Subgroups — #18084849

Order 4864.

676 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11926745	C₂	1	1	yes	maximal, characteristic
2	C₂×#11926744	C₂	1	1	yes	maximal, characteristic
3	#14569005	C₂	1	1	yes	maximal, characteristic, complemented
4	#14564441	C₂	1	1	yes	maximal, characteristic
5	C₂×#11926276	C₂	1	1	yes	maximal, characteristic, complemented
6	#14561519	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₉×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#64516	—	2	1	no	—
9	C₂²×#64527	—	2	1	no	—
10	C₂×#10597320	C₂²	1	1	yes	characteristic
11	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
12	#11926745	—	2	2	no	—
13	#11926745	—	2	2	no	—
14	#11926744	—	2	2	no	—
15	#11926744	—	2	2	no	—
16	C₂×C₄⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#10597278	—	2	1	no	—
18	C₂×#10597278	—	2	2	no	—
19	C₂×#10597266	—	2	1	no	—
20	#11926477	—	2	2	no	—
21	#11926451	—	2	1	no	—
22	#11926450	—	2	1	no	—
23	#11926442	—	2	1	no	—
24	#11926440	—	2	1	no	—
25	#11926414	C₂²	1	1	yes	characteristic
26	#11926276	—	2	2	no	—
27	C₂×C₄×Q₈×C₁₉	C₂²	1	1	yes	characteristic
28	C₂×C₁₉×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₁₉	C₂²	1	1	yes	characteristic
30	C₁₉×Q₈⋊C₈	—	2	2	no	—
31	C₂²×Q₈×C₁₉	D₄	1	1	yes	characteristic
32	C₂²×D₇₆	—	2	1	no	—
33	C₂²×D₇₆	—	2	1	no	—
34	C₂²×D₇₆	—	2	1	no	—
35	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
36	C₂²×C₈×C₁₉	—	2	1	no	—
37	C₂²×C₈×C₁₉	—	2	1	no	—
38	C₄×Q₈×C₁₉	—	2	1	no	—
39	C₄×Q₈×C₁₉	—	2	1	no	—
40	C₄×Q₈×C₁₉	—	2	1	no	—
41	C₄×Q₈×C₁₉	—	2	1	no	—
42	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
43	C₂×C₄⋊C₄×C₁₉	D₄	1	1	yes	characteristic
44	C₂×C₄²×C₁₉	—	2	1	no	—
45	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
46	C₂×#64527	—	2	4	no	—
47	C₂×#64527	—	4	2	no	—
48	C₂×#64527	—	4	2	no	—
49	C₂×C₄⋊Dic₁₉	—	2	1	no	—
50	C₂×C₄⋊Dic₁₉	—	2	1	no	—
51	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₁₉	D₄	1	2	yes	—
53	C₂×Dic₁₉⋊C₄	—	2	1	no	—
54	C₂×Dic₁₉⋊C₄	—	2	2	no	—
55	C₂×C₄×Dic₁₉	—	2	1	no	—
56	C₂²×C₁₉⋊C₈	—	2	1	no	—
57	C₂×#64516	—	2	4	no	—
58	C₂×#64516	—	4	2	no	—
59	C₂×#64516	—	4	2	no	—
60	#10597320	—	2	1	no	—
61	#10597320	—	2	1	no	—
62	#10597320	—	2	1	no	—
63	#10597320	D₄	1	2	yes	—
64	C₄×Dic₃₈	—	2	1	no	—
65	C₄×Dic₃₈	—	2	1	no	—
66	C₄×Dic₃₈	—	2	1	no	—
67	C₄×Dic₃₈	—	2	1	no	—
68	C₁₉×C₄⋊C₈	—	2	1	no	—
69	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
70	C₄×C₈×C₁₉	—	2	1	no	—
71	C₄×C₈×C₁₉	—	2	1	no	—
72	C₁₉⋊#95	—	2	2	no	—
73	C₁₉⋊#95	—	2	2	no	—
74	C₁₉⋊#95	—	2	2	no	—
75	#10597278	—	2	4	no	—
76	#10597278	—	4	4	no	—
77	#10597266	—	2	4	no	—
78	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
79	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
80	C₂³×D₁₉	—	4	1	no	—
81	C₂×Q₈×C₁₉	—	2	1	no	—
82	C₂×Q₈×C₁₉	—	2	1	no	—
83	C₂×Q₈×C₁₉	—	2	1	no	—
84	C₂×Q₈×C₁₉	—	2	1	no	—
85	C₂×Q₈×C₁₉	—	2	1	no	—
86	C₂×Q₈×C₁₉	SD₁₆	1	2	yes	complemented
87	C₂²×C₄×C₁₉	—	2	1	no	—
88	C₂²×C₄×C₁₉	—	2	1	no	—
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×D₄	1	1	yes	characteristic
92	C₂²×Dic₁₉	—	2	1	no	—
93	C₂²×Dic₁₉	—	2	2	no	—
94	C₂²×Dic₁₉	—	2	1	no	—
95	C₂×D₇₆	—	2	2	no	—
96	C₂×D₇₆	—	2	2	no	—
97	C₂×D₇₆	—	2	2	no	—
98	C₂×D₇₆	—	4	2	no	—
99	C₂×D₇₆	—	4	2	no	—
100	C₂×D₇₆	—	4	1	no	—
101	C₂×D₇₆	—	4	1	no	—
102	C₂×D₇₆	—	4	1	no	—
103	C₂×D₇₆	—	4	1	no	—
104	C₂×D₇₆	—	4	1	no	—
105	C₂×D₇₆	—	4	1	no	—
106	C₂×D₇₆	—	4	1	no	—
107	C₂×D₇₆	—	4	1	no	—
108	C₂×D₇₆	—	4	1	no	—
109	C₂×D₇₆	—	4	1	no	—
110	C₂×D₇₆	—	4	1	no	—
111	C₂×Dic₃₈	—	2	1	no	—
112	C₂×Dic₃₈	—	2	1	no	—
113	C₂×Dic₃₈	—	2	1	no	—
114	C₂×Dic₃₈	—	2	1	no	—
115	C₂×Dic₃₈	—	2	1	no	—
116	C₂×Dic₃₈	SD₁₆	1	2	yes	complemented
117	C₂×C₈×C₁₉	—	2	2	no	—
118	C₂×C₈×C₁₉	—	2	2	no	—
119	C₂×C₈×C₁₉	—	4	1	no	—
120	C₂×C₈×C₁₉	—	4	1	no	—
121	C₂×C₈×C₁₉	—	4	1	no	—
122	C₂×C₈×C₁₉	—	4	1	no	—
123	C₄⋊C₄×C₁₉	—	2	1	no	—
124	C₄⋊C₄×C₁₉	—	2	1	no	—
125	C₄⋊C₄×C₁₉	—	4	1	no	—
126	C₄⋊C₄×C₁₉	—	4	1	no	—
127	C₄²×C₁₉	—	4	1	no	—
128	C₄²×C₁₉	—	4	1	no	—
129	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₄²×C₁₉	#41	1	1	yes	characteristic
133	#64527	—	4	8	no	—
134	C₄⋊Dic₁₉	—	2	1	no	—
135	C₄⋊Dic₁₉	—	2	1	no	—
136	C₄⋊Dic₁₉	—	4	1	no	—
137	C₄⋊Dic₁₉	—	4	1	no	—
138	C₄⋊Dic₁₉	—	4	1	no	—
139	C₄⋊Dic₁₉	—	4	1	no	—
140	C₄⋊Dic₁₉	—	4	2	no	—
141	Dic₁₉⋊C₄	—	4	1	no	—
142	Dic₁₉⋊C₄	—	4	1	no	—
143	Dic₁₉⋊C₄	—	8	2	no	—
144	C₄×Dic₁₉	—	4	1	no	—
145	C₄×Dic₁₉	—	4	1	no	—
146	C₂×C₁₉⋊C₈	—	2	2	no	—
147	C₂×C₁₉⋊C₈	—	4	1	no	—
148	C₂×C₁₉⋊C₈	—	4	1	no	—
149	#64516	—	4	8	no	—
150	#10230	—	19	1	no	maximal, Sylow
151	C₂³×C₁₉	#120	1	1	yes	characteristic
152	C₂²×D₁₉	—	4	2	no	—
153	C₂²×D₁₉	—	8	1	no	—
154	C₂²×D₁₉	—	8	1	no	—
155	C₂²×D₁₉	—	8	1	no	—
156	C₂²×D₁₉	—	8	1	no	—
157	C₂²×D₁₉	—	8	1	no	—
158	C₂²×D₁₉	—	8	1	no	—
159	Q₈×C₁₉	—	2	2	no	—
160	Q₈×C₁₉	—	2	2	no	—
161	Q₈×C₁₉	—	4	1	no	—
162	Q₈×C₁₉	—	4	1	no	—
163	C₂×C₄×C₁₉	—	2	1	no	—
164	C₂×C₄×C₁₉	—	2	1	no	—
165	C₂×C₄×C₁₉	—	2	2	no	—
166	C₂×C₄×C₁₉	—	4	1	no	—
167	C₂×C₄×C₁₉	—	4	1	no	—
168	C₂×C₄×C₁₉	—	4	1	no	—
169	C₂×C₄×C₁₉	—	4	1	no	—
170	C₂×C₄×C₁₉	—	4	1	no	—
171	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
172	C₂×C₄×C₁₉	#120	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	#127	1	1	yes	characteristic
177	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
178	C₂×C₄×C₁₉	C₂×SD₁₆	1	1	yes	characteristic
179	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
180	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
181	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
182	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
184	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
185	C₂×Dic₁₉	—	2	2	no	—
186	C₂×Dic₁₉	—	4	1	no	—
187	C₂×Dic₁₉	—	4	1	no	—
188	C₂×Dic₁₉	—	4	1	no	—
189	C₂×Dic₁₉	—	4	2	no	—
190	C₂×Dic₁₉	—	4	2	no	—
191	C₂×Dic₁₉	—	4	1	no	—
192	C₂×Dic₁₉	—	4	2	no	—
193	C₂×Dic₁₉	—	4	1	no	—
194	D₇₆	—	4	4	no	—
195	D₇₆	—	4	2	no	—
196	D₇₆	—	4	2	no	—
197	D₇₆	—	4	2	no	—
198	D₇₆	—	4	2	no	—
199	D₇₆	—	8	2	no	—
200	D₇₆	—	8	1	no	—
201	D₇₆	—	8	1	no	—
202	D₇₆	—	8	1	no	—
203	D₇₆	—	8	1	no	—
204	Dic₃₈	—	2	2	no	—
205	Dic₃₈	—	2	2	no	—
206	Dic₃₈	—	4	1	no	—
207	Dic₃₈	—	4	1	no	—
208	C₈×C₁₉	—	4	2	no	—
209	C₈×C₁₉	—	4	2	no	—
210	C₁₉⋊C₈	—	4	2	no	—
211	C₂×#460	—	19	1	no	—
212	C₂×#460	—	19	1	no	—
213	#2582	—	19	1	no	—
214	#1957	—	19	1	no	—
215	C₂×Q₈⋊C₈	—	19	1	no	—
216	C₂×Q₈⋊C₈	D₁₉	1	1	yes	characteristic, complemented
217	#1296	—	19	1	no	—
218	C₂²×C₁₉	#392	1	1	yes	characteristic
219	C₂²×C₁₉	#448	1	1	yes	characteristic
220	C₂²×C₁₉	#448	1	1	yes	characteristic
221	C₂²×C₁₉	#449	1	1	yes	characteristic
222	C₂²×C₁₉	#449	1	1	yes	characteristic
223	C₂²×C₁₉	#453	1	1	yes	characteristic
224	C₂²×C₁₉	#454	1	1	yes	characteristic
225	C₂×D₁₉	—	8	2	no	—
226	C₂×D₁₉	—	8	2	no	—
227	C₂×D₁₉	—	8	2	no	—
228	C₂×D₁₉	—	16	1	no	—
229	C₂×D₁₉	—	16	1	no	—
230	C₂×D₁₉	—	16	1	no	—
231	C₂×D₁₉	—	16	1	no	—
232	C₄×C₁₉	—	2	1	no	—
233	C₄×C₁₉	—	2	1	no	—
234	C₄×C₁₉	—	4	2	no	—
235	C₄×C₁₉	—	8	1	no	—
236	C₄×C₁₉	#450	1	1	yes	characteristic
237	C₄×C₁₉	#450	1	1	yes	characteristic
238	C₄×C₁₉	#452	1	1	yes	characteristic
239	C₄×C₁₉	#452	1	1	yes	characteristic
240	C₄×C₁₉	#465	1	1	yes	characteristic
241	C₄×C₁₉	#465	1	1	yes	characteristic
242	C₄×C₁₉	#468	1	1	yes	characteristic
243	C₄×C₁₉	#468	1	1	yes	characteristic
244	Dic₁₉	—	4	2	no	—
245	Dic₁₉	—	8	2	no	—
246	Dic₁₉	—	8	1	no	—
247	C₂²×SD₁₆	—	38	1	no	—
248	C₂²×SD₁₆	—	38	1	no	—
249	C₂×#127	—	19	1	no	—
250	C₂×C₄×Q₈	—	19	1	no	—
251	C₂×C₄×Q₈	C₂×D₁₉	1	1	yes	characteristic
252	#460	—	38	2	no	—
253	#460	—	38	2	no	—
254	#460	—	38	2	no	—
255	#460	—	38	2	no	—
256	C₂×C₄⋊C₈	—	19	1	no	—
257	C₂×C₄⋊C₈	C₂×D₁₉	1	1	yes	characteristic
258	C₂×#102	—	38	1	no	—
259	C₂×#102	—	38	1	no	—
260	C₂×#102	—	38	2	no	—
261	C₂×C₄×C₈	C₂×D₁₉	1	1	yes	characteristic
262	#398	—	38	2	no	—
263	#391	—	38	1	no	—
264	#391	—	38	1	no	—
265	#389	—	38	1	no	—
266	#389	—	38	1	no	—
267	#384	—	19	1	no	—
268	Q₈⋊C₈	—	2	2	no	—
269	Q₈⋊C₈	—	38	2	no	—
270	C₂×C₁₉	#1620	1	1	yes	characteristic
271	C₂×C₁₉	#1623	1	1	yes	characteristic
272	C₂×C₁₉	#1626	1	1	yes	characteristic
273	C₂×C₁₉	#1626	1	1	yes	characteristic
274	C₂×C₁₉	#2000	1	1	yes	characteristic
275	C₂×C₁₉	#2000	1	1	yes	characteristic
276	C₂×C₁₉	#2006	1	1	yes	characteristic
277	D₁₉	—	16	2	no	—
278	C₂²×Q₈	—	19	1	no	—
279	C₂²×Q₈	D₇₆	1	1	yes	characteristic
280	C₂²×D₄	—	38	1	no	—
281	C₂²×D₄	—	38	1	no	—
282	C₂²×D₄	—	38	1	no	—
283	C₂×SD₁₆	—	38	4	no	—
284	C₂×SD₁₆	—	38	4	no	—
285	C₂×SD₁₆	—	76	2	no	—
286	C₂×SD₁₆	—	76	2	no	—
287	C₂×SD₁₆	—	76	2	no	—
288	C₂×SD₁₆	—	76	2	no	—
289	C₂²×C₈	—	2	1	no	—
290	C₂²×C₈	—	2	1	no	—
291	C₂²×C₈	—	38	1	no	—
292	#127	—	19	2	no	—
293	#127	—	38	1	no	—
294	#127	—	38	1	no	—
295	#127	—	38	1	no	—
296	C₄×Q₈	—	2	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	2	1	no	—
300	C₄×Q₈	—	38	1	no	—
301	C₄×Q₈	—	38	1	no	—
302	C₄×Q₈	—	38	1	no	—
303	C₄×Q₈	—	38	1	no	—
304	C₂×C₄⋊C₄	—	2	1	no	—
305	C₂×C₄⋊C₄	—	19	1	no	—
306	C₂×C₄⋊C₄	—	19	2	no	—
307	C₂×C₄⋊C₄	—	38	1	no	—
308	C₂×C₄⋊C₄	—	38	1	no	—
309	C₂×C₄⋊C₄	—	38	1	no	—
310	C₂×C₄⋊C₄	—	38	2	no	—
311	C₂×C₄⋊C₄	D₇₆	1	1	yes	characteristic
312	C₂×C₄²	—	2	1	no	—
313	C₂×C₄²	—	38	1	no	—
314	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
315	C₄⋊C₈	—	2	1	no	—
316	C₄⋊C₈	—	19	2	no	—
317	C₄⋊C₈	—	38	1	no	—
318	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
319	#102	—	38	4	no	—
320	#102	—	38	4	no	—
321	#102	—	76	4	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	#95	—	38	2	no	—
325	#95	—	38	2	no	—
326	#95	—	38	2	no	—
327	C₁₉	#10230	1	1	yes	characteristic, complemented, Sylow
328	C₂⁴	—	76	1	no	—
329	C₂×Q₈	—	2	1	no	—
330	C₂×Q₈	—	2	1	no	—
331	C₂×Q₈	—	2	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	19	2	no	—
335	C₂×Q₈	—	38	1	no	—
336	C₂×Q₈	—	38	1	no	—
337	C₂×Q₈	—	38	1	no	—
338	C₂×Q₈	—	38	1	no	—
339	C₂×Q₈	—	38	1	no	—
340	C₂×Q₈	#64516	1	2	yes	complemented
341	C₂×D₄	—	38	2	no	—
342	C₂×D₄	—	38	2	no	—
343	C₂×D₄	—	38	2	no	—
344	C₂×D₄	—	76	2	no	—
345	C₂×D₄	—	76	2	no	—
346	C₂×D₄	—	76	1	no	—
347	C₂×D₄	—	76	1	no	—
348	C₂×D₄	—	76	1	no	—
349	C₂×D₄	—	76	1	no	—
350	C₂×D₄	—	76	1	no	—
351	C₂×D₄	—	76	1	no	—
352	C₂×D₄	—	76	1	no	—
353	C₂×D₄	—	76	1	no	—
354	C₂×D₄	—	76	1	no	—
355	C₂×D₄	—	76	1	no	—
356	C₂×D₄	—	76	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	38	1	no	—
360	C₂²×C₄	—	38	2	no	—
361	C₂²×C₄	—	38	1	no	—
362	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
363	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
364	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
365	SD₁₆	—	76	8	no	—
366	SD₁₆	—	76	8	no	—
367	C₂×C₈	—	2	2	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	4	1	no	—
370	C₂×C₈	—	4	1	no	—
371	C₂×C₈	—	4	1	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	38	2	no	—
374	C₂×C₈	—	76	1	no	—
375	C₂×C₈	—	76	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	38	1	no	—
381	C₄⋊C₄	—	38	1	no	—
382	C₄⋊C₄	—	76	2	no	—
383	C₄⋊C₄	—	76	1	no	—
384	C₄⋊C₄	—	76	1	no	—
385	C₄⋊C₄	—	76	1	no	—
386	C₄⋊C₄	—	76	1	no	—
387	C₄⋊C₄	—	76	1	no	—
388	C₄⋊C₄	—	76	1	no	—
389	C₄⋊C₄	—	152	2	no	—
390	C₄²	—	4	1	no	—
391	C₄²	—	4	1	no	—
392	C₄²	—	76	1	no	—
393	C₄²	—	76	1	no	—
394	C₄²	#64541	1	1	yes	characteristic
395	C₄²	D₄×D₁₉	1	1	yes	characteristic
396	C₄²	D₄×D₁₉	1	1	yes	characteristic
397	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
398	C₂³	—	76	2	no	—
399	C₂³	—	152	1	no	—
400	C₂³	—	152	1	no	—
401	C₂³	—	152	1	no	—
402	C₂³	—	152	1	no	—
403	C₂³	—	152	1	no	—
404	C₂³	—	152	1	no	—
405	C₂³	#10597328	1	1	yes	characteristic
406	Q₈	—	2	2	no	—
407	Q₈	—	2	2	no	—
408	Q₈	—	4	1	no	—
409	Q₈	—	4	1	no	—
410	Q₈	—	38	2	no	—
411	Q₈	—	38	2	no	—
412	Q₈	—	76	1	no	—
413	Q₈	—	76	1	no	—
414	D₄	—	76	4	no	—
415	D₄	—	76	2	no	—
416	D₄	—	76	2	no	—
417	D₄	—	76	2	no	—
418	D₄	—	76	2	no	—
419	D₄	—	152	2	no	—
420	D₄	—	152	1	no	—
421	D₄	—	152	1	no	—
422	D₄	—	152	1	no	—
423	D₄	—	152	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	4	1	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	38	2	no	—
433	C₂×C₄	—	76	1	no	—
434	C₂×C₄	—	76	1	no	—
435	C₂×C₄	—	76	2	no	—
436	C₂×C₄	—	76	2	no	—
437	C₂×C₄	—	76	1	no	—
438	C₂×C₄	—	76	2	no	—
439	C₂×C₄	—	76	1	no	—
440	C₂×C₄	—	76	1	no	—
441	C₂×C₄	#10597328	1	1	yes	characteristic
442	C₂×C₄	#10597330	1	1	yes	characteristic
443	C₂×C₄	#10597330	1	1	yes	characteristic
444	C₂×C₄	C₂×#64516	1	1	yes	characteristic
445	C₂×C₄	#10597350	1	1	yes	characteristic
446	C₂×C₄	#10597354	1	1	yes	characteristic
447	C₂×C₄	#10597355	1	1	yes	characteristic
448	C₂×C₄	SD₁₆×D₁₉	1	1	yes	characteristic
449	C₂×C₄	#10597360	1	1	yes	characteristic
450	C₂×C₄	#10597364	1	1	yes	characteristic
451	C₂×C₄	#10597365	1	1	yes	characteristic
452	C₂×C₄	#10597376	1	1	yes	characteristic
453	C₂×C₄	#10597383	1	1	yes	characteristic
454	C₂×C₄	#10597386	1	1	yes	characteristic
455	C₈	—	4	2	no	—
456	C₈	—	4	2	no	—
457	C₈	—	76	2	no	—
458	C₂²	—	304	1	no	—
459	C₂²	—	304	1	no	—
460	C₂²	—	304	1	no	—
461	C₂²	—	304	1	no	—
462	C₂²	—	152	2	no	—
463	C₂²	—	152	2	no	—
464	C₂²	—	152	2	no	—
465	C₂²	#11926453	1	1	yes	characteristic
466	C₂²	#11926684	1	1	yes	characteristic
467	C₂²	#11926685	1	1	yes	characteristic
468	C₂²	#11926691	1	1	yes	characteristic
469	C₂²	#11926692	1	1	yes	characteristic
470	C₂²	#11926713	1	1	yes	characteristic
471	C₂²	#11926718	1	1	yes	characteristic
472	C₄	—	2	1	no	—
473	C₄	—	2	1	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	1	no	—
476	C₄	—	76	2	no	—
477	C₄	—	152	1	no	—
478	C₄	—	152	2	no	—
479	C₄	#11926693	1	1	yes	characteristic
480	C₄	#11926697	1	1	yes	characteristic
481	C₄	#11926705	1	1	yes	characteristic
482	C₄	#11926708	1	1	yes	characteristic
483	C₄	#11926773	1	1	yes	characteristic
484	C₄	#11926776	1	1	yes	characteristic
485	C₄	#11926790	1	1	yes	characteristic
486	C₄	#11926793	1	1	yes	characteristic
487	C₂	—	304	2	no	—
488	C₂	#14562696	1	1	yes	characteristic
489	C₂	#14562715	1	1	yes	characteristic
490	C₂	#14562733	1	1	yes	characteristic
491	C₂	#14562734	1	1	yes	characteristic
492	C₂	#14564637	1	1	yes	characteristic
493	C₂	#14564640	1	1	yes	characteristic
494	C₂	#14564678	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#10597328
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₂×C₁₉×Q₈⋊C₈	C₂
socle	C₂³×C₁₉	#120
prime radical	C₂×#10597320	C₂²
hypercenter	C₂×Q₈⋊C₈	D₁₉
hypocenter	C₁₉	#10230
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
3. #14569005	C₂	semidirect
5. C₂×#11926276	C₂	semidirect
6. #14561519	C₂	semidirect
7. C₂×C₁₉×Q₈⋊C₈	C₂	semidirect
86. C₂×Q₈×C₁₉	SD₁₆	semidirect
116. C₂×Dic₃₈	SD₁₆	semidirect
216. C₂×Q₈⋊C₈	D₁₉	semidirect
327. C₁₉	#10230	semidirect
340. C₂×Q₈	#64516	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11926745	2
C₂×#11926744	2
#14569005	2
#14564441	2
C₂×#11926276	2
#14561519	2
C₂×C₁₉×Q₈⋊C₈	2
#10230	19