Group #18078798 — subgroups

Subgroups — #18078798

Order 4864.

566 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14573675	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597333	C₂	1	1	yes	maximal, characteristic
3	#14564611	C₂	1	1	yes	maximal, characteristic
4	#14562133	C₂	1	1	yes	maximal, characteristic
5	#14562063	C₂	1	1	yes	maximal, characteristic
6	#14561467	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1303	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	C₂×C₄×Dic₃₈	C₂²	1	1	yes	characteristic
10	C₂×#10597333	—	2	1	no	—
11	#11926880	—	2	1	no	—
12	#11926840	C₄	1	2	yes	complemented
13	#11926755	C₄	1	2	yes	complemented
14	#11926702	—	2	1	no	—
15	C₄×Dic₇₆	—	2	2	no	—
16	#11926597	C₂²	1	1	yes	characteristic
17	C₄⋊C₄×Dic₁₉	—	2	1	no	—
18	C₄×Dic₁₉⋊C₄	—	2	1	no	—
19	#11926395	—	2	2	no	—
20	C₄²×Dic₁₉	—	2	1	no	—
21	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
22	#11926305	—	2	1	no	—
23	#11926305	—	2	1	no	—
24	#11926280	—	2	2	no	—
25	#11926274	—	2	2	no	—
26	C₁₉×#431	C₂²	1	1	yes	characteristic
27	C₁₉×#423	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₁₉	C₂²	1	1	yes	characteristic
29	C₂²×Dic₃₈	D₄	1	1	yes	characteristic
30	C₂×M₁₆×C₁₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
32	C₂×C₄²×C₁₉	—	2	1	no	—
33	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
34	#10597372	—	2	1	no	—
35	C₂×C₄⋊Dic₁₉	D₄	1	1	yes	characteristic
36	#10597370	—	2	1	no	—
37	#10597370	—	2	1	no	—
38	C₂×Dic₁₉⋊C₄	—	2	2	no	—
39	C₂×Dic₁₉⋊C₄	—	2	1	no	—
40	C₂×C₄×Dic₁₉	—	2	2	no	—
41	C₂×C₄×Dic₁₉	—	2	1	no	—
42	C₂×C₄×Dic₁₉	—	2	1	no	—
43	C₂×C₄×Dic₁₉	—	2	2	no	—
44	C₂×C₄×Dic₁₉	—	2	1	no	—
45	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₉	D₄	1	1	yes	characteristic
47	C₂×Dic₇₆	—	2	2	no	—
48	#10597333	—	2	8	no	—
49	#10597316	—	2	1	no	—
50	#10597315	C₂×C₄	1	1	yes	characteristic
51	#10597315	C₂×C₄	1	1	yes	characteristic
52	C₄×Dic₃₈	—	2	1	no	—
53	C₄×Dic₃₈	—	2	1	no	—
54	C₄×Dic₃₈	—	2	1	no	—
55	C₄×Dic₃₈	—	2	1	no	—
56	C₄×Dic₃₈	C₂×C₄	1	2	yes	—
57	C₄×Dic₃₈	D₄	1	2	yes	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	C₂×C₄	1	2	yes	—
61	C₁₉×C₂²⋊C₈	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	C₁₉×#95	D₄	1	2	yes	—
64	C₁₉⋊#95	—	2	2	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	#10597275	—	2	2	no	—
67	#10597273	—	2	2	no	—
68	#10597273	—	2	2	no	—
69	C₄⋊(C₁₉⋊C₈)	—	2	1	no	—
70	C₄×C₁₉⋊C₈	—	2	1	no	—
71	C₂²×C₄×C₁₉	—	2	2	no	—
72	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₁₉	—	2	1	no	—
76	C₂²×Dic₁₉	—	2	1	no	—
77	C₂²×Dic₁₉	—	2	1	no	—
78	C₂²×Dic₁₉	—	2	1	no	—
79	C₂×Dic₃₈	—	2	1	no	—
80	C₂×Dic₃₈	—	2	4	no	—
81	C₂×Dic₃₈	—	2	1	no	—
82	C₂×Dic₃₈	—	2	1	no	—
83	C₂×Dic₃₈	C₂²⋊C₄	1	2	yes	—
84	M₁₆×C₁₉	—	4	1	no	—
85	M₁₆×C₁₉	—	4	1	no	—
86	C₂×C₈×C₁₉	—	2	2	no	—
87	C₂×C₈×C₁₉	—	4	1	no	—
88	C₄⋊C₄×C₁₉	—	2	4	no	—
89	C₄²×C₁₉	—	4	1	no	—
90	C₄²×C₁₉	—	4	1	no	—
91	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
92	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₄²×C₁₉	#41	1	1	yes	characteristic
94	C₄²×C₁₉	#41	1	1	yes	characteristic
95	C₂²⋊Dic₁₉	—	4	1	no	—
96	C₄⋊Dic₁₉	—	2	1	no	—
97	C₄⋊Dic₁₉	—	2	1	no	—
98	C₄⋊Dic₁₉	—	2	1	no	—
99	C₄⋊Dic₁₉	—	2	1	no	—
100	C₄⋊Dic₁₉	—	2	1	no	—
101	C₄⋊Dic₁₉	C₂²⋊C₄	1	2	yes	—
102	Dic₁₉⋊C₄	—	2	8	no	—
103	Dic₁₉⋊C₄	—	2	2	no	—
104	Dic₁₉⋊C₄	—	2	2	no	—
105	Dic₁₉⋊C₄	—	4	1	no	—
106	Dic₁₉⋊C₄	—	4	1	no	—
107	C₄×Dic₁₉	—	2	8	no	—
108	C₄×Dic₁₉	—	2	4	no	—
109	C₄×Dic₁₉	—	2	2	no	—
110	C₄×Dic₁₉	—	2	2	no	—
111	C₄×Dic₁₉	—	2	1	no	—
112	C₄×Dic₁₉	—	2	1	no	—
113	C₄×Dic₁₉	—	2	1	no	—
114	C₄×Dic₁₉	—	4	2	no	—
115	C₄×Dic₁₉	—	4	4	no	—
116	C₄×Dic₁₉	—	4	1	no	—
117	C₄×Dic₁₉	Q₁₆	1	2	yes	complemented
118	C₂×C₁₉⋊C₈	—	4	1	no	—
119	Dic₇₆	—	4	4	no	—
120	#9232	—	19	1	no	maximal, Sylow
121	C₂³×C₁₉	#120	1	1	yes	characteristic
122	C₂×C₄×C₁₉	—	2	2	no	—
123	C₂×C₄×C₁₉	—	2	4	no	—
124	C₂×C₄×C₁₉	—	4	1	no	—
125	C₂×C₄×C₁₉	—	4	2	no	—
126	C₂×C₄×C₁₉	—	4	2	no	—
127	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
128	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₉	C₄×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
131	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
132	C₂×C₄×C₁₉	#123	1	1	yes	characteristic
133	C₂×C₄×C₁₉	C₂×Q₁₆	1	1	yes	characteristic
134	C₂×C₄×C₁₉	#135	1	1	yes	characteristic
135	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
136	C₂×C₄×C₁₉	#137	1	1	yes	characteristic
137	C₂×Dic₁₉	—	2	2	no	—
138	C₂×Dic₁₉	—	2	4	no	—
139	C₂×Dic₁₉	—	2	2	no	—
140	C₂×Dic₁₉	—	2	2	no	—
141	C₂×Dic₁₉	—	2	2	no	—
142	C₂×Dic₁₉	—	2	2	no	—
143	C₂×Dic₁₉	—	2	2	no	—
144	C₂×Dic₁₉	—	4	1	no	—
145	C₂×Dic₁₉	—	4	2	no	—
146	C₂×Dic₁₉	—	4	1	no	—
147	C₂×Dic₁₉	—	4	1	no	—
148	C₂×Dic₁₉	—	4	1	no	—
149	Dic₃₈	—	2	4	no	—
150	Dic₃₈	—	2	2	no	—
151	Dic₃₈	—	4	2	no	—
152	Dic₃₈	—	8	1	no	—
153	Dic₃₈	#104	1	4	yes	—
154	C₈×C₁₉	—	4	2	no	—
155	C₈×C₁₉	—	8	1	no	—
156	C₁₉⋊C₈	—	8	1	no	—
157	#3104	—	19	1	no	—
158	C₄²×Q₈	—	19	1	no	—
159	#1994	—	19	1	no	—
160	#1503	—	19	1	no	—
161	#1487	—	19	1	no	—
162	#1303	D₁₉	1	1	yes	characteristic
163	#1276	—	19	1	no	—
164	C₂²×C₁₉	—	2	1	no	—
165	C₂²×C₁₉	—	2	1	no	—
166	C₂²×C₁₉	#386	1	1	yes	characteristic
167	C₂²×C₁₉	#451	1	1	yes	characteristic
168	C₂²×C₁₉	#452	1	1	yes	characteristic
169	C₄×C₁₉	—	2	1	no	—
170	C₄×C₁₉	—	2	1	no	—
171	C₄×C₁₉	—	2	1	no	—
172	C₄×C₁₉	—	4	4	no	—
173	C₄×C₁₉	C₂×#104	1	2	yes	—
174	C₄×C₁₉	C₄×Q₁₆	1	1	yes	characteristic
175	C₄×C₁₉	#441	1	1	yes	characteristic
176	C₄×C₁₉	#462	1	1	yes	characteristic
177	C₄×C₁₉	#464	1	1	yes	characteristic
178	Dic₁₉	—	2	4	no	—
179	Dic₁₉	—	2	4	no	—
180	Dic₁₉	—	4	2	no	—
181	Dic₁₉	—	4	2	no	—
182	Dic₁₉	—	8	1	no	—
183	Dic₁₉	—	8	1	no	—
184	#533	—	19	1	no	—
185	C₂×C₄×Q₈	—	19	1	no	—
186	C₂×C₄×Q₈	—	38	1	no	—
187	#484	—	38	1	no	—
188	#477	—	19	2	no	—
189	#462	—	19	2	no	—
190	#451	—	38	1	no	—
191	C₄×Q₁₆	—	38	2	no	—
192	#431	—	19	1	no	—
193	#431	C₂×D₁₉	1	1	yes	characteristic
194	#423	C₂×D₁₉	1	1	yes	characteristic
195	C₄×C₄⋊C₄	—	38	1	no	—
196	C₄×C₄⋊C₄	—	38	1	no	—
197	C₄×C₄⋊C₄	—	38	2	no	—
198	C₄×C₄⋊C₄	C₂×D₁₉	1	1	yes	characteristic
199	C₄³	—	19	1	no	—
200	C₄³	—	38	1	no	—
201	#339	—	38	1	no	—
202	#339	—	38	1	no	—
203	#328	—	38	2	no	—
204	Q₈⋊C₈	—	38	2	no	—
205	C₂×C₁₉	—	2	1	no	—
206	C₂×C₁₉	—	2	1	no	—
207	C₂×C₁₉	#1878	1	1	yes	characteristic
208	C₂×C₁₉	#1896	1	1	yes	characteristic
209	C₂×C₁₉	#1906	1	1	yes	characteristic
210	C₂²×Q₈	—	19	1	no	—
211	C₂×Q₁₆	—	38	2	no	—
212	C₂×M₁₆	—	2	1	no	—
213	C₄⋊Q₈	—	19	1	no	—
214	C₄⋊Q₈	—	19	1	no	—
215	#125	—	38	1	no	—
216	C₂²⋊Q₈	—	38	1	no	—
217	C₂²⋊Q₈	—	38	1	no	—
218	C₄×Q₈	—	19	2	no	—
219	C₄×Q₈	—	19	2	no	—
220	C₄×Q₈	—	38	8	no	—
221	C₄×Q₈	—	38	1	no	—
222	C₄×Q₈	—	38	1	no	—
223	C₄×Q₈	—	38	1	no	—
224	C₄×Q₈	—	38	1	no	—
225	#117	—	38	1	no	—
226	C₂×C₄⋊C₄	—	2	1	no	—
227	C₂×C₄⋊C₄	—	19	1	no	—
228	C₂×C₄⋊C₄	—	38	2	no	—
229	C₂×C₄⋊C₄	—	38	1	no	—
230	C₂×C₄²	—	2	1	no	—
231	C₂×C₄²	—	19	1	no	—
232	C₂×C₄²	—	19	1	no	—
233	C₂×C₄²	—	38	2	no	—
234	C₂×C₄²	—	38	1	no	—
235	C₂×C₄²	—	38	1	no	—
236	C₂×C₄²	—	38	2	no	—
237	C₂×C₄²	—	38	1	no	—
238	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
239	#107	—	38	2	no	—
240	C₄⋊C₈	—	2	1	no	—
241	C₄⋊C₈	—	2	1	no	—
242	C₄⋊C₈	—	38	1	no	—
243	C₄⋊C₈	C₄×D₁₉	1	2	yes	—
244	#103	—	38	2	no	—
245	#103	—	38	2	no	—
246	C₂²⋊C₈	—	2	1	no	—
247	C₂²⋊C₈	—	38	1	no	—
248	C₄×C₈	—	2	1	no	—
249	C₄×C₈	—	38	1	no	—
250	#95	—	38	2	no	—
251	#95	D₇₆	1	2	yes	—
252	C₁₉	#9232	1	1	yes	characteristic, complemented, Sylow
253	C₂×Q₈	—	19	2	no	—
254	C₂×Q₈	—	38	4	no	—
255	C₂×Q₈	—	38	1	no	—
256	C₂×Q₈	—	38	1	no	—
257	C₂×Q₈	—	38	1	no	—
258	C₂²×C₄	—	2	2	no	—
259	C₂²×C₄	—	38	1	no	—
260	C₂²×C₄	—	38	1	no	—
261	C₂²×C₄	—	38	1	no	—
262	C₂²×C₄	—	38	1	no	—
263	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
264	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
265	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
266	Q₁₆	—	76	4	no	—
267	M₁₆	—	4	1	no	—
268	M₁₆	—	4	1	no	—
269	C₂×C₈	—	2	2	no	—
270	C₂×C₈	—	4	1	no	—
271	C₂×C₈	—	76	1	no	—
272	C₄⋊C₄	—	2	4	no	—
273	C₄⋊C₄	—	19	2	no	—
274	C₄⋊C₄	—	38	8	no	—
275	C₄⋊C₄	—	38	2	no	—
276	C₄⋊C₄	—	38	1	no	—
277	C₄⋊C₄	—	38	2	no	—
278	C₄⋊C₄	—	38	1	no	—
279	C₄⋊C₄	—	38	1	no	—
280	C₄⋊C₄	—	38	1	no	—
281	C₄⋊C₄	—	38	1	no	—
282	C₄⋊C₄	—	76	1	no	—
283	C₄⋊C₄	—	76	1	no	—
284	C₂²⋊C₄	—	76	1	no	—
285	C₄²	—	4	1	no	—
286	C₄²	—	4	1	no	—
287	C₄²	—	19	2	no	—
288	C₄²	—	38	4	no	—
289	C₄²	—	38	8	no	—
290	C₄²	—	38	2	no	—
291	C₄²	—	38	2	no	—
292	C₄²	—	38	1	no	—
293	C₄²	—	38	1	no	—
294	C₄²	—	38	1	no	—
295	C₄²	—	76	2	no	—
296	C₄²	—	76	4	no	—
297	C₄²	—	76	1	no	—
298	C₄²	C₂×C₄×D₁₉	1	1	yes	characteristic
299	C₄²	#64541	1	1	yes	characteristic
300	C₄²	D₄×D₁₉	1	1	yes	characteristic
301	C₄²	#64545	1	1	yes	characteristic
302	C₂³	#10597328	1	1	yes	characteristic
303	Q₈	—	19	4	no	—
304	Q₈	—	38	4	no	—
305	Q₈	—	38	2	no	—
306	Q₈	—	76	2	no	—
307	Q₈	—	152	1	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	38	2	no	—
314	C₂×C₄	—	38	4	no	—
315	C₂×C₄	—	38	2	no	—
316	C₂×C₄	—	38	2	no	—
317	C₂×C₄	—	38	2	no	—
318	C₂×C₄	—	38	2	no	—
319	C₂×C₄	—	38	2	no	—
320	C₂×C₄	—	76	1	no	—
321	C₂×C₄	—	76	2	no	—
322	C₂×C₄	—	76	1	no	—
323	C₂×C₄	—	76	1	no	—
324	C₂×C₄	—	76	1	no	—
325	C₂×C₄	C₄×D₇₆	1	1	yes	characteristic
326	C₂×C₄	C₂²⋊C₄×D₁₉	1	1	yes	characteristic
327	C₂×C₄	#10597330	1	1	yes	characteristic
328	C₂×C₄	#10597339	1	1	yes	characteristic
329	C₂×C₄	#10597340	1	1	yes	characteristic
330	C₂×C₄	#10597341	1	1	yes	characteristic
331	C₂×C₄	#10597358	1	1	yes	characteristic
332	C₂×C₄	#10597361	1	1	yes	characteristic
333	C₂×C₄	#10597361	1	1	yes	characteristic
334	C₂×C₄	Q₁₆×D₁₉	1	1	yes	characteristic
335	C₈	—	4	2	no	—
336	C₈	—	8	1	no	—
337	C₈	—	152	1	no	—
338	C₂²	—	2	1	no	—
339	C₂²	—	2	1	no	—
340	C₂²	#11926422	1	1	yes	characteristic
341	C₂²	#11926701	1	1	yes	characteristic
342	C₂²	#11926707	1	1	yes	characteristic
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	—	4	4	no	—
347	C₄	—	38	4	no	—
348	C₄	—	38	4	no	—
349	C₄	—	76	2	no	—
350	C₄	—	76	2	no	—
351	C₄	—	152	1	no	—
352	C₄	—	152	1	no	—
353	C₄	#104×D₁₉	1	2	yes	—
354	C₄	#11926638	1	1	yes	characteristic
355	C₄	#11926650	1	1	yes	characteristic
356	C₄	#11926753	1	1	yes	characteristic
357	C₄	#11926765	1	1	yes	characteristic
358	C₂	—	2	1	no	—
359	C₂	—	2	1	no	—
360	C₂	#14563977	1	1	yes	characteristic
361	C₂	#14564077	1	1	yes	characteristic
362	C₂	#14564137	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14573675

C₂

yes

maximal, characteristic

C₄×#10597333

C₂

yes

maximal, characteristic

#14564611

C₂

yes

maximal, characteristic

#14562133

C₂

yes

maximal, characteristic

#14562063

C₂

yes

maximal, characteristic

#14561467

C₂

yes

maximal, characteristic

C₁₉×#1303

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

C₂×C₄×Dic₃₈

C₂²

yes

—

—

C₄

yes

complemented

#11926755

C₄

yes

complemented

#11926702

—

C₄×Dic₇₆

—

#11926597

C₂²

yes

characteristic

C₄⋊C₄×Dic₁₉

—

C₄×Dic₁₉⋊C₄

—

#11926395

—

C₄²×Dic₁₉

—

C₄²×Dic₁₉

C₂²

yes

—

—

—

—

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₄×C₄⋊C₄×C₁₉

C₂²

yes

characteristic

C₂²×Dic₃₈

D₄

yes

characteristic

C₂×M₁₆×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

#10597372

—

C₂×C₄⋊Dic₁₉

D₄

yes

characteristic

#10597370

—

#10597370

—

C₂×Dic₁₉⋊C₄

—

C₂×Dic₁₉⋊C₄

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×C₄×Dic₁₉

D₄

yes

characteristic

C₂×Dic₇₆

—

#10597333

—

#10597316

—

#10597315

C₂×C₄

yes

characteristic

#10597315

C₂×C₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₄×Dic₃₈

C₂×C₄

yes

—

C₄×Dic₃₈

D₄

yes

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

C₂×C₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

C₁₉×#95

D₄

yes

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597275

—

#10597273

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

—

C₄×C₁₉⋊C₈

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂²×Dic₁₉

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

C₂²⋊C₄

yes

—

M₁₆×C₁₉

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

C₄²×C₁₉

yes

C₄²×C₁₉

yes

C₂²⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

100

C₄⋊Dic₁₉

—

101

C₄⋊Dic₁₉

C₂²⋊C₄

yes

—

102

Dic₁₉⋊C₄

—

103

Dic₁₉⋊C₄

—

104

Dic₁₉⋊C₄

—

105

Dic₁₉⋊C₄

—

106

Dic₁₉⋊C₄

—

107

C₄×Dic₁₉

—

108

C₄×Dic₁₉

—

109

C₄×Dic₁₉

—

110

C₄×Dic₁₉

—

111

C₄×Dic₁₉

—

112

C₄×Dic₁₉

—

113

C₄×Dic₁₉

—

114

C₄×Dic₁₉

—

115

C₄×Dic₁₉

—

116

C₄×Dic₁₉

—

117

C₄×Dic₁₉

Q₁₆

yes

complemented

118

C₂×C₁₉⋊C₈

—

119

Dic₇₆

—

120

#9232

—

maximal, Sylow

121

C₂³×C₁₉

#120

yes

characteristic

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

—

125

C₂×C₄×C₁₉

—

126

C₂×C₄×C₁₉

—

127

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

128

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

129

C₂×C₄×C₁₉

C₄×D₄

yes

characteristic

130

C₂×C₄×C₁₉

#121

yes

characteristic

131

C₂×C₄×C₁₉

#121

yes

characteristic

132

C₂×C₄×C₁₉

#123

yes

characteristic

133

C₂×C₄×C₁₉

C₂×Q₁₆

yes

characteristic

134

C₂×C₄×C₁₉

#135

yes

characteristic

135

C₂×C₄×C₁₉

#137

yes

characteristic

136

C₂×C₄×C₁₉

#137

yes

characteristic

137

C₂×Dic₁₉

—

138

C₂×Dic₁₉

—

139

C₂×Dic₁₉

—

140

C₂×Dic₁₉

—

141

C₂×Dic₁₉

—

142

C₂×Dic₁₉

—

143

C₂×Dic₁₉

—

144

C₂×Dic₁₉

—

145

C₂×Dic₁₉

—

146

C₂×Dic₁₉

—

147

C₂×Dic₁₉

—

148

C₂×Dic₁₉

—

149

Dic₃₈

—

150

Dic₃₈

—

151

Dic₃₈

—

152

Dic₃₈

—

153

Dic₃₈

#104

yes

—

154

C₈×C₁₉

—

155

C₈×C₁₉

—

156

C₁₉⋊C₈

—

157

#3104

—

158

C₄²×Q₈

—

159

#1994

—

160

#1503

—

161

#1487

—

162

#1303

D₁₉

yes

characteristic

163

#1276

—

164

C₂²×C₁₉

—

165

C₂²×C₁₉

—

166

C₂²×C₁₉

#386

yes

characteristic

167

C₂²×C₁₉

#451

yes

characteristic

168

C₂²×C₁₉

#452

yes

characteristic

169

C₄×C₁₉

—

170

C₄×C₁₉

—

171

C₄×C₁₉

—

172

C₄×C₁₉

—

173

C₄×C₁₉

C₂×#104

yes

—

174

C₄×C₁₉

C₄×Q₁₆

yes

characteristic

175

C₄×C₁₉

#441

yes

characteristic

176

C₄×C₁₉

#462

yes

characteristic

177

C₄×C₁₉

#464

yes

characteristic

178

Dic₁₉

—

179

Dic₁₉

—

180

Dic₁₉

—

181

Dic₁₉

—

182

Dic₁₉

—

183

Dic₁₉

—

184

#533

—

185

C₂×C₄×Q₈

—

186

C₂×C₄×Q₈

—

187

#484

—

188

#477

—

189

#462

—

190

#451

—

191

C₄×Q₁₆

—

192

#431

—

193

#431

C₂×D₁₉

yes

characteristic

194

#423

C₂×D₁₉

yes

characteristic

195

C₄×C₄⋊C₄

—

196

C₄×C₄⋊C₄

—

197

C₄×C₄⋊C₄

—

198

C₄×C₄⋊C₄

C₂×D₁₉

yes

characteristic

199

C₄³

—

200

C₄³

—

201

#339

—

202

#339

—

203

#328

—

204

Q₈⋊C₈

—

205

C₂×C₁₉

—

206

C₂×C₁₉

—

207

C₂×C₁₉

#1878

yes

characteristic

208

C₂×C₁₉

#1896

yes

characteristic

209

C₂×C₁₉

#1906

yes

characteristic

210

C₂²×Q₈

—

211

C₂×Q₁₆

—

212

C₂×M₁₆

—

213

C₄⋊Q₈

—

214

C₄⋊Q₈

—

215

#125

—

216

C₂²⋊Q₈

—

217

C₂²⋊Q₈

—

218

C₄×Q₈

—

219

C₄×Q₈

—

220

C₄×Q₈

—

221

C₄×Q₈

—

222

C₄×Q₈

—

223

C₄×Q₈

—

224

C₄×Q₈

—

225

#117

—

226

C₂×C₄⋊C₄

—

227

C₂×C₄⋊C₄

—

228

C₂×C₄⋊C₄

—

229

C₂×C₄⋊C₄

—

230

C₂×C₄²

—

231

C₂×C₄²

—

232

C₂×C₄²

—

233

C₂×C₄²

—

234

C₂×C₄²

—

235

C₂×C₄²

—

236

C₂×C₄²

—

237

C₂×C₄²

—

238

C₂×C₄²

C₂²×D₁₉

yes

characteristic

239

#107

—

240

C₄⋊C₈

—

241

C₄⋊C₈

—

242

C₄⋊C₈

—

243

C₄⋊C₈

C₄×D₁₉

yes

—

244

#103

—

245

#103

—

246

C₂²⋊C₈

—

247

C₂²⋊C₈

—

248

C₄×C₈

—

249

C₄×C₈

—

250

#95

—

251

#95

D₇₆

yes

—

252

C₁₉

#9232

yes

characteristic, complemented, Sylow

253

C₂×Q₈

—

254

C₂×Q₈

—

255

C₂×Q₈

—

256

C₂×Q₈

—

257

C₂×Q₈

—

258

C₂²×C₄

—

259

C₂²×C₄

—

260

C₂²×C₄

—

261

C₂²×C₄

—

262

C₂²×C₄

—

263

C₂²×C₄

C₂×D₇₆

yes

characteristic

264

C₂²×C₄

D₄×D₁₉

yes

characteristic

265

C₂²×C₄

D₄×D₁₉

yes

characteristic

266

Q₁₆

—

267

M₁₆

—

268

M₁₆

—

269

C₂×C₈

—

270

C₂×C₈

—

271

C₂×C₈

—

272

C₄⋊C₄

—

273

C₄⋊C₄

—

274

C₄⋊C₄

—

275

C₄⋊C₄

—

276

C₄⋊C₄

—

277

C₄⋊C₄

—

278

C₄⋊C₄

—

279

C₄⋊C₄

—

280

C₄⋊C₄

—

281

C₄⋊C₄

—

282

C₄⋊C₄

—

283

C₄⋊C₄

—

284

C₂²⋊C₄

—

285

C₄²

—

286

C₄²

—

287

C₄²

—

288

C₄²

—

289

C₄²

—

290

C₄²

—

291

C₄²

—

292

C₄²

—

293

C₄²

—

294

C₄²

—

295

C₄²

—

296

C₄²

—

297

C₄²

—

298

C₄²

C₂×C₄×D₁₉

yes

characteristic

299

C₄²

#64541

yes

characteristic

300

C₄²

D₄×D₁₉

yes

characteristic

301

C₄²

#64545

yes

characteristic

302

C₂³

#10597328

yes

characteristic

303

Q₈

—

304

Q₈

—

305

Q₈

—

306

Q₈

—

307

Q₈

—

152

—

308

C₂×C₄

—

309

C₂×C₄

—

310

C₂×C₄

—

311

C₂×C₄

—

312

C₂×C₄

—

313

C₂×C₄

—

314

C₂×C₄

—

315

C₂×C₄

—

316

C₂×C₄

—

317

C₂×C₄

—

318

C₂×C₄

—

319

C₂×C₄

—

320

C₂×C₄

—

321

C₂×C₄

—

322

C₂×C₄

—

323

C₂×C₄

—

324

C₂×C₄

—

325

C₂×C₄

C₄×D₇₆

yes

characteristic

326

C₂×C₄

C₂²⋊C₄×D₁₉

yes

characteristic

327

C₂×C₄

#10597330

yes

characteristic

328

C₂×C₄

#10597339

yes

characteristic

329

C₂×C₄

#10597340

yes

characteristic

330

C₂×C₄

#10597341

yes

characteristic

331

C₂×C₄

#10597358

yes

characteristic

332

C₂×C₄

#10597361

yes

characteristic

333

C₂×C₄

#10597361

yes

characteristic

334

C₂×C₄

Q₁₆×D₁₉

yes

characteristic

335

C₈

—

336

C₈

—

337

C₈

—

152

—

338

C₂²

—

339

C₂²

—

340

C₂²

#11926422

yes

characteristic

341

C₂²

#11926701

yes

characteristic

342

C₂²

#11926707

yes

characteristic

343

C₄

—

344

C₄

—

345

C₄

—

346

C₄

—

347

C₄

—

348

C₄

—

349

C₄

—

350

C₄

—

351

C₄

—

152

—

352

C₄

—

152

—

353

C₄

#104×D₁₉

yes

—

354

C₄

#11926638

yes

characteristic

355

C₄

#11926650

yes

characteristic

356

C₄

#11926753

yes

characteristic

357

C₄

#11926765

yes

characteristic

358

C₂

—

359

C₂

—

360

C₂

#14563977

yes

characteristic

361

C₂

#14564077

yes

characteristic

362

C₂

#14564137

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597330
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1303	C₂
socle	C₂²×C₁₉	#386
prime radical	C₂³×C₁₉	#120
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#1303	D₁₉
hypocenter	C₁₉	#9232
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

subgroup

G/H

center

C₂×C₄

#10597330

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1303

C₂

C₂²×C₁₉

C₂³×C₁₉

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

N	H ≅ G/N	type
12. #11926840	C₄	semidirect
13. #11926755	C₄	semidirect
117. C₄×Dic₁₉	Q₁₆	semidirect
252. C₁₉	#9232	semidirect

H ≅ G/N

type

12. #11926840

C₄

semidirect

13. #11926755

C₄

semidirect

117. C₄×Dic₁₉

Q₁₆

semidirect

252. C₁₉

#9232

semidirect

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

subgroup	index
#14573675	2
C₄×#10597333	2
#14564611	2
#14562133	2
#14562063	2
#14561467	2
C₁₉×#1303	2
#9232	19

subgroup

index

C₁₉×#1303

Subgroups — #18078798

Conjugacy classes of subgroups

Complements

Maximal subgroups