Subgroups — #18088523

Order 4864.

846 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566119	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926390	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926304	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
6	#14563328	C₂	1	1	yes	maximal, characteristic
7	C₂×C₁₉×#339	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂×#10597372	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₁₉	C₂²	1	1	yes	characteristic
12	#11926443	C₄	1	4	yes	complemented
13	#11926419	—	2	2	no	—
14	C₄×C₄⋊Dic₁₉	—	2	2	no	—
15	#11926390	—	2	2	no	—
16	#11926390	—	2	2	no	—
17	C₂×C₁₉⋊#95	—	2	2	no	—
18	#11926305	—	2	2	no	—
19	#11926304	—	2	2	no	—
20	#11926303	C₄	1	4	yes	complemented
21	#11926298	—	2	2	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#339	C₄	1	4	yes	complemented
26	C₂³×C₄×C₁₉	—	2	1	no	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
28	C₂³×Dic₁₉	—	2	1	no	—
29	C₂³×Dic₁₉	D₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₁₉×#117	—	2	1	no	—
38	C₁₉×#117	—	2	1	no	—
39	C₁₉×#117	C₂×C₄	1	2	yes	—
40	C₁₉×#117	C₂×C₄	1	2	yes	—
41	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	2	yes	—
42	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄²×C₁₉	—	2	1	no	—
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	—	2	1	no	—
46	C₂×C₄²×C₁₉	—	2	1	no	—
47	C₂×C₄²×C₁₉	C₂×C₄	1	2	yes	—
48	C₂×C₄²×C₁₉	D₄	1	2	yes	—
49	C₂×C₄²×C₁₉	Q₈	1	2	yes	—
50	C₂×C₂²⋊Dic₁₉	—	2	1	no	—
51	#10597372	—	2	1	no	—
52	#10597372	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	C₂×C₄⋊Dic₁₉	—	2	4	no	—
56	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₁₉	—	2	1	no	—
58	C₂×C₄×Dic₁₉	—	2	1	no	—
59	C₂×C₄×Dic₁₉	—	2	1	no	—
60	C₂×C₄×Dic₁₉	—	2	1	no	—
61	C₂×C₄×Dic₁₉	—	2	1	no	—
62	C₂×C₄×Dic₁₉	—	2	1	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂×C₄×Dic₁₉	—	2	1	no	—
65	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
66	C₂×C₄×Dic₁₉	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
68	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
69	C₂×C₄×Dic₁₉	Q₈	1	2	yes	—
70	C₂×#64520	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	—	2	1	no	—
75	C₂×#64520	C₂×C₄	1	2	yes	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₁₉⋊#95	—	2	8	no	—
78	C₁₉⋊#95	—	2	4	no	—
79	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₉	—	2	2	no	—
81	C₂²×C₄×C₁₉	—	2	2	no	—
82	C₂²×C₄×C₁₉	—	2	2	no	—
83	C₂²×C₄×C₁₉	—	2	2	no	—
84	C₂²×C₄×C₁₉	—	4	4	no	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
92	C₂²×C₄×C₁₉	C₂×Q₈	1	1	yes	characteristic
93	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
94	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
95	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
96	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
97	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
98	C₂²×C₄×C₁₉	#41	1	1	yes	characteristic
99	C₂²×Dic₁₉	—	2	2	no	—
100	C₂²×Dic₁₉	—	2	2	no	—
101	C₂²×Dic₁₉	—	2	2	no	—
102	C₂²×Dic₁₉	—	2	2	no	—
103	C₂²×Dic₁₉	—	2	2	no	—
104	C₂²×Dic₁₉	—	2	2	no	—
105	C₂²×Dic₁₉	—	4	4	no	—
106	C₂²×Dic₁₉	—	4	4	no	—
107	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
108	M₁₆×C₁₉	—	2	2	no	—
109	M₁₆×C₁₉	—	2	2	no	—
110	M₁₆×C₁₉	—	4	1	no	—
111	M₁₆×C₁₉	—	4	1	no	—
112	C₂×C₈×C₁₉	—	2	2	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₄⋊C₄×C₁₉	—	2	2	no	—
116	C₄⋊C₄×C₁₉	C₄²	1	4	yes	—
117	C₂²⋊C₄×C₁₉	—	2	2	no	—
118	C₂²⋊C₄×C₁₉	—	2	2	no	—
119	C₄²×C₁₉	—	2	2	no	—
120	C₄²×C₁₉	—	2	2	no	—
121	C₄²×C₁₉	—	2	2	no	—
122	C₄²×C₁₉	—	2	2	no	—
123	C₄²×C₁₉	—	2	2	no	—
124	C₄²×C₁₉	C₄⋊C₄	1	4	yes	complemented
125	C₂²⋊Dic₁₉	—	4	1	no	—
126	C₂²⋊Dic₁₉	—	4	1	no	—
127	C₄⋊Dic₁₉	—	2	2	no	—
128	C₄⋊Dic₁₉	—	2	2	no	—
129	C₄⋊Dic₁₉	—	4	8	no	—
130	C₄×Dic₁₉	—	2	2	no	—
131	C₄×Dic₁₉	—	2	2	no	—
132	C₄×Dic₁₉	—	2	2	no	—
133	C₄×Dic₁₉	—	2	2	no	—
134	C₄×Dic₁₉	—	2	2	no	—
135	C₄×Dic₁₉	—	2	2	no	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	4	1	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	complemented
140	#64520	—	2	2	no	—
141	#64520	—	2	2	no	—
142	#64520	—	4	1	no	—
143	#64520	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	2	2	no	—
145	C₂×C₁₉⋊C₈	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	#10879	—	19	1	no	maximal, Sylow
148	C₂³×C₁₉	—	2	4	no	—
149	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
151	C₂³×C₁₉	C₄×D₄	1	1	yes	characteristic
152	C₂³×C₁₉	#120	1	1	yes	characteristic
153	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
154	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₁₉	#123	1	1	yes	characteristic
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	2	4	no	—
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	4	no	—
160	C₂×C₄×C₁₉	—	4	4	no	—
161	C₂×C₄×C₁₉	—	4	4	no	—
162	C₂×C₄×C₁₉	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
181	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
186	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
187	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
189	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
190	C₂×Dic₁₉	—	2	4	no	—
191	C₂×Dic₁₉	—	2	4	no	—
192	C₂×Dic₁₉	—	2	4	no	—
193	C₂×Dic₁₉	—	2	4	no	—
194	C₂×Dic₁₉	—	4	4	no	—
195	C₂×Dic₁₉	—	4	4	no	—
196	C₂×Dic₁₉	—	4	4	no	—
197	C₂×Dic₁₉	—	4	4	no	—
198	C₂×Dic₁₉	—	4	4	no	—
199	C₂×Dic₁₉	—	4	2	no	—
200	C₂×Dic₁₉	—	4	4	no	—
201	C₈×C₁₉	—	4	2	no	—
202	C₁₉⋊C₈	—	4	2	no	—
203	#2296	—	19	1	no	—
204	C₂×#376	—	19	1	no	—
205	C₂×#339	—	19	1	no	—
206	C₂×#339	—	19	1	no	—
207	C₂×#339	—	19	1	no	—
208	C₂×#339	D₁₉	1	1	yes	characteristic
209	#1728	—	19	1	no	—
210	C₂²×C₁₉	—	2	2	no	—
211	C₂²×C₁₉	—	2	2	no	—
212	C₂²×C₁₉	—	2	2	no	—
213	C₂²×C₁₉	—	2	2	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
217	C₂²×C₁₉	#385	1	1	yes	characteristic
218	C₂²×C₁₉	#385	1	1	yes	characteristic
219	C₂²×C₁₉	#386	1	1	yes	characteristic
220	C₂²×C₁₉	#387	1	1	yes	characteristic
221	C₂²×C₁₉	#387	1	1	yes	characteristic
222	C₂²×C₁₉	#391	1	1	yes	characteristic
223	C₂²×C₁₉	#421	1	4	yes	—
224	C₄×C₁₉	—	4	4	no	—
225	C₄×C₁₉	—	4	4	no	—
226	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
227	C₄×C₁₉	C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₄×C₁₉	#387	1	1	yes	characteristic
229	C₄×C₁₉	#387	1	1	yes	characteristic
230	C₄×C₁₉	#388	1	1	yes	characteristic
231	C₄×C₁₉	#388	1	1	yes	characteristic
232	C₄×C₁₉	#389	1	1	yes	characteristic
233	C₄×C₁₉	#389	1	1	yes	characteristic
234	Dic₁₉	—	4	4	no	—
235	Dic₁₉	—	4	4	no	—
236	Dic₁₉	—	8	2	no	—
237	C₂²×M₁₆	—	19	1	no	—
238	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
239	C₂×#117	—	19	1	no	—
240	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
241	C₂²×C₄²	—	19	1	no	—
242	C₂²×C₄²	—	19	1	no	—
243	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
244	#389	—	19	4	no	—
245	#385	—	38	2	no	—
246	C₄×C₄⋊C₄	—	38	2	no	—
247	#376	—	38	2	no	—
248	#376	—	38	2	no	—
249	C₂×#95	—	38	2	no	—
250	#339	—	19	4	no	—
251	#339	—	38	2	no	—
252	#339	—	38	2	no	—
253	#339	Dic₁₉	1	4	yes	complemented
254	#336	—	38	2	no	—
255	C₂×C₁₉	—	2	1	no	—
256	C₂×C₁₉	—	2	1	no	—
257	C₂×C₁₉	—	2	1	no	—
258	C₂×C₁₉	—	2	1	no	—
259	C₂×C₁₉	#1436	1	1	yes	characteristic
260	C₂×C₁₉	#1759	1	2	yes	—
261	C₂×C₁₉	#1897	1	2	yes	—
262	C₂×C₁₉	#1995	1	2	yes	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	—	19	2	no	—
265	C₂³×C₄	—	38	1	no	—
266	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
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	—	38	1	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	C₂×Dic₁₉	1	2	yes	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	38	1	no	—
281	#117	—	2	1	no	—
282	#117	—	2	1	no	—
283	#117	—	38	1	no	—
284	#117	—	38	1	no	—
285	#117	—	38	1	no	—
286	#117	—	38	1	no	—
287	#117	C₄×D₁₉	1	2	yes	—
288	#117	C₂×Dic₁₉	1	2	yes	—
289	C₂×C₄⋊C₄	—	19	2	no	—
290	C₂×C₄⋊C₄	—	38	4	no	—
291	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	38	1	no	—
294	C₂×C₄²	—	2	1	no	—
295	C₂×C₄²	—	2	1	no	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	19	2	no	—
299	C₂×C₄²	—	19	2	no	—
300	C₂×C₄²	—	19	2	no	—
301	C₂×C₄²	—	19	2	no	—
302	C₂×C₄²	—	19	2	no	—
303	C₂×C₄²	—	38	1	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	C₂×C₄²	—	38	1	no	—
309	C₂×C₄²	—	38	1	no	—
310	C₂×C₄²	—	38	1	no	—
311	C₂×C₄²	Dic₃₈	1	2	yes	—
312	C₂×C₄²	D₇₆	1	2	yes	—
313	C₂×C₄²	C₂×Dic₁₉	1	2	yes	—
314	#95	—	38	4	no	—
315	#95	—	38	8	no	—
316	C₁₉	#10879	1	1	yes	characteristic, complemented, Sylow
317	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	4	4	no	—
323	C₂²×C₄	—	19	4	no	—
324	C₂²×C₄	—	38	2	no	—
325	C₂²×C₄	—	38	2	no	—
326	C₂²×C₄	—	38	2	no	—
327	C₂²×C₄	—	38	2	no	—
328	C₂²×C₄	—	38	2	no	—
329	C₂²×C₄	—	38	2	no	—
330	C₂²×C₄	—	76	4	no	—
331	C₂²×C₄	—	76	4	no	—
332	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
333	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
335	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
336	C₂²×C₄	#64541	1	1	yes	characteristic
337	C₂²×C₄	#64541	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
340	C₂²×C₄	#64543	1	1	yes	characteristic
341	C₂²×C₄	#64543	1	1	yes	characteristic
342	C₂²×C₄	#64543	1	1	yes	characteristic
343	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
344	C₂²×C₄	#64545	1	1	yes	characteristic
345	C₂²×C₄	C₂²×Dic₁₉	1	1	yes	characteristic
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	1	no	—
349	M₁₆	—	4	1	no	—
350	M₁₆	—	38	2	no	—
351	M₁₆	—	38	2	no	—
352	M₁₆	—	76	1	no	—
353	M₁₆	—	76	1	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	4	1	no	—
356	C₂×C₈	—	4	1	no	—
357	C₂×C₈	—	38	2	no	—
358	C₂×C₈	—	76	1	no	—
359	C₂×C₈	—	76	1	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	38	2	no	—
362	C₄⋊C₄	—	38	2	no	—
363	C₄⋊C₄	—	76	8	no	—
364	C₄⋊C₄	C₄×Dic₁₉	1	4	yes	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	2	2	no	—
367	C₂²⋊C₄	—	76	1	no	—
368	C₂²⋊C₄	—	76	1	no	—
369	C₄²	—	2	2	no	—
370	C₄²	—	2	2	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	2	2	no	—
373	C₄²	—	2	2	no	—
374	C₄²	—	19	4	no	—
375	C₄²	—	38	2	no	—
376	C₄²	—	38	2	no	—
377	C₄²	—	38	2	no	—
378	C₄²	—	38	2	no	—
379	C₄²	—	38	2	no	—
380	C₄²	—	38	2	no	—
381	C₄²	—	38	2	no	—
382	C₄²	—	76	1	no	—
383	C₄²	—	76	1	no	—
384	C₄²	C₄⋊Dic₁₉	1	4	yes	complemented
385	C₂³	—	2	4	no	—
386	C₂³	#10597324	1	1	yes	characteristic
387	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
388	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
389	C₂³	#10597328	1	1	yes	characteristic
390	C₂³	#10597340	1	1	yes	characteristic
391	C₂³	#10597342	1	1	yes	characteristic
392	C₂³	D₄×Dic₁₉	1	1	yes	characteristic
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	4	no	—
395	C₂×C₄	—	4	4	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	38	4	no	—
400	C₂×C₄	—	38	4	no	—
401	C₂×C₄	—	38	4	no	—
402	C₂×C₄	—	38	4	no	—
403	C₂×C₄	—	76	4	no	—
404	C₂×C₄	—	76	4	no	—
405	C₂×C₄	—	76	4	no	—
406	C₂×C₄	—	76	4	no	—
407	C₂×C₄	—	76	4	no	—
408	C₂×C₄	—	76	4	no	—
409	C₂×C₄	—	76	2	no	—
410	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
411	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
412	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
413	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
414	C₂×C₄	#10597323	1	1	yes	characteristic
415	C₂×C₄	#10597324	1	1	yes	characteristic
416	C₂×C₄	#10597325	1	1	yes	characteristic
417	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
418	C₂×C₄	#10597329	1	1	yes	characteristic
419	C₂×C₄	#10597330	1	1	yes	characteristic
420	C₂×C₄	#10597331	1	1	yes	characteristic
421	C₂×C₄	#10597332	1	1	yes	characteristic
422	C₂×C₄	#10597333	1	1	yes	characteristic
423	C₂×C₄	#10597334	1	1	yes	characteristic
424	C₂×C₄	#10597335	1	1	yes	characteristic
425	C₂×C₄	#10597336	1	1	yes	characteristic
426	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
427	C₂×C₄	#10597338	1	1	yes	characteristic
428	C₂×C₄	#10597339	1	1	yes	characteristic
429	C₂×C₄	#10597341	1	1	yes	characteristic
430	C₂×C₄	#10597343	1	1	yes	characteristic
431	C₂×C₄	#10597344	1	1	yes	characteristic
432	C₂×C₄	C₂×C₄×Dic₁₉	1	1	yes	characteristic
433	C₂×C₄	C₂×C₄⋊Dic₁₉	1	1	yes	characteristic
434	C₂×C₄	#10597372	1	1	yes	characteristic
435	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
436	C₂×C₄	D₄×Dic₁₉	1	1	yes	characteristic
437	C₂×C₄	Q₈×Dic₁₉	1	1	yes	characteristic
438	C₈	—	4	2	no	—
439	C₈	—	76	2	no	—
440	C₂²	—	2	2	no	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	2	no	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	2	no	—
445	C₂²	—	2	2	no	—
446	C₂²	C₂²⋊C₄×Dic₁₉	1	1	yes	characteristic
447	C₂²	#11926418	1	1	yes	characteristic
448	C₂²	#11926419	1	1	yes	characteristic
449	C₂²	#11926422	1	1	yes	characteristic
450	C₂²	#11926430	1	1	yes	characteristic
451	C₂²	#11926431	1	1	yes	characteristic
452	C₂²	#11926448	1	1	yes	characteristic
453	C₂²	#11926559	1	4	yes	—
454	C₄	—	4	4	no	—
455	C₄	—	4	4	no	—
456	C₄	—	76	4	no	—
457	C₄	—	76	4	no	—
458	C₄	—	152	2	no	—
459	C₄	C₄×C₄⋊Dic₁₉	1	1	yes	characteristic
460	C₄	C₄⋊C₄×Dic₁₉	1	1	yes	characteristic
461	C₄	#11926427	1	1	yes	characteristic
462	C₄	#11926429	1	1	yes	characteristic
463	C₄	#11926436	1	1	yes	characteristic
464	C₄	#11926437	1	1	yes	characteristic
465	C₄	#11926441	1	1	yes	characteristic
466	C₄	#11926443	1	1	yes	characteristic
467	C₂	—	2	1	no	—
468	C₂	—	2	1	no	—
469	C₂	—	2	1	no	—
470	C₂	—	2	1	no	—
471	C₂	#14561869	1	1	yes	characteristic
472	C₂	#14563447	1	2	yes	—
473	C₂	#14564082	1	2	yes	—
474	C₂	#14564614	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₄×D₁₉
commutator	C₂×C₄×C₁₉	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₂×C₁₉×#339	C₂
socle	C₂³×C₁₉	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	C₂×#339	D₁₉
hypocenter	C₁₉	#10879
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂×#339

Complements

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

N	H ≅ G/N	type
12. #11926443	C₄	semidirect
20. #11926303	C₄	semidirect
25. C₁₉×#339	C₄	semidirect
124. C₄²×C₁₉	C₄⋊C₄	semidirect
139. C₄×Dic₁₉	C₄⋊C₄	semidirect
253. #339	Dic₁₉	semidirect
316. C₁₉	#10879	semidirect
384. C₄²	C₄⋊Dic₁₉	semidirect

Maximal subgroups

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

subgroup	index
#14566119	2
C₂×#11926390	2
C₂×#11926305	2
C₂×#11926304	2
C₂×#11926303	2
#14563328	2
C₂×C₁₉×#339	2
#10879	19