Subgroups — C₂×#11927351 #14578391

Order 2432.

1460 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10597436	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#10597435	C₂	1	1	yes	maximal, characteristic, complemented
3	#11927351	C₂	1	16	yes	maximal, direct product factor
4	C₂×#10597364	C₂	1	2	yes	maximal, complemented
5	C₂×#10597397	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#10597395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#10597357	C₂	1	2	yes	maximal, complemented
8	C₂×#10597362	C₂	1	2	yes	maximal, complemented
9	C₂²×#64516	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×SD₁₆×D₁₉	C₂	1	2	yes	maximal, complemented
11	C₂×#10597347	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₉×#135	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic
14	C₂×#41×C₁₉	C₂²	1	1	yes	characteristic, complemented
15	#10597436	—	2	4	no	—
16	#10597436	C₂²	1	8	yes	complemented
17	#10597435	—	2	4	no	—
18	#10597435	C₂²	1	8	yes	complemented
19	C₂×#64545	C₂²	1	2	yes	—
20	C₂×Q₈×D₁₉	C₂²	1	2	yes	complemented
21	C₂×#64543	—	2	2	no	—
22	C₂×#64543	C₂²	1	2	yes	complemented
23	C₂×D₄×D₁₉	—	2	2	no	—
24	C₂×D₄×D₁₉	C₂²	1	2	yes	—
25	C₂×#64541	—	2	1	no	—
26	C₂×#64541	—	2	1	no	—
27	C₂×#64541	C₂²	1	1	yes	characteristic
28	C₂²×D₇₆	—	2	1	no	—
29	C₂²×D₇₆	C₂²	1	1	yes	characteristic
30	C₂²×Dic₃₈	—	2	1	no	—
31	C₂²×Dic₃₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₉×#135	C₂²	1	8	yes	complemented
33	C₂×Q₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
35	C₂×SD₁₆×C₁₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
37	C₂²×C₈×C₁₉	C₂²	1	1	yes	characteristic, complemented
38	#10597397	C₂²	1	8	yes	complemented
39	#10597395	C₂²	1	8	yes	complemented
40	C₂×#64528	C₂²	1	2	yes	complemented
41	C₂×#64527	C₂²	1	2	yes	complemented
42	C₂×#64526	C₂²	1	2	yes	complemented
43	C₂×#64525	C₂²	1	2	yes	complemented
44	C₂×#64520	C₂²	1	1	yes	characteristic, complemented
45	#10597364	C₂²	1	16	yes	complemented
46	#10597362	C₂²	1	16	yes	complemented
47	SD₁₆×D₁₉	C₂²	1	16	yes	complemented
48	#10597357	C₂²	1	16	yes	complemented
49	C₂×#64516	C₂²	1	2	yes	complemented
50	C₂×#64516	C₂²	1	2	yes	complemented
51	C₂×#64516	C₂²	1	8	yes	complemented
52	#10597347	C₂²	1	8	yes	complemented
53	C₂×#64515	C₂²	1	2	yes	complemented
54	C₂×C₈×D₁₉	C₂²	1	2	yes	complemented
55	C₂³×D₁₉	—	2	1	no	—
56	C₂³×D₁₉	—	2	2	no	—
57	#41×C₁₉	—	2	2	no	—
58	#41×C₁₉	—	2	2	no	—
59	#41×C₁₉	C₂³	1	4	yes	—
60	#41×C₁₉	C₂³	1	4	yes	complemented
61	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
62	C₂×Q₈×C₁₉	C₂³	1	1	yes	characteristic
63	C₂×D₄×C₁₉	—	2	1	no	—
64	C₂×D₄×C₁₉	—	2	1	no	—
65	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
66	C₂×D₄×C₁₉	C₂³	1	1	yes	characteristic
67	C₂²×C₄×C₁₉	—	2	1	no	—
68	C₂²×C₄×C₁₉	—	2	1	no	—
69	C₂²×C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₉	—	2	2	no	—
71	C₂×C₂²⋊D₁₉	—	2	2	no	—
72	C₂×C₂²⋊D₁₉	D₄	1	2	yes	—
73	C₂²×Dic₁₉	—	2	1	no	—
74	C₂²×Dic₁₉	—	2	2	no	—
75	#64545	—	2	4	no	—
76	#64545	C₂³	1	8	yes	—
77	Q₈×D₁₉	—	2	4	no	—
78	Q₈×D₁₉	C₂³	1	8	yes	complemented
79	#64543	—	2	16	no	—
80	#64543	—	2	4	no	—
81	#64543	C₂³	1	8	yes	complemented
82	D₄×D₁₉	—	2	16	no	—
83	D₄×D₁₉	—	2	4	no	—
84	D₄×D₁₉	C₂³	1	8	yes	—
85	#64541	—	2	8	no	—
86	#64541	—	2	8	no	—
87	#64541	D₄	1	4	yes	—
88	#64541	C₂³	1	4	yes	—
89	C₂×D₇₆	—	2	2	no	—
90	C₂×D₇₆	—	2	1	no	—
91	C₂×D₇₆	—	2	2	no	—
92	C₂×D₇₆	—	2	8	no	—
93	C₂×D₇₆	D₄	1	1	yes	characteristic
94	C₂×D₇₆	C₂³	1	2	yes	—
95	C₂×D₇₆	C₂³	1	4	yes	—
96	C₂×C₄×D₁₉	—	2	2	no	—
97	C₂×C₄×D₁₉	—	2	2	no	—
98	C₂×C₄×D₁₉	C₂³	1	2	yes	—
99	C₂×Dic₃₈	—	2	1	no	—
100	C₂×Dic₃₈	—	2	2	no	—
101	C₂×Dic₃₈	—	2	2	no	—
102	C₂×Dic₃₈	—	2	8	no	—
103	C₂×Dic₃₈	D₄	1	1	yes	characteristic
104	C₂×Dic₃₈	C₂³	1	2	yes	—
105	C₂×Dic₃₈	C₂³	1	4	yes	complemented
106	Q₁₆×C₁₉	C₂³	1	4	yes	complemented
107	SD₁₆×C₁₉	C₂³	1	4	yes	complemented
108	SD₁₆×C₁₉	C₂³	1	4	yes	complemented
109	D₈×C₁₉	C₂³	1	4	yes	complemented
110	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₁₉	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₁₉	C₂³	1	4	yes	complemented
113	#64528	C₂³	1	8	yes	complemented
114	#64527	C₂³	1	8	yes	complemented
115	#64526	C₂³	1	8	yes	complemented
116	#64525	C₂³	1	8	yes	complemented
117	#64520	C₂³	1	4	yes	complemented
118	C₂×C₁₉⋊C₈	C₂³	1	2	yes	—
119	#64516	C₂³	1	8	yes	complemented
120	#64516	C₂³	1	8	yes	complemented
121	#64515	C₂³	1	8	yes	complemented
122	C₈×D₁₉	C₂³	1	8	yes	complemented
123	C₂³×C₁₉	—	2	1	no	—
124	C₂³×C₁₉	—	2	1	no	—
125	C₂³×C₁₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₁₉	—	2	2	no	—
127	C₂²×D₁₉	—	2	4	no	—
128	C₂²×D₁₉	—	2	8	no	—
129	C₂²×D₁₉	—	8	4	no	—
130	C₂²×D₁₉	—	8	2	no	—
131	C₂²×D₁₉	C₂×D₄	1	2	yes	—
132	Q₈×C₁₉	—	2	1	no	—
133	Q₈×C₁₉	—	2	1	no	—
134	Q₈×C₁₉	C₂⁴	1	2	yes	—
135	Q₈×C₁₉	C₂⁴	1	2	yes	—
136	D₄×C₁₉	—	2	4	no	—
137	D₄×C₁₉	—	2	4	no	—
138	D₄×C₁₉	—	2	1	no	—
139	D₄×C₁₉	—	2	1	no	—
140	D₄×C₁₉	C₂⁴	1	2	yes	—
141	D₄×C₁₉	C₂⁴	1	2	yes	—
142	C₂×C₄×C₁₉	—	2	1	no	—
143	C₂×C₄×C₁₉	—	2	1	no	—
144	C₂×C₄×C₁₉	—	2	4	no	—
145	C₂×C₄×C₁₉	—	2	4	no	—
146	C₂×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×C₁₉	C₂×D₄	1	2	yes	—
148	C₂×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
149	C₂×C₄×C₁₉	C₂⁴	1	2	yes	—
150	C₂²⋊D₁₉	—	2	8	no	—
151	C₂²⋊D₁₉	—	2	8	no	—
152	C₂²⋊D₁₉	C₂×D₄	1	8	yes	—
153	C₂×Dic₁₉	—	2	2	no	—
154	C₂×Dic₁₉	—	2	4	no	—
155	C₂×Dic₁₉	—	2	8	no	—
156	C₂×Dic₁₉	C₂×D₄	1	2	yes	—
157	D₇₆	—	2	8	no	—
158	D₇₆	—	2	4	no	—
159	D₇₆	—	2	2	no	—
160	D₇₆	C₂×D₄	1	4	yes	—
161	D₇₆	C₂⁴	1	4	yes	—
162	C₄×D₁₉	—	2	8	no	—
163	C₄×D₁₉	—	2	8	no	—
164	C₄×D₁₉	C₂×D₄	1	4	yes	—
165	C₄×D₁₉	C₂⁴	1	4	yes	—
166	Dic₃₈	—	2	4	no	—
167	Dic₃₈	—	2	2	no	—
168	Dic₃₈	—	2	8	no	—
169	Dic₃₈	C₂×D₄	1	4	yes	—
170	Dic₃₈	C₂⁴	1	4	yes	—
171	C₈×C₁₉	C₂⁴	1	2	yes	—
172	C₈×C₁₉	C₂⁴	1	2	yes	—
173	C₁₉⋊C₈	C₂⁴	1	4	yes	—
174	C₂×#577	—	19	1	no	maximal, Sylow
175	C₂²×C₁₉	—	2	2	no	—
176	C₂²×C₁₉	—	2	2	no	—
177	C₂²×C₁₉	—	2	2	no	—
178	C₂²×C₁₉	—	4	2	no	—
179	C₂²×C₁₉	—	4	2	no	—
180	C₂²×C₁₉	C₂²×D₄	1	2	yes	—
181	C₂²×C₁₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×D₁₉	—	2	4	no	—
183	C₂×D₁₉	—	2	4	no	—
184	C₂×D₁₉	—	4	4	no	—
185	C₂×D₁₉	—	8	8	no	—
186	C₂×D₁₉	—	8	4	no	—
187	C₂×D₁₉	C₂²×D₄	1	4	yes	—
188	C₄×C₁₉	—	2	2	no	—
189	C₄×C₁₉	—	2	2	no	—
190	C₄×C₁₉	C₂²×D₄	1	2	yes	—
191	C₄×C₁₉	C₂²×D₄	1	1	yes	characteristic
192	C₄×C₁₉	C₂⁵	1	1	yes	characteristic
193	Dic₁₉	—	2	4	no	—
194	Dic₁₉	C₂²×D₄	1	4	yes	—
195	C₂×2₋¹⁺⁴	—	19	1	no	—
196	C₂×H(5,𝔽₂)	—	19	1	no	—
197	#577	—	19	16	no	—
198	C₂×#137	—	19	1	no	—
199	C₂×#137	—	19	2	no	—
200	C₂×AGL(1,ℤ/8)	—	19	1	no	—
201	C₂×AGL(1,ℤ/8)	—	19	2	no	—
202	C₂×#135	—	19	2	no	—
203	C₂×#135	D₁₉	1	1	yes	characteristic, complemented
204	C₂²×SD₁₆	—	19	2	no	—
205	C₂²×SD₁₆	—	19	1	no	—
206	C₂×#131	—	19	1	no	—
207	C₂×C₁₉	—	2	2	no	—
208	C₂×C₁₉	—	4	2	no	—
209	C₂×C₁₉	—	4	2	no	—
210	C₂×C₁₉	#577	1	2	yes	complemented
211	C₂×C₁₉	C₂³×D₄	1	1	yes	characteristic
212	D₁₉	—	2	4	no	—
213	D₁₉	—	4	4	no	—
214	2₋¹⁺⁴	—	19	8	no	—
215	2₋¹⁺⁴	—	38	4	no	—
216	H(5,𝔽₂)	—	19	8	no	—
217	H(5,𝔽₂)	—	38	4	no	—
218	C₂×#41	—	19	1	no	—
219	C₂×#41	—	19	2	no	—
220	C₂×#41	—	19	2	no	—
221	C₂×#41	—	38	1	no	—
222	C₂×#41	—	38	1	no	—
223	C₂×#41	—	38	2	no	—
224	C₂×#41	C₂×D₁₉	1	1	yes	characteristic
225	C₂×#41	C₂×D₁₉	1	1	yes	characteristic, complemented
226	C₂²×Q₈	—	19	2	no	—
227	C₂²×Q₈	—	19	1	no	—
228	C₂²×Q₈	—	38	1	no	—
229	C₂²×D₄	—	19	2	no	—
230	C₂²×D₄	—	19	1	no	—
231	C₂²×D₄	—	38	1	no	—
232	C₂²×D₄	—	38	2	no	—
233	#137	—	19	8	no	—
234	#137	—	19	16	no	—
235	AGL(1,ℤ/8)	—	19	8	no	—
236	AGL(1,ℤ/8)	—	19	16	no	—
237	#135	—	19	16	no	—
238	#135	C₂×D₁₉	1	8	yes	complemented
239	C₂×Q₁₆	—	19	2	no	—
240	C₂×Q₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
241	C₂×SD₁₆	—	19	2	no	—
242	C₂×SD₁₆	—	19	2	no	—
243	C₂×SD₁₆	—	19	16	no	—
244	C₂×SD₁₆	—	19	2	no	—
245	C₂×SD₁₆	—	19	2	no	—
246	C₂×SD₁₆	—	19	8	no	—
247	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
248	C₂×SD₁₆	C₂×D₁₉	1	1	yes	characteristic, complemented
249	C₂×D₈	—	19	2	no	—
250	C₂×D₈	C₂×D₁₉	1	1	yes	characteristic, complemented
251	#131	—	19	8	no	—
252	C₂×M₁₆	—	19	1	no	—
253	C₂×M₁₆	—	19	2	no	—
254	C₂²×C₈	—	19	2	no	—
255	C₂²×C₈	C₂×D₁₉	1	1	yes	characteristic, complemented
256	C₁₉	C₂×#577	1	1	yes	characteristic, complemented, Sylow
257	C₂⁴	—	38	2	no	—
258	C₂⁴	—	38	1	no	—
259	#41	—	2	2	no	—
260	#41	—	2	2	no	—
261	#41	—	19	4	no	—
262	#41	—	19	4	no	—
263	#41	—	19	8	no	—
264	#41	—	19	8	no	—
265	#41	—	38	8	no	—
266	#41	—	38	8	no	—
267	#41	—	38	4	no	—
268	#41	—	38	4	no	—
269	#41	—	38	16	no	—
270	#41	C₂²×D₁₉	1	4	yes	—
271	#41	C₂²×D₁₉	1	4	yes	complemented
272	C₂×Q₈	—	19	1	no	—
273	C₂×Q₈	—	19	8	no	—
274	C₂×Q₈	—	19	2	no	—
275	C₂×Q₈	—	19	4	no	—
276	C₂×Q₈	—	38	2	no	—
277	C₂×Q₈	—	38	8	no	—
278	C₂×Q₈	—	38	4	no	—
279	C₂×Q₈	—	38	1	no	—
280	C₂×Q₈	—	38	2	no	—
281	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
282	C₂×Q₈	C₂²×D₁₉	1	1	yes	characteristic
283	C₂×D₄	—	2	1	no	—
284	C₂×D₄	—	2	1	no	—
285	C₂×D₄	—	19	2	no	—
286	C₂×D₄	—	19	8	no	—
287	C₂×D₄	—	19	1	no	—
288	C₂×D₄	—	19	2	no	—
289	C₂×D₄	—	19	4	no	—
290	C₂×D₄	—	38	8	no	—
291	C₂×D₄	—	38	2	no	—
292	C₂×D₄	—	38	4	no	—
293	C₂×D₄	—	38	2	no	—
294	C₂×D₄	—	38	16	no	—
295	C₂×D₄	—	38	2	no	—
296	C₂×D₄	—	38	1	no	—
297	C₂×D₄	—	38	2	no	—
298	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
299	C₂×D₄	C₂²×D₁₉	1	1	yes	characteristic
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	1	no	—
302	C₂²×C₄	—	19	2	no	—
303	C₂²×C₄	—	38	2	no	—
304	C₂²×C₄	—	38	2	no	—
305	C₂²×C₄	—	38	2	no	—
306	C₂²×C₄	—	38	1	no	—
307	C₂²×C₄	C₂²×D₁₉	1	1	yes	characteristic
308	Q₁₆	—	19	8	no	—
309	Q₁₆	C₂²×D₁₉	1	4	yes	complemented
310	SD₁₆	—	19	8	no	—
311	SD₁₆	—	19	8	no	—
312	SD₁₆	—	19	8	no	—
313	SD₁₆	—	19	8	no	—
314	SD₁₆	C₂²×D₁₉	1	4	yes	complemented
315	SD₁₆	C₂²×D₁₉	1	4	yes	complemented
316	D₈	—	19	8	no	—
317	D₈	C₂²×D₁₉	1	4	yes	complemented
318	M₁₆	—	19	4	no	—
319	M₁₆	—	19	8	no	—
320	C₂×C₈	—	19	2	no	—
321	C₂×C₈	—	19	8	no	—
322	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
323	C₂×C₈	C₂²×D₁₉	1	1	yes	characteristic
324	C₂×C₈	C₂²×D₁₉	1	4	yes	complemented
325	C₂³	—	2	1	no	—
326	C₂³	—	2	1	no	—
327	C₂³	—	19	2	no	—
328	C₂³	—	38	8	no	—
329	C₂³	—	38	2	no	—
330	C₂³	—	38	4	no	—
331	C₂³	—	152	2	no	—
332	C₂³	—	152	4	no	—
333	C₂³	D₄×D₁₉	1	1	yes	characteristic
334	Q₈	—	2	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	19	4	no	—
337	Q₈	—	19	4	no	—
338	Q₈	—	38	8	no	—
339	Q₈	—	38	4	no	—
340	Q₈	—	38	2	no	—
341	Q₈	C₂³×D₁₉	1	2	yes	—
342	Q₈	C₂³×D₁₉	1	2	yes	—
343	D₄	—	2	4	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	19	8	no	—
348	D₄	—	19	4	no	—
349	D₄	—	19	4	no	—
350	D₄	—	38	8	no	—
351	D₄	—	38	8	no	—
352	D₄	—	38	8	no	—
353	D₄	—	38	4	no	—
354	D₄	—	38	2	no	—
355	D₄	C₂³×D₁₉	1	2	yes	—
356	D₄	C₂³×D₁₉	1	2	yes	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	19	2	no	—
362	C₂×C₄	—	19	4	no	—
363	C₂×C₄	—	19	4	no	—
364	C₂×C₄	—	38	8	no	—
365	C₂×C₄	—	38	8	no	—
366	C₂×C₄	—	38	8	no	—
367	C₂×C₄	—	38	4	no	—
368	C₂×C₄	—	38	2	no	—
369	C₂×C₄	D₄×D₁₉	1	2	yes	—
370	C₂×C₄	D₄×D₁₉	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₁₉	1	2	yes	—
372	C₂×C₄	C₂³×D₁₉	1	1	yes	characteristic
373	C₈	—	19	4	no	—
374	C₈	C₂³×D₁₉	1	2	yes	—
375	C₈	C₂³×D₁₉	1	2	yes	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	19	4	no	—
382	C₂²	—	38	4	no	—
383	C₂²	—	38	4	no	—
384	C₂²	—	76	4	no	—
385	C₂²	—	152	4	no	—
386	C₂²	—	152	8	no	—
387	C₂²	C₂×D₄×D₁₉	1	2	yes	—
388	C₂²	C₂×D₄×D₁₉	1	1	yes	characteristic
389	C₄	—	2	2	no	—
390	C₄	—	2	2	no	—
391	C₄	—	19	4	no	—
392	C₄	—	38	4	no	—
393	C₄	C₂×D₄×D₁₉	1	2	yes	—
394	C₄	C₂×D₄×D₁₉	1	1	yes	characteristic
395	C₄	C₂⁴×D₁₉	1	1	yes	characteristic
396	C₂	—	2	2	no	—
397	C₂	—	4	2	no	—
398	C₂	—	4	2	no	—
399	C₂	—	38	4	no	—
400	C₂	—	76	4	no	—
401	C₂	#11927351	1	2	yes	direct product factor
402	C₂	C₂²×D₄×D₁₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₉
commutator, cosocle	C₄×C₁₉	C₂⁵
Frattini	C₄	C₂⁴×D₁₉
Fitting	C₂×C₁₉×#135	C₂
socle	C₂²×C₁₉	C₂²×D₄
hypercenter	C₂×#135	D₁₉
hypocenter	C₁₉	C₂×#577
LCS	G ▷ C₄×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#10597436	C₂	semidirect
2. C₂×#10597435	C₂	semidirect
3. #11927351	C₂	direct (N × H)
4. C₂×#10597364	C₂	semidirect
5. C₂×#10597397	C₂	semidirect
6. C₂×#10597395	C₂	semidirect
7. C₂×#10597357	C₂	semidirect
8. C₂×#10597362	C₂	semidirect
9. C₂²×#64516	C₂	semidirect
10. C₂×SD₁₆×D₁₉	C₂	semidirect
11. C₂×#10597347	C₂	semidirect
12. C₂×C₁₉×#135	C₂	semidirect
14. C₂×#41×C₁₉	C₂²	semidirect
16. #10597436	C₂²	semidirect
18. #10597435	C₂²	semidirect
20. C₂×Q₈×D₁₉	C₂²	semidirect
22. C₂×#64543	C₂²	semidirect
31. C₂²×Dic₃₈	C₂²	semidirect
32. C₁₉×#135	C₂²	semidirect
33. C₂×Q₁₆×C₁₉	C₂²	semidirect
34. C₂×SD₁₆×C₁₉	C₂²	semidirect
35. C₂×SD₁₆×C₁₉	C₂²	semidirect
36. C₂×D₈×C₁₉	C₂²	semidirect
37. C₂²×C₈×C₁₉	C₂²	semidirect
38. #10597397	C₂²	semidirect
39. #10597395	C₂²	semidirect
40. C₂×#64528	C₂²	semidirect
41. C₂×#64527	C₂²	semidirect
42. C₂×#64526	C₂²	semidirect
43. C₂×#64525	C₂²	semidirect
44. C₂×#64520	C₂²	semidirect
45. #10597364	C₂²	semidirect
46. #10597362	C₂²	semidirect
47. SD₁₆×D₁₉	C₂²	semidirect
48. #10597357	C₂²	semidirect
49. C₂×#64516	C₂²	semidirect
50. C₂×#64516	C₂²	semidirect
51. C₂×#64516	C₂²	semidirect
52. #10597347	C₂²	semidirect
53. C₂×#64515	C₂²	semidirect
54. C₂×C₈×D₁₉	C₂²	semidirect
60. #41×C₁₉	C₂³	semidirect
78. Q₈×D₁₉	C₂³	semidirect
81. #64543	C₂³	semidirect
105. C₂×Dic₃₈	C₂³	semidirect
106. Q₁₆×C₁₉	C₂³	semidirect
107. SD₁₆×C₁₉	C₂³	semidirect
108. SD₁₆×C₁₉	C₂³	semidirect
109. D₈×C₁₉	C₂³	semidirect
112. C₂×C₈×C₁₉	C₂³	semidirect
113. #64528	C₂³	semidirect
114. #64527	C₂³	semidirect
115. #64526	C₂³	semidirect
116. #64525	C₂³	semidirect
117. #64520	C₂³	semidirect
119. #64516	C₂³	semidirect
120. #64516	C₂³	semidirect
121. #64515	C₂³	semidirect
122. C₈×D₁₉	C₂³	semidirect
203. C₂×#135	D₁₉	semidirect
210. C₂×C₁₉	#577	semidirect
225. C₂×#41	C₂×D₁₉	semidirect
238. #135	C₂×D₁₉	semidirect
240. C₂×Q₁₆	C₂×D₁₉	semidirect
247. C₂×SD₁₆	C₂×D₁₉	semidirect
248. C₂×SD₁₆	C₂×D₁₉	semidirect
250. C₂×D₈	C₂×D₁₉	semidirect
255. C₂²×C₈	C₂×D₁₉	semidirect
256. C₁₉	C₂×#577	semidirect
271. #41	C₂²×D₁₉	semidirect
309. Q₁₆	C₂²×D₁₉	semidirect
314. SD₁₆	C₂²×D₁₉	semidirect
315. SD₁₆	C₂²×D₁₉	semidirect
317. D₈	C₂²×D₁₉	semidirect
324. C₂×C₈	C₂²×D₁₉	semidirect
401. C₂	#11927351	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#10597436	2
C₂×#10597435	2
#11927351	2
C₂×#10597364	2
C₂×#10597397	2
C₂×#10597395	2
C₂×#10597357	2
C₂×#10597362	2
C₂²×#64516	2
C₂×SD₁₆×D₁₉	2
C₂×#10597347	2
C₂×C₁₉×#135	2
C₂×#577	19

Subgroups — C2×#11927351 #14578391

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11927351 #14578391