Group #18085276 — subgroups

Subgroups — #18085276

Order 4864.

528 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 528 conjugacy classes of subgroups — too many to draw. Only its 107 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	#14574585	C₂	1	1	yes	maximal, characteristic
2	#14574583	C₂	1	1	yes	maximal, characteristic
3	#14572012	C₂	1	1	yes	maximal, characteristic
4	#14564611	C₂	1	1	yes	maximal, characteristic
5	#14562317	C₂	1	1	yes	maximal, characteristic
6	#14561467	C₂	1	1	yes	maximal, characteristic
7	C₁₉×#1548	C₂	1	1	yes	maximal, characteristic
8	#11927101	C₂²	1	1	yes	characteristic
9	C₂×#10597315	C₂²	1	1	yes	characteristic
10	#11926924	—	2	1	no	—
11	#11926923	—	2	1	no	—
12	#11926895	—	2	1	no	—
13	#11926894	—	2	1	no	—
14	#11926755	—	2	2	no	—
15	#11926751	—	2	2	no	—
16	#11926702	—	2	2	no	—
17	#11926700	—	2	2	no	—
18	#11926597	C₂²	1	1	yes	characteristic
19	#11926451	—	2	2	no	—
20	#11926449	—	2	2	no	—
21	#11926409	—	2	2	no	—
22	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
23	#11926305	—	2	2	no	—
24	#11926292	—	2	2	no	—
25	C₂×C₁₉×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₉×#431	C₂²	1	1	yes	characteristic
27	C₁₉×#423	C₂²	1	1	yes	characteristic
28	C₁₉×#333	—	2	2	no	—
29	C₂²×Q₈×C₁₉	D₄	1	2	yes	—
30	C₂²×Dic₃₈	D₄	1	2	yes	—
31	C₂×M₁₆×C₁₉	—	2	1	no	—
32	C₁₉×C₄⋊Q₈	—	2	1	no	—
33	C₁₉×C₄⋊Q₈	—	2	1	no	—
34	C₁₉×C₄⋊Q₈	—	2	1	no	—
35	C₁₉×C₄⋊Q₈	—	2	1	no	—
36	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
37	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
38	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
39	C₂×#64528	—	2	4	no	—
40	#10597372	—	2	1	no	—
41	C₂×C₄⋊Dic₁₉	—	2	1	no	—
42	C₂×C₄⋊Dic₁₉	—	2	1	no	—
43	#10597370	—	2	1	no	—
44	#10597370	—	2	1	no	—
45	C₂×C₄×Dic₁₉	—	2	1	no	—
46	C₂×C₄×Dic₁₉	—	2	1	no	—
47	C₂×C₄×Dic₁₉	D₄	1	2	yes	—
48	C₂×Dic₇₆	—	2	4	no	—
49	#10597316	—	2	1	no	—
50	#10597315	—	2	1	no	—
51	#10597315	—	2	1	no	—
52	#10597315	—	2	1	no	—
53	#10597315	—	2	1	no	—
54	#10597315	D₄	1	1	yes	characteristic
55	#10597315	D₄	1	1	yes	characteristic
56	C₄×Dic₃₈	—	2	1	no	—
57	C₄×Dic₃₈	—	2	1	no	—
58	C₁₉×C₄⋊C₈	—	2	1	no	—
59	C₁₉×C₄⋊C₈	—	2	1	no	—
60	C₁₉×C₄⋊C₈	D₄	1	2	yes	—
61	C₁₉×C₂²⋊C₈	—	2	1	no	—
62	C₄×C₈×C₁₉	—	2	1	no	—
63	#10597292	—	2	4	no	—
64	C₁₉⋊#95	—	2	8	no	—
65	C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
66	#10597273	—	2	4	no	—
67	C₄⋊(C₁₉⋊C₈)	D₄	1	2	yes	—
68	C₄×C₁₉⋊C₈	—	2	1	no	—
69	C₂×Q₈×C₁₉	—	2	2	no	—
70	C₂×Q₈×C₁₉	—	2	2	no	—
71	C₂×Q₈×C₁₉	—	4	4	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₁₉	—	2	2	no	—
77	C₂²×Dic₁₉	—	2	2	no	—
78	C₂×Dic₃₈	—	2	1	no	—
79	C₂×Dic₃₈	—	2	2	no	—
80	C₂×Dic₃₈	—	2	1	no	—
81	C₂×Dic₃₈	—	2	2	no	—
82	C₂×Dic₃₈	—	4	4	no	—
83	M₁₆×C₁₉	—	4	2	no	—
84	C₂×C₈×C₁₉	—	2	2	no	—
85	C₂×C₈×C₁₉	—	4	1	no	—
86	C₄⋊C₄×C₁₉	—	4	1	no	—
87	C₄⋊C₄×C₁₉	—	4	1	no	—
88	C₄⋊C₄×C₁₉	—	4	1	no	—
89	C₄⋊C₄×C₁₉	—	4	1	no	—
90	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
91	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
92	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₄²×C₁₉	#41	1	1	yes	characteristic
94	C₂²⋊Dic₁₉	—	4	1	no	—
95	#64528	—	8	4	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	—	4	1	no	—
101	C₄⋊Dic₁₉	—	4	1	no	—
102	C₄⋊Dic₁₉	—	4	1	no	—
103	C₄⋊Dic₁₉	—	4	1	no	—
104	Dic₁₉⋊C₄	—	4	1	no	—
105	Dic₁₉⋊C₄	—	4	1	no	—
106	C₄×Dic₁₉	—	2	2	no	—
107	C₄×Dic₁₉	—	4	2	no	—
108	C₄×Dic₁₉	—	4	2	no	—
109	C₄×Dic₁₉	—	4	1	no	—
110	C₄×Dic₁₉	Q₁₆	1	4	yes	complemented
111	C₂×C₁₉⋊C₈	—	2	2	no	—
112	Dic₇₆	—	8	4	no	—
113	#10297	—	19	1	no	maximal, Sylow
114	C₂³×C₁₉	#120	1	1	yes	characteristic
115	Q₈×C₁₉	—	4	4	no	—
116	Q₈×C₁₉	—	8	2	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	2	no	—
119	C₂×C₄×C₁₉	—	4	4	no	—
120	C₂×C₄×C₁₉	—	4	2	no	—
121	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
122	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
123	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
124	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
125	C₂×C₄×C₁₉	#121	1	1	yes	characteristic
126	C₂×C₄×C₁₉	#127	1	1	yes	characteristic
127	C₂×C₄×C₁₉	C₂×Q₁₆	1	2	yes	—
128	C₂×C₄×C₁₉	#137	1	2	yes	—
129	C₂×Dic₁₉	—	2	4	no	—
130	C₂×Dic₁₉	—	4	2	no	—
131	C₂×Dic₁₉	—	4	2	no	—
132	C₂×Dic₁₉	—	4	4	no	—
133	C₂×Dic₁₉	—	4	1	no	—
134	C₂×Dic₁₉	—	4	1	no	—
135	C₂×Dic₁₉	—	4	2	no	—
136	Dic₃₈	—	4	2	no	—
137	Dic₃₈	—	4	4	no	—
138	Dic₃₈	—	4	2	no	—
139	Dic₃₈	—	8	2	no	—
140	C₈×C₁₉	—	4	2	no	—
141	C₈×C₁₉	—	8	1	no	—
142	C₁₉⋊C₈	—	4	2	no	—
143	#3209	—	19	1	no	—
144	#3209	—	19	1	no	—
145	#2862	—	19	1	no	—
146	#1994	—	19	1	no	—
147	#1548	—	19	1	no	—
148	#1548	D₁₉	1	1	yes	characteristic
149	#1276	—	19	1	no	—
150	C₂²×C₁₉	—	2	1	no	—
151	C₂²×C₁₉	—	2	1	no	—
152	C₂²×C₁₉	#392	1	1	yes	characteristic
153	C₂²×C₁₉	#451	1	2	yes	—
154	C₄×C₁₉	—	2	1	no	—
155	C₄×C₁₉	—	2	1	no	—
156	C₄×C₁₉	—	8	2	no	—
157	C₄×C₁₉	#455	1	2	yes	—
158	C₄×C₁₉	#455	1	2	yes	—
159	C₄×C₁₉	#462	1	2	yes	—
160	C₄×C₁₉	#494	1	1	yes	characteristic
161	C₄×C₁₉	#497	1	1	yes	characteristic
162	Dic₁₉	—	4	4	no	—
163	Dic₁₉	—	8	2	no	—
164	Dic₁₉	—	8	1	no	—
165	Dic₁₉	—	8	1	no	—
166	#533	—	19	1	no	—
167	C₂×C₄⋊Q₈	—	19	1	no	—
168	C₂×C₄⋊Q₈	C₂×D₁₉	1	1	yes	characteristic
169	#494	—	38	1	no	—
170	#494	—	38	1	no	—
171	#487	—	38	1	no	—
172	#487	—	38	1	no	—
173	#462	—	38	2	no	—
174	#462	—	38	2	no	—
175	#451	—	38	2	no	—
176	#451	—	38	2	no	—
177	#431	—	19	1	no	—
178	#431	C₂×D₁₉	1	1	yes	characteristic
179	#423	C₂×D₁₉	1	1	yes	characteristic
180	#391	—	38	2	no	—
181	#391	—	38	2	no	—
182	#382	—	38	2	no	—
183	C₄³	—	19	1	no	—
184	#339	—	38	2	no	—
185	#333	—	2	2	no	—
186	#333	—	38	2	no	—
187	C₂×C₁₉	—	2	2	no	—
188	C₂×C₁₉	#2004	1	1	yes	characteristic
189	C₂×C₁₉	#2004	1	1	yes	characteristic
190	C₂×C₁₉	#2016	1	1	yes	characteristic
191	C₂²×Q₈	—	19	2	no	—
192	C₂²×Q₈	D₇₆	1	2	yes	—
193	C₂×Q₁₆	—	38	4	no	—
194	C₂×Q₁₆	—	38	4	no	—
195	C₂×M₁₆	—	2	1	no	—
196	C₄⋊Q₈	—	2	1	no	—
197	C₄⋊Q₈	—	2	1	no	—
198	C₄⋊Q₈	—	2	1	no	—
199	C₄⋊Q₈	—	2	1	no	—
200	C₄⋊Q₈	—	19	1	no	—
201	C₄⋊Q₈	—	19	1	no	—
202	C₄⋊Q₈	—	38	1	no	—
203	C₄⋊Q₈	—	38	1	no	—
204	C₄⋊Q₈	—	38	1	no	—
205	C₄⋊Q₈	—	38	1	no	—
206	#125	—	38	1	no	—
207	C₂²⋊Q₈	—	38	1	no	—
208	C₂²⋊Q₈	—	38	1	no	—
209	C₄×Q₈	—	38	1	no	—
210	C₄×Q₈	—	38	1	no	—
211	#117	—	38	1	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	—	2	1	no	—
214	C₂×C₄⋊C₄	—	38	1	no	—
215	C₂×C₄⋊C₄	—	38	1	no	—
216	C₂×C₄²	—	19	2	no	—
217	C₂×C₄²	—	38	1	no	—
218	C₂×C₄²	—	38	1	no	—
219	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
220	C₄⋊C₈	—	2	1	no	—
221	C₄⋊C₈	—	2	1	no	—
222	C₄⋊C₈	—	19	2	no	—
223	C₄⋊C₈	C₂²⋊D₁₉	1	2	yes	—
224	#103	—	38	4	no	—
225	#103	—	38	4	no	—
226	C₂²⋊C₈	—	2	1	no	—
227	C₂²⋊C₈	—	38	1	no	—
228	C₄×C₈	—	2	1	no	—
229	C₄×C₈	—	38	1	no	—
230	#95	—	38	8	no	—
231	C₁₉	#10297	1	1	yes	characteristic, complemented, Sylow
232	C₂×Q₈	—	2	2	no	—
233	C₂×Q₈	—	2	2	no	—
234	C₂×Q₈	—	4	4	no	—
235	C₂×Q₈	—	38	2	no	—
236	C₂×Q₈	—	38	1	no	—
237	C₂×Q₈	—	38	1	no	—
238	C₂×Q₈	—	38	2	no	—
239	C₂×Q₈	—	76	4	no	—
240	C₂²×C₄	—	2	2	no	—
241	C₂²×C₄	—	38	2	no	—
242	C₂²×C₄	—	38	2	no	—
243	C₂²×C₄	C₂×D₇₆	1	1	yes	characteristic
244	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
245	C₂²×C₄	D₄×D₁₉	1	1	yes	characteristic
246	Q₁₆	—	152	4	no	—
247	Q₁₆	—	152	4	no	—
248	M₁₆	—	4	2	no	—
249	C₂×C₈	—	2	2	no	—
250	C₂×C₈	—	4	1	no	—
251	C₂×C₈	—	38	2	no	—
252	C₄⋊C₄	—	4	1	no	—
253	C₄⋊C₄	—	4	1	no	—
254	C₄⋊C₄	—	4	1	no	—
255	C₄⋊C₄	—	4	1	no	—
256	C₄⋊C₄	—	38	1	no	—
257	C₄⋊C₄	—	38	1	no	—
258	C₄⋊C₄	—	38	1	no	—
259	C₄⋊C₄	—	38	1	no	—
260	C₄⋊C₄	—	76	1	no	—
261	C₄⋊C₄	—	76	1	no	—
262	C₄⋊C₄	—	76	1	no	—
263	C₄⋊C₄	—	76	1	no	—
264	C₄⋊C₄	—	76	1	no	—
265	C₄⋊C₄	—	76	1	no	—
266	C₂²⋊C₄	—	76	1	no	—
267	C₄²	—	19	4	no	—
268	C₄²	—	38	2	no	—
269	C₄²	—	76	2	no	—
270	C₄²	—	76	2	no	—
271	C₄²	—	76	1	no	—
272	C₄²	#64541	1	1	yes	characteristic
273	C₄²	D₄×D₁₉	1	1	yes	characteristic
274	C₄²	D₄×D₁₉	1	1	yes	characteristic
275	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
276	C₂³	#10597328	1	1	yes	characteristic
277	Q₈	—	4	4	no	—
278	Q₈	—	8	2	no	—
279	Q₈	—	76	2	no	—
280	Q₈	—	76	4	no	—
281	Q₈	—	76	2	no	—
282	Q₈	—	152	2	no	—
283	C₂×C₄	—	2	2	no	—
284	C₂×C₄	—	2	2	no	—
285	C₂×C₄	—	4	4	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	38	4	no	—
288	C₂×C₄	—	76	2	no	—
289	C₂×C₄	—	76	2	no	—
290	C₂×C₄	—	76	4	no	—
291	C₂×C₄	—	76	1	no	—
292	C₂×C₄	—	76	1	no	—
293	C₂×C₄	—	76	2	no	—
294	C₂×C₄	#10597328	1	1	yes	characteristic
295	C₂×C₄	#10597330	1	1	yes	characteristic
296	C₂×C₄	#10597330	1	1	yes	characteristic
297	C₂×C₄	#10597361	1	2	yes	—
298	C₂×C₄	Q₁₆×D₁₉	1	2	yes	—
299	C₂×C₄	#10597376	1	1	yes	characteristic
300	C₂×C₄	#10597383	1	1	yes	characteristic
301	C₂×C₄	#10597386	1	1	yes	characteristic
302	C₈	—	4	2	no	—
303	C₈	—	8	1	no	—
304	C₈	—	76	2	no	—
305	C₂²	—	2	1	no	—
306	C₂²	—	2	1	no	—
307	C₂²	#11926453	1	1	yes	characteristic
308	C₂²	#11926701	1	2	yes	—
309	C₄	—	2	1	no	—
310	C₄	—	2	1	no	—
311	C₄	—	8	2	no	—
312	C₄	—	76	4	no	—
313	C₄	—	152	2	no	—
314	C₄	—	152	1	no	—
315	C₄	—	152	1	no	—
316	C₄	#11926720	1	2	yes	—
317	C₄	#11926724	1	2	yes	—
318	C₄	#11926753	1	2	yes	—
319	C₄	#11926922	1	1	yes	characteristic
320	C₄	#11926935	1	1	yes	characteristic
321	C₂	—	2	2	no	—
322	C₂	#14564665	1	1	yes	characteristic
323	C₂	#14564666	1	1	yes	characteristic
324	C₂	#14564736	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14574585

C₂

yes

maximal, characteristic

#14574583

C₂

yes

maximal, characteristic

#14572012

C₂

yes

maximal, characteristic

#14564611

C₂

yes

maximal, characteristic

#14562317

C₂

yes

maximal, characteristic

#14561467

C₂

yes

maximal, characteristic

C₁₉×#1548

C₂

yes

maximal, characteristic

#11927101

C₂²

yes

characteristic

C₂×#10597315

C₂²

yes

—

—

—

—

—

—

—

—

C₂²

yes

—

—

—

C₄²×Dic₁₉

C₂²

yes

characteristic

#11926305

—

#11926292

—

C₂×C₁₉×C₄⋊Q₈

C₂²

yes

characteristic

C₁₉×#431

C₂²

yes

characteristic

C₁₉×#423

C₂²

yes

characteristic

C₁₉×#333

—

C₂²×Q₈×C₁₉

D₄

yes

—

C₂²×Dic₃₈

D₄

yes

—

C₂×M₁₆×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×#64528

—

#10597372

—

C₂×C₄⋊Dic₁₉

—

C₂×C₄⋊Dic₁₉

—

#10597370

—

#10597370

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

D₄

yes

—

C₂×Dic₇₆

—

—

—

—

—

—

D₄

yes

characteristic

#10597315

D₄

yes

characteristic

C₄×Dic₃₈

—

C₄×Dic₃₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

—

C₁₉×C₄⋊C₈

D₄

yes

—

C₁₉×C₂²⋊C₈

—

C₄×C₈×C₁₉

—

#10597292

—

C₁₉⋊#95

—

C₂²⋊(C₁₉⋊C₈)

—

#10597273

—

C₄⋊(C₁₉⋊C₈)

D₄

yes

—

C₄×C₁₉⋊C₈

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

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

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

C₂×Dic₃₈

—

M₁₆×C₁₉

—

C₂×C₈×C₁₉

—

C₂×C₈×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄²×C₁₉

#41

yes

characteristic

C₂²⋊Dic₁₉

—

#64528

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

C₄⋊Dic₁₉

—

100

C₄⋊Dic₁₉

—

101

C₄⋊Dic₁₉

—

102

C₄⋊Dic₁₉

—

103

C₄⋊Dic₁₉

—

104

Dic₁₉⋊C₄

—

105

Dic₁₉⋊C₄

—

106

C₄×Dic₁₉

—

107

C₄×Dic₁₉

—

108

C₄×Dic₁₉

—

109

C₄×Dic₁₉

—

110

C₄×Dic₁₉

Q₁₆

yes

complemented

111

C₂×C₁₉⋊C₈

—

112

Dic₇₆

—

113

#10297

—

maximal, Sylow

114

C₂³×C₁₉

#120

yes

characteristic

115

Q₈×C₁₉

—

116

Q₈×C₁₉

—

117

C₂×C₄×C₁₉

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

#120

yes

characteristic

122

C₂×C₄×C₁₉

#120

yes

characteristic

123

C₂×C₄×C₁₉

#121

yes

characteristic

124

C₂×C₄×C₁₉

#121

yes

characteristic

125

C₂×C₄×C₁₉

#121

yes

characteristic

126

C₂×C₄×C₁₉

#127

yes

characteristic

127

C₂×C₄×C₁₉

C₂×Q₁₆

yes

—

128

C₂×C₄×C₁₉

#137

yes

—

129

C₂×Dic₁₉

—

130

C₂×Dic₁₉

—

131

C₂×Dic₁₉

—

132

C₂×Dic₁₉

—

133

C₂×Dic₁₉

—

134

C₂×Dic₁₉

—

135

C₂×Dic₁₉

—

136

Dic₃₈

—

137

Dic₃₈

—

138

Dic₃₈

—

139

Dic₃₈

—

140

C₈×C₁₉

—

141

C₈×C₁₉

—

142

C₁₉⋊C₈

—

143

#3209

—

144

#3209

—

145

#2862

—

146

#1994

—

147

#1548

—

148

#1548

D₁₉

yes

characteristic

149

#1276

—

150

C₂²×C₁₉

—

151

C₂²×C₁₉

—

152

C₂²×C₁₉

#392

yes

characteristic

153

C₂²×C₁₉

#451

yes

—

154

C₄×C₁₉

—

155

C₄×C₁₉

—

156

C₄×C₁₉

—

157

C₄×C₁₉

#455

yes

—

158

C₄×C₁₉

#455

yes

—

159

C₄×C₁₉

#462

yes

—

160

C₄×C₁₉

#494

yes

characteristic

161

C₄×C₁₉

#497

yes

characteristic

162

Dic₁₉

—

163

Dic₁₉

—

164

Dic₁₉

—

165

Dic₁₉

—

166

#533

—

167

C₂×C₄⋊Q₈

—

168

C₂×C₄⋊Q₈

C₂×D₁₉

yes

characteristic

169

#494

—

170

#494

—

171

#487

—

172

#487

—

173

#462

—

174

#462

—

175

#451

—

176

#451

—

177

#431

—

178

#431

C₂×D₁₉

yes

characteristic

179

#423

C₂×D₁₉

yes

characteristic

180

#391

—

181

#391

—

182

#382

—

183

C₄³

—

184

#339

—

185

#333

—

186

#333

—

187

C₂×C₁₉

—

188

C₂×C₁₉

#2004

yes

characteristic

189

C₂×C₁₉

#2004

yes

characteristic

190

C₂×C₁₉

#2016

yes

characteristic

191

C₂²×Q₈

—

192

C₂²×Q₈

D₇₆

yes

—

193

C₂×Q₁₆

—

194

C₂×Q₁₆

—

195

C₂×M₁₆

—

196

C₄⋊Q₈

—

197

C₄⋊Q₈

—

198

C₄⋊Q₈

—

199

C₄⋊Q₈

—

200

C₄⋊Q₈

—

201

C₄⋊Q₈

—

202

C₄⋊Q₈

—

203

C₄⋊Q₈

—

204

C₄⋊Q₈

—

205

C₄⋊Q₈

—

206

#125

—

207

C₂²⋊Q₈

—

208

C₂²⋊Q₈

—

209

C₄×Q₈

—

210

C₄×Q₈

—

211

#117

—

212

C₂×C₄⋊C₄

—

213

C₂×C₄⋊C₄

—

214

C₂×C₄⋊C₄

—

215

C₂×C₄⋊C₄

—

216

C₂×C₄²

—

217

C₂×C₄²

—

218

C₂×C₄²

—

219

C₂×C₄²

C₂²×D₁₉

yes

characteristic

220

C₄⋊C₈

—

221

C₄⋊C₈

—

222

C₄⋊C₈

—

223

C₄⋊C₈

C₂²⋊D₁₉

yes

—

224

#103

—

225

#103

—

226

C₂²⋊C₈

—

227

C₂²⋊C₈

—

228

C₄×C₈

—

229

C₄×C₈

—

230

#95

—

231

C₁₉

#10297

yes

characteristic, complemented, Sylow

232

C₂×Q₈

—

233

C₂×Q₈

—

234

C₂×Q₈

—

235

C₂×Q₈

—

236

C₂×Q₈

—

237

C₂×Q₈

—

238

C₂×Q₈

—

239

C₂×Q₈

—

240

C₂²×C₄

—

241

C₂²×C₄

—

242

C₂²×C₄

—

243

C₂²×C₄

C₂×D₇₆

yes

characteristic

244

C₂²×C₄

D₄×D₁₉

yes

characteristic

245

C₂²×C₄

D₄×D₁₉

yes

characteristic

246

Q₁₆

—

152

—

247

Q₁₆

—

152

—

248

M₁₆

—

249

C₂×C₈

—

250

C₂×C₈

—

251

C₂×C₈

—

252

C₄⋊C₄

—

253

C₄⋊C₄

—

254

C₄⋊C₄

—

255

C₄⋊C₄

—

256

C₄⋊C₄

—

257

C₄⋊C₄

—

258

C₄⋊C₄

—

259

C₄⋊C₄

—

260

C₄⋊C₄

—

261

C₄⋊C₄

—

262

C₄⋊C₄

—

263

C₄⋊C₄

—

264

C₄⋊C₄

—

265

C₄⋊C₄

—

266

C₂²⋊C₄

—

267

C₄²

—

268

C₄²

—

269

C₄²

—

270

C₄²

—

271

C₄²

—

272

C₄²

#64541

yes

characteristic

273

C₄²

D₄×D₁₉

yes

characteristic

274

C₄²

D₄×D₁₉

yes

characteristic

275

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

276

C₂³

#10597328

yes

characteristic

277

Q₈

—

278

Q₈

—

279

Q₈

—

280

Q₈

—

281

Q₈

—

282

Q₈

—

152

—

283

C₂×C₄

—

284

C₂×C₄

—

285

C₂×C₄

—

286

C₂×C₄

—

287

C₂×C₄

—

288

C₂×C₄

—

289

C₂×C₄

—

290

C₂×C₄

—

291

C₂×C₄

—

292

C₂×C₄

—

293

C₂×C₄

—

294

C₂×C₄

#10597328

yes

characteristic

295

C₂×C₄

#10597330

yes

characteristic

296

C₂×C₄

#10597330

yes

characteristic

297

C₂×C₄

#10597361

yes

—

298

C₂×C₄

Q₁₆×D₁₉

yes

—

299

C₂×C₄

#10597376

yes

characteristic

300

C₂×C₄

#10597383

yes

characteristic

301

C₂×C₄

#10597386

yes

characteristic

302

C₈

—

303

C₈

—

304

C₈

—

305

C₂²

—

306

C₂²

—

307

C₂²

#11926453

yes

characteristic

308

C₂²

#11926701

yes

—

309

C₄

—

310

C₄

—

311

C₄

—

312

C₄

—

313

C₄

—

152

—

314

C₄

—

152

—

315

C₄

—

152

—

316

C₄

#11926720

yes

—

317

C₄

#11926724

yes

—

318

C₄

#11926753

yes

—

319

C₄

#11926922

yes

characteristic

320

C₄

#11926935

yes

characteristic

321

C₂

—

322

C₂

#14564665

yes

characteristic

323

C₂

#14564666

yes

characteristic

324

C₂

#14564736

yes

characteristic

	subgroup	G/H
center	C₂²	#11926453
commutator, cosocle	C₂×C₄²×C₁₉	C₂³
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#1548	C₂
socle	C₂²×C₁₉	#392
prime radical	C₂³×C₁₉	#120
hypercenter	#1548	D₁₉
hypocenter	C₁₉	#10297
LCS	G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

subgroup

G/H

center

C₂²

#11926453

commutator, cosocle

C₂×C₄²×C₁₉

C₂³

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#1548

C₂

C₂²×C₁₉

C₂³×C₁₉

D₁₉

C₁₉

G ▷ C₂×C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1548

N	H ≅ G/N	type
110. C₄×Dic₁₉	Q₁₆	semidirect
231. C₁₉	#10297	semidirect

H ≅ G/N

type

110. C₄×Dic₁₉

Q₁₆

semidirect

231. C₁₉

#10297

semidirect

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

subgroup	index
#14574585	2
#14574583	2
#14572012	2
#14564611	2
#14562317	2
#14561467	2
C₁₉×#1548	2
#10297	19

subgroup

index

C₁₉×#1548

Subgroups — #18085276

Conjugacy classes of subgroups

Complements

Maximal subgroups