Subgroups — #18089376

Order 4864.

1242 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×#11926553	C₂	1	2	yes	maximal
2	C₂²×#10597293	C₂	1	2	yes	maximal
3	C₂×#11926309	C₂	1	1	yes	maximal, characteristic
4	#14563331	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₁₆×C₁₉	C₂	1	1	yes	maximal, characteristic
6	C₂²×#64520	C₂²	1	1	yes	characteristic
7	C₂²×#64520	C₂²	1	2	yes	—
8	C₂×#10597372	C₂²	1	1	yes	characteristic
9	#11926553	—	2	4	no	—
10	#11926553	—	2	4	no	—
11	C₂×#10597292	—	2	4	no	—
12	C₂×#10597293	—	2	4	no	—
13	C₂×#10597293	—	2	4	no	—
14	C₂×#10597293	—	2	4	no	—
15	#11926309	—	2	2	no	—
16	#11926298	—	2	2	no	—
17	C₂³×Q₈×C₁₉	C₂²	1	2	yes	—
18	C₂²×Q₁₆×C₁₉	—	2	4	no	—
19	C₂²×Q₁₆×C₁₉	—	2	4	no	—
20	C₂²×Q₁₆×C₁₉	—	2	2	no	—
21	C₂²×Q₁₆×C₁₉	—	2	2	no	—
22	C₂²×Q₁₆×C₁₉	C₄	1	4	yes	complemented
23	C₂³×C₈×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×Q₈×C₁₉	—	2	2	no	—
25	C₂²×Q₈×C₁₉	—	2	2	no	—
26	C₂²×Q₈×C₁₉	—	2	2	no	—
27	C₂²×Q₈×C₁₉	—	2	2	no	—
28	C₂²×Q₈×C₁₉	—	2	2	no	—
29	C₂²×Q₈×C₁₉	—	2	2	no	—
30	C₂²×Q₈×C₁₉	—	2	2	no	—
31	C₂²×Q₈×C₁₉	—	2	2	no	—
32	C₂²×Q₈×C₁₉	—	2	2	no	—
33	C₂²×Q₈×C₁₉	—	2	2	no	—
34	C₂²×Q₈×C₁₉	—	2	2	no	—
35	C₂²×Q₈×C₁₉	C₂×C₄	1	4	yes	—
36	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
37	C₂²×Q₈×C₁₉	D₄	1	4	yes	—
38	C₂³×C₄×C₁₉	—	2	2	no	—
39	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
40	C₂×Q₁₆×C₁₉	—	2	8	no	—
41	C₂×Q₁₆×C₁₉	—	2	16	no	—
42	C₂×Q₁₆×C₁₉	—	2	8	no	—
43	C₂×Q₁₆×C₁₉	—	2	16	no	—
44	C₂×Q₁₆×C₁₉	—	2	8	no	—
45	C₂²×C₈×C₁₉	—	2	2	no	—
46	C₂²×C₈×C₁₉	—	2	2	no	—
47	C₂²×C₈×C₁₉	C₂×C₄	1	2	yes	—
48	C₂²×C₈×C₁₉	D₄	1	2	yes	—
49	C₂²×C₈×C₁₉	D₄	1	2	yes	—
50	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
51	#10597372	—	2	2	no	—
52	#10597372	—	2	2	no	—
53	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×#64520	—	2	2	no	—
56	C₂×#64520	—	2	1	no	—
57	C₂×#64520	—	2	2	no	—
58	C₂×#64520	—	2	2	no	—
59	C₂×#64520	—	2	2	no	—
60	C₂×#64520	—	2	2	no	—
61	C₂×#64520	—	2	2	no	—
62	C₂×#64520	—	2	2	no	—
63	C₂×#64520	D₄	1	4	yes	—
64	C₂×#64520	D₄	1	2	yes	—
65	C₂²×C₁₉⋊C₈	—	2	2	no	—
66	C₂²×C₁₉⋊C₈	—	2	1	no	—
67	#10597293	—	2	16	no	—
68	#10597292	—	2	16	no	—
69	C₂⁴×C₁₉	#41	1	1	yes	characteristic
70	C₂×Q₈×C₁₉	—	2	4	no	—
71	C₂×Q₈×C₁₉	—	2	4	no	—
72	C₂×Q₈×C₁₉	—	2	4	no	—
73	C₂×Q₈×C₁₉	—	2	4	no	—
74	C₂×Q₈×C₁₉	—	2	4	no	—
75	C₂×Q₈×C₁₉	—	2	4	no	—
76	C₂×Q₈×C₁₉	—	2	4	no	—
77	C₂×Q₈×C₁₉	—	2	4	no	—
78	C₂×Q₈×C₁₉	—	2	4	no	—
79	C₂×Q₈×C₁₉	—	2	4	no	—
80	C₂×Q₈×C₁₉	—	2	4	no	—
81	C₂×Q₈×C₁₉	—	2	4	no	—
82	C₂×Q₈×C₁₉	—	2	4	no	—
83	C₂×Q₈×C₁₉	—	2	4	no	—
84	C₂×Q₈×C₁₉	—	2	4	no	—
85	C₂×Q₈×C₁₉	—	4	2	no	—
86	C₂×Q₈×C₁₉	—	4	2	no	—
87	C₂×Q₈×C₁₉	—	4	2	no	—
88	C₂×Q₈×C₁₉	—	4	2	no	—
89	C₂×Q₈×C₁₉	—	4	2	no	—
90	C₂×Q₈×C₁₉	—	4	2	no	—
91	C₂×Q₈×C₁₉	—	4	2	no	—
92	C₂×Q₈×C₁₉	—	4	2	no	—
93	C₂×Q₈×C₁₉	—	4	2	no	—
94	C₂×Q₈×C₁₉	—	4	2	no	—
95	C₂×Q₈×C₁₉	—	4	2	no	—
96	C₂×Q₈×C₁₉	—	4	2	no	—
97	C₂×Q₈×C₁₉	C₂²⋊C₄	1	8	yes	—
98	C₂²×C₄×C₁₉	—	2	4	no	—
99	C₂²×C₄×C₁₉	—	2	4	no	—
100	C₂²×C₄×C₁₉	—	2	4	no	—
101	C₂²×C₄×C₁₉	—	4	2	no	—
102	C₂²×C₄×C₁₉	—	4	2	no	—
103	C₂²×C₄×C₁₉	—	4	2	no	—
104	C₂²×C₄×C₁₉	—	4	2	no	—
105	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
114	C₂²×C₄×C₁₉	#41	1	2	yes	—
115	C₂²×Dic₁₉	—	2	2	no	—
116	Q₁₆×C₁₉	—	2	32	no	—
117	C₂×C₈×C₁₉	—	2	4	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	2	4	no	—
120	C₂×C₈×C₁₉	—	2	2	no	—
121	C₂×C₈×C₁₉	C₂²⋊C₄	1	4	yes	—
122	C₂²⋊Dic₁₉	—	4	2	no	—
123	C₄⋊Dic₁₉	—	2	4	no	—
124	C₄×Dic₁₉	—	4	1	no	—
125	C₄×Dic₁₉	—	4	1	no	—
126	#64520	—	2	4	no	—
127	#64520	—	2	4	no	—
128	#64520	—	2	4	no	—
129	#64520	—	4	2	no	—
130	#64520	—	4	2	no	—
131	#64520	—	4	2	no	—
132	C₂×C₁₉⋊C₈	—	2	4	no	—
133	C₂×C₁₉⋊C₈	—	2	2	no	—
134	C₂×C₁₉⋊C₈	—	4	1	no	—
135	C₂×C₁₉⋊C₈	—	4	2	no	—
136	C₂×C₁₉⋊C₈	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	4	2	no	—
138	#11029	—	19	1	no	maximal, Sylow
139	C₂³×C₁₉	—	2	4	no	—
140	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
141	C₂³×C₁₉	#121	1	1	yes	characteristic
142	C₂³×C₁₉	#121	1	2	yes	—
143	C₂³×C₁₉	#123	1	2	yes	—
144	C₂³×C₁₉	#124	1	1	yes	characteristic
145	Q₈×C₁₉	—	2	8	no	—
146	Q₈×C₁₉	—	2	8	no	—
147	Q₈×C₁₉	—	4	4	no	—
148	Q₈×C₁₉	—	4	4	no	—
149	Q₈×C₁₉	—	4	4	no	—
150	Q₈×C₁₉	—	4	4	no	—
151	Q₈×C₁₉	—	4	4	no	—
152	Q₈×C₁₉	—	4	4	no	—
153	C₂×C₄×C₁₉	—	2	8	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	4	4	no	—
156	C₂×C₄×C₁₉	—	4	4	no	—
157	C₂×C₄×C₁₉	—	4	4	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₁₉	#120	1	2	yes	—
165	C₂×C₄×C₁₉	#120	1	2	yes	—
166	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#120	1	2	yes	—
168	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#121	1	2	yes	—
170	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	2	yes	—
172	C₂×C₄×C₁₉	#121	1	2	yes	—
173	C₂×C₄×C₁₉	#121	1	2	yes	—
174	C₂×C₄×C₁₉	#123	1	2	yes	—
175	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
178	C₂×Dic₁₉	—	4	2	no	—
179	C₂×Dic₁₉	—	4	4	no	—
180	C₈×C₁₉	—	2	4	no	—
181	C₁₉⋊C₈	—	4	4	no	—
182	C₁₉⋊C₈	—	4	2	no	—
183	C₂³×Q₁₆	D₁₉	1	1	yes	characteristic
184	C₂×#419	—	19	2	no	—
185	C₂²×#101	—	19	2	no	—
186	C₂×#341	—	19	1	no	—
187	#1729	—	19	1	no	—
188	C₂²×C₁₉	—	2	2	no	—
189	C₂²×C₁₉	—	2	2	no	—
190	C₂²×C₁₉	—	2	4	no	—
191	C₂²×C₁₉	—	2	4	no	—
192	C₂²×C₁₉	#386	1	2	yes	—
193	C₂²×C₁₉	#390	1	1	yes	characteristic
194	C₂²×C₁₉	#392	1	1	yes	characteristic
195	C₂²×C₁₉	#394	1	2	yes	—
196	C₂²×C₁₉	#394	1	1	yes	characteristic
197	C₂²×C₁₉	#473	1	4	yes	—
198	C₄×C₁₉	—	4	8	no	—
199	C₄×C₁₉	#379	1	1	yes	characteristic
200	C₄×C₁₉	#386	1	2	yes	—
201	C₄×C₁₉	#390	1	1	yes	characteristic
202	C₄×C₁₉	#392	1	2	yes	—
203	C₄×C₁₉	#392	1	1	yes	characteristic
204	C₄×C₁₉	#394	1	1	yes	characteristic
205	Dic₁₉	—	8	2	no	—
206	C₂³×Q₈	C₂×D₁₉	1	2	yes	—
207	C₂²×Q₁₆	—	2	4	no	—
208	C₂²×Q₁₆	—	2	4	no	—
209	C₂²×Q₁₆	—	2	2	no	—
210	C₂²×Q₁₆	—	2	2	no	—
211	C₂²×Q₁₆	Dic₁₉	1	4	yes	complemented
212	C₂²×M₁₆	—	19	1	no	—
213	C₂²×M₁₆	—	19	2	no	—
214	C₂³×C₈	C₂×D₁₉	1	1	yes	characteristic
215	C₂×#117	—	19	1	no	—
216	#419	—	38	4	no	—
217	#419	—	38	4	no	—
218	C₂×#103	—	38	4	no	—
219	C₂×#101	—	38	4	no	—
220	C₂×#101	—	38	4	no	—
221	C₂×#101	—	38	4	no	—
222	#341	—	38	2	no	—
223	#336	—	38	2	no	—
224	C₂×C₁₉	—	2	2	no	—
225	C₂×C₁₉	—	2	2	no	—
226	C₂×C₁₉	#1438	1	1	yes	characteristic
227	C₂×C₁₉	#1979	1	2	yes	—
228	C₂×C₁₉	#2020	1	2	yes	—
229	C₂×C₁₉	#2047	1	2	yes	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	2	no	—
235	C₂²×Q₈	—	2	2	no	—
236	C₂²×Q₈	—	2	2	no	—
237	C₂²×Q₈	—	2	2	no	—
238	C₂²×Q₈	—	2	2	no	—
239	C₂²×Q₈	—	2	2	no	—
240	C₂²×Q₈	—	2	2	no	—
241	C₂²×Q₈	C₂×Dic₁₉	1	4	yes	—
242	C₂²×Q₈	C₂²⋊D₁₉	1	4	yes	—
243	C₂²×Q₈	C₂²⋊D₁₉	1	4	yes	—
244	C₂³×C₄	—	2	2	no	—
245	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
246	C₂×Q₁₆	—	2	8	no	—
247	C₂×Q₁₆	—	2	16	no	—
248	C₂×Q₁₆	—	2	8	no	—
249	C₂×Q₁₆	—	2	16	no	—
250	C₂×Q₁₆	—	2	8	no	—
251	C₂×M₁₆	—	19	2	no	—
252	C₂×M₁₆	—	19	4	no	—
253	C₂×M₁₆	—	38	1	no	—
254	C₂×M₁₆	—	38	2	no	—
255	C₂×M₁₆	—	38	2	no	—
256	C₂×M₁₆	—	38	2	no	—
257	C₂×M₁₆	—	38	2	no	—
258	C₂×M₁₆	—	38	2	no	—
259	C₂×M₁₆	—	38	2	no	—
260	C₂×M₁₆	—	38	2	no	—
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	38	2	no	—
264	C₂²×C₈	—	38	1	no	—
265	C₂²×C₈	C₂×Dic₁₉	1	2	yes	—
266	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
267	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
268	#117	—	38	2	no	—
269	#117	—	38	2	no	—
270	C₂×C₄⋊C₄	—	19	2	no	—
271	C₂×C₂²⋊C₄	—	38	1	no	—
272	C₂×C₄²	—	38	1	no	—
273	#103	—	38	16	no	—
274	#101	—	38	16	no	—
275	C₁₉	#11029	1	1	yes	characteristic, complemented, Sylow
276	C₂⁴	#64543	1	1	yes	characteristic
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	2	4	no	—
279	C₂×Q₈	—	2	4	no	—
280	C₂×Q₈	—	2	4	no	—
281	C₂×Q₈	—	2	4	no	—
282	C₂×Q₈	—	2	4	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	4	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	4	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×Q₈	—	2	4	no	—
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×Q₈	—	2	4	no	—
292	C₂×Q₈	—	4	2	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	4	2	no	—
295	C₂×Q₈	—	4	2	no	—
296	C₂×Q₈	—	4	2	no	—
297	C₂×Q₈	—	4	2	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	4	2	no	—
300	C₂×Q₈	—	4	2	no	—
301	C₂×Q₈	—	4	2	no	—
302	C₂×Q₈	—	4	2	no	—
303	C₂×Q₈	—	4	2	no	—
304	C₂×Q₈	C₂²⋊Dic₁₉	1	8	yes	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	4	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	—	4	2	no	—
310	C₂²×C₄	—	4	2	no	—
311	C₂²×C₄	—	4	2	no	—
312	C₂²×C₄	—	38	2	no	—
313	C₂²×C₄	D₄×D₁₉	1	2	yes	—
314	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
316	C₂²×C₄	#64543	1	1	yes	characteristic
317	C₂²×C₄	#64543	1	2	yes	—
318	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
319	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
320	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
322	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
323	Q₁₆	—	2	32	no	—
324	M₁₆	—	38	4	no	—
325	M₁₆	—	38	4	no	—
326	M₁₆	—	38	4	no	—
327	M₁₆	—	76	2	no	—
328	M₁₆	—	76	2	no	—
329	M₁₆	—	76	2	no	—
330	C₂×C₈	—	2	4	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	38	4	no	—
335	C₂×C₈	—	38	2	no	—
336	C₂×C₈	—	76	2	no	—
337	C₂×C₈	—	76	1	no	—
338	C₂×C₈	—	76	2	no	—
339	C₂×C₈	—	76	1	no	—
340	C₂×C₈	C₂²⋊Dic₁₉	1	4	yes	—
341	C₄⋊C₄	—	38	4	no	—
342	C₂²⋊C₄	—	76	2	no	—
343	C₄²	—	76	1	no	—
344	C₄²	—	76	1	no	—
345	C₂³	—	2	4	no	—
346	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
347	C₂³	#10597381	1	2	yes	—
348	C₂³	#10597382	1	1	yes	characteristic
349	C₂³	#10597384	1	1	yes	characteristic
350	C₂³	#10597385	1	2	yes	—
351	Q₈	—	2	8	no	—
352	Q₈	—	2	8	no	—
353	Q₈	—	4	4	no	—
354	Q₈	—	4	4	no	—
355	Q₈	—	4	4	no	—
356	Q₈	—	4	4	no	—
357	Q₈	—	4	4	no	—
358	Q₈	—	4	4	no	—
359	C₂×C₄	—	2	8	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	4	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	—	4	4	no	—
366	C₂×C₄	—	76	4	no	—
367	C₂×C₄	—	76	2	no	—
368	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
369	C₂×C₄	D₄×Dic₁₉	1	2	yes	—
370	C₂×C₄	#10597381	1	2	yes	—
371	C₂×C₄	#10597382	1	1	yes	characteristic
372	C₂×C₄	#10597383	1	2	yes	—
373	C₂×C₄	#10597383	1	2	yes	—
374	C₂×C₄	#10597384	1	2	yes	—
375	C₂×C₄	#10597384	1	1	yes	characteristic
376	C₂×C₄	#10597385	1	2	yes	—
377	C₂×C₄	#10597385	1	2	yes	—
378	C₂×C₄	#10597385	1	2	yes	—
379	C₂×C₄	#10597386	1	1	yes	characteristic
380	C₂×C₄	#10597386	1	1	yes	characteristic
381	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
382	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
383	C₂×C₄	#10597399	1	1	yes	characteristic
384	C₂×C₄	#10597399	1	2	yes	—
385	C₂×C₄	#10597399	1	1	yes	characteristic
386	C₈	—	2	4	no	—
387	C₈	—	76	4	no	—
388	C₈	—	76	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	2	4	no	—
391	C₂²	—	2	2	no	—
392	C₂²	—	2	2	no	—
393	C₂²	#11926424	1	2	yes	—
394	C₂²	#11926447	1	1	yes	characteristic
395	C₂²	#11926452	1	1	yes	characteristic
396	C₂²	#11926458	1	2	yes	—
397	C₂²	#11926458	1	1	yes	characteristic
398	C₂²	#11926816	1	4	yes	—
399	C₄	—	4	8	no	—
400	C₄	—	152	2	no	—
401	C₄	#11926400	1	1	yes	characteristic
402	C₄	#11926424	1	2	yes	—
403	C₄	#11926447	1	1	yes	characteristic
404	C₄	#11926452	1	2	yes	—
405	C₄	#11926452	1	1	yes	characteristic
406	C₄	#11926458	1	1	yes	characteristic
407	C₂	—	2	2	no	—
408	C₂	—	2	2	no	—
409	C₂	#14561876	1	1	yes	characteristic
410	C₂	#14564551	1	2	yes	—
411	C₂	#14564754	1	2	yes	—
412	C₂	#14564900	1	2	yes	—

	subgroup	G/H
center	C₂³	#10597384
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂³×Q₁₆×C₁₉	C₂
socle	C₂³×C₁₉	#121
prime radical	C₂⁴×C₁₉	#41
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂³×Q₁₆	D₁₉
hypocenter	C₁₉	#11029
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×Q₁₆

Complements

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

N	H ≅ G/N	type
22. C₂²×Q₁₆×C₁₉	C₄	semidirect
211. C₂²×Q₁₆	Dic₁₉	semidirect
275. C₁₉	#11029	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926553	2
C₂²×#10597293	2
C₂×#11926309	2
#14563331	2
C₂³×Q₁₆×C₁₉	2
#11029	19