Subgroups — SD₁₆×C₂²⋊D₁₉ #14575325

Order 2432.

546 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×SD₁₆×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
2	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic
4	#11926915	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926773	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926770	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926747	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926742	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926695	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926693	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926683	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926681	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×SD₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₉	—	2	1	no	—
19	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
21	C₂×SD₁₆×C₁₉	—	2	4	no	—
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	#10597399	—	2	1	no	—
28	#10597392	—	2	1	no	—
29	#10597392	C₂²	1	1	yes	characteristic, complemented
30	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
31	#10597390	—	2	1	no	—
32	#10597390	C₂²	1	1	yes	characteristic, complemented
33	C₂×#64527	C₂²	1	1	yes	characteristic, complemented
34	C₂×#64527	C₂²	1	1	yes	characteristic, complemented
35	#10597386	C₂²	1	1	yes	characteristic
36	#10597385	—	2	1	no	—
37	#10597384	C₂²	1	1	yes	characteristic
38	#10597383	—	2	1	no	—
39	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
40	C₂×#64526	C₂²	1	1	yes	characteristic
41	C₂×#64526	C₂²	1	1	yes	characteristic, complemented
42	#10597376	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊D₁₉	—	2	1	no	—
44	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
45	#10597370	—	2	1	no	—
46	#10597370	C₂²	1	1	yes	characteristic, complemented
47	SD₁₆×D₁₉	—	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	#10597292	C₂²	1	1	yes	characteristic, complemented
52	#10597289	C₂²	1	1	yes	characteristic
53	#10597289	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#10597278	C₂²	1	1	yes	characteristic, complemented
56	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
57	#10597274	C₂²	1	1	yes	characteristic, complemented
58	#10597273	C₂²	1	1	yes	characteristic, complemented
59	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₁₉	—	2	1	no	—
62	C₂³×D₁₉	—	2	1	no	—
63	C₂×Q₈×C₁₉	—	2	1	no	—
64	C₂×Q₈×C₁₉	—	2	2	no	—
65	C₂×Q₈×C₁₉	—	4	1	no	—
66	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
67	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	1	no	—
70	C₂×D₄×C₁₉	—	4	1	no	—
71	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	4	4	no	—
81	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
82	C₂²×Dic₁₉	—	2	1	no	—
83	Q₈×D₁₉	—	2	2	no	—
84	Q₈×D₁₉	—	4	1	no	—
85	D₄×D₁₉	—	2	2	no	—
86	D₄×D₁₉	—	4	1	no	—
87	C₂×D₇₆	C₂³	1	1	yes	characteristic
88	C₂×C₄×D₁₉	—	2	1	no	—
89	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
90	C₂×Dic₃₈	—	2	1	no	—
91	C₂×Dic₃₈	C₂³	1	1	yes	characteristic
92	SD₁₆×C₁₉	—	2	2	no	—
93	SD₁₆×C₁₉	—	2	2	no	—
94	SD₁₆×C₁₉	—	2	2	no	—
95	SD₁₆×C₁₉	D₄	1	4	yes	complemented
96	C₂×C₈×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	D₄	1	1	yes	characteristic
103	#64527	—	2	2	no	—
104	#64527	—	4	1	no	—
105	#64526	—	2	2	no	—
106	#64526	—	4	1	no	—
107	(C₂×D₁₉)⋊C₄	—	2	1	no	—
108	(C₂×D₁₉)⋊C₄	—	2	1	no	—
109	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
110	C₄⋊Dic₁₉	—	2	1	no	—
111	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
112	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
113	Dic₁₉⋊C₄	—	2	1	no	—
114	Dic₁₉⋊C₄	—	2	1	no	—
115	Dic₁₉⋊C₄	—	2	1	no	—
116	Dic₁₉⋊C₄	—	2	1	no	—
117	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
122	#64516	—	2	2	no	—
123	C₈×D₁₉	—	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	—	4	2	no	—
132	C₂²×D₁₉	—	4	2	no	—
133	C₂²×D₁₉	—	8	1	no	—
134	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
135	Q₈×C₁₉	—	2	1	no	—
136	Q₈×C₁₉	—	2	1	no	—
137	Q₈×C₁₉	—	2	1	no	—
138	Q₈×C₁₉	—	4	2	no	—
139	Q₈×C₁₉	C₂×D₄	1	2	yes	complemented
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	2	1	no	—
142	D₄×C₁₉	—	2	1	no	—
143	D₄×C₁₉	—	4	2	no	—
144	D₄×C₁₉	C₂×D₄	1	2	yes	—
145	C₂×C₄×C₁₉	—	2	1	no	—
146	C₂×C₄×C₁₉	—	2	1	no	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	4	2	no	—
150	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
151	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₉	—	8	1	no	—
157	C₂²⋊D₁₉	SD₁₆	1	4	yes	direct product factor
158	C₂×Dic₁₉	—	2	1	no	—
159	C₂×Dic₁₉	—	2	1	no	—
160	C₂×Dic₁₉	—	2	1	no	—
161	C₂×Dic₁₉	—	4	2	no	—
162	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
163	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
165	D₇₆	—	2	1	no	—
166	D₇₆	—	2	1	no	—
167	C₄×D₁₉	—	2	1	no	—
168	C₄×D₁₉	—	2	1	no	—
169	C₄×D₁₉	—	4	2	no	—
170	Dic₃₈	—	2	1	no	—
171	Dic₃₈	—	2	1	no	—
172	Dic₃₈	—	4	2	no	—
173	C₈×C₁₉	—	2	1	no	—
174	C₈×C₁₉	C₂×D₄	1	2	yes	complemented
175	C₁₉⋊C₈	—	2	1	no	—
176	C₁₉⋊C₈	—	2	1	no	—
177	D₄×SD₁₆	—	19	1	no	maximal, Sylow
178	C₂²×C₁₉	—	2	1	no	—
179	C₂²×C₁₉	—	2	1	no	—
180	C₂²×C₁₉	—	2	2	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	—	8	4	no	—
187	C₂²×C₁₉	C₂×SD₁₆	1	2	yes	complemented
188	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×D₁₉	—	2	1	no	—
190	C₂×D₁₉	—	2	1	no	—
191	C₂×D₁₉	—	4	1	no	—
192	C₂×D₁₉	—	4	1	no	—
193	C₂×D₁₉	—	4	1	no	—
194	C₂×D₁₉	—	8	4	no	—
195	C₂×D₁₉	C₂×SD₁₆	1	2	yes	complemented
196	C₄×C₁₉	—	2	2	no	—
197	C₄×C₁₉	—	2	1	no	—
198	C₄×C₁₉	—	4	1	no	—
199	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
200	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
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	Dic₁₉	C₂×SD₁₆	1	2	yes	complemented
207	C₂²×SD₁₆	—	19	1	no	—
208	C₂²×SD₁₆	D₁₉	1	1	yes	characteristic, complemented
209	D₄×Q₈	—	19	1	no	—
210	D₄²	—	19	1	no	—
211	#492	—	19	1	no	—
212	#465	—	19	1	no	—
213	#465	—	19	1	no	—
214	#461	—	19	1	no	—
215	#460	—	19	1	no	—
216	#450	—	19	1	no	—
217	#450	—	19	1	no	—
218	#448	—	19	1	no	—
219	#448	—	19	1	no	—
220	C₄×SD₁₆	—	19	1	no	—
221	C₈×D₄	—	19	1	no	—
222	C₂×C₁₉	—	2	2	no	—
223	C₂×C₁₉	—	4	2	no	—
224	C₂×C₁₉	—	8	1	no	—
225	C₂×C₁₉	D₄²	1	1	yes	characteristic
226	C₂×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
227	C₂×C₁₉	#577	1	1	yes	characteristic
228	D₁₉	—	2	2	no	—
229	D₁₉	—	8	1	no	—
230	C₂²×Q₈	—	19	1	no	—
231	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
232	C₂²×D₄	—	19	1	no	—
233	C₂²×D₄	—	38	1	no	—
234	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	19	1	no	—
237	C₂×SD₁₆	—	19	1	no	—
238	C₂×SD₁₆	—	19	1	no	—
239	C₂×SD₁₆	—	19	1	no	—
240	C₂×SD₁₆	—	19	1	no	—
241	C₂×SD₁₆	—	38	4	no	—
242	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
243	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
244	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
245	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
246	C₂²×C₈	—	19	1	no	—
247	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
248	C₄⋊Q₈	—	19	1	no	—
249	C₄⋊Q₈	—	38	1	no	—
250	#127	—	19	1	no	—
251	C₂²⋊Q₈	—	19	1	no	—
252	C₂²⋊Q₈	—	19	1	no	—
253	C₂²⋊Q₈	—	38	1	no	—
254	C₂²⋊Q₈	—	38	1	no	—
255	#121	—	19	1	no	—
256	#121	—	19	1	no	—
257	#121	—	38	1	no	—
258	#120	—	38	1	no	—
259	#120	—	38	1	no	—
260	C₄×Q₈	—	19	1	no	—
261	C₄×D₄	—	19	1	no	—
262	C₄×D₄	—	19	1	no	—
263	C₄×D₄	—	38	1	no	—
264	#106	—	19	1	no	—
265	C₄⋊C₈	—	19	1	no	—
266	#103	—	19	1	no	—
267	#103	—	19	1	no	—
268	#103	—	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	C₄×C₈	—	19	1	no	—
275	C₁₉	D₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	—	2	1	no	—
277	C₂⁴	—	38	1	no	—
278	C₂×Q₈	—	2	1	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	4	1	no	—
281	C₂×Q₈	—	19	1	no	—
282	C₂×Q₈	—	38	1	no	—
283	C₂×Q₈	—	38	2	no	—
284	C₂×Q₈	—	76	1	no	—
285	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
286	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	19	1	no	—
291	C₂×D₄	—	19	1	no	—
292	C₂×D₄	—	38	1	no	—
293	C₂×D₄	—	38	1	no	—
294	C₂×D₄	—	38	1	no	—
295	C₂×D₄	—	38	2	no	—
296	C₂×D₄	—	38	1	no	—
297	C₂×D₄	—	38	1	no	—
298	C₂×D₄	—	76	1	no	—
299	C₂×D₄	—	76	4	no	—
300	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
301	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	19	1	no	—
304	C₂²×C₄	—	38	1	no	—
305	C₂²×C₄	—	38	1	no	—
306	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
307	SD₁₆	—	2	2	no	—
308	SD₁₆	—	2	2	no	—
309	SD₁₆	—	2	2	no	—
310	SD₁₆	—	38	2	no	—
311	SD₁₆	—	38	2	no	—
312	SD₁₆	—	38	2	no	—
313	SD₁₆	—	76	1	no	—
314	SD₁₆	—	76	1	no	—
315	SD₁₆	C₂²⋊D₁₉	1	4	yes	direct product factor
316	C₂×C₈	—	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	C₄⋊C₄	—	38	1	no	—
328	C₄⋊C₄	—	38	1	no	—
329	C₄⋊C₄	—	38	1	no	—
330	C₂²⋊C₄	—	19	1	no	—
331	C₂²⋊C₄	—	19	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	C₂²⋊C₄	—	38	1	no	—
337	C₄²	—	19	1	no	—
338	C₄²	—	38	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	—	76	2	no	—
347	C₂³	—	76	2	no	—
348	C₂³	—	152	1	no	—
349	C₂³	D₄×D₁₉	1	1	yes	characteristic
350	Q₈	—	2	1	no	—
351	Q₈	—	2	1	no	—
352	Q₈	—	2	1	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	38	1	no	—
355	Q₈	—	38	1	no	—
356	Q₈	—	76	2	no	—
357	Q₈	C₂×C₂²⋊D₁₉	1	2	yes	complemented
358	D₄	—	2	1	no	—
359	D₄	—	2	1	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	19	4	no	—
363	D₄	—	38	1	no	—
364	D₄	—	38	1	no	—
365	D₄	—	76	2	no	—
366	D₄	—	76	2	no	—
367	D₄	—	76	2	no	—
368	D₄	—	76	2	no	—
369	D₄	—	152	1	no	—
370	D₄	C₂×C₂²⋊D₁₉	1	2	yes	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	19	1	no	—
377	C₂×C₄	—	19	1	no	—
378	C₂×C₄	—	19	1	no	—
379	C₂×C₄	—	38	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	—	76	2	no	—
385	C₂×C₄	—	76	2	no	—
386	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
387	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
388	C₈	—	2	1	no	—
389	C₈	—	38	1	no	—
390	C₈	—	38	1	no	—
391	C₈	C₂×C₂²⋊D₁₉	1	2	yes	complemented
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	2	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	—	8	4	no	—
401	C₂²	—	19	2	no	—
402	C₂²	—	38	1	no	—
403	C₂²	—	38	1	no	—
404	C₂²	—	76	1	no	—
405	C₂²	—	76	1	no	—
406	C₂²	—	76	1	no	—
407	C₂²	—	152	4	no	—
408	C₂²	SD₁₆×D₁₉	1	2	yes	complemented
409	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
410	C₄	—	2	1	no	—
411	C₄	—	2	2	no	—
412	C₄	—	4	1	no	—
413	C₄	—	19	2	no	—
414	C₄	—	38	1	no	—
415	C₄	—	38	1	no	—
416	C₄	—	76	1	no	—
417	C₄	—	76	1	no	—
418	C₄	—	76	1	no	—
419	C₄	#10597430	1	1	yes	characteristic
420	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
421	C₂	—	2	2	no	—
422	C₂	—	4	2	no	—
423	C₂	—	8	1	no	—
424	C₂	—	38	2	no	—
425	C₂	—	152	1	no	—
426	C₂	D₄×C₂²⋊D₁₉	1	1	yes	characteristic
427	C₂	C₂×SD₁₆×D₁₉	1	1	yes	characteristic
428	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	C₂²×SD₁₆×C₁₉	C₂
socle	C₂²×C₁₉	C₂²×D₄
prime radical	D₄×C₂²⋊D₁₉	C₂
hypercenter	C₂²×SD₁₆	D₁₉
hypocenter	C₁₉	D₄×SD₁₆
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×D₁₉	C₂	semidirect
2. Q₈×C₂²⋊D₁₉	C₂	semidirect
4. #11926915	C₂	semidirect
5. #11926773	C₂	semidirect
6. #11926770	C₂	semidirect
7. #11926747	C₂	semidirect
8. #11926742	C₂	semidirect
9. #11926695	C₂	semidirect
10. #11926693	C₂	semidirect
11. #11926683	C₂	semidirect
12. #11926681	C₂	semidirect
13. SD₁₆×Dic₁₉	C₂	semidirect
14. C₈×C₂²⋊D₁₉	C₂	semidirect
15. C₂²×SD₁₆×C₁₉	C₂	semidirect
16. C₂²×Q₈×C₁₉	C₂²	semidirect
19. C₂×Q₈×D₁₉	C₂²	semidirect
24. C₂×SD₁₆×C₁₉	C₂²	semidirect
25. C₂×SD₁₆×C₁₉	C₂²	semidirect
26. C₂²×C₈×C₁₉	C₂²	semidirect
29. #10597392	C₂²	semidirect
30. Q₈×Dic₁₉	C₂²	semidirect
32. #10597390	C₂²	semidirect
33. C₂×#64527	C₂²	semidirect
34. C₂×#64527	C₂²	semidirect
41. C₂×#64526	C₂²	semidirect
46. #10597370	C₂²	semidirect
48. C₂×#64516	C₂²	semidirect
49. C₂×C₈×D₁₉	C₂²	semidirect
50. #10597292	C₂²	semidirect
51. #10597292	C₂²	semidirect
53. #10597289	C₂²	semidirect
54. C₂²⋊(C₁₉⋊C₈)	C₂²	semidirect
55. #10597278	C₂²	semidirect
56. (C₂×D₁₉)⋊C₈	C₂²	semidirect
57. #10597274	C₂²	semidirect
58. #10597273	C₂²	semidirect
59. Dic₁₉⋊C₈	C₂²	semidirect
60. C₈×Dic₁₉	C₂²	semidirect
95. SD₁₆×C₁₉	D₄	semidirect
139. Q₈×C₁₉	C₂×D₄	semidirect
157. C₂²⋊D₁₉	SD₁₆	direct (N × H)
174. C₈×C₁₉	C₂×D₄	semidirect
187. C₂²×C₁₉	C₂×SD₁₆	semidirect
195. C₂×D₁₉	C₂×SD₁₆	semidirect
206. Dic₁₉	C₂×SD₁₆	semidirect
208. C₂²×SD₁₆	D₁₉	semidirect
231. C₂²×Q₈	C₂×D₁₉	semidirect
244. C₂×SD₁₆	C₂×D₁₉	semidirect
245. C₂×SD₁₆	C₂×D₁₉	semidirect
247. C₂²×C₈	C₂×D₁₉	semidirect
275. C₁₉	D₄×SD₁₆	semidirect
315. SD₁₆	C₂²⋊D₁₉	direct (N × H)
357. Q₈	C₂×C₂²⋊D₁₉	semidirect
391. C₈	C₂×C₂²⋊D₁₉	semidirect
408. C₂²	SD₁₆×D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₉	2
Q₈×C₂²⋊D₁₉	2
D₄×C₂²⋊D₁₉	2
#11926915	2
#11926773	2
#11926770	2
#11926747	2
#11926742	2
#11926695	2
#11926693	2
#11926683	2
#11926681	2
SD₁₆×Dic₁₉	2
C₈×C₂²⋊D₁₉	2
C₂²×SD₁₆×C₁₉	2
D₄×SD₁₆	19

Subgroups — SD16×C22⋊D19 #14575325

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — SD₁₆×C₂²⋊D₁₉ #14575325