Subgroups — #14575249

Order 2432.

556 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597360	C₂	1	1	yes	maximal, characteristic, complemented
2	#11927213	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#11926919	C₂	1	1	yes	maximal, characteristic, complemented
5	#11926797	C₂	1	1	yes	maximal, characteristic, complemented
6	#11926794	C₂	1	1	yes	maximal, characteristic, complemented
7	#11926742	C₂	1	1	yes	maximal, characteristic, complemented
8	#11926737	C₂	1	1	yes	maximal, characteristic, complemented
9	#11926689	C₂	1	1	yes	maximal, characteristic, complemented
10	#11926688	C₂	1	1	yes	maximal, characteristic, complemented
11	#11926678	C₂	1	1	yes	maximal, characteristic, complemented
12	#11926676	C₂	1	1	yes	maximal, characteristic, complemented
13	SD₁₆×Dic₁₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#11926620	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₁₉×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄×C₁₉	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₉	—	2	1	no	—
19	C₂×#64545	C₂²	1	1	yes	characteristic, complemented
20	C₂×D₄×D₁₉	C₂²	1	1	yes	characteristic
21	C₁₉×AGL(1,ℤ/8)	—	2	4	no	—
22	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic
23	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic
25	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×M₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
27	#10597399	—	2	1	no	—
28	Q₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×#64527	C₂²	1	1	yes	characteristic, complemented
30	#10597386	—	2	1	no	—
31	#10597386	C₂²	1	1	yes	characteristic
32	#10597386	C₂²	1	1	yes	characteristic, complemented
33	#10597385	—	2	1	no	—
34	#10597384	—	2	1	no	—
35	#10597384	C₂²	1	1	yes	characteristic
36	#10597384	C₂²	1	1	yes	characteristic, complemented
37	#10597383	—	2	1	no	—
38	D₄×Dic₁₉	C₂²	1	1	yes	characteristic
39	C₂×#64525	C₂²	1	1	yes	characteristic
40	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
41	C₂×#64525	C₂²	1	1	yes	characteristic, complemented
42	#10597376	—	2	1	no	—
43	#10597376	C₂²	1	1	yes	characteristic
44	#10597376	C₂²	1	1	yes	characteristic, complemented
45	C₄×C₂²⋊D₁₉	—	2	1	no	—
46	C₄×C₂²⋊D₁₉	C₂²	1	1	yes	characteristic
47	#10597360	—	2	4	no	—
48	C₂×D₁₅₂	C₂²	1	1	yes	characteristic, complemented
49	C₂×#64515	C₂²	1	1	yes	characteristic, complemented
50	#10597292	C₂²	1	1	yes	characteristic, complemented
51	#10597289	C₂²	1	1	yes	characteristic
52	#10597289	C₂²	1	1	yes	characteristic, complemented
53	#10597289	C₂²	1	1	yes	characteristic, complemented
54	C₂²⋊(C₁₉⋊C₈)	C₂²	1	1	yes	characteristic, complemented
55	#10597278	C₂²	1	1	yes	characteristic, complemented
56	#10597278	C₂²	1	1	yes	characteristic, complemented
57	(C₂×D₁₉)⋊C₈	C₂²	1	1	yes	characteristic, complemented
58	#10597274	C₂²	1	1	yes	characteristic, complemented
59	Dic₁₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
60	C₈×Dic₁₉	C₂²	1	1	yes	characteristic, complemented
61	C₂⁴×C₁₉	—	2	1	no	—
62	C₂³×D₁₉	—	2	1	no	—
63	#41×C₁₉	—	2	2	no	—
64	#41×C₁₉	—	4	1	no	—
65	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₉	—	2	2	no	—
67	C₂×D₄×C₁₉	—	2	1	no	—
68	C₂×D₄×C₁₉	—	2	1	no	—
69	C₂×D₄×C₁₉	—	4	1	no	—
70	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
72	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	—	2	1	no	—
74	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₉	—	2	1	no	—
76	C₂×C₂²⋊D₁₉	—	2	1	no	—
77	C₂×C₂²⋊D₁₉	—	2	1	no	—
78	C₂×C₂²⋊D₁₉	—	2	1	no	—
79	C₂×C₂²⋊D₁₉	—	2	1	no	—
80	C₂×C₂²⋊D₁₉	—	2	1	no	—
81	C₂×C₂²⋊D₁₉	—	2	1	no	—
82	C₂×C₂²⋊D₁₉	—	2	1	no	—
83	C₂×C₂²⋊D₁₉	—	2	1	no	—
84	C₂×C₂²⋊D₁₉	—	4	4	no	—
85	C₂×C₂²⋊D₁₉	D₄	1	1	yes	characteristic
86	C₂²×Dic₁₉	—	2	1	no	—
87	#64545	—	2	2	no	—
88	#64545	—	4	1	no	—
89	D₄×D₁₉	—	2	2	no	—
90	D₄×D₁₉	—	4	1	no	—
91	C₂×D₇₆	—	2	1	no	—
92	C₂×D₇₆	C₂³	1	1	yes	characteristic
93	C₂×D₇₆	C₂³	1	1	yes	characteristic
94	C₂×C₄×D₁₉	—	2	1	no	—
95	C₂×C₄×D₁₉	C₂³	1	1	yes	characteristic
96	SD₁₆×C₁₉	—	2	2	no	—
97	SD₁₆×C₁₉	D₄	1	4	yes	complemented
98	D₈×C₁₉	—	2	2	no	—
99	D₈×C₁₉	—	2	2	no	—
100	M₁₆×C₁₉	—	2	2	no	—
101	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
102	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
103	C₂²⋊Dic₁₉	—	2	1	no	—
104	C₂²⋊Dic₁₉	—	2	1	no	—
105	C₂²⋊Dic₁₉	—	2	1	no	—
106	C₂²⋊Dic₁₉	D₄	1	1	yes	characteristic
107	#64527	—	2	2	no	—
108	#64525	—	2	2	no	—
109	#64525	—	4	1	no	—
110	#64525	—	4	1	no	—
111	(C₂×D₁₉)⋊C₄	—	2	1	no	—
112	(C₂×D₁₉)⋊C₄	—	2	1	no	—
113	(C₂×D₁₉)⋊C₄	D₄	1	1	yes	characteristic
114	C₄⋊Dic₁₉	—	2	1	no	—
115	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
116	C₄⋊Dic₁₉	C₂³	1	1	yes	characteristic
117	Dic₁₉⋊C₄	D₄	1	1	yes	characteristic
118	C₄×Dic₁₉	—	2	1	no	—
119	C₄×Dic₁₉	C₂³	1	1	yes	characteristic
120	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
121	C₂×C₁₉⋊C₈	C₂³	1	1	yes	characteristic
122	D₁₅₂	—	2	2	no	—
123	#64515	—	2	2	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	—	2	1	no	—
126	C₂³×C₁₉	—	2	1	no	—
127	C₂³×C₁₉	—	4	2	no	—
128	C₂³×C₁₉	—	4	2	no	—
129	C₂³×C₁₉	—	8	1	no	—
130	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
131	C₂²×D₁₉	—	2	1	no	—
132	C₂²×D₁₉	—	2	1	no	—
133	C₂²×D₁₉	—	4	2	no	—
134	C₂²×D₁₉	—	4	2	no	—
135	C₂²×D₁₉	—	8	1	no	—
136	C₂²×D₁₉	C₂×D₄	1	1	yes	characteristic
137	Q₈×C₁₉	—	2	1	no	—
138	Q₈×C₁₉	C₂×D₄	1	2	yes	complemented
139	D₄×C₁₉	—	2	1	no	—
140	D₄×C₁₉	—	2	1	no	—
141	D₄×C₁₉	—	2	1	no	—
142	D₄×C₁₉	—	2	1	no	—
143	D₄×C₁₉	—	2	1	no	—
144	D₄×C₁₉	—	4	2	no	—
145	D₄×C₁₉	—	4	2	no	—
146	D₄×C₁₉	C₂×D₄	1	2	yes	—
147	C₂×C₄×C₁₉	—	2	1	no	—
148	C₂×C₄×C₁₉	—	2	1	no	—
149	C₂×C₄×C₁₉	—	2	1	no	—
150	C₂×C₄×C₁₉	—	4	2	no	—
151	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
153	C₂²⋊D₁₉	—	2	2	no	—
154	C₂²⋊D₁₉	—	4	2	no	—
155	C₂²⋊D₁₉	—	4	2	no	—
156	C₂²⋊D₁₉	—	4	2	no	—
157	C₂²⋊D₁₉	—	4	2	no	—
158	C₂²⋊D₁₉	—	4	2	no	—
159	C₂²⋊D₁₉	—	8	1	no	—
160	C₂²⋊D₁₉	—	8	1	no	—
161	C₂²⋊D₁₉	—	8	1	no	—
162	C₂²⋊D₁₉	—	8	1	no	—
163	C₂×Dic₁₉	—	2	1	no	—
164	C₂×Dic₁₉	—	2	1	no	—
165	C₂×Dic₁₉	—	4	2	no	—
166	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
167	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
168	C₂×Dic₁₉	C₂×D₄	1	1	yes	characteristic
169	D₇₆	—	2	1	no	—
170	D₇₆	—	2	1	no	—
171	D₇₆	—	2	1	no	—
172	D₇₆	—	2	1	no	—
173	D₇₆	—	4	2	no	—
174	C₄×D₁₉	—	2	1	no	—
175	C₄×D₁₉	—	2	1	no	—
176	C₄×D₁₉	—	4	2	no	—
177	C₈×C₁₉	—	2	1	no	—
178	C₈×C₁₉	C₂×D₄	1	2	yes	complemented
179	C₁₉⋊C₈	—	2	1	no	—
180	C₁₉⋊C₈	—	2	1	no	—
181	#3274	—	19	1	no	maximal, Sylow
182	C₂²×C₁₉	—	2	2	no	—
183	C₂²×C₁₉	—	2	1	no	—
184	C₂²×C₁₉	—	2	1	no	—
185	C₂²×C₁₉	—	2	1	no	—
186	C₂²×C₁₉	—	4	1	no	—
187	C₂²×C₁₉	—	4	1	no	—
188	C₂²×C₁₉	—	4	1	no	—
189	C₂²×C₁₉	—	4	1	no	—
190	C₂²×C₁₉	—	4	1	no	—
191	C₂²×C₁₉	—	4	1	no	—
192	C₂²×C₁₉	—	4	1	no	—
193	C₂²×C₁₉	—	4	1	no	—
194	C₂²×C₁₉	—	8	4	no	—
195	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×D₁₉	—	2	1	no	—
197	C₂×D₁₉	—	2	1	no	—
198	C₂×D₁₉	—	2	1	no	—
199	C₂×D₁₉	—	4	1	no	—
200	C₂×D₁₉	—	4	1	no	—
201	C₂×D₁₉	—	4	1	no	—
202	C₂×D₁₉	—	4	1	no	—
203	C₂×D₁₉	—	4	1	no	—
204	C₂×D₁₉	—	4	1	no	—
205	C₂×D₁₉	—	8	4	no	—
206	C₄×C₁₉	—	2	2	no	—
207	C₄×C₁₉	—	2	1	no	—
208	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
209	C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
210	Dic₁₉	—	2	1	no	—
211	Dic₁₉	—	2	1	no	—
212	Dic₁₉	—	4	1	no	—
213	Dic₁₉	—	4	1	no	—
214	Dic₁₉	AGL(1,ℤ/8)	1	2	yes	complemented
215	C₂×AGL(1,ℤ/8)	—	19	1	no	—
216	C₂×AGL(1,ℤ/8)	D₁₉	1	1	yes	characteristic, complemented
217	#550	—	19	1	no	—
218	D₄²	—	19	1	no	—
219	#493	—	19	1	no	—
220	#469	—	19	1	no	—
221	#469	—	19	1	no	—
222	#460	—	19	1	no	—
223	#459	—	19	1	no	—
224	#449	—	19	1	no	—
225	#449	—	19	1	no	—
226	#447	—	19	1	no	—
227	#447	—	19	1	no	—
228	C₄×SD₁₆	—	19	1	no	—
229	#436	—	19	1	no	—
230	C₂×C₁₉	—	4	2	no	—
231	C₂×C₁₉	—	4	1	no	—
232	C₂×C₁₉	—	8	1	no	—
233	C₂×C₁₉	—	8	1	no	—
234	C₂×C₁₉	D₄²	1	1	yes	characteristic
235	C₂×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂×C₁₉	#576	1	1	yes	characteristic
237	D₁₉	—	4	1	no	—
238	D₁₉	—	8	1	no	—
239	D₁₉	—	8	1	no	—
240	C₂×#41	—	19	1	no	—
241	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
242	C₂²×D₄	—	19	1	no	—
243	C₂²×D₄	—	38	1	no	—
244	C₂²×D₄	C₂×D₁₉	1	1	yes	characteristic
245	AGL(1,ℤ/8)	—	2	4	no	—
246	AGL(1,ℤ/8)	—	38	4	no	—
247	C₂×SD₁₆	—	19	1	no	—
248	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic
249	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
250	C₂×D₈	—	19	1	no	—
251	C₂×D₈	—	19	1	no	—
252	C₂×D₈	—	19	1	no	—
253	C₂×D₈	—	19	1	no	—
254	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic
255	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
256	C₂×M₁₆	—	19	1	no	—
257	C₂×M₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
258	#127	—	19	1	no	—
259	#127	—	19	1	no	—
260	#127	—	38	1	no	—
261	#121	—	19	1	no	—
262	#121	—	19	1	no	—
263	#121	—	19	1	no	—
264	#121	—	19	1	no	—
265	#121	—	38	1	no	—
266	#121	—	38	1	no	—
267	#121	—	38	1	no	—
268	#120	—	38	1	no	—
269	#120	—	38	1	no	—
270	C₄×Q₈	—	19	1	no	—
271	C₄×D₄	—	19	1	no	—
272	C₄×D₄	—	19	1	no	—
273	C₄×D₄	—	38	1	no	—
274	#106	—	19	1	no	—
275	C₄⋊C₈	—	19	1	no	—
276	#103	—	19	1	no	—
277	#102	—	19	1	no	—
278	#102	—	19	1	no	—
279	#102	—	19	1	no	—
280	#102	—	19	1	no	—
281	#102	—	19	1	no	—
282	C₂²⋊C₈	—	19	1	no	—
283	C₂²⋊C₈	—	19	1	no	—
284	C₄×C₈	—	19	1	no	—
285	C₁₉	#3274	1	1	yes	characteristic, complemented, Sylow
286	C₂⁴	—	2	1	no	—
287	C₂⁴	—	38	1	no	—
288	#41	—	2	2	no	—
289	#41	—	4	1	no	—
290	#41	—	38	2	no	—
291	#41	—	76	1	no	—
292	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	1	no	—
295	C₂×D₄	—	2	1	no	—
296	C₂×D₄	—	4	1	no	—
297	C₂×D₄	—	19	1	no	—
298	C₂×D₄	—	19	1	no	—
299	C₂×D₄	—	19	1	no	—
300	C₂×D₄	—	38	1	no	—
301	C₂×D₄	—	38	1	no	—
302	C₂×D₄	—	38	1	no	—
303	C₂×D₄	—	38	1	no	—
304	C₂×D₄	—	38	1	no	—
305	C₂×D₄	—	38	1	no	—
306	C₂×D₄	—	38	2	no	—
307	C₂×D₄	—	38	1	no	—
308	C₂×D₄	—	38	1	no	—
309	C₂×D₄	—	38	1	no	—
310	C₂×D₄	—	38	1	no	—
311	C₂×D₄	—	76	1	no	—
312	C₂×D₄	—	76	4	no	—
313	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
314	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
315	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	19	1	no	—
318	C₂²×C₄	—	38	1	no	—
319	C₂²×C₄	—	38	1	no	—
320	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
321	SD₁₆	—	2	2	no	—
322	SD₁₆	—	38	2	no	—
323	SD₁₆	C₂²⋊D₁₉	1	4	yes	complemented
324	D₈	—	2	2	no	—
325	D₈	—	2	2	no	—
326	D₈	—	38	2	no	—
327	D₈	—	38	2	no	—
328	D₈	—	76	1	no	—
329	D₈	—	76	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	38	2	no	—
332	C₂×C₈	—	19	1	no	—
333	C₂×C₈	—	19	1	no	—
334	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
335	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
336	C₄⋊C₄	—	19	1	no	—
337	C₄⋊C₄	—	19	1	no	—
338	C₄⋊C₄	—	19	1	no	—
339	C₄⋊C₄	—	38	1	no	—
340	C₂²⋊C₄	—	19	1	no	—
341	C₂²⋊C₄	—	19	1	no	—
342	C₂²⋊C₄	—	38	1	no	—
343	C₂²⋊C₄	—	38	1	no	—
344	C₂²⋊C₄	—	38	1	no	—
345	C₂²⋊C₄	—	38	1	no	—
346	C₂²⋊C₄	—	38	1	no	—
347	C₄²	—	19	1	no	—
348	C₄²	—	38	1	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	—	4	2	no	—
354	C₂³	—	8	1	no	—
355	C₂³	—	19	1	no	—
356	C₂³	—	38	1	no	—
357	C₂³	—	38	1	no	—
358	C₂³	—	76	2	no	—
359	C₂³	—	76	2	no	—
360	C₂³	—	152	1	no	—
361	C₂³	D₄×D₁₉	1	1	yes	characteristic
362	Q₈	—	2	1	no	—
363	Q₈	C₂×C₂²⋊D₁₉	1	2	yes	complemented
364	D₄	—	2	1	no	—
365	D₄	—	2	1	no	—
366	D₄	—	2	1	no	—
367	D₄	—	2	1	no	—
368	D₄	—	2	1	no	—
369	D₄	—	4	2	no	—
370	D₄	—	4	2	no	—
371	D₄	—	38	2	no	—
372	D₄	—	38	1	no	—
373	D₄	—	38	1	no	—
374	D₄	—	38	1	no	—
375	D₄	—	38	1	no	—
376	D₄	—	76	2	no	—
377	D₄	—	76	2	no	—
378	D₄	—	76	2	no	—
379	D₄	—	76	2	no	—
380	D₄	—	76	2	no	—
381	D₄	—	76	2	no	—
382	D₄	—	152	1	no	—
383	D₄	—	152	1	no	—
384	D₄	—	152	1	no	—
385	D₄	—	152	1	no	—
386	D₄	C₂×C₂²⋊D₁₉	1	2	yes	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	19	1	no	—
392	C₂×C₄	—	19	1	no	—
393	C₂×C₄	—	19	1	no	—
394	C₂×C₄	—	38	1	no	—
395	C₂×C₄	—	38	1	no	—
396	C₂×C₄	—	38	1	no	—
397	C₂×C₄	—	38	1	no	—
398	C₂×C₄	—	76	2	no	—
399	C₂×C₄	—	76	2	no	—
400	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
402	C₈	—	2	1	no	—
403	C₈	—	38	1	no	—
404	C₈	—	38	1	no	—
405	C₈	C₂×C₂²⋊D₁₉	1	2	yes	complemented
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	1	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	4	1	no	—
411	C₂²	—	4	1	no	—
412	C₂²	—	4	1	no	—
413	C₂²	—	4	1	no	—
414	C₂²	—	4	1	no	—
415	C₂²	—	4	1	no	—
416	C₂²	—	4	1	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	38	1	no	—
420	C₂²	—	38	1	no	—
421	C₂²	—	38	1	no	—
422	C₂²	—	76	1	no	—
423	C₂²	—	76	1	no	—
424	C₂²	—	76	1	no	—
425	C₂²	—	76	1	no	—
426	C₂²	—	76	1	no	—
427	C₂²	—	76	1	no	—
428	C₂²	—	152	4	no	—
429	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	2	no	—
432	C₄	—	19	2	no	—
433	C₄	—	38	1	no	—
434	C₄	—	38	1	no	—
435	C₄	—	76	1	no	—
436	C₄	—	76	1	no	—
437	C₄	#10597430	1	1	yes	characteristic
438	C₄	C₂²×C₂²⋊D₁₉	1	1	yes	characteristic
439	C₂	—	4	1	no	—
440	C₂	—	4	2	no	—
441	C₂	—	8	1	no	—
442	C₂	—	8	1	no	—
443	C₂	—	76	1	no	—
444	C₂	—	152	1	no	—
445	C₂	—	152	1	no	—
446	C₂	D₄×C₂²⋊D₁₉	1	1	yes	characteristic
447	C₂	AGL(1,ℤ/8)×D₁₉	1	1	yes	characteristic
448	C₂	#11927348	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₂×C₄×C₁₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₉
Fitting	C₂×C₁₉×AGL(1,ℤ/8)	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×AGL(1,ℤ/8)	D₁₉
hypocenter	C₁₉	#3274
LCS	G ▷ C₂×C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. C₂×#10597360	C₂	semidirect
2. #11927213	C₂	semidirect
3. D₄×C₂²⋊D₁₉	C₂	semidirect
4. #11926919	C₂	semidirect
5. #11926797	C₂	semidirect
6. #11926794	C₂	semidirect
7. #11926742	C₂	semidirect
8. #11926737	C₂	semidirect
9. #11926689	C₂	semidirect
10. #11926688	C₂	semidirect
11. #11926678	C₂	semidirect
12. #11926676	C₂	semidirect
13. SD₁₆×Dic₁₉	C₂	semidirect
14. #11926620	C₂	semidirect
15. C₂×C₁₉×AGL(1,ℤ/8)	C₂	semidirect
16. C₂×#41×C₁₉	C₂²	semidirect
19. C₂×#64545	C₂²	semidirect
23. C₂×SD₁₆×C₁₉	C₂²	semidirect
25. C₂×D₈×C₁₉	C₂²	semidirect
26. C₂×M₁₆×C₁₉	C₂²	semidirect
28. Q₈×Dic₁₉	C₂²	semidirect
29. C₂×#64527	C₂²	semidirect
32. #10597386	C₂²	semidirect
36. #10597384	C₂²	semidirect
40. C₂×#64525	C₂²	semidirect
41. C₂×#64525	C₂²	semidirect
44. #10597376	C₂²	semidirect
48. C₂×D₁₅₂	C₂²	semidirect
49. C₂×#64515	C₂²	semidirect
50. #10597292	C₂²	semidirect
52. #10597289	C₂²	semidirect
53. #10597289	C₂²	semidirect
54. C₂²⋊(C₁₉⋊C₈)	C₂²	semidirect
55. #10597278	C₂²	semidirect
56. #10597278	C₂²	semidirect
57. (C₂×D₁₉)⋊C₈	C₂²	semidirect
58. #10597274	C₂²	semidirect
59. Dic₁₉⋊C₈	C₂²	semidirect
60. C₈×Dic₁₉	C₂²	semidirect
97. SD₁₆×C₁₉	D₄	semidirect
138. Q₈×C₁₉	C₂×D₄	semidirect
178. C₈×C₁₉	C₂×D₄	semidirect
214. Dic₁₉	AGL(1,ℤ/8)	semidirect
216. C₂×AGL(1,ℤ/8)	D₁₉	semidirect
241. C₂×#41	C₂×D₁₉	semidirect
249. C₂×SD₁₆	C₂×D₁₉	semidirect
255. C₂×D₈	C₂×D₁₉	semidirect
257. C₂×M₁₆	C₂×D₁₉	semidirect
285. C₁₉	#3274	semidirect
323. SD₁₆	C₂²⋊D₁₉	semidirect
363. Q₈	C₂×C₂²⋊D₁₉	semidirect
405. C₈	C₂×C₂²⋊D₁₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10597360	2
#11927213	2
D₄×C₂²⋊D₁₉	2
#11926919	2
#11926797	2
#11926794	2
#11926742	2
#11926737	2
#11926689	2
#11926688	2
#11926678	2
#11926676	2
SD₁₆×Dic₁₉	2
#11926620	2
C₂×C₁₉×AGL(1,ℤ/8)	2
#3274	19