Subgroups — #14572361

Order 2432.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597353	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#64515	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927053	C₂	1	1	yes	maximal, characteristic
4	#11926621	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926620	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926617	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926612	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926612	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄×C₁₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926569	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926509	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₈×D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926501	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₉×#435	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#64541	C₂²	1	1	yes	characteristic
17	C₂²×C₄×D₁₉	C₂²	1	1	yes	characteristic
18	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
19	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic
20	C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
21	#10597385	C₄	1	1	yes	characteristic
22	#10597383	C₄	1	1	yes	characteristic
23	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
25	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic
26	C₂²×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
27	#10597353	—	2	4	no	—
28	C₂×#64515	—	2	4	no	—
29	C₂×#64515	C₂²	1	1	yes	characteristic
30	C₂×#64515	C₂²	1	1	yes	characteristic
31	C₂×#64515	C₂²	1	1	yes	characteristic
32	C₂×#64515	C₂²	1	1	yes	characteristic
33	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic
36	C₂×C₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
37	#10597342	C₄	1	1	yes	characteristic
38	#10597340	C₄	1	1	yes	characteristic
39	#10597330	C₄	1	1	yes	characteristic
40	#10597329	C₄	1	1	yes	characteristic
41	#10597328	C₄	1	1	yes	characteristic
42	#10597324	C₄	1	1	yes	characteristic
43	C₄×D₇₆	C₂²	1	1	yes	characteristic
44	#10597318	C₂²	1	1	yes	characteristic
45	C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic
47	C₁₉×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
48	C₁₉×#97	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
50	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
51	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
52	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic
53	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
54	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
55	#10597272	C₂²	1	1	yes	characteristic, complemented
56	Dic₁₉⋊C₈	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	C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
60	C₄×C₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₉	C₂×C₄	1	1	yes	characteristic
62	C₂×D₄×C₁₉	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
64	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊D₁₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₂²⋊D₁₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×Dic₁₉	C₂×C₄	1	1	yes	characteristic
70	#64541	—	2	2	no	—
71	#64541	—	2	2	no	—
72	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
73	C₂×D₇₆	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄×D₁₉	—	2	2	no	—
75	C₂×C₄×D₁₉	—	2	2	no	—
76	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×D₁₉	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
79	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
81	C₂×Dic₃₈	C₂×C₄	1	1	yes	characteristic
82	M₁₆×C₁₉	—	2	2	no	—
83	C₂×C₈×C₁₉	—	2	2	no	—
84	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
85	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
86	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
87	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
88	C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
89	C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
91	C₄²×C₁₉	C₂³	1	1	yes	characteristic
92	C₂²⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
93	C₂²⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
94	(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₁₉)⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₄⋊Dic₁₉	C₂×C₄	1	1	yes	characteristic
101	Dic₁₉⋊C₄	C₂×C₄	1	1	yes	characteristic
102	Dic₁₉⋊C₄	C₂×C₄	1	1	yes	characteristic
103	Dic₁₉⋊C₄	C₂×C₄	1	1	yes	characteristic
104	Dic₁₉⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
106	C₂×C₁₉⋊C₈	—	2	2	no	—
107	C₂×C₁₉⋊C₈	—	2	2	no	—
108	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
109	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
110	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
112	#64515	—	2	2	no	—
113	#64515	—	2	2	no	—
114	#64515	—	2	2	no	—
115	#64515	—	2	2	no	—
116	#64515	D₄	1	4	yes	complemented
117	C₈×D₁₉	—	2	2	no	—
118	C₈×D₁₉	—	2	2	no	—
119	C₈×D₁₉	—	2	2	no	—
120	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
121	C₂³×C₁₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×D₁₉	—	2	2	no	—
123	C₂²×D₁₉	—	2	2	no	—
124	C₂²×D₁₉	—	4	1	no	—
125	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₁₉	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₁₉	—	2	2	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	2	1	no	—
131	C₂×C₄×C₁₉	—	2	1	no	—
132	C₂×C₄×C₁₉	—	2	1	no	—
133	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₁₉	—	2	2	no	—
139	C₂²⋊D₁₉	—	2	2	no	—
140	C₂²⋊D₁₉	—	2	2	no	—
141	C₂²⋊D₁₉	—	4	1	no	—
142	C₂×Dic₁₉	—	2	2	no	—
143	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₉	C₂²×C₄	1	1	yes	characteristic
148	D₇₆	—	2	2	no	—
149	D₇₆	—	4	1	no	—
150	C₄×D₁₉	—	2	2	no	—
151	C₄×D₁₉	—	2	1	no	—
152	C₄×D₁₉	—	2	1	no	—
153	C₄×D₁₉	—	2	1	no	—
154	C₄×D₁₉	—	2	1	no	—
155	C₄×D₁₉	—	2	2	no	—
156	C₄×D₁₉	C₂×D₄	1	2	yes	—
157	C₄×D₁₉	#41	1	2	yes	—
158	Dic₃₈	—	2	2	no	—
159	C₈×C₁₉	—	2	1	no	—
160	C₈×C₁₉	—	2	1	no	—
161	C₈×C₁₉	—	2	1	no	—
162	C₈×C₁₉	C₂×D₄	1	2	yes	—
163	C₁₉⋊C₈	—	2	1	no	—
164	C₁₉⋊C₈	—	2	1	no	—
165	C₁₉⋊C₈	—	2	1	no	—
166	C₁₉⋊C₈	C₂×D₄	1	2	yes	—
167	#2933	—	19	1	no	maximal, Sylow
168	C₂²×C₁₉	—	2	1	no	—
169	C₂²×C₁₉	—	2	1	no	—
170	C₂²×C₁₉	—	2	1	no	—
171	C₂²×C₁₉	—	2	1	no	—
172	C₂²×C₁₉	—	2	1	no	—
173	C₂²×C₁₉	#131	1	2	yes	complemented
174	C₂²×C₁₉	C₂³×C₄	1	1	yes	characteristic
175	C₂×D₁₉	—	2	1	no	—
176	C₂×D₁₉	—	2	1	no	—
177	C₂×D₁₉	—	2	1	no	—
178	C₂×D₁₉	—	2	1	no	—
179	C₂×D₁₉	—	2	1	no	—
180	C₂×D₁₉	—	2	1	no	—
181	C₂×D₁₉	—	2	1	no	—
182	C₂×D₁₉	—	2	1	no	—
183	C₂×D₁₉	—	4	4	no	—
184	C₂×D₁₉	C₄×D₄	1	2	yes	—
185	C₄×C₁₉	—	2	1	no	—
186	C₄×C₁₉	—	2	1	no	—
187	C₄×C₁₉	—	2	1	no	—
188	C₄×C₁₉	—	2	1	no	—
189	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
190	C₄×C₁₉	C₂×#41	1	1	yes	characteristic
191	Dic₁₉	—	2	1	no	—
192	Dic₁₉	—	2	1	no	—
193	Dic₁₉	—	2	1	no	—
194	Dic₁₉	—	2	1	no	—
195	Dic₁₉	C₄×D₄	1	2	yes	—
196	C₂×#131	—	19	1	no	—
197	C₂²×M₁₆	—	19	1	no	—
198	#525	—	19	1	no	—
199	#436	—	19	1	no	—
200	#436	—	19	1	no	—
201	#435	—	19	1	no	—
202	#435	—	19	1	no	—
203	#435	—	19	1	no	—
204	#435	D₁₉	1	1	yes	characteristic, complemented
205	C₈×D₄	—	19	1	no	—
206	C₈×D₄	—	19	1	no	—
207	#424	—	19	1	no	—
208	#408	—	19	1	no	—
209	C₂×C₂²⋊C₈	—	19	1	no	—
210	#405	—	19	1	no	—
211	C₂×C₁₉	—	2	2	no	—
212	C₂×C₁₉	—	4	1	no	—
213	C₂×C₁₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂×C₁₉	C₂×#131	1	1	yes	characteristic
215	C₂×C₁₉	#568	1	1	yes	characteristic
216	D₁₉	—	2	2	no	—
217	D₁₉	—	4	1	no	—
218	D₁₉	—	4	1	no	—
219	C₂×#41	—	19	1	no	—
220	C₂³×C₄	—	19	1	no	—
221	#131	—	38	4	no	—
222	C₂×M₁₆	—	19	1	no	—
223	C₂×M₁₆	—	19	1	no	—
224	C₂×M₁₆	—	19	1	no	—
225	C₂×M₁₆	—	19	1	no	—
226	C₂×M₁₆	—	19	1	no	—
227	C₂×M₁₆	—	38	4	no	—
228	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
229	C₂²×C₈	—	19	1	no	—
230	C₂²×C₈	—	19	1	no	—
231	C₂²×C₈	—	19	1	no	—
232	C₂²×C₈	—	19	1	no	—
233	C₂²×C₈	—	19	1	no	—
234	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic
235	#123	—	19	1	no	—
236	#123	—	19	1	no	—
237	C₂²⋊Q₈	—	19	1	no	—
238	C₂²⋊Q₈	—	19	1	no	—
239	#121	—	19	1	no	—
240	#121	—	19	1	no	—
241	#120	—	19	1	no	—
242	#120	—	19	1	no	—
243	C₄×D₄	—	19	1	no	—
244	C₄×D₄	—	19	1	no	—
245	C₄×D₄	—	19	1	no	—
246	C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
247	#117	—	19	1	no	—
248	C₄⋊C₈	—	19	1	no	—
249	C₄⋊C₈	—	19	1	no	—
250	C₄⋊C₈	—	19	1	no	—
251	C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
252	C₂²⋊C₈	—	19	1	no	—
253	C₂²⋊C₈	—	19	1	no	—
254	C₂²⋊C₈	—	19	1	no	—
255	C₂²⋊C₈	—	19	1	no	—
256	C₂²⋊C₈	—	19	1	no	—
257	C₂²⋊C₈	—	19	1	no	—
258	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic
259	C₂²⋊C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
260	#97	—	19	1	no	—
261	#97	C₂×D₁₉	1	1	yes	characteristic, complemented
262	C₄×C₈	—	19	1	no	—
263	C₄×C₈	—	19	1	no	—
264	C₁₉	#2933	1	1	yes	characteristic, complemented, Sylow
265	C₂⁴	—	19	1	no	—
266	#41	—	38	2	no	—
267	#41	—	38	2	no	—
268	C₂×Q₈	—	19	1	no	—
269	C₂×D₄	—	19	1	no	—
270	C₂×D₄	—	19	1	no	—
271	C₂×D₄	—	19	1	no	—
272	C₂×D₄	—	19	1	no	—
273	C₂×D₄	—	19	1	no	—
274	C₂×D₄	—	19	1	no	—
275	C₂×D₄	C₄×D₁₉	1	1	yes	characteristic
276	C₂²×C₄	—	19	1	no	—
277	C₂²×C₄	—	19	1	no	—
278	C₂²×C₄	—	19	1	no	—
279	C₂²×C₄	—	19	1	no	—
280	C₂²×C₄	—	19	1	no	—
281	C₂²×C₄	—	19	1	no	—
282	C₂²×C₄	—	38	2	no	—
283	C₂²×C₄	—	38	2	no	—
284	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
285	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
286	M₁₆	—	2	2	no	—
287	M₁₆	—	19	4	no	—
288	M₁₆	—	38	2	no	—
289	M₁₆	—	38	2	no	—
290	M₁₆	—	38	2	no	—
291	M₁₆	—	38	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	19	1	no	—
294	C₂×C₈	—	19	1	no	—
295	C₂×C₈	—	19	1	no	—
296	C₂×C₈	—	19	1	no	—
297	C₂×C₈	—	38	2	no	—
298	C₂×C₈	—	38	2	no	—
299	C₂×C₈	—	38	2	no	—
300	C₂×C₈	—	38	2	no	—
301	C₂×C₈	—	38	2	no	—
302	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
304	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
305	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
306	C₄⋊C₄	—	19	1	no	—
307	C₄⋊C₄	—	19	1	no	—
308	C₄⋊C₄	—	19	1	no	—
309	C₄⋊C₄	—	19	1	no	—
310	C₄⋊C₄	—	19	1	no	—
311	C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
312	C₂²⋊C₄	—	19	1	no	—
313	C₂²⋊C₄	—	19	1	no	—
314	C₂²⋊C₄	—	19	1	no	—
315	C₂²⋊C₄	—	19	1	no	—
316	C₂²⋊C₄	—	19	1	no	—
317	C₂²⋊C₄	—	19	1	no	—
318	C₂²⋊C₄	—	19	1	no	—
319	C₂²⋊C₄	—	19	1	no	—
320	C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
321	C₂²⋊C₄	C₄×D₁₉	1	1	yes	characteristic
322	C₄²	—	19	1	no	—
323	C₄²	C₂²×D₁₉	1	1	yes	characteristic
324	C₂³	—	19	1	no	—
325	C₂³	—	19	1	no	—
326	C₂³	—	19	1	no	—
327	C₂³	—	38	2	no	—
328	C₂³	—	38	2	no	—
329	C₂³	—	76	1	no	—
330	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
331	C₂³	C₂×C₄×D₁₉	1	1	yes	characteristic
332	Q₈	—	38	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	38	2	no	—
335	D₄	—	38	2	no	—
336	D₄	—	38	2	no	—
337	D₄	—	38	2	no	—
338	D₄	—	76	1	no	—
339	D₄	—	76	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	19	1	no	—
345	C₂×C₄	—	19	2	no	—
346	C₂×C₄	—	19	2	no	—
347	C₂×C₄	—	19	1	no	—
348	C₂×C₄	—	19	1	no	—
349	C₂×C₄	—	19	1	no	—
350	C₂×C₄	—	19	1	no	—
351	C₂×C₄	—	38	2	no	—
352	C₂×C₄	—	38	2	no	—
353	C₂×C₄	—	38	2	no	—
354	C₂×C₄	—	38	1	no	—
355	C₂×C₄	—	38	1	no	—
356	C₂×C₄	—	38	1	no	—
357	C₂×C₄	—	38	1	no	—
358	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
359	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
360	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
361	C₂×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
362	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
363	C₈	—	2	1	no	—
364	C₈	—	2	1	no	—
365	C₈	—	2	1	no	—
366	C₈	—	19	2	no	—
367	C₈	—	38	1	no	—
368	C₈	—	38	1	no	—
369	C₈	—	38	1	no	—
370	C₈	D₄×D₁₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	19	2	no	—
377	C₂²	—	38	1	no	—
378	C₂²	—	38	1	no	—
379	C₂²	—	38	1	no	—
380	C₂²	—	38	1	no	—
381	C₂²	—	38	1	no	—
382	C₂²	—	38	1	no	—
383	C₂²	—	38	1	no	—
384	C₂²	—	38	1	no	—
385	C₂²	—	76	4	no	—
386	C₂²	#10597353	1	2	yes	complemented
387	C₂²	C₂²×C₄×D₁₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	19	2	no	—
393	C₄	—	38	1	no	—
394	C₄	—	38	1	no	—
395	C₄	—	38	1	no	—
396	C₄	—	38	1	no	—
397	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
398	C₄	#41×D₁₉	1	1	yes	characteristic
399	C₂	—	2	2	no	—
400	C₂	—	4	1	no	—
401	C₂	—	38	2	no	—
402	C₂	—	76	1	no	—
403	C₂	—	76	1	no	—
404	C₂	C₄×D₄×D₁₉	1	1	yes	characteristic
405	C₂	C₂×#10597353	1	1	yes	characteristic
406	C₂	#11927309	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×D₁₉
commutator, socle	C₂²×C₁₉	C₂³×C₄
Fitting	C₁₉×#435	C₂
prime radical	#11927053	C₂
cosocle	C₂×C₄×C₁₉	C₂⁴
hypercenter	#435	D₁₉
hypocenter	C₁₉	#2933
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ #435

Complements

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

N	H ≅ G/N	type
1. C₂×#10597353	C₂	semidirect
2. C₂²×#64515	C₂	semidirect
4. #11926621	C₂	semidirect
5. #11926620	C₂	semidirect
6. #11926617	C₂	semidirect
7. #11926612	C₂	semidirect
8. #11926612	C₂	semidirect
9. D₄×C₁₉⋊C₈	C₂	semidirect
10. C₈×C₂²⋊D₁₉	C₂	semidirect
11. #11926569	C₂	semidirect
12. #11926509	C₂	semidirect
13. C₂²⋊C₈×D₁₉	C₂	semidirect
14. #11926501	C₂	semidirect
15. C₁₉×#435	C₂	semidirect
18. C₂×M₁₆×C₁₉	C₂²	semidirect
26. C₂²×C₁₉⋊C₈	C₂²	semidirect
33. C₂×#64515	C₂²	semidirect
36. C₂×C₈×D₁₉	C₂²	semidirect
45. C₁₉×C₄⋊C₈	C₂²	semidirect
47. C₁₉×C₂²⋊C₈	C₂²	semidirect
48. C₁₉×#97	C₂²	semidirect
50. C₂²⋊(C₁₉⋊C₈)	C₂²	semidirect
53. (C₂×D₁₉)⋊C₈	C₂²	semidirect
54. (C₂×D₁₉)⋊C₈	C₂²	semidirect
55. #10597272	C₂²	semidirect
56. Dic₁₉⋊C₈	C₂²	semidirect
57. Dic₁₉⋊C₈	C₂²	semidirect
58. C₈×Dic₁₉	C₂²	semidirect
59. C₄⋊(C₁₉⋊C₈)	C₂²	semidirect
60. C₄×C₁₉⋊C₈	C₂²	semidirect
116. #64515	D₄	semidirect
173. C₂²×C₁₉	#131	semidirect
204. #435	D₁₉	semidirect
228. C₂×M₁₆	C₂×D₁₉	semidirect
251. C₄⋊C₈	C₂×D₁₉	semidirect
259. C₂²⋊C₈	C₂×D₁₉	semidirect
261. #97	C₂×D₁₉	semidirect
264. C₁₉	#2933	semidirect
386. C₂²	#10597353	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597353	2
C₂²×#64515	2
#11927053	2
#11926621	2
#11926620	2
#11926617	2
#11926612	2
D₄×C₁₉⋊C₈	2
C₈×C₂²⋊D₁₉	2
#11926569	2
#11926509	2
C₂²⋊C₈×D₁₉	2
#11926501	2
C₁₉×#435	2
#2933	19