Subgroups — #18091313

Order 4864.

686 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926409	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926313	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
5	#14563328	C₂	1	1	yes	maximal, characteristic
6	#14563328	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#343	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂²×C₄⋊Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926409	—	2	2	no	—
13	#11926409	—	2	2	no	—
14	C₂×C₁₉⋊#95	C₄	1	4	yes	—
15	#11926313	—	2	2	no	—
16	#11926312	—	2	2	no	—
17	#11926312	—	2	2	no	—
18	#11926298	—	2	2	no	—
19	#11926298	—	2	2	no	—
20	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
21	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
23	C₁₉×#343	—	2	2	no	—
24	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
25	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
26	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
27	C₂³×Dic₁₉	C₂×C₄	1	2	yes	—
28	C₂×M₁₆×C₁₉	—	2	1	no	—
29	C₂×M₁₆×C₁₉	—	2	1	no	—
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₂×M₁₆×C₁₉	—	2	1	no	—
33	C₂×M₁₆×C₁₉	—	2	1	no	—
34	C₂×M₁₆×C₁₉	—	2	1	no	—
35	C₂×M₁₆×C₁₉	—	2	1	no	—
36	C₂×M₁₆×C₁₉	—	2	1	no	—
37	C₂×M₁₆×C₁₉	—	2	1	no	—
38	C₂×M₁₆×C₁₉	D₄	1	2	yes	—
39	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
44	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
45	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
46	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
47	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
48	C₂×C₄⋊Dic₁₉	—	2	1	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	—	2	1	no	—
52	C₂×C₄⋊Dic₁₉	—	2	1	no	—
53	C₂×C₄⋊Dic₁₉	—	2	1	no	—
54	C₂×C₄×Dic₁₉	—	2	1	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂×C₄×Dic₁₉	—	2	1	no	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
59	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
60	C₂×#64520	—	2	1	no	—
61	C₂×#64520	—	2	1	no	—
62	C₂×#64520	—	2	1	no	—
63	C₂×#64520	—	2	1	no	—
64	C₂×#64520	—	2	1	no	—
65	C₂×#64520	—	2	1	no	—
66	C₂×#64520	—	2	1	no	—
67	C₂×#64520	—	2	1	no	—
68	C₂×#64520	—	2	1	no	—
69	C₂×#64520	—	2	1	no	—
70	C₂×#64520	D₄	1	2	yes	—
71	C₂×#64520	Q₈	1	2	yes	—
72	C₂²×C₁₉⋊C₈	—	2	1	no	—
73	C₂²×C₁₉⋊C₈	—	2	1	no	—
74	C₁₉⋊#95	—	2	8	no	—
75	C₂⁴×C₁₉	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₉	—	2	2	no	—
77	C₂²×C₄×C₁₉	—	2	2	no	—
78	C₂²×C₄×C₁₉	—	2	2	no	—
79	C₂²×C₄×C₁₉	—	4	4	no	—
80	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×Dic₁₉	—	2	2	no	—
95	C₂²×Dic₁₉	—	2	2	no	—
96	C₂²×Dic₁₉	—	2	2	no	—
97	C₂²×Dic₁₉	—	2	2	no	—
98	C₂²×Dic₁₉	—	2	2	no	—
99	C₂²×Dic₁₉	—	4	2	no	—
100	C₂²×Dic₁₉	—	4	2	no	—
101	C₂²×Dic₁₉	—	4	4	no	—
102	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
103	M₁₆×C₁₉	—	2	2	no	—
104	M₁₆×C₁₉	—	2	2	no	—
105	M₁₆×C₁₉	—	2	2	no	—
106	M₁₆×C₁₉	—	2	2	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	M₁₆×C₁₉	—	4	1	no	—
109	M₁₆×C₁₉	—	4	1	no	—
110	M₁₆×C₁₉	—	4	1	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₂×C₈×C₁₉	—	4	1	no	—
117	C₄⋊C₄×C₁₉	—	4	1	no	—
118	C₄⋊C₄×C₁₉	—	4	1	no	—
119	C₄⋊C₄×C₁₉	—	4	1	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊Dic₁₉	—	4	1	no	—
122	C₄⋊Dic₁₉	—	4	1	no	—
123	C₄⋊Dic₁₉	—	4	1	no	—
124	C₄⋊Dic₁₉	—	4	1	no	—
125	C₄×Dic₁₉	—	2	2	no	—
126	C₄×Dic₁₉	—	2	2	no	—
127	C₄×Dic₁₉	—	2	2	no	—
128	C₄×Dic₁₉	—	2	2	no	—
129	#64520	—	2	2	no	—
130	#64520	—	2	2	no	—
131	#64520	—	2	2	no	—
132	#64520	—	2	2	no	—
133	#64520	—	4	1	no	—
134	#64520	—	4	1	no	—
135	#64520	—	4	1	no	—
136	#64520	—	4	1	no	—
137	C₂×C₁₉⋊C₈	—	2	2	no	—
138	C₂×C₁₉⋊C₈	—	2	2	no	—
139	C₂×C₁₉⋊C₈	—	4	1	no	—
140	C₂×C₁₉⋊C₈	—	4	1	no	—
141	C₂×C₁₉⋊C₈	—	4	1	no	—
142	C₂×C₁₉⋊C₈	—	4	1	no	—
143	#11355	—	19	1	no	maximal, Sylow
144	C₂³×C₁₉	—	2	2	no	—
145	C₂³×C₁₉	—	2	2	no	—
146	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₁₉	#117	1	1	yes	characteristic
148	C₂³×C₁₉	#117	1	1	yes	characteristic
149	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
150	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
151	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
152	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₁₉	—	4	2	no	—
154	C₂×C₄×C₁₉	—	4	4	no	—
155	C₂×C₄×C₁₉	—	8	2	no	—
156	C₂×C₄×C₁₉	—	8	2	no	—
157	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
158	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
159	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
160	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
161	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
168	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
169	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
170	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
184	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
185	C₂×Dic₁₉	—	2	4	no	—
186	C₂×Dic₁₉	—	2	4	no	—
187	C₂×Dic₁₉	—	2	4	no	—
188	C₂×Dic₁₉	—	4	4	no	—
189	C₂×Dic₁₉	—	4	4	no	—
190	C₂×Dic₁₉	—	4	2	no	—
191	C₂×Dic₁₉	—	4	4	no	—
192	C₂×Dic₁₉	—	8	2	no	—
193	C₂×Dic₁₉	—	8	2	no	—
194	C₈×C₁₉	—	4	2	no	—
195	C₈×C₁₉	—	4	2	no	—
196	C₁₉⋊C₈	—	4	2	no	—
197	C₁₉⋊C₈	—	4	2	no	—
198	C₂×#382	—	19	1	no	—
199	C₂×#343	—	19	1	no	—
200	C₂×#343	—	19	1	no	—
201	C₂×#343	—	19	1	no	—
202	C₂×#343	D₁₉	1	1	yes	characteristic
203	#1728	—	19	1	no	—
204	#1728	—	19	1	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	2	1	no	—
208	C₂²×C₁₉	—	2	1	no	—
209	C₂²×C₁₉	—	2	1	no	—
210	C₂²×C₁₉	—	2	1	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	#381	1	1	yes	characteristic
214	C₂²×C₁₉	#387	1	1	yes	characteristic
215	C₂²×C₁₉	#387	1	1	yes	characteristic
216	C₂²×C₁₉	#387	1	1	yes	characteristic
217	C₂²×C₁₉	#387	1	1	yes	characteristic
218	C₂²×C₁₉	#390	1	1	yes	characteristic
219	C₂²×C₁₉	#391	1	1	yes	characteristic
220	C₂²×C₁₉	#413	1	2	yes	—
221	C₂²×C₁₉	#413	1	2	yes	—
222	C₄×C₁₉	—	8	2	no	—
223	C₄×C₁₉	#397	1	1	yes	characteristic
224	C₄×C₁₉	#397	1	1	yes	characteristic
225	C₄×C₁₉	#398	1	1	yes	characteristic
226	C₄×C₁₉	#398	1	1	yes	characteristic
227	C₄×C₁₉	#399	1	1	yes	characteristic
228	C₄×C₁₉	#399	1	1	yes	characteristic
229	C₄×C₁₉	#400	1	1	yes	characteristic
230	C₄×C₁₉	#400	1	1	yes	characteristic
231	Dic₁₉	—	4	4	no	—
232	Dic₁₉	—	8	2	no	—
233	C₂²×M₁₆	—	19	1	no	—
234	C₂²×M₁₆	—	19	1	no	—
235	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
236	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
237	C₂²×C₄⋊C₄	—	19	1	no	—
238	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
239	C₂²×C₄²	—	19	1	no	—
240	#382	—	38	2	no	—
241	#382	—	38	2	no	—
242	C₂×#95	—	19	4	no	—
243	#343	—	2	2	no	—
244	#343	—	38	2	no	—
245	#343	—	38	2	no	—
246	#343	—	38	2	no	—
247	#336	—	38	2	no	—
248	#336	—	38	2	no	—
249	C₂×C₁₉	—	2	1	no	—
250	C₂×C₁₉	—	2	1	no	—
251	C₂×C₁₉	—	2	1	no	—
252	C₂×C₁₉	—	2	1	no	—
253	C₂×C₁₉	#1445	1	1	yes	characteristic
254	C₂×C₁₉	#1822	1	2	yes	—
255	C₂×C₁₉	#1967	1	1	yes	characteristic
256	C₂×C₁₉	#1967	1	1	yes	characteristic
257	C₂×C₁₉	#1998	1	2	yes	—
258	C₂³×C₄	—	19	2	no	—
259	C₂³×C₄	—	19	2	no	—
260	C₂³×C₄	C₄×D₁₉	1	2	yes	—
261	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
262	C₂×M₁₆	—	2	1	no	—
263	C₂×M₁₆	—	2	1	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	2	1	no	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	2	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	2	1	no	—
271	C₂×M₁₆	—	2	1	no	—
272	C₂×M₁₆	—	19	2	no	—
273	C₂×M₁₆	—	19	2	no	—
274	C₂×M₁₆	—	38	1	no	—
275	C₂×M₁₆	—	38	1	no	—
276	C₂×M₁₆	—	38	1	no	—
277	C₂×M₁₆	—	38	1	no	—
278	C₂×M₁₆	—	38	1	no	—
279	C₂×M₁₆	—	38	1	no	—
280	C₂×M₁₆	—	38	1	no	—
281	C₂×M₁₆	—	38	1	no	—
282	C₂×M₁₆	—	38	1	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	Dic₃₈	1	2	yes	—
285	C₂×M₁₆	C₂²⋊D₁₉	1	2	yes	—
286	C₂²×C₈	—	2	1	no	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	C₂²×C₈	—	38	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	1	no	—
295	C₂×C₄⋊C₄	—	2	1	no	—
296	C₂×C₄⋊C₄	—	38	1	no	—
297	C₂×C₄⋊C₄	—	38	1	no	—
298	C₂×C₄⋊C₄	—	38	1	no	—
299	C₂×C₄⋊C₄	—	38	1	no	—
300	C₂×C₄⋊C₄	—	38	1	no	—
301	C₂×C₄⋊C₄	—	38	1	no	—
302	C₂×C₄²	—	19	2	no	—
303	C₂×C₄²	—	19	2	no	—
304	C₂×C₄²	—	38	1	no	—
305	C₂×C₄²	—	38	1	no	—
306	C₂×C₄²	—	38	1	no	—
307	C₂×C₄²	—	38	1	no	—
308	#95	—	38	8	no	—
309	C₁₉	#11355	1	1	yes	characteristic, complemented, Sylow
310	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	19	4	no	—
316	C₂²×C₄	—	38	2	no	—
317	C₂²×C₄	—	38	2	no	—
318	C₂²×C₄	—	38	2	no	—
319	C₂²×C₄	—	38	2	no	—
320	C₂²×C₄	—	38	2	no	—
321	C₂²×C₄	—	76	2	no	—
322	C₂²×C₄	—	76	2	no	—
323	C₂²×C₄	—	76	4	no	—
324	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
325	C₂²×C₄	#64541	1	1	yes	characteristic
326	C₂²×C₄	#64541	1	1	yes	characteristic
327	C₂²×C₄	#64541	1	1	yes	characteristic
328	C₂²×C₄	#64541	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
330	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
332	C₂²×C₄	#64543	1	1	yes	characteristic
333	C₂²×C₄	#64543	1	1	yes	characteristic
334	C₂²×C₄	#64543	1	1	yes	characteristic
335	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
336	C₂²×C₄	#64545	1	1	yes	characteristic
337	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
338	M₁₆	—	2	2	no	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	2	2	no	—
341	M₁₆	—	2	2	no	—
342	M₁₆	—	4	1	no	—
343	M₁₆	—	4	1	no	—
344	M₁₆	—	4	1	no	—
345	M₁₆	—	4	1	no	—
346	M₁₆	—	38	2	no	—
347	M₁₆	—	38	2	no	—
348	M₁₆	—	38	2	no	—
349	M₁₆	—	38	2	no	—
350	M₁₆	—	76	1	no	—
351	M₁₆	—	76	1	no	—
352	M₁₆	—	76	1	no	—
353	M₁₆	—	76	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	4	1	no	—
358	C₂×C₈	—	4	1	no	—
359	C₂×C₈	—	4	1	no	—
360	C₂×C₈	—	38	2	no	—
361	C₂×C₈	—	38	2	no	—
362	C₂×C₈	—	76	1	no	—
363	C₂×C₈	—	76	1	no	—
364	C₂×C₈	—	76	1	no	—
365	C₂×C₈	—	76	1	no	—
366	C₄⋊C₄	—	4	1	no	—
367	C₄⋊C₄	—	4	1	no	—
368	C₄⋊C₄	—	4	1	no	—
369	C₄⋊C₄	—	4	1	no	—
370	C₄⋊C₄	—	76	1	no	—
371	C₄⋊C₄	—	76	1	no	—
372	C₄⋊C₄	—	76	1	no	—
373	C₄⋊C₄	—	76	1	no	—
374	C₄²	—	38	2	no	—
375	C₄²	—	38	2	no	—
376	C₄²	—	38	2	no	—
377	C₄²	—	38	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
381	C₂³	#10597318	1	1	yes	characteristic
382	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
383	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
384	C₂³	#10597333	1	1	yes	characteristic
385	C₂³	#10597338	1	1	yes	characteristic
386	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	8	2	no	—
390	C₂×C₄	—	8	2	no	—
391	C₂×C₄	—	38	4	no	—
392	C₂×C₄	—	38	4	no	—
393	C₂×C₄	—	38	4	no	—
394	C₂×C₄	—	76	4	no	—
395	C₂×C₄	—	76	4	no	—
396	C₂×C₄	—	76	2	no	—
397	C₂×C₄	—	76	4	no	—
398	C₂×C₄	—	152	2	no	—
399	C₂×C₄	—	152	2	no	—
400	C₂×C₄	#10597316	1	1	yes	characteristic
401	C₂×C₄	#10597322	1	1	yes	characteristic
402	C₂×C₄	#10597324	1	1	yes	characteristic
403	C₂×C₄	#10597324	1	1	yes	characteristic
404	C₂×C₄	#10597325	1	1	yes	characteristic
405	C₂×C₄	#10597325	1	1	yes	characteristic
406	C₂×C₄	#10597329	1	1	yes	characteristic
407	C₂×C₄	#10597329	1	1	yes	characteristic
408	C₂×C₄	#10597329	1	1	yes	characteristic
409	C₂×C₄	#10597330	1	1	yes	characteristic
410	C₂×C₄	#10597331	1	1	yes	characteristic
411	C₂×C₄	#10597331	1	1	yes	characteristic
412	C₂×C₄	#10597334	1	1	yes	characteristic
413	C₂×C₄	#10597335	1	1	yes	characteristic
414	C₂×C₄	#10597335	1	1	yes	characteristic
415	C₂×C₄	#10597336	1	1	yes	characteristic
416	C₂×C₄	#10597340	1	1	yes	characteristic
417	C₂×C₄	#10597340	1	1	yes	characteristic
418	C₂×C₄	#10597340	1	1	yes	characteristic
419	C₂×C₄	#10597342	1	1	yes	characteristic
420	C₂×C₄	#10597342	1	1	yes	characteristic
421	C₂×C₄	#10597344	1	1	yes	characteristic
422	C₂×C₄	#10597370	1	1	yes	characteristic
423	C₂×C₄	#10597375	1	1	yes	characteristic
424	C₂×C₄	#10597381	1	1	yes	characteristic
425	C₂×C₄	#10597385	1	1	yes	characteristic
426	C₂×C₄	#10597386	1	1	yes	characteristic
427	C₂×C₄	#10597392	1	1	yes	characteristic
428	C₈	—	4	2	no	—
429	C₈	—	4	2	no	—
430	C₈	—	76	2	no	—
431	C₈	—	76	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	1	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	2	2	no	—
440	C₂²	#11926406	1	1	yes	characteristic
441	C₂²	#11926425	1	1	yes	characteristic
442	C₂²	#11926426	1	1	yes	characteristic
443	C₂²	#11926428	1	1	yes	characteristic
444	C₂²	#11926431	1	1	yes	characteristic
445	C₂²	#11926444	1	1	yes	characteristic
446	C₂²	#11926448	1	1	yes	characteristic
447	C₂²	#11926525	1	2	yes	—
448	C₂²	#11926527	1	2	yes	—
449	C₄	—	8	2	no	—
450	C₄	—	76	4	no	—
451	C₄	—	152	2	no	—
452	C₄	#11926472	1	1	yes	characteristic
453	C₄	#11926473	1	1	yes	characteristic
454	C₄	#11926477	1	1	yes	characteristic
455	C₄	#11926478	1	1	yes	characteristic
456	C₄	#11926479	1	1	yes	characteristic
457	C₄	#11926480	1	1	yes	characteristic
458	C₄	#11926485	1	1	yes	characteristic
459	C₄	#11926486	1	1	yes	characteristic
460	C₂	—	2	1	no	—
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	2	1	no	—
464	C₂	#14561901	1	1	yes	characteristic
465	C₂	#14563717	1	2	yes	—
466	C₂	#14564481	1	1	yes	characteristic
467	C₂	#14564483	1	1	yes	characteristic
468	C₂	#14564626	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²⋊C₄×D₁₉
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#343	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#343	D₁₉
hypocenter	C₁₉	#11355
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#343

Complements

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

N	H ≅ G/N	type
309. C₁₉	#11355	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926409	2
C₂×#11926313	2
C₂×#11926312	2
#14563328	2
C₂×C₁₉×#343	2
#11355	19