Subgroups — #14567453

Order 2432.

584 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597324	C₂	1	1	yes	maximal, characteristic, complemented
2	#11926483	C₂	1	1	yes	maximal, characteristic, complemented
3	#11926477	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926467	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926456	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926450	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926428	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926424	C₂	1	1	yes	maximal, characteristic
9	#11926424	C₂	1	1	yes	maximal, characteristic
10	#11926419	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926417	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926417	C₂	1	1	yes	maximal, characteristic, complemented
13	#11926404	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₉⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₄×C₁₉	C₂	1	1	yes	maximal, characteristic
16	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₉	C₂²	1	1	yes	characteristic
19	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
20	C₂³×Dic₁₉	C₂²	1	1	yes	characteristic
21	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic
22	C₄×D₄×C₁₉	—	2	4	no	—
23	C₂×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
24	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
26	C₂×C₄²×C₁₉	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₁₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
36	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
37	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
38	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
39	C₂×Dic₁₉⋊C₄	C₂²	1	1	yes	characteristic
40	#10597324	—	2	4	no	—
41	C₁₉⋊#95	C₂²	1	1	yes	characteristic
42	C₁₉⋊#95	C₂²	1	1	yes	characteristic
43	C₁₉⋊#95	C₂²	1	1	yes	characteristic
44	C₁₉⋊#95	C₂²	1	1	yes	characteristic
45	C₁₉⋊#95	C₂²	1	1	yes	characteristic
46	C₁₉⋊#95	C₂²	1	1	yes	characteristic
47	C₁₉⋊#95	C₂²	1	1	yes	characteristic
48	C₁₉⋊#95	C₂²	1	1	yes	characteristic
49	C₁₉⋊#95	C₂²	1	1	yes	characteristic
50	C₁₉⋊#95	C₂²	1	1	yes	characteristic
51	C₁₉⋊#95	C₂²	1	1	yes	characteristic
52	C₁₉⋊#95	C₂²	1	1	yes	characteristic
53	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
54	C₂⁴×C₁₉	C₂³	1	1	yes	characteristic
55	C₂×D₄×C₁₉	—	2	2	no	—
56	C₂×D₄×C₁₉	—	2	2	no	—
57	C₂×D₄×C₁₉	Q₈	1	4	yes	complemented
58	C₂²×C₄×C₁₉	—	2	2	no	—
59	C₂²×C₄×C₁₉	—	2	2	no	—
60	C₂²×C₄×C₁₉	—	2	2	no	—
61	C₂²×C₄×C₁₉	—	2	2	no	—
62	C₂²×C₄×C₁₉	—	4	1	no	—
63	C₂²×C₄×C₁₉	—	4	1	no	—
64	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
65	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
69	C₂²×Dic₁₉	—	2	2	no	—
70	C₂²×Dic₁₉	—	2	2	no	—
71	C₂²×Dic₁₉	—	2	2	no	—
72	C₂²×Dic₁₉	—	4	1	no	—
73	C₂²×Dic₁₉	—	4	1	no	—
74	C₂²×Dic₁₉	—	4	1	no	—
75	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
76	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
77	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
78	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
79	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
80	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
81	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
82	C₂²×Dic₁₉	C₂³	1	1	yes	characteristic
83	C₂×Dic₃₈	—	2	2	no	—
84	C₂×Dic₃₈	—	2	2	no	—
85	C₂×Dic₃₈	—	4	1	no	—
86	C₄⋊C₄×C₁₉	—	2	2	no	—
87	C₂²⋊C₄×C₁₉	—	2	2	no	—
88	C₂²⋊C₄×C₁₉	D₄	1	4	yes	—
89	C₄²×C₁₉	—	2	2	no	—
90	C₂²⋊Dic₁₉	—	2	2	no	—
91	C₂²⋊Dic₁₉	—	2	2	no	—
92	C₂²⋊Dic₁₉	—	2	2	no	—
93	C₂²⋊Dic₁₉	—	4	1	no	—
94	C₂²⋊Dic₁₉	—	4	1	no	—
95	C₂²⋊Dic₁₉	—	4	1	no	—
96	C₄⋊Dic₁₉	—	2	2	no	—
97	C₄⋊Dic₁₉	—	4	1	no	—
98	C₄⋊Dic₁₉	—	4	1	no	—
99	Dic₁₉⋊C₄	—	2	2	no	—
100	Dic₁₉⋊C₄	—	2	2	no	—
101	Dic₁₉⋊C₄	—	2	2	no	—
102	Dic₁₉⋊C₄	—	4	1	no	—
103	C₂³×C₁₉	—	2	1	no	—
104	C₂³×C₁₉	—	2	1	no	—
105	C₂³×C₁₉	—	2	1	no	—
106	C₂³×C₁₉	—	2	1	no	—
107	C₂³×C₁₉	—	2	1	no	—
108	C₂³×C₁₉	—	2	1	no	—
109	C₂³×C₁₉	—	2	1	no	—
110	C₂³×C₁₉	—	2	1	no	—
111	C₂³×C₁₉	—	2	1	no	—
112	C₂³×C₁₉	—	2	1	no	—
113	C₂³×C₁₉	C₂×D₄	1	2	yes	—
114	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
115	C₂³×C₁₉	C₂×Q₈	1	2	yes	—
116	C₂³×C₁₉	#41	1	2	yes	—
117	C₂³×C₁₉	C₂⁴	1	1	yes	characteristic
118	D₄×C₁₉	—	2	8	no	—
119	C₂×C₄×C₁₉	—	2	1	no	—
120	C₂×C₄×C₁₉	—	2	1	no	—
121	C₂×C₄×C₁₉	—	2	1	no	—
122	C₂×C₄×C₁₉	—	2	1	no	—
123	C₂×C₄×C₁₉	—	2	1	no	—
124	C₂×C₄×C₁₉	—	2	1	no	—
125	C₂×C₄×C₁₉	—	2	1	no	—
126	C₂×C₄×C₁₉	—	2	1	no	—
127	C₂×C₄×C₁₉	—	2	1	no	—
128	C₂×C₄×C₁₉	—	2	1	no	—
129	C₂×C₄×C₁₉	—	2	1	no	—
130	C₂×C₄×C₁₉	—	4	4	no	—
131	C₂×C₄×C₁₉	—	4	4	no	—
132	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
134	C₂×C₄×C₁₉	C₂×Q₈	1	2	yes	—
135	C₂×C₄×C₁₉	#41	1	2	yes	—
136	C₂×Dic₁₉	—	2	1	no	—
137	C₂×Dic₁₉	—	2	1	no	—
138	C₂×Dic₁₉	—	2	1	no	—
139	C₂×Dic₁₉	—	2	1	no	—
140	C₂×Dic₁₉	—	2	1	no	—
141	C₂×Dic₁₉	—	2	1	no	—
142	C₂×Dic₁₉	—	2	1	no	—
143	C₂×Dic₁₉	—	2	1	no	—
144	C₂×Dic₁₉	—	2	1	no	—
145	C₂×Dic₁₉	—	2	1	no	—
146	C₂×Dic₁₉	—	2	1	no	—
147	C₂×Dic₁₉	—	2	1	no	—
148	C₂×Dic₁₉	—	2	1	no	—
149	C₂×Dic₁₉	—	2	1	no	—
150	C₂×Dic₁₉	—	2	1	no	—
151	C₂×Dic₁₉	—	2	1	no	—
152	C₂×Dic₁₉	—	2	1	no	—
153	C₂×Dic₁₉	—	2	1	no	—
154	C₂×Dic₁₉	—	2	1	no	—
155	C₂×Dic₁₉	—	2	1	no	—
156	C₂×Dic₁₉	—	2	1	no	—
157	C₂×Dic₁₉	—	2	1	no	—
158	C₂×Dic₁₉	—	2	1	no	—
159	C₂×Dic₁₉	—	4	4	no	—
160	C₂×Dic₁₉	—	4	4	no	—
161	C₂×Dic₁₉	#41	1	2	yes	—
162	Dic₃₈	—	4	4	no	—
163	#2450	—	19	1	no	maximal, Sylow
164	C₂²×C₁₉	—	2	2	no	—
165	C₂²×C₁₉	—	2	2	no	—
166	C₂²×C₁₉	—	2	2	no	—
167	C₂²×C₁₉	—	2	2	no	—
168	C₂²×C₁₉	—	2	2	no	—
169	C₂²×C₁₉	—	2	2	no	—
170	C₂²×C₁₉	—	2	2	no	—
171	C₂²×C₁₉	—	2	2	no	—
172	C₂²×C₁₉	—	2	2	no	—
173	C₂²×C₁₉	—	4	1	no	—
174	C₂²×C₁₉	—	4	1	no	—
175	C₂²×C₁₉	—	4	1	no	—
176	C₂²×C₁₉	—	4	1	no	—
177	C₂²×C₁₉	C₂²⋊Q₈	1	4	yes	—
178	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
179	C₂²×C₁₉	C₂²×Q₈	1	1	yes	characteristic
180	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
181	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
182	C₂²×C₁₉	C₂×#41	1	1	yes	characteristic
183	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
184	C₂²×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
185	C₄×C₁₉	—	2	2	no	—
186	C₄×C₁₉	—	2	2	no	—
187	C₄×C₁₉	—	2	2	no	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	4	1	no	—
190	Dic₁₉	—	2	2	no	—
191	Dic₁₉	—	4	1	no	—
192	Dic₁₉	—	4	1	no	—
193	Dic₁₉	—	4	1	no	—
194	Dic₁₉	—	4	1	no	—
195	Dic₁₉	—	4	1	no	—
196	Dic₁₉	—	4	1	no	—
197	Dic₁₉	—	4	1	no	—
198	C₂×C₂²⋊Q₈	—	19	1	no	—
199	C₂×C₄×D₄	D₁₉	1	1	yes	characteristic
200	#400	—	19	1	no	—
201	#398	—	19	1	no	—
202	#396	—	19	1	no	—
203	#393	—	19	1	no	—
204	#391	—	19	1	no	—
205	#387	—	19	1	no	—
206	#386	—	19	1	no	—
207	#386	—	19	1	no	—
208	#385	—	19	1	no	—
209	#385	—	19	1	no	—
210	#385	—	19	1	no	—
211	#380	—	19	1	no	—
212	C₂×#95	—	19	1	no	—
213	C₂×C₁₉	—	2	4	no	—
214	C₂×C₁₉	—	4	2	no	—
215	C₂×C₁₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
216	C₂×C₁₉	#529	1	1	yes	characteristic
217	C₂×C₁₉	#538	1	1	yes	characteristic
218	C₂×C₁₉	#546	1	1	yes	characteristic
219	C₂×C₁₉	#546	1	1	yes	characteristic
220	C₂×C₁₉	#554	1	1	yes	characteristic
221	C₂×C₁₉	#554	1	1	yes	characteristic
222	C₂²×Q₈	—	19	1	no	—
223	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
224	C₂³×C₄	—	19	1	no	—
225	C₂³×C₄	—	19	1	no	—
226	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
227	C₂³×C₄	C₂×D₁₉	1	1	yes	characteristic
228	C₂²⋊Q₈	—	38	4	no	—
229	C₄×D₄	—	2	4	no	—
230	C₂×C₄⋊C₄	—	19	1	no	—
231	C₂×C₄⋊C₄	—	19	1	no	—
232	C₂×C₄⋊C₄	—	19	1	no	—
233	C₂×C₄⋊C₄	—	19	1	no	—
234	C₂×C₄⋊C₄	—	19	1	no	—
235	C₂×C₄⋊C₄	—	19	1	no	—
236	C₂×C₄⋊C₄	—	19	1	no	—
237	C₂×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
238	C₂×C₂²⋊C₄	—	19	1	no	—
239	C₂×C₂²⋊C₄	—	19	1	no	—
240	C₂×C₂²⋊C₄	—	19	1	no	—
241	C₂×C₂²⋊C₄	—	19	1	no	—
242	C₂×C₂²⋊C₄	—	19	1	no	—
243	C₂×C₂²⋊C₄	—	19	1	no	—
244	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
245	C₂×C₂²⋊C₄	C₂×D₁₉	1	1	yes	characteristic
246	C₂×C₄²	C₂×D₁₉	1	1	yes	characteristic
247	#95	—	19	1	no	—
248	#95	—	19	1	no	—
249	#95	—	19	1	no	—
250	#95	—	19	1	no	—
251	#95	—	19	1	no	—
252	#95	—	19	1	no	—
253	#95	—	19	1	no	—
254	#95	—	19	1	no	—
255	#95	—	19	1	no	—
256	#95	—	19	1	no	—
257	#95	—	19	1	no	—
258	#95	—	19	1	no	—
259	C₁₉	#2450	1	1	yes	characteristic, complemented, Sylow
260	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
261	C₂⁴	C₂²×D₁₉	1	1	yes	characteristic
262	C₂×Q₈	—	38	2	no	—
263	C₂×Q₈	—	38	2	no	—
264	C₂×Q₈	—	76	1	no	—
265	C₂×D₄	—	2	2	no	—
266	C₂×D₄	—	2	2	no	—
267	C₂×D₄	Dic₃₈	1	4	yes	complemented
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	4	1	no	—
274	C₂²×C₄	—	19	1	no	—
275	C₂²×C₄	—	19	1	no	—
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	—	38	2	no	—
285	C₂²×C₄	—	76	1	no	—
286	C₂²×C₄	—	76	1	no	—
287	C₂²×C₄	—	76	1	no	—
288	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
289	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
290	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
291	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
292	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
293	C₄⋊C₄	—	2	2	no	—
294	C₄⋊C₄	—	38	2	no	—
295	C₄⋊C₄	—	38	2	no	—
296	C₄⋊C₄	—	38	2	no	—
297	C₄⋊C₄	—	38	2	no	—
298	C₄⋊C₄	—	76	1	no	—
299	C₄⋊C₄	—	76	1	no	—
300	C₄⋊C₄	—	76	1	no	—
301	C₂²⋊C₄	—	2	2	no	—
302	C₂²⋊C₄	—	38	2	no	—
303	C₂²⋊C₄	—	38	2	no	—
304	C₂²⋊C₄	—	38	2	no	—
305	C₂²⋊C₄	—	76	1	no	—
306	C₂²⋊C₄	—	76	1	no	—
307	C₂²⋊C₄	—	76	1	no	—
308	C₂²⋊C₄	C₂²⋊D₁₉	1	4	yes	—
309	C₄²	—	2	2	no	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	C₂×Dic₃₈	1	2	yes	—
321	C₂³	C₂×Dic₃₈	1	2	yes	—
322	C₂³	#64541	1	2	yes	—
323	C₂³	C₂×C₂²⋊D₁₉	1	2	yes	—
324	C₂³	C₂³×D₁₉	1	1	yes	characteristic
325	Q₈	—	76	4	no	—
326	D₄	—	2	8	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	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	4	4	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	—	19	2	no	—
341	C₂×C₄	—	38	1	no	—
342	C₂×C₄	—	38	1	no	—
343	C₂×C₄	—	38	1	no	—
344	C₂×C₄	—	38	1	no	—
345	C₂×C₄	—	38	1	no	—
346	C₂×C₄	—	38	1	no	—
347	C₂×C₄	—	38	1	no	—
348	C₂×C₄	—	38	1	no	—
349	C₂×C₄	—	38	1	no	—
350	C₂×C₄	—	38	1	no	—
351	C₂×C₄	—	38	1	no	—
352	C₂×C₄	—	38	1	no	—
353	C₂×C₄	—	38	1	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	—	38	1	no	—
359	C₂×C₄	—	38	1	no	—
360	C₂×C₄	—	38	1	no	—
361	C₂×C₄	—	38	1	no	—
362	C₂×C₄	—	38	1	no	—
363	C₂×C₄	—	38	1	no	—
364	C₂×C₄	—	76	4	no	—
365	C₂×C₄	—	76	4	no	—
366	C₂×C₄	C₂×Dic₃₈	1	2	yes	—
367	C₂×C₄	#64543	1	2	yes	—
368	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
369	C₂×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	1	no	—
380	C₂²	—	4	1	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	#10597370	1	4	yes	—
384	C₂²	C₂²×Dic₃₈	1	1	yes	characteristic
385	C₂²	C₂×#64541	1	1	yes	characteristic
386	C₂²	C₂×#64543	1	1	yes	characteristic
387	C₂²	#10597430	1	1	yes	characteristic
388	C₂²	#41×D₁₉	1	1	yes	characteristic
389	C₂²	#10597435	1	1	yes	characteristic
390	C₂²	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
391	C₄	—	2	2	no	—
392	C₄	—	2	2	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	4	1	no	—
396	C₄	—	38	2	no	—
397	C₄	—	76	1	no	—
398	C₄	—	76	1	no	—
399	C₄	—	76	1	no	—
400	C₄	—	76	1	no	—
401	C₄	—	76	1	no	—
402	C₄	—	76	1	no	—
403	C₄	—	76	1	no	—
404	C₂	—	2	4	no	—
405	C₂	—	4	2	no	—
406	C₂	C₂×#10597370	1	1	yes	characteristic
407	C₂	#11927074	1	1	yes	characteristic
408	C₂	#11927127	1	1	yes	characteristic
409	C₂	#11927182	1	1	yes	characteristic
410	C₂	#11927188	1	1	yes	characteristic
411	C₂	#11927251	1	1	yes	characteristic
412	C₂	#11927253	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₉
commutator, socle, cosocle	C₂³×C₁₉	C₂⁴
Fitting	C₂×C₄×D₄×C₁₉	C₂
prime radical	C₂²×D₄×C₁₉	C₂²
hypercenter	C₂×C₄×D₄	D₁₉
hypocenter	C₁₉	#2450
LCS	G ▷ C₂³×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#10597324	C₂	semidirect
2. #11926483	C₂	semidirect
3. #11926477	C₂	semidirect
4. #11926467	C₂	semidirect
5. #11926456	C₂	semidirect
6. #11926450	C₂	semidirect
7. #11926428	C₂	semidirect
10. #11926419	C₂	semidirect
11. #11926417	C₂	semidirect
12. #11926417	C₂	semidirect
13. #11926404	C₂	semidirect
14. C₂×C₁₉⋊#95	C₂	semidirect
57. C₂×D₄×C₁₉	Q₈	semidirect
259. C₁₉	#2450	semidirect
267. C₂×D₄	Dic₃₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597324	2
#11926483	2
#11926477	2
#11926467	2
#11926456	2
#11926450	2
#11926428	2
#11926424	2
#11926419	2
#11926417	2
#11926404	2
C₂×C₁₉⋊#95	2
C₂×C₄×D₄×C₁₉	2
#2450	19