Subgroups — #41×C₂²⋊D₁₉ #14577120

Order 2432.

1648 conjugacy classes of subgroups.

The subgroup lattice has 432 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	#11927213	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11927205	C₂	1	1	yes	maximal, characteristic, complemented
5	#11927201	C₂	1	1	yes	maximal, characteristic, complemented
6	#11927193	C₂	1	3	yes	maximal, complemented
7	#11927188	C₂	1	3	yes	maximal, complemented
8	#11927182	C₂	1	3	yes	maximal, complemented
9	D₄×C₂²⋊D₁₉	C₂	1	3	yes	maximal, complemented
10	#11927090	C₂	1	3	yes	maximal, complemented
11	#11927055	C₂	1	3	yes	maximal, complemented
12	#11927051	C₂	1	3	yes	maximal, complemented
13	#41×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₄×C₂²⋊D₁₉	C₂	1	3	yes	maximal, complemented
15	C₂²×#41×C₁₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	—	2	8	no	—
17	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
18	C₂×#41×C₁₉	C₂²	1	3	yes	complemented
19	C₂×#41×C₁₉	C₂²	1	3	yes	complemented
20	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
21	C₂²×Q₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
22	C₂²×D₄×C₁₉	C₂²	1	3	yes	complemented
23	C₂³×C₄×C₁₉	C₂²	1	3	yes	complemented
24	C₂²×C₂²⋊D₁₉	C₂²	1	3	yes	—
25	#41×D₁₉	—	2	8	no	—
26	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×#64543	C₂²	1	3	yes	complemented
29	C₂×D₄×D₁₉	C₂²	1	3	yes	complemented
30	C₂×#64541	C₂²	1	3	yes	complemented
31	C₂²×C₄×D₁₉	C₂²	1	3	yes	complemented
32	#10597399	C₂²	1	6	yes	complemented
33	C₂×C₂²⋊Dic₁₉	C₂²	1	3	yes	complemented
34	#10597393	C₂²	1	3	yes	complemented
35	#10597392	C₂²	1	3	yes	complemented
36	#10597392	C₂²	1	3	yes	complemented
37	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
38	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
39	#10597390	C₂²	1	3	yes	complemented
40	#10597386	C₂²	1	3	yes	complemented
41	#10597385	C₂²	1	6	yes	complemented
42	#10597385	C₂²	1	6	yes	complemented
43	#10597384	C₂²	1	3	yes	complemented
44	#10597384	C₂²	1	3	yes	complemented
45	#10597383	C₂²	1	6	yes	complemented
46	#10597382	C₂²	1	3	yes	complemented
47	#10597381	C₂²	1	6	yes	complemented
48	D₄×Dic₁₉	C₂²	1	3	yes	complemented
49	D₄×Dic₁₉	C₂²	1	3	yes	complemented
50	#10597376	C₂²	1	3	yes	complemented
51	#10597376	C₂²	1	3	yes	complemented
52	#10597375	C₂²	1	6	yes	complemented
53	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	—
54	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
56	C₄×C₂²⋊D₁₉	C₂²	1	6	yes	complemented
57	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
58	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
59	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
60	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
61	C₄×C₂²⋊D₁₉	C₂²	1	3	yes	complemented
62	C₂×(C₂×D₁₉)⋊C₄	C₂²	1	3	yes	complemented
63	#10597372	C₂²	1	3	yes	complemented
64	#10597370	C₂²	1	3	yes	complemented
65	#10597370	C₂²	1	3	yes	complemented
66	C₂×Dic₁₉⋊C₄	C₂²	1	3	yes	complemented
67	C₂×C₄×Dic₁₉	C₂²	1	3	yes	complemented
68	C₂⁴×C₁₉	C₂³	1	3	yes	—
69	C₂³×D₁₉	C₂³	1	3	yes	—
70	#41×C₁₉	—	2	4	no	—
71	#41×C₁₉	—	2	12	no	—
72	#41×C₁₉	—	2	12	no	—
73	#41×C₁₉	D₄	1	8	yes	complemented
74	C₂×Q₈×C₁₉	—	2	4	no	—
75	C₂×Q₈×C₁₉	C₂³	1	3	yes	—
76	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
77	C₂×D₄×C₁₉	—	2	12	no	—
78	C₂×D₄×C₁₉	C₂³	1	6	yes	—
79	C₂×D₄×C₁₉	C₂³	1	3	yes	—
80	C₂×D₄×C₁₉	C₂³	1	3	yes	—
81	C₂²×C₄×C₁₉	—	2	12	no	—
82	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
83	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
84	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
86	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
87	C₂²×C₄×C₁₉	C₂³	1	3	yes	—
88	C₂×C₂²⋊D₁₉	—	2	12	no	—
89	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
90	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
91	C₂×C₂²⋊D₁₉	C₂³	1	3	yes	—
92	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
93	C₂×C₂²⋊D₁₉	C₂³	1	6	yes	—
94	C₂×C₂²⋊D₁₉	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₉	C₂³	1	3	yes	—
96	C₂²×Dic₁₉	C₂³	1	3	yes	—
97	C₂²×Dic₁₉	C₂³	1	3	yes	—
98	#64545	—	2	4	no	—
99	Q₈×D₁₉	—	2	4	no	—
100	#64543	—	2	12	no	—
101	D₄×D₁₉	—	2	12	no	—
102	#64541	—	2	12	no	—
103	C₂×D₇₆	C₂³	1	3	yes	—
104	C₂×C₄×D₁₉	—	2	12	no	—
105	C₂×C₄×D₁₉	C₂³	1	3	yes	—
106	C₂×C₄×D₁₉	C₂³	1	3	yes	—
107	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₉	C₂³	1	3	yes	—
109	C₂×Dic₃₈	C₂³	1	3	yes	—
110	C₂²⋊Dic₁₉	C₂³	1	6	yes	—
111	C₂²⋊Dic₁₉	C₂³	1	3	yes	—
112	C₂²⋊Dic₁₉	C₂³	1	6	yes	—
113	C₂²⋊Dic₁₉	C₂³	1	3	yes	—
114	C₂²⋊Dic₁₉	C₂³	1	1	yes	characteristic
115	C₂²⋊Dic₁₉	C₂³	1	3	yes	—
116	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
117	(C₂×D₁₉)⋊C₄	C₂³	1	6	yes	—
118	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
119	(C₂×D₁₉)⋊C₄	C₂³	1	3	yes	—
120	(C₂×D₁₉)⋊C₄	C₂³	1	1	yes	characteristic
121	C₄⋊Dic₁₉	C₂³	1	3	yes	—
122	C₄⋊Dic₁₉	C₂³	1	3	yes	—
123	Dic₁₉⋊C₄	C₂³	1	3	yes	—
124	Dic₁₉⋊C₄	C₂³	1	6	yes	—
125	Dic₁₉⋊C₄	C₂³	1	3	yes	—
126	Dic₁₉⋊C₄	C₂³	1	1	yes	characteristic
127	Dic₁₉⋊C₄	C₂³	1	3	yes	—
128	C₄×Dic₁₉	C₂³	1	3	yes	—
129	C₄×Dic₁₉	C₂³	1	3	yes	—
130	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₉	C₂³	1	3	yes	—
132	C₂³×C₁₉	—	2	6	no	—
133	C₂³×C₁₉	—	2	6	no	—
134	C₂³×C₁₉	—	4	3	no	—
135	C₂³×C₁₉	C₂⁴	1	3	yes	—
136	C₂³×C₁₉	C₂⁴	1	3	yes	—
137	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
138	C₂²×D₁₉	—	2	6	no	—
139	C₂²×D₁₉	—	2	6	no	—
140	C₂²×D₁₉	—	4	3	no	—
141	C₂²×D₁₉	C₂⁴	1	3	yes	—
142	C₂²×D₁₉	C₂⁴	1	1	yes	characteristic
143	Q₈×C₁₉	—	2	6	no	—
144	Q₈×C₁₉	C₂×D₄	1	4	yes	complemented
145	D₄×C₁₉	—	2	12	no	—
146	D₄×C₁₉	—	2	6	no	—
147	D₄×C₁₉	C₂×D₄	1	12	yes	complemented
148	C₂×C₄×C₁₉	—	2	6	no	—
149	C₂×C₄×C₁₉	—	2	2	no	—
150	C₂×C₄×C₁₉	—	2	6	no	—
151	C₂×C₄×C₁₉	—	2	6	no	—
152	C₂×C₄×C₁₉	—	2	6	no	—
153	C₂×C₄×C₁₉	C₂×D₄	1	12	yes	complemented
154	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
155	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
156	C₂×C₄×C₁₉	C₂⁴	1	3	yes	—
157	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
158	C₂²⋊D₁₉	—	2	12	no	—
159	C₂²⋊D₁₉	—	2	6	no	—
160	C₂²⋊D₁₉	—	2	6	no	—
161	C₂²⋊D₁₉	—	2	6	no	—
162	C₂²⋊D₁₉	—	4	6	no	—
163	C₂²⋊D₁₉	#41	1	4	yes	direct product factor
164	C₂×Dic₁₉	—	2	6	no	—
165	C₂×Dic₁₉	—	2	6	no	—
166	C₂×Dic₁₉	—	4	3	no	—
167	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
168	C₂×Dic₁₉	C₂⁴	1	3	yes	—
169	C₂×Dic₁₉	C₂⁴	1	3	yes	—
170	C₂×Dic₁₉	C₂⁴	1	3	yes	—
171	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
172	C₂×Dic₁₉	C₂⁴	1	1	yes	characteristic
173	D₇₆	—	2	6	no	—
174	C₄×D₁₉	—	2	2	no	—
175	C₄×D₁₉	—	2	6	no	—
176	C₄×D₁₉	—	2	6	no	—
177	C₄×D₁₉	—	2	6	no	—
178	Dic₃₈	—	2	6	no	—
179	D₄×#41	—	19	1	no	maximal, Sylow
180	C₂²×C₁₉	—	2	1	no	—
181	C₂²×C₁₉	—	2	3	no	—
182	C₂²×C₁₉	—	2	3	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	3	no	—
185	C₂²×C₁₉	—	2	3	no	—
186	C₂²×C₁₉	—	2	3	no	—
187	C₂²×C₁₉	—	4	12	no	—
188	C₂²×C₁₉	C₂²×D₄	1	6	yes	—
189	C₂²×C₁₉	C₂×#41	1	2	yes	complemented
190	C₂²×C₁₉	C₂⁵	1	1	yes	characteristic
191	C₂×D₁₉	—	2	1	no	—
192	C₂×D₁₉	—	2	1	no	—
193	C₂×D₁₉	—	2	3	no	—
194	C₂×D₁₉	—	2	3	no	—
195	C₂×D₁₉	—	2	3	no	—
196	C₂×D₁₉	—	4	12	no	—
197	C₂×D₁₉	C₂×#41	1	2	yes	complemented
198	C₄×C₁₉	—	2	1	no	—
199	C₄×C₁₉	—	2	3	no	—
200	C₄×C₁₉	C₂²×D₄	1	6	yes	—
201	C₄×C₁₉	C₂²×D₄	1	2	yes	—
202	Dic₁₉	—	2	3	no	—
203	Dic₁₉	—	2	1	no	—
204	Dic₁₉	—	2	3	no	—
205	Dic₁₉	—	2	1	no	—
206	Dic₁₉	—	2	3	no	—
207	Dic₁₉	C₂×#41	1	2	yes	complemented
208	C₂²×#41	—	19	1	no	—
209	C₂²×#41	D₁₉	1	1	yes	characteristic, complemented
210	#550	—	19	1	no	—
211	D₄×Q₈	—	19	1	no	—
212	#548	—	19	1	no	—
213	#548	—	19	1	no	—
214	#547	—	19	3	no	—
215	#546	—	19	3	no	—
216	#546	—	19	3	no	—
217	D₄²	—	19	3	no	—
218	#532	—	19	3	no	—
219	#525	—	19	3	no	—
220	#525	—	19	3	no	—
221	C₄×#41	—	19	1	no	—
222	C₂×C₄×D₄	—	19	3	no	—
223	C₂×C₁₉	—	2	6	no	—
224	C₂×C₁₉	—	2	2	no	—
225	C₂×C₁₉	—	4	3	no	—
226	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
227	C₂×C₁₉	C₂²×#41	1	1	yes	characteristic
228	C₂×C₁₉	#585	1	1	yes	characteristic
229	D₁₉	—	2	2	no	—
230	D₁₉	—	4	3	no	—
231	C₂×#41	—	2	8	no	—
232	C₂×#41	—	19	1	no	—
233	C₂×#41	—	19	3	no	—
234	C₂×#41	—	19	3	no	—
235	C₂×#41	—	38	8	no	—
236	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
237	C₂×#41	C₂×D₁₉	1	3	yes	complemented
238	C₂×#41	C₂×D₁₉	1	3	yes	complemented
239	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
240	C₂²×Q₈	—	19	1	no	—
241	C₂²×Q₈	C₂×D₁₉	1	1	yes	characteristic, complemented
242	C₂²×D₄	—	19	3	no	—
243	C₂²×D₄	—	19	3	no	—
244	C₂²×D₄	C₂×D₁₉	1	3	yes	complemented
245	C₂³×C₄	—	19	3	no	—
246	C₂³×C₄	C₂×D₁₉	1	3	yes	complemented
247	C₄⋊Q₈	—	19	3	no	—
248	#127	—	19	3	no	—
249	#124	—	19	3	no	—
250	#124	—	19	3	no	—
251	#123	—	19	6	no	—
252	#123	—	19	6	no	—
253	C₂²⋊Q₈	—	19	3	no	—
254	C₂²⋊Q₈	—	19	3	no	—
255	C₂²⋊Q₈	—	19	3	no	—
256	C₂²⋊Q₈	—	19	3	no	—
257	#121	—	19	3	no	—
258	#121	—	19	3	no	—
259	#121	—	19	6	no	—
260	#121	—	19	6	no	—
261	#121	—	19	3	no	—
262	#121	—	19	3	no	—
263	#120	—	19	6	no	—
264	#120	—	19	6	no	—
265	C₄×Q₈	—	19	1	no	—
266	C₄×Q₈	—	19	1	no	—
267	C₄×D₄	—	19	3	no	—
268	C₄×D₄	—	19	3	no	—
269	C₄×D₄	—	19	1	no	—
270	C₄×D₄	—	19	3	no	—
271	C₄×D₄	—	19	3	no	—
272	C₄×D₄	—	19	3	no	—
273	C₄×D₄	—	19	3	no	—
274	C₄×D₄	—	19	3	no	—
275	C₄×D₄	—	19	3	no	—
276	C₄×D₄	—	19	3	no	—
277	C₄×D₄	—	19	6	no	—
278	#117	—	19	3	no	—
279	C₂×C₄⋊C₄	—	19	3	no	—
280	C₂×C₂²⋊C₄	—	19	3	no	—
281	C₂×C₂²⋊C₄	—	19	3	no	—
282	C₂×C₄²	—	19	3	no	—
283	C₁₉	D₄×#41	1	1	yes	characteristic, complemented, Sylow
284	C₂⁴	—	19	3	no	—
285	C₂⁴	C₂²×D₁₉	1	3	yes	—
286	#41	—	2	4	no	—
287	#41	—	2	12	no	—
288	#41	—	2	12	no	—
289	#41	—	38	4	no	—
290	#41	—	38	12	no	—
291	#41	—	38	12	no	—
292	#41	C₂²⋊D₁₉	1	8	yes	direct product factor
293	C₂×Q₈	—	2	4	no	—
294	C₂×Q₈	—	19	3	no	—
295	C₂×Q₈	—	38	4	no	—
296	C₂×Q₈	C₂²×D₁₉	1	3	yes	—
297	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
298	C₂×D₄	—	2	12	no	—
299	C₂×D₄	—	19	1	no	—
300	C₂×D₄	—	19	3	no	—
301	C₂×D₄	—	19	3	no	—
302	C₂×D₄	—	19	3	no	—
303	C₂×D₄	—	19	6	no	—
304	C₂×D₄	—	19	6	no	—
305	C₂×D₄	—	19	3	no	—
306	C₂×D₄	—	38	12	no	—
307	C₂×D₄	—	38	12	no	—
308	C₂×D₄	C₂²×D₁₉	1	6	yes	—
309	C₂×D₄	C₂²×D₁₉	1	3	yes	—
310	C₂×D₄	C₂²×D₁₉	1	3	yes	—
311	C₂²×C₄	—	2	12	no	—
312	C₂²×C₄	—	19	3	no	—
313	C₂²×C₄	—	19	3	no	—
314	C₂²×C₄	—	19	3	no	—
315	C₂²×C₄	—	19	3	no	—
316	C₂²×C₄	—	19	3	no	—
317	C₂²×C₄	—	19	1	no	—
318	C₂²×C₄	—	19	3	no	—
319	C₂²×C₄	—	38	12	no	—
320	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
321	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
322	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
323	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
325	C₂²×C₄	C₂²×D₁₉	1	3	yes	—
326	C₄⋊C₄	—	19	1	no	—
327	C₄⋊C₄	—	19	3	no	—
328	C₄⋊C₄	—	19	3	no	—
329	C₄⋊C₄	—	19	3	no	—
330	C₄⋊C₄	—	19	6	no	—
331	C₄⋊C₄	—	19	3	no	—
332	C₄⋊C₄	—	19	3	no	—
333	C₂²⋊C₄	—	19	1	no	—
334	C₂²⋊C₄	—	19	3	no	—
335	C₂²⋊C₄	—	19	3	no	—
336	C₂²⋊C₄	—	19	3	no	—
337	C₂²⋊C₄	—	19	6	no	—
338	C₂²⋊C₄	—	19	6	no	—
339	C₂²⋊C₄	—	19	1	no	—
340	C₂²⋊C₄	—	19	3	no	—
341	C₂²⋊C₄	—	19	3	no	—
342	C₂²⋊C₄	—	19	3	no	—
343	C₂²⋊C₄	—	19	6	no	—
344	C₄²	—	19	3	no	—
345	C₄²	—	19	3	no	—
346	C₄²	—	19	1	no	—
347	C₄²	—	19	3	no	—
348	C₂³	—	2	6	no	—
349	C₂³	—	2	6	no	—
350	C₂³	—	4	3	no	—
351	C₂³	—	19	1	no	—
352	C₂³	—	19	3	no	—
353	C₂³	—	38	6	no	—
354	C₂³	—	38	6	no	—
355	C₂³	—	76	3	no	—
356	C₂³	C₂³×D₁₉	1	3	yes	—
357	C₂³	C₂³×D₁₉	1	1	yes	characteristic
358	C₂³	C₂³×D₁₉	1	3	yes	—
359	Q₈	—	2	6	no	—
360	Q₈	—	38	6	no	—
361	Q₈	C₂×C₂²⋊D₁₉	1	4	yes	complemented
362	D₄	—	2	12	no	—
363	D₄	—	2	6	no	—
364	D₄	—	19	4	no	—
365	D₄	—	38	6	no	—
366	D₄	—	38	6	no	—
367	D₄	—	38	6	no	—
368	D₄	—	38	12	no	—
369	D₄	—	38	6	no	—
370	D₄	—	76	6	no	—
371	D₄	C₂×C₂²⋊D₁₉	1	12	yes	complemented
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	6	no	—
375	C₂×C₄	—	2	6	no	—
376	C₂×C₄	—	2	6	no	—
377	C₂×C₄	—	19	1	no	—
378	C₂×C₄	—	19	1	no	—
379	C₂×C₄	—	19	3	no	—
380	C₂×C₄	—	19	3	no	—
381	C₂×C₄	—	19	1	no	—
382	C₂×C₄	—	19	3	no	—
383	C₂×C₄	—	38	6	no	—
384	C₂×C₄	—	38	6	no	—
385	C₂×C₄	—	38	2	no	—
386	C₂×C₄	—	38	6	no	—
387	C₂×C₄	—	38	6	no	—
388	C₂×C₄	—	38	6	no	—
389	C₂×C₄	—	76	3	no	—
390	C₂×C₄	C₂×C₂²⋊D₁₉	1	12	yes	complemented
391	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₉	1	3	yes	—
393	C₂×C₄	C₂³×D₁₉	1	3	yes	—
394	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
395	C₂²	—	2	1	no	—
396	C₂²	—	2	3	no	—
397	C₂²	—	2	3	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	3	no	—
400	C₂²	—	2	3	no	—
401	C₂²	—	2	3	no	—
402	C₂²	—	4	12	no	—
403	C₂²	—	19	2	no	—
404	C₂²	—	38	1	no	—
405	C₂²	—	38	1	no	—
406	C₂²	—	38	3	no	—
407	C₂²	—	38	3	no	—
408	C₂²	—	38	3	no	—
409	C₂²	—	76	12	no	—
410	C₂²	#41×D₁₉	1	2	yes	complemented
411	C₂²	C₂²×C₂²⋊D₁₉	1	6	yes	—
412	C₂²	C₂⁴×D₁₉	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	3	no	—
415	C₄	—	19	2	no	—
416	C₄	—	38	1	no	—
417	C₄	—	38	3	no	—
418	C₄	—	38	3	no	—
419	C₄	—	38	1	no	—
420	C₄	—	38	3	no	—
421	C₄	C₂²×C₂²⋊D₁₉	1	2	yes	—
422	C₄	C₂²×C₂²⋊D₁₉	1	6	yes	—
423	C₂	—	2	2	no	—
424	C₂	—	2	6	no	—
425	C₂	—	4	3	no	—
426	C₂	—	38	2	no	—
427	C₂	—	76	3	no	—
428	C₂	C₂³×C₂²⋊D₁₉	1	1	yes	characteristic
429	C₂	C₂×#41×D₁₉	1	1	yes	characteristic
430	C₂	#11927380	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₉
commutator, socle, cosocle	C₂²×C₁₉	C₂⁵
Frattini	C₂²	C₂⁴×D₁₉
Fitting	C₂²×#41×C₁₉	C₂
hypercenter	C₂²×#41	D₁₉
hypocenter	C₁₉	D₄×#41
LCS	G ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₉	C₂	semidirect
2. #11927213	C₂	semidirect
3. Q₈×C₂²⋊D₁₉	C₂	semidirect
4. #11927205	C₂	semidirect
5. #11927201	C₂	semidirect
6. #11927193	C₂	semidirect
7. #11927188	C₂	semidirect
8. #11927182	C₂	semidirect
9. D₄×C₂²⋊D₁₉	C₂	semidirect
10. #11927090	C₂	semidirect
11. #11927055	C₂	semidirect
12. #11927051	C₂	semidirect
13. #41×Dic₁₉	C₂	semidirect
14. C₂×C₄×C₂²⋊D₁₉	C₂	semidirect
15. C₂²×#41×C₁₉	C₂	semidirect
18. C₂×#41×C₁₉	C₂²	semidirect
19. C₂×#41×C₁₉	C₂²	semidirect
20. C₂×#41×C₁₉	C₂²	semidirect
21. C₂²×Q₈×C₁₉	C₂²	semidirect
22. C₂²×D₄×C₁₉	C₂²	semidirect
23. C₂³×C₄×C₁₉	C₂²	semidirect
26. C₂×#64545	C₂²	semidirect
27. C₂×Q₈×D₁₉	C₂²	semidirect
28. C₂×#64543	C₂²	semidirect
29. C₂×D₄×D₁₉	C₂²	semidirect
30. C₂×#64541	C₂²	semidirect
31. C₂²×C₄×D₁₉	C₂²	semidirect
32. #10597399	C₂²	semidirect
33. C₂×C₂²⋊Dic₁₉	C₂²	semidirect
34. #10597393	C₂²	semidirect
35. #10597392	C₂²	semidirect
36. #10597392	C₂²	semidirect
37. Q₈×Dic₁₉	C₂²	semidirect
38. Q₈×Dic₁₉	C₂²	semidirect
39. #10597390	C₂²	semidirect
40. #10597386	C₂²	semidirect
41. #10597385	C₂²	semidirect
42. #10597385	C₂²	semidirect
43. #10597384	C₂²	semidirect
44. #10597384	C₂²	semidirect
45. #10597383	C₂²	semidirect
46. #10597382	C₂²	semidirect
47. #10597381	C₂²	semidirect
48. D₄×Dic₁₉	C₂²	semidirect
49. D₄×Dic₁₉	C₂²	semidirect
50. #10597376	C₂²	semidirect
51. #10597376	C₂²	semidirect
52. #10597375	C₂²	semidirect
55. C₄×C₂²⋊D₁₉	C₂²	semidirect
56. C₄×C₂²⋊D₁₉	C₂²	semidirect
57. C₄×C₂²⋊D₁₉	C₂²	semidirect
58. C₄×C₂²⋊D₁₉	C₂²	semidirect
59. C₄×C₂²⋊D₁₉	C₂²	semidirect
60. C₄×C₂²⋊D₁₉	C₂²	semidirect
61. C₄×C₂²⋊D₁₉	C₂²	semidirect
62. C₂×(C₂×D₁₉)⋊C₄	C₂²	semidirect
63. #10597372	C₂²	semidirect
64. #10597370	C₂²	semidirect
65. #10597370	C₂²	semidirect
66. C₂×Dic₁₉⋊C₄	C₂²	semidirect
67. C₂×C₄×Dic₁₉	C₂²	semidirect
73. #41×C₁₉	D₄	semidirect
144. Q₈×C₁₉	C₂×D₄	semidirect
147. D₄×C₁₉	C₂×D₄	semidirect
153. C₂×C₄×C₁₉	C₂×D₄	semidirect
163. C₂²⋊D₁₉	#41	direct (N × H)
189. C₂²×C₁₉	C₂×#41	semidirect
197. C₂×D₁₉	C₂×#41	semidirect
207. Dic₁₉	C₂×#41	semidirect
209. C₂²×#41	D₁₉	semidirect
237. C₂×#41	C₂×D₁₉	semidirect
238. C₂×#41	C₂×D₁₉	semidirect
239. C₂×#41	C₂×D₁₉	semidirect
241. C₂²×Q₈	C₂×D₁₉	semidirect
244. C₂²×D₄	C₂×D₁₉	semidirect
246. C₂³×C₄	C₂×D₁₉	semidirect
283. C₁₉	D₄×#41	semidirect
292. #41	C₂²⋊D₁₉	direct (N × H)
361. Q₈	C₂×C₂²⋊D₁₉	semidirect
371. D₄	C₂×C₂²⋊D₁₉	semidirect
390. C₂×C₄	C₂×C₂²⋊D₁₉	semidirect
410. C₂²	#41×D₁₉	semidirect

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
#11927213	2
Q₈×C₂²⋊D₁₉	2
#11927205	2
#11927201	2
#11927193	2
#11927188	2
#11927182	2
D₄×C₂²⋊D₁₉	2
#11927090	2
#11927055	2
#11927051	2
#41×Dic₁₉	2
C₂×C₄×C₂²⋊D₁₉	2
C₂²×#41×C₁₉	2
D₄×#41	19

Subgroups — #41×C22⋊D19 #14577120

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #41×C₂²⋊D₁₉ #14577120