	—
60	C₂³×D₁₉	—	2	2	no	—
61	C₂³×D₁₉	—	2	2	no	—
62	C₂³×D₁₉	—	2	8	no	—
63	C₂³×D₁₉	—	4	8	no	—
64	C₂³×D₁₉	D₄	1	1	yes	characteristic
65	#41×C₁₉	—	2	2	no	—
66	#41×C₁₉	C₂³	1	4	yes	complemented
67	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic, complemented
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	2	2	no	—
71	C₂×D₄×C₁₉	C₂³	1	2	yes	—
72	C₂×D₄×C₁₉	C₂³	1	4	yes	complemented
73	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic, complemented
74	C₂²×C₄×C₁₉	—	2	1	no	—
75	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	2	no	—
80	C₂×C₂²⋊D₁₉	—	2	2	no	—
81	C₂×C₂²⋊D₁₉	—	2	8	no	—
82	C₂²×Dic₁₉	—	2	1	no	—
83	C₂²×Dic₁₉	D₄	1	1	yes	characteristic
84	#64545	—	2	2	no	—
85	#64545	C₂³	1	4	yes	complemented
86	Q₈×D₁₉	—	2	2	no	—
87	Q₈×D₁₉	C₂³	1	4	yes	complemented
88	#64543	—	2	8	no	—
89	#64543	—	2	2	no	—
90	#64543	C₂³	1	4	yes	complemented
91	D₄×D₁₉	—	2	8	no	—
92	D₄×D₁₉	—	2	4	no	—
93	D₄×D₁₉	—	2	8	no	—
94	D₄×D₁₉	—	2	8	no	—
95	D₄×D₁₉	—	2	4	no	—
96	D₄×D₁₉	—	2	2	no	—
97	D₄×D₁₉	C₂³	1	8	yes	—
98	D₄×D₁₉	C₂³	1	8	yes	complemented
99	D₄×D₁₉	C₂³	1	4	yes	complemented
100	#64541	—	2	2	no	—
101	#64541	—	2	8	no	—
102	#64541	C₂³	1	4	yes	complemented
103	C₂×D₇₆	—	2	1	no	—
104	C₂×D₇₆	—	2	2	no	—
105	C₂×D₇₆	—	2	1	no	—
106	C₂×D₇₆	C₂³	1	2	yes	—
107	C₂×D₇₆	C₂³	1	4	yes	complemented
108	C₂×D₇₆	C₂³	1	1	yes	characteristic, complemented
109	C₂×C₄×D₁₉	—	2	1	no	—
110	C₂×C₄×D₁₉	—	2	1	no	—
111	C₂×C₄×D₁₉	—	2	1	no	—
112	C₂×C₄×D₁₉	—	2	8	no	—
113	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
114	C₂×C₄×D₁₉	D₄	1	1	yes	characteristic
115	C₂×C₄×D₁₉	D₄	1	4	yes	—
116	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
117	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
118	C₂×C₄×D₁₉	C₂³	1	4	yes	—
119	C₂×Dic₃₈	—	2	1	no	—
120	C₂×Dic₃₈	C₂³	1	1	yes	characteristic, complemented
121	SD₁₆×C₁₉	C₂³	1	8	yes	complemented
122	D₈×C₁₉	C₂³	1	8	yes	complemented
123	M₁₆×C₁₉	C₂³	1	4	yes	complemented
124	C₂×C₈×C₁₉	C₂³	1	2	yes	complemented
125	#64527	C₂³	1	8	yes	complemented
126	#64526	C₂³	1	8	yes	complemented
127	#64525	C₂³	1	8	yes	complemented
128	#64525	C₂³	1	8	yes	complemented
129	#64520	C₂³	1	4	yes	complemented
130	C₂×C₁₉⋊C₈	C₂³	1	2	yes	complemented
131	D₁₅₂	C₂³	1	8	yes	complemented
132	#64516	C₂³	1	8	yes	complemented
133	#64515	C₂³	1	8	yes	complemented
134	C₈×D₁₉	C₂³	1	8	yes	complemented
135	C₂³×C₁₉	—	2	1	no	—
136	C₂³×C₁₉	—	2	2	no	—
137	C₂³×C₁₉	—	2	4	no	—
138	C₂³×C₁₉	—	4	4	no	—
139	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×D₁₉	—	2	4	no	—
141	C₂²×D₁₉	—	2	1	no	—
142	C₂²×D₁₉	—	2	2	no	—
143	C₂²×D₁₉	—	2	4	no	—
144	C₂²×D₁₉	—	2	4	no	—
145	C₂²×D₁₉	—	2	8	no	—
146	C₂²×D₁₉	—	2	8	no	—
147	C₂²×D₁₉	—	4	8	no	—
148	C₂²×D₁₉	—	4	32	no	—
149	C₂²×D₁₉	—	4	4	no	—
150	C₂²×D₁₉	—	4	4	no	—
151	C₂²×D₁₉	—	4	8	no	—
152	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
153	C₂²×D₁₉	C₂×D₄	1	4	yes	—
154	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
155	Q₈×C₁₉	—	2	1	no	—
156	Q₈×C₁₉	C₂⁴	1	2	yes	complemented
157	D₄×C₁₉	—	2	4	no	—
158	D₄×C₁₉	—	2	2	no	—
159	D₄×C₁₉	—	2	4	no	—
160	D₄×C₁₉	—	2	1	no	—
161	D₄×C₁₉	C₂⁴	1	4	yes	—
162	D₄×C₁₉	C₂⁴	1	2	yes	complemented
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	4	no	—
165	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
167	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
169	C₂²⋊D₁₉	—	2	4	no	—
170	C₂²⋊D₁₉	—	2	4	no	—
171	C₂²⋊D₁₉	—	2	4	no	—
172	C₂²⋊D₁₉	—	2	8	no	—
173	C₂²⋊D₁₉	—	2	8	no	—
174	C₂×Dic₁₉	—	2	1	no	—
175	C₂×Dic₁₉	—	2	4	no	—
176	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
177	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
178	C₂×Dic₁₉	C₂×D₄	1	4	yes	—
179	D₇₆	—	2	4	no	—
180	D₇₆	—	2	2	no	—
181	D₇₆	—	2	4	no	—
182	D₇₆	—	2	1	no	—
183	D₇₆	C₂⁴	1	4	yes	—
184	D₇₆	C₂⁴	1	2	yes	complemented
185	C₄×D₁₉	—	2	4	no	—
186	C₄×D₁₉	—	2	4	no	—
187	C₄×D₁₉	—	2	4	no	—
188	C₄×D₁₉	C₂×D₄	1	4	yes	—
189	C₄×D₁₉	C₂×D₄	1	4	yes	—
190	C₄×D₁₉	C₂×D₄	1	2	yes	—
191	C₄×D₁₉	C₂×D₄	1	2	yes	—
192	C₄×D₁₉	C₂⁴	1	2	yes	—
193	C₄×D₁₉	C₂⁴	1	2	yes	—
194	Dic₃₈	—	2	1	no	—
195	Dic₃₈	—	2	4	no	—
196	Dic₃₈	C₂⁴	1	2	yes	complemented
197	C₈×C₁₉	C₂⁴	1	4	yes	complemented
198	C₁₉⋊C₈	C₂⁴	1	4	yes	complemented
199	C₂²×AGL(1,ℤ/8)	—	19	1	no	maximal, Sylow
200	C₂²×C₁₉	—	2	2	no	—
201	C₂²×C₁₉	—	2	2	no	—
202	C₂²×C₁₉	—	2	4	no	—
203	C₂²×C₁₉	—	4	8	no	—
204	C₂²×C₁₉	—	4	4	no	—
205	C₂²×C₁₉	—	4	2	no	—
206	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
207	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
208	C₂×D₁₉	—	2	2	no	—
209	C₂×D₁₉	—	2	8	no	—
210	C₂×D₁₉	—	2	2	no	—
211	C₂×D₁₉	—	2	4	no	—
212	C₂×D₁₉	—	4	16	no	—
213	C₂×D₁₉	—	4	8	no	—
214	C₂×D₁₉	—	4	2	no	—
215	C₂×D₁₉	—	4	4	no	—
216	C₂×D₁₉	—	4	8	no	—
217	C₂×D₁₉	—	4	16	no	—
218	C₂×D₁₉	AGL(1,ℤ/8)	1	4	yes	direct product factor
219	C₂×D₁₉	C₂²×D₄	1	2	yes	—
220	C₂×D₁₉	C₂²×D₄	1	2	yes	—
221	C₄×C₁₉	—	2	2	no	—
222	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
223	C₄×C₁₉	C₂²×D₄	1	2	yes	—
224	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
225	Dic₁₉	—	2	2	no	—
226	Dic₁₉	C₂²×D₄	1	2	yes	—
227	Dic₁₉	C₂²×D₄	1	2	yes	—
228	C₂²×#41	—	19	1	no	—
229	C₂³×D₄	—	19	1	no	—
230	C₂×AGL(1,ℤ/8)	—	19	1	no	—
231	C₂×AGL(1,ℤ/8)	—	19	1	no	—
232	C₂×AGL(1,ℤ/8)	—	19	16	no	—
233	C₂×AGL(1,ℤ/8)	—	19	2	no	—
234	C₂×AGL(1,ℤ/8)	—	19	2	no	—
235	C₂×AGL(1,ℤ/8)	—	19	1	no	—
236	C₂×AGL(1,ℤ/8)	D₁₉	1	1	yes	characteristic, direct product factor
237	C₂²×SD₁₆	—	19	2	no	—
238	C₂²×D₈	—	19	2	no	—
239	C₂²×M₁₆	—	19	1	no	—
240	C₂×C₁₉	—	2	2	no	—
241	C₂×C₁₉	—	4	4	no	—
242	C₂×C₁₉	—	4	2	no	—
243	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	2	yes	complemented
244	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
245	D₁₉	—	2	2	no	—
246	D₁₉	—	4	2	no	—
247	D₁₉	—	4	4	no	—
248	D₁₉	C₂×AGL(1,ℤ/8)	1	4	yes	direct product factor
249	C₂⁵	—	38	1	no	—
250	C₂×#41	—	19	8	no	—
251	C₂×#41	—	19	1	no	—
252	C₂×#41	—	19	1	no	—
253	C₂×#41	—	19	1	no	—
254	C₂×#41	—	38	1	no	—
255	C₂×#41	—	38	1	no	—
256	C₂×#41	—	38	4	no	—
257	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
258	C₂²×Q₈	—	19	1	no	—
259	C₂²×D₄	—	19	2	no	—
260	C₂²×D₄	—	19	2	no	—
261	C₂²×D₄	—	19	1	no	—
262	C₂²×D₄	—	19	8	no	—
263	C₂²×D₄	—	19	1	no	—
264	C₂²×D₄	—	38	1	no	—
265	C₂²×D₄	—	38	4	no	—
266	C₂²×D₄	—	38	1	no	—
267	C₂²×D₄	—	38	1	no	—
268	C₂²×D₄	—	38	1	no	—
269	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic, complemented
270	C₂³×C₄	—	19	1	no	—
271	C₂³×C₄	—	38	1	no	—
272	AGL(1,ℤ/8)	—	19	8	no	—
273	AGL(1,ℤ/8)	—	19	8	no	—
274	AGL(1,ℤ/8)	—	19	16	no	—
275	AGL(1,ℤ/8)	—	19	16	no	—
276	AGL(1,ℤ/8)	—	19	8	no	—
277	AGL(1,ℤ/8)	C₂×D₁₉	1	8	yes	direct product factor
278	C₂×SD₁₆	—	19	2	no	—
279	C₂×SD₁₆	—	19	2	no	—
280	C₂×SD₁₆	—	19	16	no	—
281	C₂×SD₁₆	—	19	2	no	—
282	C₂×SD₁₆	C₂×D₁₉	1	2	yes	complemented
283	C₂×D₈	—	19	2	no	—
284	C₂×D₈	—	19	2	no	—
285	C₂×D₈	—	19	16	no	—
286	C₂×D₈	—	19	2	no	—
287	C₂×D₈	C₂×D₁₉	1	2	yes	complemented
288	C₂×M₁₆	—	19	1	no	—
289	C₂×M₁₆	—	19	8	no	—
290	C₂×M₁₆	—	19	2	no	—
291	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
292	C₂²×C₈	—	19	2	no	—
293	C₁₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
294	C₂⁴	—	2	1	no	—
295	C₂⁴	—	19	1	no	—
296	C₂⁴	—	38	1	no	—
297	C₂⁴	—	38	8	no	—
298	C₂⁴	—	38	2	no	—
299	C₂⁴	—	38	2	no	—
300	C₂⁴	—	38	1	no	—
301	C₂⁴	—	76	8	no	—
302	#41	—	2	2	no	—
303	#41	—	19	4	no	—
304	#41	—	19	4	no	—
305	#41	—	19	4	no	—
306	#41	—	38	8	no	—
307	#41	—	38	8	no	—
308	#41	—	38	2	no	—
309	#41	—	38	2	no	—
310	#41	—	38	2	no	—
311	#41	C₂²×D₁₉	1	4	yes	complemented
312	C₂×Q₈	—	19	4	no	—
313	C₂×Q₈	—	19	1	no	—
314	C₂×Q₈	—	38	1	no	—
315	C₂×Q₈	—	38	2	no	—
316	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic, complemented
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	19	8	no	—
321	C₂×D₄	—	19	8	no	—
322	C₂×D₄	—	19	4	no	—
323	C₂×D₄	—	19	2	no	—
324	C₂×D₄	—	19	1	no	—
325	C₂×D₄	—	19	4	no	—
326	C₂×D₄	—	38	1	no	—
327	C₂×D₄	—	38	8	no	—
328	C₂×D₄	—	38	4	no	—
329	C₂×D₄	—	38	4	no	—
330	C₂×D₄	—	38	8	no	—
331	C₂×D₄	—	38	2	no	—
332	C₂×D₄	—	38	8	no	—
333	C₂×D₄	—	38	2	no	—
334	C₂×D₄	—	38	2	no	—
335	C₂×D₄	—	38	1	no	—
336	C₂×D₄	—	38	8	no	—
337	C₂×D₄	—	38	1	no	—
338	C₂×D₄	—	38	1	no	—
339	C₂×D₄	—	38	2	no	—
340	C₂×D₄	—	38	1	no	—
341	C₂×D₄	C₂²×D₁₉	1	2	yes	—
342	C₂×D₄	C₂²×D₁₉	1	4	yes	complemented
343	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic, complemented
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	19	1	no	—
346	C₂²×C₄	—	19	1	no	—
347	C₂²×C₄	—	19	4	no	—
348	C₂²×C₄	—	19	1	no	—
349	C₂²×C₄	—	19	1	no	—
350	C₂²×C₄	—	19	4	no	—
351	C₂²×C₄	—	19	1	no	—
352	C₂²×C₄	—	38	1	no	—
353	C₂²×C₄	—	38	8	no	—
354	C₂²×C₄	—	38	1	no	—
355	C₂²×C₄	—	38	1	no	—
356	C₂²×C₄	—	38	1	no	—
357	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
358	SD₁₆	—	19	8	no	—
359	SD₁₆	—	19	8	no	—
360	SD₁₆	—	19	8	no	—
361	SD₁₆	C₂²×D₁₉	1	8	yes	complemented
362	D₈	—	19	8	no	—
363	D₈	—	19	8	no	—
364	D₈	—	19	8	no	—
365	D₈	C₂²×D₁₉	1	8	yes	complemented
366	M₁₆	—	19	4	no	—
367	M₁₆	—	19	8	no	—
368	M₁₆	C₂²×D₁₉	1	4	yes	complemented
369	C₂×C₈	—	19	2	no	—
370	C₂×C₈	—	19	8	no	—
371	C₂×C₈	C₂²×D₁₉	1	2	yes	complemented
372	C₂³	—	2	4	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	2	no	—
375	C₂³	—	4	4	no	—
376	C₂³	—	19	1	no	—
377	C₂³	—	19	4	no	—
378	C₂³	—	19	1	no	—
379	C₂³	—	38	4	no	—
380	C₂³	—	38	4	no	—
381	C₂³	—	38	8	no	—
382	C₂³	—	38	8	no	—
383	C₂³	—	38	4	no	—
384	C₂³	—	38	1	no	—
385	C₂³	—	38	2	no	—
386	C₂³	—	76	4	no	—
387	C₂³	—	76	8	no	—
388	C₂³	—	76	4	no	—
389	C₂³	—	76	32	no	—
390	C₂³	—	76	8	no	—
391	C₂³	D₄×D₁₉	1	1	yes	characteristic
392	Q₈	—	2	1	no	—
393	Q₈	—	19	2	no	—
394	Q₈	—	38	4	no	—
395	Q₈	—	38	1	no	—
396	Q₈	C₂³×D₁₉	1	2	yes	complemented
397	D₄	—	2	4	no	—
398	D₄	—	2	2	no	—
399	D₄	—	2	4	no	—
400	D₄	—	2	1	no	—
401	D₄	—	19	2	no	—
402	D₄	—	19	4	no	—
403	D₄	—	38	4	no	—
404	D₄	—	38	8	no	—
405	D₄	—	38	8	no	—
406	D₄	—	38	4	no	—
407	D₄	—	38	4	no	—
408	D₄	—	38	4	no	—
409	D₄	—	38	4	no	—
410	D₄	—	38	2	no	—
411	D₄	—	38	1	no	—
412	D₄	C₂³×D₁₉	1	4	yes	—
413	D₄	C₂³×D₁₉	1	2	yes	complemented
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	19	4	no	—
417	C₂×C₄	—	19	1	no	—
418	C₂×C₄	—	19	1	no	—
419	C₂×C₄	—	19	4	no	—
420	C₂×C₄	—	19	2	no	—
421	C₂×C₄	—	19	2	no	—
422	C₂×C₄	—	19	4	no	—
423	C₂×C₄	—	19	2	no	—
424	C₂×C₄	—	19	2	no	—
425	C₂×C₄	—	38	4	no	—
426	C₂×C₄	—	38	4	no	—
427	C₂×C₄	—	38	4	no	—
428	C₂×C₄	—	38	1	no	—
429	C₂×C₄	—	38	4	no	—
430	C₂×C₄	D₄×D₁₉	1	2	yes	—
431	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₉	1	2	yes	—
433	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
434	C₈	—	19	4	no	—
435	C₈	C₂³×D₁₉	1	4	yes	complemented
436	C₂²	—	2	2	no	—
437	C₂²	—	2	2	no	—
438	C₂²	—	2	4	no	—
439	C₂²	—	4	8	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	19	4	no	—
443	C₂²	—	19	2	no	—
444	C₂²	—	19	2	no	—
445	C₂²	—	38	8	no	—
446	C₂²	—	38	2	no	—
447	C₂²	—	38	2	no	—
448	C₂²	—	38	4	no	—
449	C₂²	—	76	8	no	—
450	C₂²	—	76	16	no	—
451	C₂²	—	76	8	no	—
452	C₂²	—	76	16	no	—
453	C₂²	—	76	4	no	—
454	C₂²	—	76	2	no	—
455	C₂²	C₂×D₄×D₁₉	1	2	yes	—
456	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	19	2	no	—
459	C₄	—	19	2	no	—
460	C₄	—	38	2	no	—
461	C₄	C₂×D₄×D₁₉	1	2	yes	—
462	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
463	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
464	C₂	—	2	2	no	—
465	C₂	—	4	4	no	—
466	C₂	—	4	2	no	—
467	C₂	—	19	4	no	—
468	C₂	—	38	2	no	—
469	C₂	—	76	4	no	—
470	C₂	—	76	2	no	—
471	C₂	AGL(1,ℤ/8)×D₁₉	1	2	yes	direct product factor
472	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×AGL(1,ℤ/8)	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₉
hypocenter	C₁₉	C₂²×AGL(1,ℤ/8)
LCS	G ▷ 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×#41×D₁₉	C₂	semidirect
2. C₂²×D₄×D₁₉	C₂	semidirect
3. C₂×#10597354	C₂	semidirect
4. C₂×#10597360	C₂	semidirect
5. C₂×#10597378	C₂	semidirect
6. C₂×#10597395	C₂	semidirect
7. C₂×#10597357	C₂	semidirect
8. AGL(1,ℤ/8)×D₁₉	C₂	direct (N × H)
9. C₂×SD₁₆×D₁₉	C₂	semidirect
10. C₂×D₈×D₁₉	C₂	semidirect
11. C₂×M₁₆×D₁₉	C₂	semidirect
12. C₂×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
14. C₂×#41×C₁₉	C₂²	semidirect
15. C₂²×D₄×C₁₉	C₂²	semidirect
18. #41×D₁₉	C₂²	semidirect
19. C₂×#64545	C₂²	semidirect
20. C₂×Q₈×D₁₉	C₂²	semidirect
22. C₂×#64543	C₂²	semidirect
28. C₂×D₄×D₁₉	C₂²	semidirect
29. C₂×D₄×D₁₉	C₂²	semidirect
30. C₂×D₄×D₁₉	C₂²	semidirect
32. C₂×#64541	C₂²	semidirect
33. C₂²×D₇₆	C₂²	semidirect
36. C₁₉×AGL(1,ℤ/8)	C₂²	semidirect
37. C₂×SD₁₆×C₁₉	C₂²	semidirect
38. C₂×D₈×C₁₉	C₂²	semidirect
39. C₂×M₁₆×C₁₉	C₂²	semidirect
40. #10597395	C₂²	semidirect
41. C₂×#64527	C₂²	semidirect
42. C₂×#64526	C₂²	semidirect
43. #10597378	C₂²	semidirect
44. C₂×#64525	C₂²	semidirect
45. C₂×#64525	C₂²	semidirect
46. C₂×#64520	C₂²	semidirect
47. #10597360	C₂²	semidirect
48. SD₁₆×D₁₉	C₂²	semidirect
49. #10597357	C₂²	semidirect
50. D₈×D₁₉	C₂²	semidirect
51. #10597354	C₂²	semidirect
52. M₁₆×D₁₉	C₂²	semidirect
53. C₂×D₁₅₂	C₂²	semidirect
54. C₂×#64516	C₂²	semidirect
55. C₂×#64515	C₂²	semidirect
56. C₂×C₈×D₁₉	C₂²	semidirect
66. #41×C₁₉	C₂³	semidirect
67. C₂×Q₈×C₁₉	C₂³	semidirect
72. C₂×D₄×C₁₉	C₂³	semidirect
73. C₂×D₄×C₁₉	C₂³	semidirect
85. #64545	C₂³	semidirect
87. Q₈×D₁₉	C₂³	semidirect
90. #64543	C₂³	semidirect
98. D₄×D₁₉	C₂³	semidirect
99. D₄×D₁₉	C₂³	semidirect
102. #64541	C₂³	semidirect
107. C₂×D₇₆	C₂³	semidirect
108. C₂×D₇₆	C₂³	semidirect
120. C₂×Dic₃₈	C₂³	semidirect
121. SD₁₆×C₁₉	C₂³	semidirect
122. D₈×C₁₉	C₂³	semidirect
123. M₁₆×C₁₉	C₂³	semidirect
124. C₂×C₈×C₁₉	C₂³	semidirect
125. #64527	C₂³	semidirect
126. #64526	C₂³	semidirect
127. #64525	C₂³	semidirect
128. #64525	C₂³	semidirect
129. #64520	C₂³	semidirect
130. C₂×C₁₉⋊C₈	C₂³	semidirect
131. D₁₅₂	C₂³	semidirect
132. #64516	C₂³	semidirect
133. #64515	C₂³	semidirect
134. C₈×D₁₉	C₂³	semidirect
156. Q₈×C₁₉	C₂⁴	semidirect
162. D₄×C₁₉	C₂⁴	semidirect
184. D₇₆	C₂⁴	semidirect
196. Dic₃₈	C₂⁴	semidirect
197. C₈×C₁₉	C₂⁴	semidirect
198. C₁₉⋊C₈	C₂⁴	semidirect
218. C₂×D₁₉	AGL(1,ℤ/8)	direct (N × H)
236. C₂×AGL(1,ℤ/8)	D₁₉	direct (N × H)
243. C₂×C₁₉	C₂×AGL(1,ℤ/8)	semidirect
248. D₁₉	C₂×AGL(1,ℤ/8)	direct (N × H)
257. C₂×#41	C₂×D₁₉	semidirect
269. C₂²×D₄	C₂×D₁₉	semidirect
277. AGL(1,ℤ/8)	C₂×D₁₉	direct (N × H)
282. C₂×SD₁₆	C₂×D₁₉	semidirect
287. C₂×D₈	C₂×D₁₉	semidirect
291. C₂×M₁₆	C₂×D₁₉	semidirect
293. C₁₉	C₂²×AGL(1,ℤ/8)	semidirect
311. #41	C₂²×D₁₉	semidirect
316. C₂×Q₈	C₂²×D₁₉	semidirect
342. C₂×D₄	C₂²×D₁₉	semidirect
343. C₂×D₄	C₂²×D₁₉	semidirect
361. SD₁₆	C₂²×D₁₉	semidirect
365. D₈	C₂²×D₁₉	semidirect
368. M₁₆	C₂²×D₁₉	semidirect
371. C₂×C₈	C₂²×D₁₉	semidirect
396. Q₈	C₂³×D₁₉	semidirect
413. D₄	C₂³×D₁₉	semidirect
435. C₈	C₂³×D₁₉	semidirect
471. C₂	AGL(1,ℤ/8)×D₁₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₉	2
C₂²×D₄×D₁₉	2
C₂×#10597354	2
C₂×#10597360	2
C₂×#10597378	2
C₂×#10597395	2
C₂×#10597357	2
AGL(1,ℤ/8)×D₁₉	2
C₂×SD₁₆×D₁₉	2
C₂×D₈×D₁₉	2
C₂×M₁₆×D₁₉	2
C₂×C₁₉×AGL(1,ℤ/8)	2
C₂²×AGL(1,ℤ/8)	19

Subgroups — C2×AGL(1,ℤ/8)×D19 #14578365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×AGL(1,ℤ/8)×D₁₉ #14578365