Subgroups — #18090467

Order 4864.

762 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14566251	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926409	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926312	C₂	1	1	yes	maximal, characteristic
4	#14563354	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926305	C₂	1	1	yes	maximal, characteristic
6	C₂×#11926303	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1736	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	#11926442	—	2	2	no	—
13	#11926440	—	2	2	no	—
14	#11926409	—	2	2	no	—
15	#11926409	C₄	1	4	yes	complemented
16	#11926402	—	2	2	no	—
17	C₂×C₁₉⋊#95	—	2	2	no	—
18	#11926312	—	2	2	no	—
19	#11926306	—	2	2	no	—
20	#11926305	—	2	2	no	—
21	#11926303	—	2	2	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×C₁₉×#117	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#340	—	2	2	no	—
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	Q₈	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	—	2	1	no	—
40	C₁₉×#117	—	2	1	no	—
41	C₂×C₄⋊C₄×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	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊C₄×C₁₉	D₄	1	2	yes	—
48	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
49	C₂×C₄²×C₁₉	—	2	1	no	—
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	1	no	—
56	C₂×C₄⋊Dic₁₉	—	2	1	no	—
57	C₂×C₄⋊Dic₁₉	—	2	1	no	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
61	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
62	C₂×Dic₁₉⋊C₄	—	2	4	no	—
63	C₂×C₄×Dic₁₉	—	2	1	no	—
64	C₂×C₄×Dic₁₉	—	2	1	no	—
65	C₂×C₄×Dic₁₉	—	2	1	no	—
66	C₂×C₄×Dic₁₉	—	2	1	no	—
67	C₂×C₄×Dic₁₉	C₂×C₄	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	Q₈	1	2	yes	—
76	C₂²×C₁₉⋊C₈	—	2	1	no	—
77	C₁₉⋊#95	—	2	4	no	—
78	C₁₉⋊#95	—	2	8	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	—	4	4	no	—
83	C₂²×C₄×C₁₉	—	4	1	no	—
84	C₂²×C₄×C₁₉	—	4	1	no	—
85	C₂²×C₄×C₁₉	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₉	C₂×D₄	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×Q₈	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	2	no	—
106	C₂²×Dic₁₉	—	4	2	no	—
107	C₂²×Dic₁₉	—	4	4	no	—
108	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
109	M₁₆×C₁₉	—	2	2	no	—
110	M₁₆×C₁₉	—	2	2	no	—
111	M₁₆×C₁₉	—	4	1	no	—
112	M₁₆×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	2	2	no	—
114	C₂×C₈×C₁₉	—	4	1	no	—
115	C₂×C₈×C₁₉	—	4	1	no	—
116	C₄⋊C₄×C₁₉	—	2	2	no	—
117	C₄⋊C₄×C₁₉	—	2	2	no	—
118	C₄⋊C₄×C₁₉	—	2	2	no	—
119	C₄⋊C₄×C₁₉	—	2	2	no	—
120	C₄⋊C₄×C₁₉	—	4	1	no	—
121	C₄⋊C₄×C₁₉	—	4	1	no	—
122	C₂²⋊C₄×C₁₉	—	4	1	no	—
123	C₂²⋊C₄×C₁₉	—	4	1	no	—
124	C₄²×C₁₉	—	4	1	no	—
125	C₄²×C₁₉	—	4	1	no	—
126	C₂²⋊Dic₁₉	—	4	1	no	—
127	C₂²⋊Dic₁₉	—	4	1	no	—
128	C₄⋊Dic₁₉	—	2	2	no	—
129	C₄⋊Dic₁₉	—	2	2	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	Dic₁₉⋊C₄	—	8	4	no	—
135	C₄×Dic₁₉	—	2	2	no	—
136	C₄×Dic₁₉	—	2	2	no	—
137	C₄×Dic₁₉	—	2	2	no	—
138	C₄×Dic₁₉	—	4	1	no	—
139	C₄×Dic₁₉	—	4	1	no	—
140	C₄×Dic₁₉	C₄⋊C₄	1	4	yes	complemented
141	#64520	—	2	2	no	—
142	#64520	—	2	2	no	—
143	#64520	—	4	1	no	—
144	#64520	—	4	1	no	—
145	C₂×C₁₉⋊C₈	—	2	2	no	—
146	C₂×C₁₉⋊C₈	—	4	1	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	#11211	—	19	1	no	maximal, Sylow
149	C₂³×C₁₉	—	2	2	no	—
150	C₂³×C₁₉	—	2	2	no	—
151	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
152	C₂³×C₁₉	#120	1	1	yes	characteristic
153	C₂³×C₁₉	#121	1	1	yes	characteristic
154	C₂³×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
155	C₂³×C₁₉	#123	1	1	yes	characteristic
156	C₂³×C₁₉	#124	1	1	yes	characteristic
157	C₂³×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₁₉	—	4	4	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	—	4	2	no	—
162	C₂×C₄×C₁₉	—	4	2	no	—
163	C₂×C₄×C₁₉	—	8	2	no	—
164	C₂×C₄×C₁₉	—	8	2	no	—
165	C₂×C₄×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#117	1	1	yes	characteristic
167	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₄×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
175	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
179	C₂×C₄×C₁₉	C₂²⋊Q₈	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	C₂²⋊Q₈	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#123	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	#125	1	1	yes	characteristic
188	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
189	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
190	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
191	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
192	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
193	C₂×Dic₁₉	—	2	4	no	—
194	C₂×Dic₁₉	—	2	4	no	—
195	C₂×Dic₁₉	—	4	4	no	—
196	C₂×Dic₁₉	—	4	2	no	—
197	C₂×Dic₁₉	—	4	2	no	—
198	C₂×Dic₁₉	—	4	4	no	—
199	C₂×Dic₁₉	—	4	4	no	—
200	C₂×Dic₁₉	—	4	4	no	—
201	C₂×Dic₁₉	—	4	2	no	—
202	C₂×Dic₁₉	—	4	2	no	—
203	C₂×Dic₁₉	—	4	2	no	—
204	C₂×Dic₁₉	—	8	2	no	—
205	C₈×C₁₉	—	4	2	no	—
206	C₁₉⋊C₈	—	4	2	no	—
207	#2316	—	19	1	no	—
208	C₂×#382	—	19	1	no	—
209	C₂×#343	—	19	1	no	—
210	#1736	—	19	1	no	—
211	#1736	D₁₉	1	1	yes	characteristic
212	C₂×#339	—	19	1	no	—
213	C₂×#339	—	19	1	no	—
214	C₂²×C₁₉	—	2	2	no	—
215	C₂²×C₁₉	—	2	2	no	—
216	C₂²×C₁₉	—	2	1	no	—
217	C₂²×C₁₉	—	2	1	no	—
218	C₂²×C₁₉	—	2	1	no	—
219	C₂²×C₁₉	—	2	1	no	—
220	C₂²×C₁₉	—	2	2	no	—
221	C₂²×C₁₉	—	2	2	no	—
222	C₂²×C₁₉	#380	1	1	yes	characteristic
223	C₂²×C₁₉	#386	1	1	yes	characteristic
224	C₂²×C₁₉	#391	1	1	yes	characteristic
225	C₂²×C₁₉	#394	1	1	yes	characteristic
226	C₂²×C₁₉	#395	1	1	yes	characteristic
227	C₂²×C₁₉	#398	1	1	yes	characteristic
228	C₂²×C₁₉	#400	1	1	yes	characteristic
229	C₂²×C₁₉	#454	1	2	yes	—
230	C₂²×C₁₉	#455	1	2	yes	—
231	C₄×C₁₉	—	8	2	no	—
232	C₄×C₁₉	—	8	2	no	—
233	C₄×C₁₉	#387	1	1	yes	characteristic
234	C₄×C₁₉	#387	1	1	yes	characteristic
235	C₄×C₁₉	#389	1	1	yes	characteristic
236	C₄×C₁₉	#389	1	1	yes	characteristic
237	C₄×C₁₉	#396	1	1	yes	characteristic
238	C₄×C₁₉	#396	1	1	yes	characteristic
239	C₄×C₁₉	#398	1	1	yes	characteristic
240	C₄×C₁₉	#398	1	1	yes	characteristic
241	Dic₁₉	—	4	4	no	—
242	Dic₁₉	—	4	4	no	—
243	Dic₁₉	—	8	2	no	—
244	C₂²×M₁₆	—	19	1	no	—
245	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
246	C₂×#117	—	19	1	no	—
247	C₂×#117	C₂×D₁₉	1	1	yes	characteristic
248	C₂²×C₄⋊C₄	—	19	1	no	—
249	C₂²×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
250	C₂²×C₄²	—	19	1	no	—
251	#389	—	38	2	no	—
252	#389	—	38	2	no	—
253	#382	—	19	4	no	—
254	#382	—	38	2	no	—
255	#380	—	38	2	no	—
256	C₂×#95	—	38	2	no	—
257	#343	—	38	2	no	—
258	#340	—	2	2	no	—
259	#340	—	38	2	no	—
260	#339	—	38	2	no	—
261	#339	—	38	2	no	—
262	C₂×C₁₉	—	2	1	no	—
263	C₂×C₁₉	—	2	1	no	—
264	C₂×C₁₉	—	2	1	no	—
265	C₂×C₁₉	—	2	1	no	—
266	C₂×C₁₉	#1441	1	1	yes	characteristic
267	C₂×C₁₉	#1885	1	1	yes	characteristic
268	C₂×C₁₉	#1888	1	1	yes	characteristic
269	C₂×C₁₉	#2040	1	2	yes	—
270	C₂×C₁₉	#2061	1	2	yes	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	—	19	2	no	—
273	C₂³×C₄	—	38	1	no	—
274	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	2	1	no	—
277	C₂×M₁₆	—	2	1	no	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	1	no	—
280	C₂×M₁₆	—	19	2	no	—
281	C₂×M₁₆	—	38	1	no	—
282	C₂×M₁₆	—	38	1	no	—
283	C₂×M₁₆	—	38	1	no	—
284	C₂×M₁₆	—	38	1	no	—
285	C₂×M₁₆	—	38	1	no	—
286	C₂×M₁₆	Dic₃₈	1	2	yes	—
287	C₂²×C₈	—	2	1	no	—
288	C₂²×C₈	—	38	1	no	—
289	#117	—	2	1	no	—
290	#117	—	2	1	no	—
291	#117	—	2	1	no	—
292	#117	—	2	1	no	—
293	#117	—	38	1	no	—
294	#117	—	38	1	no	—
295	#117	—	38	1	no	—
296	#117	—	38	1	no	—
297	C₂×C₄⋊C₄	—	2	1	no	—
298	C₂×C₄⋊C₄	—	2	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	19	2	no	—
303	C₂×C₄⋊C₄	—	19	2	no	—
304	C₂×C₄⋊C₄	—	19	2	no	—
305	C₂×C₄⋊C₄	—	38	1	no	—
306	C₂×C₄⋊C₄	—	38	1	no	—
307	C₂×C₄⋊C₄	—	38	1	no	—
308	C₂×C₄⋊C₄	—	38	1	no	—
309	C₂×C₄⋊C₄	—	38	4	no	—
310	C₂×C₄⋊C₄	C₄×D₁₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂²⋊D₁₉	1	2	yes	—
312	C₂×C₂²⋊C₄	—	2	1	no	—
313	C₂×C₂²⋊C₄	—	38	1	no	—
314	C₂×C₄²	—	2	1	no	—
315	C₂×C₄²	—	19	2	no	—
316	C₂×C₄²	—	19	2	no	—
317	C₂×C₄²	—	19	2	no	—
318	C₂×C₄²	—	38	1	no	—
319	C₂×C₄²	—	38	1	no	—
320	C₂×C₄²	—	38	1	no	—
321	C₂×C₄²	—	38	1	no	—
322	#95	—	38	8	no	—
323	#95	—	38	4	no	—
324	C₁₉	#11211	1	1	yes	characteristic, complemented, Sylow
325	C₂⁴	D₄×D₁₉	1	1	yes	characteristic
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	4	4	no	—
329	C₂²×C₄	—	4	1	no	—
330	C₂²×C₄	—	4	1	no	—
331	C₂²×C₄	—	19	4	no	—
332	C₂²×C₄	—	38	2	no	—
333	C₂²×C₄	—	38	2	no	—
334	C₂²×C₄	—	38	2	no	—
335	C₂²×C₄	—	38	2	no	—
336	C₂²×C₄	—	38	2	no	—
337	C₂²×C₄	—	38	2	no	—
338	C₂²×C₄	—	76	2	no	—
339	C₂²×C₄	—	76	2	no	—
340	C₂²×C₄	—	76	4	no	—
341	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
342	C₂²×C₄	C₂×C₄×D₁₉	1	1	yes	characteristic
343	C₂²×C₄	#64541	1	1	yes	characteristic
344	C₂²×C₄	#64541	1	1	yes	characteristic
345	C₂²×C₄	#64541	1	1	yes	characteristic
346	C₂²×C₄	#64541	1	1	yes	characteristic
347	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
349	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
350	C₂²×C₄	#64543	1	1	yes	characteristic
351	C₂²×C₄	#64543	1	1	yes	characteristic
352	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
353	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
354	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	4	1	no	—
358	M₁₆	—	4	1	no	—
359	M₁₆	—	38	2	no	—
360	M₁₆	—	38	2	no	—
361	M₁₆	—	76	1	no	—
362	M₁₆	—	76	1	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	4	1	no	—
365	C₂×C₈	—	4	1	no	—
366	C₂×C₈	—	38	2	no	—
367	C₂×C₈	—	76	1	no	—
368	C₂×C₈	—	76	1	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	2	2	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	2	2	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	38	2	no	—
376	C₄⋊C₄	—	38	2	no	—
377	C₄⋊C₄	—	38	2	no	—
378	C₄⋊C₄	—	38	2	no	—
379	C₄⋊C₄	—	38	2	no	—
380	C₄⋊C₄	—	38	2	no	—
381	C₄⋊C₄	—	152	4	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	4	1	no	—
384	C₂²⋊C₄	—	76	1	no	—
385	C₂²⋊C₄	—	76	1	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	—	19	4	no	—
389	C₄²	—	38	2	no	—
390	C₄²	—	38	2	no	—
391	C₄²	—	38	2	no	—
392	C₄²	—	76	1	no	—
393	C₄²	—	76	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
397	C₂³	#10597329	1	1	yes	characteristic
398	C₂³	#10597330	1	1	yes	characteristic
399	C₂³	#10597331	1	1	yes	characteristic
400	C₂³	#10597334	1	1	yes	characteristic
401	C₂³	#10597342	1	1	yes	characteristic
402	C₂³	#10597383	1	1	yes	characteristic
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	8	2	no	—
409	C₂×C₄	—	8	2	no	—
410	C₂×C₄	—	38	4	no	—
411	C₂×C₄	—	38	4	no	—
412	C₂×C₄	—	76	4	no	—
413	C₂×C₄	—	76	2	no	—
414	C₂×C₄	—	76	2	no	—
415	C₂×C₄	—	76	4	no	—
416	C₂×C₄	—	76	4	no	—
417	C₂×C₄	—	76	4	no	—
418	C₂×C₄	—	76	2	no	—
419	C₂×C₄	—	76	2	no	—
420	C₂×C₄	—	76	2	no	—
421	C₂×C₄	—	152	2	no	—
422	C₂×C₄	C₄×Dic₃₈	1	1	yes	characteristic
423	C₂×C₄	#10597316	1	1	yes	characteristic
424	C₂×C₄	#10597318	1	1	yes	characteristic
425	C₂×C₄	#10597322	1	1	yes	characteristic
426	C₂×C₄	#10597324	1	1	yes	characteristic
427	C₂×C₄	#10597324	1	1	yes	characteristic
428	C₂×C₄	#10597325	1	1	yes	characteristic
429	C₂×C₄	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
430	C₂×C₄	#10597329	1	1	yes	characteristic
431	C₂×C₄	#10597330	1	1	yes	characteristic
432	C₂×C₄	#10597330	1	1	yes	characteristic
433	C₂×C₄	#10597330	1	1	yes	characteristic
434	C₂×C₄	#10597333	1	1	yes	characteristic
435	C₂×C₄	#10597334	1	1	yes	characteristic
436	C₂×C₄	#10597335	1	1	yes	characteristic
437	C₂×C₄	#10597335	1	1	yes	characteristic
438	C₂×C₄	#10597335	1	1	yes	characteristic
439	C₂×C₄	C₄⋊C₄×D₁₉	1	1	yes	characteristic
440	C₂×C₄	#10597342	1	1	yes	characteristic
441	C₂×C₄	#10597342	1	1	yes	characteristic
442	C₂×C₄	#10597342	1	1	yes	characteristic
443	C₂×C₄	#10597342	1	1	yes	characteristic
444	C₂×C₄	#10597370	1	1	yes	characteristic
445	C₂×C₄	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
446	C₂×C₄	#10597375	1	1	yes	characteristic
447	C₂×C₄	#10597384	1	1	yes	characteristic
448	C₂×C₄	#10597385	1	1	yes	characteristic
449	C₂×C₄	#10597390	1	1	yes	characteristic
450	C₈	—	4	2	no	—
451	C₈	—	76	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	1	no	—
455	C₂²	—	2	1	no	—
456	C₂²	—	2	1	no	—
457	C₂²	—	2	1	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	2	no	—
460	C₂²	#11926403	1	1	yes	characteristic
461	C₂²	#11926420	1	1	yes	characteristic
462	C₂²	#11926448	1	1	yes	characteristic
463	C₂²	#11926459	1	1	yes	characteristic
464	C₂²	#11926464	1	1	yes	characteristic
465	C₂²	#11926478	1	1	yes	characteristic
466	C₂²	#11926485	1	1	yes	characteristic
467	C₂²	#11926715	1	2	yes	—
468	C₂²	#11926720	1	2	yes	—
469	C₄	—	8	2	no	—
470	C₄	—	8	2	no	—
471	C₄	—	76	4	no	—
472	C₄	—	76	4	no	—
473	C₄	—	152	2	no	—
474	C₄	#11926426	1	1	yes	characteristic
475	C₄	#11926428	1	1	yes	characteristic
476	C₄	#11926439	1	1	yes	characteristic
477	C₄	#11926441	1	1	yes	characteristic
478	C₄	#11926467	1	1	yes	characteristic
479	C₄	#11926468	1	1	yes	characteristic
480	C₄	#11926475	1	1	yes	characteristic
481	C₄	#11926478	1	1	yes	characteristic
482	C₂	—	2	1	no	—
483	C₂	—	2	1	no	—
484	C₂	—	2	1	no	—
485	C₂	—	2	1	no	—
486	C₂	#14561886	1	1	yes	characteristic
487	C₂	#14564020	1	1	yes	characteristic
488	C₂	#14564035	1	1	yes	characteristic
489	C₂	#14564862	1	2	yes	—
490	C₂	#14564983	1	2	yes	—

	subgroup	G/H
center	C₂³	#10597383
commutator	C₂²×C₄×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1736	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂⁴×C₁₉	C₂×D₄
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1736	D₁₉
hypocenter	C₁₉	#11211
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1736

Complements

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

N	H ≅ G/N	type
15. #11926409	C₄	semidirect
140. C₄×Dic₁₉	C₄⋊C₄	semidirect
324. C₁₉	#11211	semidirect

Maximal subgroups

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

subgroup	index
#14566251	2
C₂×#11926409	2
C₂×#11926312	2
#14563354	2
C₂×#11926305	2
C₂×#11926303	2
C₁₉×#1736	2
#11211	19