Subgroups — #18090545

Order 4864.

706 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14572198	C₂	1	1	yes	maximal, characteristic
2	#14566118	C₂	1	1	yes	maximal, characteristic
3	C₂×#11926316	C₂	1	1	yes	maximal, characteristic
4	C₂×#11926315	C₂	1	1	yes	maximal, characteristic
5	#14563373	C₂	1	1	yes	maximal, characteristic
6	#14563329	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1728	C₂	1	1	yes	maximal, characteristic
8	C₂²×#64520	C₂²	1	1	yes	characteristic
9	C₂²×#64520	C₂²	1	1	yes	characteristic
10	C₂×#10597372	C₂²	1	1	yes	characteristic
11	C₂×#10597372	C₂²	1	1	yes	characteristic
12	#11926572	—	2	2	no	—
13	#11926570	—	2	2	no	—
14	#11926567	—	2	2	no	—
15	#11926442	—	2	2	no	—
16	#11926417	C₄	1	4	yes	—
17	C₄×Dic₁₉⋊C₄	—	2	2	no	—
18	#11926316	—	2	2	no	—
19	#11926315	—	2	2	no	—
20	#11926312	—	2	2	no	—
21	#11926299	—	2	2	no	—
22	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₁₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
25	C₁₉×#336	—	2	2	no	—
26	C₂³×C₄×C₁₉	C₂×C₄	1	2	yes	—
27	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
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	—	2	1	no	—
39	C₂×M₁₆×C₁₉	Q₈	1	2	yes	—
40	C₂²×C₈×C₁₉	—	2	1	no	—
41	C₂²×C₈×C₁₉	D₄	1	2	yes	—
42	C₂×C₄²×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	—	2	1	no	—
48	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊Dic₁₉	C₂×C₄	1	2	yes	—
50	#10597372	—	2	1	no	—
51	#10597372	—	2	1	no	—
52	#10597372	—	2	1	no	—
53	#10597372	—	2	1	no	—
54	#10597372	—	2	1	no	—
55	#10597372	—	2	1	no	—
56	#10597372	D₄	1	2	yes	—
57	#10597372	Q₈	1	2	yes	—
58	C₂×C₄⋊Dic₁₉	—	2	1	no	—
59	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
60	C₂×Dic₁₉⋊C₄	—	2	4	no	—
61	C₂×C₄×Dic₁₉	—	2	1	no	—
62	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
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	—	2	1	no	—
71	C₂×#64520	—	2	1	no	—
72	C₂×#64520	—	2	1	no	—
73	C₂×#64520	—	2	1	no	—
74	C₂×#64520	Q₈	1	2	yes	—
75	C₂²×C₁₉⋊C₈	—	2	1	no	—
76	C₂²×C₁₉⋊C₈	D₄	1	2	yes	—
77	C₁₉⋊#95	—	2	4	no	—
78	Dic₁₉⋊C₈	—	2	8	no	—
79	C₂⁴×C₁₉	C₂²×C₄	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	—	4	4	no	—
84	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₉	C₂×D₄	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×Q₈	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	#41	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×Dic₁₉	—	2	2	no	—
99	C₂²×Dic₁₉	C₂²⋊C₄	1	4	yes	—
100	M₁₆×C₁₉	—	2	2	no	—
101	M₁₆×C₁₉	—	2	2	no	—
102	M₁₆×C₁₉	—	4	1	no	—
103	M₁₆×C₁₉	—	4	1	no	—
104	M₁₆×C₁₉	—	4	1	no	—
105	M₁₆×C₁₉	—	4	1	no	—
106	M₁₆×C₁₉	—	4	1	no	—
107	M₁₆×C₁₉	—	4	1	no	—
108	C₂×C₈×C₁₉	—	2	2	no	—
109	C₂×C₈×C₁₉	—	2	2	no	—
110	C₂×C₈×C₁₉	—	2	2	no	—
111	C₂×C₈×C₁₉	—	2	2	no	—
112	C₂×C₈×C₁₉	—	4	1	no	—
113	C₂×C₈×C₁₉	—	4	1	no	—
114	C₄²×C₁₉	—	4	1	no	—
115	C₄²×C₁₉	—	4	1	no	—
116	C₄²×C₁₉	—	4	1	no	—
117	C₄²×C₁₉	—	4	1	no	—
118	C₂²⋊Dic₁₉	—	2	2	no	—
119	C₂²⋊Dic₁₉	—	2	2	no	—
120	C₂²⋊Dic₁₉	—	2	2	no	—
121	C₂²⋊Dic₁₉	C₄⋊C₄	1	4	yes	—
122	C₄⋊Dic₁₉	—	2	2	no	—
123	C₄⋊Dic₁₉	—	2	2	no	—
124	C₄⋊Dic₁₉	—	2	2	no	—
125	C₄⋊Dic₁₉	—	2	2	no	—
126	Dic₁₉⋊C₄	—	4	8	no	—
127	C₄×Dic₁₉	—	2	2	no	—
128	C₄×Dic₁₉	—	2	2	no	—
129	C₄×Dic₁₉	—	2	2	no	—
130	C₄×Dic₁₉	—	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	#64520	—	4	1	no	—
138	#64520	—	4	1	no	—
139	C₂×C₁₉⋊C₈	—	2	2	no	—
140	C₂×C₁₉⋊C₈	—	2	2	no	—
141	C₂×C₁₉⋊C₈	—	2	2	no	—
142	C₂×C₁₉⋊C₈	—	2	2	no	—
143	C₂×C₁₉⋊C₈	—	4	1	no	—
144	C₂×C₁₉⋊C₈	—	4	1	no	—
145	#11223	—	19	1	no	maximal, Sylow
146	C₂³×C₁₉	—	4	2	no	—
147	C₂³×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂³×C₁₉	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂³×C₁₉	#117	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	C₄×Q₈	1	1	yes	characteristic
153	C₂³×C₁₉	C₄×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₁₉	—	2	4	no	—
155	C₂×C₄×C₁₉	—	2	4	no	—
156	C₂×C₄×C₁₉	—	2	4	no	—
157	C₂×C₄×C₁₉	—	4	2	no	—
158	C₂×C₄×C₁₉	—	4	2	no	—
159	C₂×C₄×C₁₉	—	4	2	no	—
160	C₂×C₄×C₁₉	—	4	2	no	—
161	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
162	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
163	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
164	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
165	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
166	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
167	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
168	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
169	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
170	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
171	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
172	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
173	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
174	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
175	C₂×C₄×C₁₉	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
177	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
178	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#124	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
181	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
182	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#125	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
185	C₂×C₄×C₁₉	#126	1	1	yes	characteristic
186	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
187	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
188	C₂×C₄×C₁₉	C₄⋊Q₈	1	1	yes	characteristic
189	C₂×Dic₁₉	—	2	4	no	—
190	C₂×Dic₁₉	—	2	4	no	—
191	C₂×Dic₁₉	—	4	4	no	—
192	C₂×Dic₁₉	—	4	4	no	—
193	C₈×C₁₉	—	4	2	no	—
194	C₈×C₁₉	—	4	2	no	—
195	C₁₉⋊C₈	—	4	2	no	—
196	C₁₉⋊C₈	—	4	2	no	—
197	#2905	—	19	1	no	—
198	#2296	—	19	1	no	—
199	C₂×#344	—	19	1	no	—
200	C₂×#344	—	19	1	no	—
201	#1742	—	19	1	no	—
202	#1728	—	19	1	no	—
203	#1728	D₁₉	1	1	yes	characteristic
204	C₂²×C₁₉	—	2	2	no	—
205	C₂²×C₁₉	—	2	2	no	—
206	C₂²×C₁₉	—	2	2	no	—
207	C₂²×C₁₉	—	4	1	no	—
208	C₂²×C₁₉	—	4	1	no	—
209	C₂²×C₁₉	—	4	1	no	—
210	C₂²×C₁₉	—	4	1	no	—
211	C₂²×C₁₉	#380	1	1	yes	characteristic
212	C₂²×C₁₉	#386	1	1	yes	characteristic
213	C₂²×C₁₉	#387	1	1	yes	characteristic
214	C₂²×C₁₉	#387	1	1	yes	characteristic
215	C₂²×C₁₉	#389	1	1	yes	characteristic
216	C₂²×C₁₉	#389	1	1	yes	characteristic
217	C₂²×C₁₉	#391	1	1	yes	characteristic
218	C₄×C₁₉	—	4	4	no	—
219	C₄×C₁₉	#394	1	1	yes	characteristic
220	C₄×C₁₉	#395	1	1	yes	characteristic
221	C₄×C₁₉	#396	1	1	yes	characteristic
222	C₄×C₁₉	#396	1	1	yes	characteristic
223	C₄×C₁₉	#398	1	1	yes	characteristic
224	C₄×C₁₉	#398	1	1	yes	characteristic
225	C₄×C₁₉	#398	1	1	yes	characteristic
226	C₄×C₁₉	#400	1	1	yes	characteristic
227	Dic₁₉	—	4	4	no	—
228	Dic₁₉	—	4	4	no	—
229	C₂²×M₁₆	—	19	1	no	—
230	C₂²×M₁₆	—	19	1	no	—
231	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
232	C₂²×M₁₆	C₂×D₁₉	1	1	yes	characteristic
233	C₂×#117	—	19	1	no	—
234	C₂×#117	—	19	1	no	—
235	C₂²×C₄²	C₂×D₁₉	1	1	yes	characteristic
236	#424	—	38	2	no	—
237	#424	—	38	2	no	—
238	#423	—	38	2	no	—
239	#389	—	38	2	no	—
240	#385	—	19	4	no	—
241	C₄×C₄⋊C₄	—	38	2	no	—
242	#344	—	38	2	no	—
243	#344	—	38	2	no	—
244	#343	—	38	2	no	—
245	#336	—	2	2	no	—
246	#336	—	38	2	no	—
247	C₂×C₁₉	—	2	1	no	—
248	C₂×C₁₉	—	2	1	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	#1441	1	1	yes	characteristic
254	C₂×C₁₉	#1891	1	2	yes	—
255	C₂³×C₄	C₄×D₁₉	1	2	yes	—
256	C₂³×C₄	C₂²×D₁₉	1	1	yes	characteristic
257	C₂×M₁₆	—	2	1	no	—
258	C₂×M₁₆	—	2	1	no	—
259	C₂×M₁₆	—	2	1	no	—
260	C₂×M₁₆	—	2	1	no	—
261	C₂×M₁₆	—	2	1	no	—
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	—	19	2	no	—
269	C₂×M₁₆	—	38	1	no	—
270	C₂×M₁₆	—	38	1	no	—
271	C₂×M₁₆	—	38	1	no	—
272	C₂×M₁₆	—	38	1	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	—	38	1	no	—
279	C₂×M₁₆	—	38	1	no	—
280	C₂×M₁₆	Dic₃₈	1	2	yes	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	19	2	no	—
283	C₂²×C₈	—	38	1	no	—
284	C₂²×C₈	C₂²⋊D₁₉	1	2	yes	—
285	#117	—	19	2	no	—
286	#117	—	19	2	no	—
287	#117	—	38	1	no	—
288	#117	—	38	1	no	—
289	#117	—	38	1	no	—
290	#117	—	38	1	no	—
291	#117	—	38	1	no	—
292	#117	—	38	1	no	—
293	C₂×C₄⋊C₄	—	19	2	no	—
294	C₂×C₄⋊C₄	—	38	1	no	—
295	C₂×C₄⋊C₄	—	38	4	no	—
296	C₂×C₂²⋊C₄	—	19	2	no	—
297	C₂×C₂²⋊C₄	—	19	2	no	—
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	—	2	1	no	—
300	C₂×C₄²	—	2	1	no	—
301	C₂×C₄²	—	2	1	no	—
302	C₂×C₄²	—	2	1	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	19	2	no	—
305	C₂×C₄²	—	38	1	no	—
306	C₄⋊C₈	—	38	8	no	—
307	#95	—	38	4	no	—
308	C₁₉	#11223	1	1	yes	characteristic, complemented, Sylow
309	C₂⁴	C₂×C₄×D₁₉	1	1	yes	characteristic
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	4	4	no	—
314	C₂²×C₄	—	19	4	no	—
315	C₂²×C₄	—	38	2	no	—
316	C₂²×C₄	C₂×Dic₃₈	1	1	yes	characteristic
317	C₂²×C₄	#64541	1	1	yes	characteristic
318	C₂²×C₄	#64541	1	1	yes	characteristic
319	C₂²×C₄	#64541	1	1	yes	characteristic
320	C₂²×C₄	#64541	1	1	yes	characteristic
321	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
322	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
323	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
325	C₂²×C₄	#64543	1	1	yes	characteristic
326	C₂²×C₄	#64543	1	1	yes	characteristic
327	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
328	C₂²×C₄	Q₈×D₁₉	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	2	no	—
332	M₁₆	—	4	1	no	—
333	M₁₆	—	4	1	no	—
334	M₁₆	—	4	1	no	—
335	M₁₆	—	4	1	no	—
336	M₁₆	—	4	1	no	—
337	M₁₆	—	4	1	no	—
338	M₁₆	—	38	2	no	—
339	M₁₆	—	38	2	no	—
340	M₁₆	—	76	1	no	—
341	M₁₆	—	76	1	no	—
342	M₁₆	—	76	1	no	—
343	M₁₆	—	76	1	no	—
344	M₁₆	—	76	1	no	—
345	M₁₆	—	76	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	4	1	no	—
351	C₂×C₈	—	4	1	no	—
352	C₂×C₈	—	38	2	no	—
353	C₂×C₈	—	38	2	no	—
354	C₂×C₈	—	38	2	no	—
355	C₂×C₈	—	38	2	no	—
356	C₂×C₈	—	76	1	no	—
357	C₂×C₈	—	76	1	no	—
358	C₄⋊C₄	—	38	2	no	—
359	C₄⋊C₄	—	38	2	no	—
360	C₄⋊C₄	—	38	2	no	—
361	C₄⋊C₄	—	38	2	no	—
362	C₄⋊C₄	—	76	8	no	—
363	C₂²⋊C₄	—	19	4	no	—
364	C₂²⋊C₄	—	38	2	no	—
365	C₂²⋊C₄	—	38	2	no	—
366	C₂²⋊C₄	—	38	2	no	—
367	C₄²	—	4	1	no	—
368	C₄²	—	4	1	no	—
369	C₄²	—	4	1	no	—
370	C₄²	—	4	1	no	—
371	C₄²	—	38	2	no	—
372	C₄²	—	38	2	no	—
373	C₄²	—	38	2	no	—
374	C₄²	—	38	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	C₄×Dic₃₈	1	1	yes	characteristic
377	C₂³	#10597318	1	1	yes	characteristic
378	C₂³	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
379	C₂³	(C₂²⋊D₁₉)⋊C₄	1	1	yes	characteristic
380	C₂³	#10597333	1	1	yes	characteristic
381	C₂³	C₄⋊C₄×D₁₉	1	1	yes	characteristic
382	C₂³	C₄×C₂²⋊D₁₉	1	1	yes	characteristic
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	4	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	2	no	—
390	C₂×C₄	—	38	4	no	—
391	C₂×C₄	—	38	4	no	—
392	C₂×C₄	—	76	4	no	—
393	C₂×C₄	—	76	4	no	—
394	C₂×C₄	#10597316	1	1	yes	characteristic
395	C₂×C₄	#10597322	1	1	yes	characteristic
396	C₂×C₄	#10597324	1	1	yes	characteristic
397	C₂×C₄	#10597324	1	1	yes	characteristic
398	C₂×C₄	#10597325	1	1	yes	characteristic
399	C₂×C₄	#10597329	1	1	yes	characteristic
400	C₂×C₄	#10597329	1	1	yes	characteristic
401	C₂×C₄	#10597330	1	1	yes	characteristic
402	C₂×C₄	#10597330	1	1	yes	characteristic
403	C₂×C₄	#10597330	1	1	yes	characteristic
404	C₂×C₄	#10597330	1	1	yes	characteristic
405	C₂×C₄	#10597331	1	1	yes	characteristic
406	C₂×C₄	#10597334	1	1	yes	characteristic
407	C₂×C₄	#10597334	1	1	yes	characteristic
408	C₂×C₄	#10597335	1	1	yes	characteristic
409	C₂×C₄	#10597335	1	1	yes	characteristic
410	C₂×C₄	#10597335	1	1	yes	characteristic
411	C₂×C₄	#10597342	1	1	yes	characteristic
412	C₂×C₄	#10597342	1	1	yes	characteristic
413	C₂×C₄	#10597342	1	1	yes	characteristic
414	C₂×C₄	#10597342	1	1	yes	characteristic
415	C₂×C₄	#10597342	1	1	yes	characteristic
416	C₂×C₄	#10597370	1	1	yes	characteristic
417	C₂×C₄	#10597375	1	1	yes	characteristic
418	C₂×C₄	#10597383	1	1	yes	characteristic
419	C₂×C₄	#10597384	1	1	yes	characteristic
420	C₂×C₄	#10597385	1	1	yes	characteristic
421	C₂×C₄	#10597390	1	1	yes	characteristic
422	C₈	—	4	2	no	—
423	C₈	—	4	2	no	—
424	C₈	—	76	2	no	—
425	C₈	—	76	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	1	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	#11926403	1	1	yes	characteristic
434	C₂²	#11926420	1	1	yes	characteristic
435	C₂²	#11926426	1	1	yes	characteristic
436	C₂²	#11926428	1	1	yes	characteristic
437	C₂²	#11926439	1	1	yes	characteristic
438	C₂²	#11926441	1	1	yes	characteristic
439	C₂²	#11926448	1	1	yes	characteristic
440	C₄	—	4	4	no	—
441	C₄	—	76	4	no	—
442	C₄	—	76	4	no	—
443	C₄	#11926459	1	1	yes	characteristic
444	C₄	#11926464	1	1	yes	characteristic
445	C₄	#11926467	1	1	yes	characteristic
446	C₄	#11926468	1	1	yes	characteristic
447	C₄	#11926475	1	1	yes	characteristic
448	C₄	#11926478	1	1	yes	characteristic
449	C₄	#11926478	1	1	yes	characteristic
450	C₄	#11926485	1	1	yes	characteristic
451	C₂	—	2	1	no	—
452	C₂	—	2	1	no	—
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	2	1	no	—
457	C₂	#14561886	1	1	yes	characteristic
458	C₂	#14564050	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#10597383
commutator, prime radical	C₂⁴×C₁₉	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₁₉
Fitting	C₁₉×#1728	C₂
socle	C₂²×C₁₉	#386
cosocle	C₂³×C₄×C₁₉	C₂³
hypercenter	#1728	D₁₉
hypocenter	C₁₉	#11223
LCS	G ▷ C₂⁴×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1728

Complements

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

N	H ≅ G/N	type
308. C₁₉	#11223	semidirect

Maximal subgroups

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

subgroup	index
#14572198	2
#14566118	2
C₂×#11926316	2
C₂×#11926315	2
#14563373	2
#14563329	2
C₁₉×#1728	2
#11223	19