Group #18075098 — subgroups

Subgroups — #18075098

Order 4864.

728 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 728 conjugacy classes of subgroups — too many to draw. Only its 139 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	#14564613	C₂	1	2	yes	maximal, complemented
2	#14564464	C₂	1	1	yes	maximal, characteristic
3	#14562373	C₂	1	2	yes	maximal, complemented
4	#14562370	C₂	1	1	yes	maximal, characteristic
5	C₁₉×#3550	C₂	1	1	yes	maximal, characteristic
6	#11926568	C₂²	1	2	yes	—
7	#11926568	C₂²	1	1	yes	characteristic
8	C₂×#10597294	—	2	2	no	—
9	C₄²×Dic₁₉	C₂²	1	1	yes	characteristic
10	#11926303	—	2	4	no	—
11	#11926293	—	2	1	no	—
12	#11926290	—	2	2	no	—
13	#11926290	—	2	2	no	—
14	#11926288	—	2	1	no	—
15	C₁₉×#563	C₄	1	4	yes	complemented
16	C₁₉×#559	—	2	1	no	—
17	Q₈²×C₁₉	—	2	1	no	—
18	C₁₉×#556	—	2	2	no	—
19	D₄×Q₈×C₁₉	—	2	2	no	—
20	C₁₉×#542	—	2	4	no	—
21	C₁₉×#536	—	2	2	no	—
22	C₁₉×#533	C₂²	1	2	yes	—
23	C₁₉×#532	C₂²	1	1	yes	characteristic
24	C₂×#41×C₁₉	D₄	1	2	yes	—
25	C₂²×Q₈×C₁₉	—	2	2	no	—
26	C₁₉×C₄⋊Q₈	—	2	4	no	—
27	C₁₉×C₄⋊Q₈	—	2	4	no	—
28	C₁₉×C₄⋊Q₈	D₄	1	1	yes	characteristic
29	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
30	C₁₉×C₄⋊Q₈	D₄	1	2	yes	—
31	C₁₉×#127	D₄	1	1	yes	characteristic
32	C₁₉×#126	—	2	8	no	—
33	C₁₉×#125	C₂×C₄	1	4	yes	—
34	C₁₉×#124	—	2	4	no	—
35	C₁₉×#124	—	2	4	no	—
36	C₁₉×#124	C₂×C₄	1	2	yes	—
37	C₁₉×#123	—	2	4	no	—
38	C₁₉×#123	—	2	4	no	—
39	C₁₉×C₂²⋊Q₈	—	2	4	no	—
40	C₁₉×C₂²⋊Q₈	—	2	2	no	—
41	C₁₉×C₂²⋊Q₈	—	2	2	no	—
42	C₁₉×C₂²⋊Q₈	—	2	8	no	—
43	C₁₉×#121	—	2	2	no	—
44	C₄×Q₈×C₁₉	—	2	4	no	—
45	C₄×Q₈×C₁₉	—	2	2	no	—
46	C₄×Q₈×C₁₉	—	2	2	no	—
47	C₄×D₄×C₁₉	—	2	4	no	—
48	C₄×D₄×C₁₉	—	2	2	no	—
49	C₁₉×#117	—	2	2	no	—
50	C₁₉×#117	D₄	1	4	yes	—
51	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
52	C₂×C₄×Dic₁₉	—	2	1	no	—
53	C₂×C₄×Dic₁₉	—	2	2	no	—
54	C₂×#64520	—	2	1	no	—
55	C₂×#64520	—	2	2	no	—
56	#10597294	—	4	4	no	—
57	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
58	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
59	C₄⋊(C₁₉⋊C₈)	—	2	2	no	—
60	#41×C₁₉	—	4	2	no	—
61	#41×C₁₉	—	4	2	no	—
62	C₂×Q₈×C₁₉	—	2	4	no	—
63	C₂×Q₈×C₁₉	—	2	2	no	—
64	C₂×Q₈×C₁₉	—	2	2	no	—
65	C₂×Q₈×C₁₉	—	8	2	no	—
66	C₂×Q₈×C₁₉	—	8	2	no	—
67	C₂×Q₈×C₁₉	C₂²⋊C₄	1	2	yes	—
68	C₂×D₄×C₁₉	—	2	2	no	—
69	C₂×D₄×C₁₉	—	2	2	no	—
70	C₂×D₄×C₁₉	C₂²⋊C₄	1	2	yes	—
71	C₂²×C₄×C₁₉	—	2	4	no	—
72	C₂²×C₄×C₁₉	—	2	2	no	—
73	C₂²×C₄×C₁₉	C₂×D₄	1	2	yes	—
74	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
75	C₂²×Dic₁₉	—	4	1	no	—
76	C₄⋊C₄×C₁₉	—	2	8	no	—
77	C₄⋊C₄×C₁₉	—	2	4	no	—
78	C₄⋊C₄×C₁₉	—	2	4	no	—
79	C₄⋊C₄×C₁₉	—	2	2	no	—
80	C₄⋊C₄×C₁₉	—	2	2	no	—
81	C₄⋊C₄×C₁₉	—	2	2	no	—
82	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
83	C₄⋊C₄×C₁₉	C₂²⋊C₄	1	4	yes	—
84	C₂²⋊C₄×C₁₉	—	2	4	no	—
85	C₂²⋊C₄×C₁₉	—	2	8	no	—
86	C₂²⋊C₄×C₁₉	—	2	4	no	—
87	C₂²⋊C₄×C₁₉	—	2	4	no	—
88	C₄²×C₁₉	—	2	4	no	—
89	C₄²×C₁₉	—	2	4	no	—
90	C₄²×C₁₉	C₂²×C₄	1	1	yes	characteristic
91	C₄²×C₁₉	C₂×D₄	1	2	yes	—
92	C₄²×C₁₉	C₂×D₄	1	1	yes	characteristic
93	C₄×Dic₁₉	—	2	2	no	—
94	C₄×Dic₁₉	—	2	4	no	—
95	C₄×Dic₁₉	—	4	2	no	—
96	C₄×Dic₁₉	—	4	1	no	—
97	#64520	—	4	2	no	—
98	#64520	—	4	4	no	—
99	C₂×C₁₉⋊C₈	—	4	1	no	—
100	C₂×C₁₉⋊C₈	—	4	2	no	—
101	#8531	—	19	1	no	maximal, Sylow
102	C₂³×C₁₉	—	2	2	no	—
103	C₂³×C₁₉	#120	1	1	yes	characteristic
104	Q₈×C₁₉	—	4	2	no	—
105	Q₈×C₁₉	—	4	2	no	—
106	Q₈×C₁₉	—	4	2	no	—
107	Q₈×C₁₉	—	4	2	no	—
108	Q₈×C₁₉	—	4	2	no	—
109	Q₈×C₁₉	—	8	4	no	—
110	D₄×C₁₉	—	4	2	no	—
111	D₄×C₁₉	—	4	2	no	—
112	D₄×C₁₉	—	4	2	no	—
113	D₄×C₁₉	—	8	2	no	—
114	C₂×C₄×C₁₉	—	2	1	no	—
115	C₂×C₄×C₁₉	—	2	2	no	—
116	C₂×C₄×C₁₉	—	2	1	no	—
117	C₂×C₄×C₁₉	—	2	2	no	—
118	C₂×C₄×C₁₉	—	2	4	no	—
119	C₂×C₄×C₁₉	—	2	2	no	—
120	C₂×C₄×C₁₉	—	2	4	no	—
121	C₂×C₄×C₁₉	—	4	2	no	—
122	C₂×C₄×C₁₉	—	4	2	no	—
123	C₂×C₄×C₁₉	—	8	4	no	—
124	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	2	yes	—
125	C₂×C₄×C₁₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₁₉	#120	1	1	yes	characteristic
127	C₂×C₄×C₁₉	#120	1	2	yes	—
128	C₂×Dic₁₉	—	4	2	no	—
129	C₂×Dic₁₉	—	4	4	no	—
130	C₁₉⋊C₈	—	8	1	no	—
131	C₁₉⋊C₈	—	8	2	no	—
132	#3550	D₁₉	1	1	yes	characteristic
133	#1994	—	19	2	no	—
134	#1962	—	19	1	no	—
135	#1561	—	19	2	no	—
136	#1560	—	19	1	no	—
137	C₂²×C₁₉	—	2	1	no	—
138	C₂²×C₁₉	—	2	2	no	—
139	C₂²×C₁₉	—	4	2	no	—
140	C₂²×C₁₉	—	4	4	no	—
141	C₂²×C₁₉	#379	1	1	yes	characteristic
142	C₄×C₁₉	—	2	1	no	—
143	C₄×C₁₉	—	2	2	no	—
144	C₄×C₁₉	—	4	2	no	—
145	C₄×C₁₉	—	4	4	no	—
146	C₄×C₁₉	—	4	4	no	—
147	C₄×C₁₉	#453	1	1	yes	characteristic
148	C₄×C₁₉	#454	1	2	yes	—
149	C₄×C₁₉	#455	1	1	yes	characteristic
150	C₄×C₁₉	#456	1	2	yes	—
151	Dic₁₉	—	4	4	no	—
152	#563	Dic₁₉	1	4	yes	complemented
153	#559	—	2	1	no	—
154	Q₈²	—	2	1	no	—
155	#556	—	2	2	no	—
156	D₄×Q₈	—	2	2	no	—
157	#542	—	2	4	no	—
158	#536	—	2	2	no	—
159	#533	C₂×D₁₉	1	2	yes	—
160	#532	C₂×D₁₉	1	1	yes	characteristic
161	#423	—	19	2	no	—
162	#423	—	19	1	no	—
163	C₂×#104	—	38	2	no	—
164	C₄³	—	19	1	no	—
165	#339	—	38	4	no	—
166	#333	—	38	1	no	—
167	#332	—	38	2	no	—
168	#332	—	38	2	no	—
169	#331	—	38	1	no	—
170	C₂×C₁₉	—	4	1	no	—
171	C₂×C₁₉	—	8	2	no	—
172	C₂×C₁₉	#1792	1	1	yes	characteristic
173	C₂×C₁₉	#1793	1	2	yes	—
174	C₂×#41	C₂²⋊D₁₉	1	2	yes	—
175	C₂²×Q₈	—	2	2	no	—
176	C₂×M₁₆	—	38	2	no	—
177	C₂×M₁₆	—	38	1	no	—
178	C₄⋊Q₈	—	2	4	no	—
179	C₄⋊Q₈	—	2	4	no	—
180	C₄⋊Q₈	C₂²⋊D₁₉	1	1	yes	characteristic
181	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
182	C₄⋊Q₈	C₂²⋊D₁₉	1	2	yes	—
183	#127	C₂²⋊D₁₉	1	1	yes	characteristic
184	#126	—	2	8	no	—
185	#125	C₂×Dic₁₉	1	4	yes	—
186	#124	—	2	4	no	—
187	#124	—	2	4	no	—
188	#124	C₂×Dic₁₉	1	2	yes	—
189	#123	—	2	4	no	—
190	#123	—	2	4	no	—
191	C₂²⋊Q₈	—	2	4	no	—
192	C₂²⋊Q₈	—	2	2	no	—
193	C₂²⋊Q₈	—	2	2	no	—
194	C₂²⋊Q₈	—	2	8	no	—
195	#121	—	2	2	no	—
196	C₄×Q₈	—	2	4	no	—
197	C₄×Q₈	—	2	2	no	—
198	C₄×Q₈	—	2	2	no	—
199	C₄×D₄	—	2	4	no	—
200	C₄×D₄	—	2	2	no	—
201	#117	—	2	2	no	—
202	#117	C₂²⋊D₁₉	1	4	yes	—
203	C₂×C₄²	—	38	2	no	—
204	C₂×C₄²	—	38	1	no	—
205	C₂×C₄²	C₂²×D₁₉	1	1	yes	characteristic
206	C₄⋊C₈	—	38	2	no	—
207	C₄⋊C₈	—	38	2	no	—
208	C₄⋊C₈	—	38	2	no	—
209	#104	—	76	4	no	—
210	C₁₉	#8531	1	1	yes	characteristic, complemented, Sylow
211	#41	—	4	2	no	—
212	#41	—	4	2	no	—
213	C₂×Q₈	—	2	4	no	—
214	C₂×Q₈	—	2	2	no	—
215	C₂×Q₈	—	2	2	no	—
216	C₂×Q₈	—	8	2	no	—
217	C₂×Q₈	—	8	2	no	—
218	C₂×Q₈	C₂²⋊Dic₁₉	1	2	yes	—
219	C₂×D₄	—	2	2	no	—
220	C₂×D₄	—	2	2	no	—
221	C₂×D₄	C₂²⋊Dic₁₉	1	2	yes	—
222	C₂²×C₄	—	2	4	no	—
223	C₂²×C₄	—	2	2	no	—
224	C₂²×C₄	—	76	1	no	—
225	C₂²×C₄	C₂×C₂²⋊D₁₉	1	2	yes	—
226	C₂²×C₄	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
227	M₁₆	—	76	2	no	—
228	M₁₆	—	76	4	no	—
229	C₂×C₈	—	76	1	no	—
230	C₂×C₈	—	76	2	no	—
231	C₄⋊C₄	—	2	8	no	—
232	C₄⋊C₄	—	2	4	no	—
233	C₄⋊C₄	—	2	4	no	—
234	C₄⋊C₄	—	2	2	no	—
235	C₄⋊C₄	—	2	2	no	—
236	C₄⋊C₄	—	2	2	no	—
237	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
238	C₄⋊C₄	C₂²⋊Dic₁₉	1	4	yes	—
239	C₂²⋊C₄	—	2	4	no	—
240	C₂²⋊C₄	—	2	8	no	—
241	C₂²⋊C₄	—	2	4	no	—
242	C₂²⋊C₄	—	2	4	no	—
243	C₄²	—	2	4	no	—
244	C₄²	—	2	4	no	—
245	C₄²	—	38	2	no	—
246	C₄²	—	38	4	no	—
247	C₄²	—	76	2	no	—
248	C₄²	—	76	1	no	—
249	C₄²	C₂²×Dic₁₉	1	1	yes	characteristic
250	C₄²	C₂×C₂²⋊D₁₉	1	2	yes	—
251	C₄²	C₂×C₂²⋊D₁₉	1	1	yes	characteristic
252	C₂³	—	2	2	no	—
253	C₂³	#10597399	1	1	yes	characteristic
254	Q₈	—	4	2	no	—
255	Q₈	—	4	2	no	—
256	Q₈	—	4	2	no	—
257	Q₈	—	4	2	no	—
258	Q₈	—	4	2	no	—
259	Q₈	—	8	4	no	—
260	D₄	—	4	2	no	—
261	D₄	—	4	2	no	—
262	D₄	—	4	2	no	—
263	D₄	—	8	2	no	—
264	C₂×C₄	—	2	1	no	—
265	C₂×C₄	—	2	2	no	—
266	C₂×C₄	—	2	1	no	—
267	C₂×C₄	—	2	2	no	—
268	C₂×C₄	—	2	4	no	—
269	C₂×C₄	—	2	2	no	—
270	C₂×C₄	—	2	4	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	2	no	—
273	C₂×C₄	—	8	4	no	—
274	C₂×C₄	—	76	2	no	—
275	C₂×C₄	—	76	4	no	—
276	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	2	yes	—
277	C₂×C₄	C₂×C₂²⋊Dic₁₉	1	1	yes	characteristic
278	C₂×C₄	#10597399	1	1	yes	characteristic
279	C₂×C₄	#10597399	1	2	yes	—
280	C₈	—	152	1	no	—
281	C₈	—	152	2	no	—
282	C₂²	—	2	1	no	—
283	C₂²	—	2	2	no	—
284	C₂²	—	4	2	no	—
285	C₂²	—	4	4	no	—
286	C₂²	#11926400	1	1	yes	characteristic
287	C₄	—	2	1	no	—
288	C₄	—	2	2	no	—
289	C₄	—	4	2	no	—
290	C₄	—	4	4	no	—
291	C₄	—	4	4	no	—
292	C₄	—	76	4	no	—
293	C₄	#11926712	1	1	yes	characteristic
294	C₄	#11926717	1	2	yes	—
295	C₄	#11926722	1	1	yes	characteristic
296	C₄	#11926727	1	2	yes	—
297	C₂	—	4	1	no	—
298	C₂	—	8	2	no	—
299	C₂	#14563589	1	1	yes	characteristic
300	C₂	#14563594	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#14564613

C₂

yes

maximal, complemented

#14564464

C₂

yes

maximal, characteristic

#14562373

C₂

yes

maximal, complemented

#14562370

C₂

yes

maximal, characteristic

C₁₉×#3550

C₂

yes

maximal, characteristic

#11926568

C₂²

yes

—

#11926568

C₂²

yes

characteristic

C₂×#10597294

—

C₄²×Dic₁₉

C₂²

yes

—

—

—

—

—

C₁₉×#563

C₄

yes

complemented

C₁₉×#559

—

Q₈²×C₁₉

—

C₁₉×#556

—

D₄×Q₈×C₁₉

—

C₁₉×#542

—

C₁₉×#536

—

C₁₉×#533

C₂²

yes

—

C₁₉×#532

C₂²

yes

characteristic

C₂×#41×C₁₉

D₄

yes

—

C₂²×Q₈×C₁₉

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

—

C₁₉×C₄⋊Q₈

D₄

yes

characteristic

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×C₄⋊Q₈

D₄

yes

—

C₁₉×#127

D₄

yes

characteristic

C₁₉×#126

—

C₁₉×#125

C₂×C₄

yes

—

C₁₉×#124

—

C₁₉×#124

—

C₁₉×#124

C₂×C₄

yes

—

C₁₉×#123

—

C₁₉×#123

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×C₂²⋊Q₈

—

C₁₉×#121

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×Q₈×C₁₉

—

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₁₉×#117

—

C₁₉×#117

D₄

yes

—

C₂×C₄²×C₁₉

C₂³

yes

characteristic

C₂×C₄×Dic₁₉

—

C₂×C₄×Dic₁₉

—

C₂×#64520

—

C₂×#64520

—

#10597294

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

C₄⋊(C₁₉⋊C₈)

—

#41×C₁₉

—

#41×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

—

C₂×Q₈×C₁₉

C₂²⋊C₄

yes

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₂×D₄

yes

—

C₂²×C₄×C₁₉

C₂×D₄

yes

characteristic

C₂²×Dic₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₄⋊C₄×C₁₉

C₂²⋊C₄

yes

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

C₂²×C₄

yes

characteristic

C₄²×C₁₉

C₂×D₄

yes

—

C₄²×C₁₉

C₂×D₄

yes

characteristic

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

C₄×Dic₁₉

—

#64520

—

#64520

—

C₂×C₁₉⋊C₈

—

100

C₂×C₁₉⋊C₈

—

101

#8531

—

maximal, Sylow

102

C₂³×C₁₉

—

103

C₂³×C₁₉

#120

yes

characteristic

104

Q₈×C₁₉

—

105

Q₈×C₁₉

—

106

Q₈×C₁₉

—

107

Q₈×C₁₉

—

108

Q₈×C₁₉

—

109

Q₈×C₁₉

—

110

D₄×C₁₉

—

111

D₄×C₁₉

—

112

D₄×C₁₉

—

113

D₄×C₁₉

—

114

C₂×C₄×C₁₉

—

115

C₂×C₄×C₁₉

—

116

C₂×C₄×C₁₉

—

117

C₂×C₄×C₁₉

—

118

C₂×C₄×C₁₉

—

119

C₂×C₄×C₁₉

—

120

C₂×C₄×C₁₉

—

121

C₂×C₄×C₁₉

—

122

C₂×C₄×C₁₉

—

123

C₂×C₄×C₁₉

—

124

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

—

125

C₂×C₄×C₁₉

C₂×C₂²⋊C₄

yes

characteristic

126

C₂×C₄×C₁₉

#120

yes

characteristic

127

C₂×C₄×C₁₉

#120

yes

—

128

C₂×Dic₁₉

—

129

C₂×Dic₁₉

—

130

C₁₉⋊C₈

—

131

C₁₉⋊C₈

—

132

#3550

D₁₉

yes

characteristic

133

#1994

—

134

#1962

—

135

#1561

—

136

#1560

—

137

C₂²×C₁₉

—

138

C₂²×C₁₉

—

139

C₂²×C₁₉

—

140

C₂²×C₁₉

—

141

C₂²×C₁₉

#379

yes

characteristic

142

C₄×C₁₉

—

143

C₄×C₁₉

—

144

C₄×C₁₉

—

145

C₄×C₁₉

—

146

C₄×C₁₉

—

147

C₄×C₁₉

#453

yes

characteristic

148

C₄×C₁₉

#454

yes

—

149

C₄×C₁₉

#455

yes

characteristic

150

C₄×C₁₉

#456

yes

—

151

Dic₁₉

—

152

#563

Dic₁₉

yes

complemented

153

#559

—

154

Q₈²

—

155

#556

—

156

D₄×Q₈

—

157

#542

—

158

#536

—

159

#533

C₂×D₁₉

yes

—

160

#532

C₂×D₁₉

yes

characteristic

161

#423

—

162

#423

—

163

C₂×#104

—

164

C₄³

—

165

#339

—

166

#333

—

167

#332

—

168

#332

—

169

#331

—

170

C₂×C₁₉

—

171

C₂×C₁₉

—

172

C₂×C₁₉

#1792

yes

characteristic

173

C₂×C₁₉

#1793

yes

—

174

C₂×#41

C₂²⋊D₁₉

yes

—

175

C₂²×Q₈

—

176

C₂×M₁₆

—

177

C₂×M₁₆

—

178

C₄⋊Q₈

—

179

C₄⋊Q₈

—

180

C₄⋊Q₈

C₂²⋊D₁₉

yes

characteristic

181

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

182

C₄⋊Q₈

C₂²⋊D₁₉

yes

—

183

#127

C₂²⋊D₁₉

yes

characteristic

184

#126

—

185

#125

C₂×Dic₁₉

yes

—

186

#124

—

187

#124

—

188

#124

C₂×Dic₁₉

yes

—

189

#123

—

190

#123

—

191

C₂²⋊Q₈

—

192

C₂²⋊Q₈

—

193

C₂²⋊Q₈

—

194

C₂²⋊Q₈

—

195

#121

—

196

C₄×Q₈

—

197

C₄×Q₈

—

198

C₄×Q₈

—

199

C₄×D₄

—

200

C₄×D₄

—

201

#117

—

202

#117

C₂²⋊D₁₉

yes

—

203

C₂×C₄²

—

204

C₂×C₄²

—

205

C₂×C₄²

C₂²×D₁₉

yes

characteristic

206

C₄⋊C₈

—

207

C₄⋊C₈

—

208

C₄⋊C₈

—

209

#104

—

210

C₁₉

#8531

yes

characteristic, complemented, Sylow

211

#41

—

212

#41

—

213

C₂×Q₈

—

214

C₂×Q₈

—

215

C₂×Q₈

—

216

C₂×Q₈

—

217

C₂×Q₈

—

218

C₂×Q₈

C₂²⋊Dic₁₉

yes

—

219

C₂×D₄

—

220

C₂×D₄

—

221

C₂×D₄

C₂²⋊Dic₁₉

yes

—

222

C₂²×C₄

—

223

C₂²×C₄

—

224

C₂²×C₄

—

225

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

—

226

C₂²×C₄

C₂×C₂²⋊D₁₉

yes

characteristic

227

M₁₆

—

228

M₁₆

—

229

C₂×C₈

—

230

C₂×C₈

—

231

C₄⋊C₄

—

232

C₄⋊C₄

—

233

C₄⋊C₄

—

234

C₄⋊C₄

—

235

C₄⋊C₄

—

236

C₄⋊C₄

—

237

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

238

C₄⋊C₄

C₂²⋊Dic₁₉

yes

—

239

C₂²⋊C₄

—

240

C₂²⋊C₄

—

241

C₂²⋊C₄

—

242

C₂²⋊C₄

—

243

C₄²

—

244

C₄²

—

245

C₄²

—

246

C₄²

—

247

C₄²

—

248

C₄²

—

249

C₄²

C₂²×Dic₁₉

yes

characteristic

250

C₄²

C₂×C₂²⋊D₁₉

yes

—

251

C₄²

C₂×C₂²⋊D₁₉

yes

characteristic

252

C₂³

—

253

C₂³

#10597399

yes

characteristic

254

Q₈

—

255

Q₈

—

256

Q₈

—

257

Q₈

—

258

Q₈

—

259

Q₈

—

260

D₄

—

261

D₄

—

262

D₄

—

263

D₄

—

264

C₂×C₄

—

265

C₂×C₄

—

266

C₂×C₄

—

267

C₂×C₄

—

268

C₂×C₄

—

269

C₂×C₄

—

270

C₂×C₄

—

271

C₂×C₄

—

272

C₂×C₄

—

273

C₂×C₄

—

274

C₂×C₄

—

275

C₂×C₄

—

276

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

—

277

C₂×C₄

C₂×C₂²⋊Dic₁₉

yes

characteristic

278

C₂×C₄

#10597399

yes

characteristic

279

C₂×C₄

#10597399

yes

—

280

C₈

—

152

—

281

C₈

—

152

—

282

C₂²

—

283

C₂²

—

284

C₂²

—

285

C₂²

—

286

C₂²

#11926400

yes

characteristic

287

C₄

—

288

C₄

—

289

C₄

—

290

C₄

—

291

C₄

—

292

C₄

—

293

C₄

#11926712

yes

characteristic

294

C₄

#11926717

yes

—

295

C₄

#11926722

yes

characteristic

296

C₄

#11926727

yes

—

297

C₂

—

298

C₂

—

299

C₂

#14563589

yes

characteristic

300

C₂

#14563594

yes

—

	subgroup	G/H
center	C₂²	#11926400
commutator	C₄²×C₁₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₉
Fitting	C₁₉×#3550	C₂
socle	C₂²×C₁₉	#379
prime radical	C₁₉×#532	C₂²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	#3550	D₁₉
hypocenter	C₁₉	#8531
LCS	G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3550

subgroup

G/H

center

C₂²

#11926400

commutator

C₄²×C₁₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₉

Fitting

C₁₉×#3550

C₂

socle

C₂²×C₁₉

#379

prime radical

C₁₉×#532

C₂²

cosocle

C₂×C₄²×C₁₉

C₂³

D₁₉

C₁₉

G ▷ C₄²×C₁₉ ▷ C₂²×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3550

N	H ≅ G/N	type
1. #14564613	C₂	semidirect
3. #14562373	C₂	semidirect
15. C₁₉×#563	C₄	semidirect
152. #563	Dic₁₉	semidirect
210. C₁₉	#8531	semidirect

H ≅ G/N

type

1. #14564613

C₂

semidirect

3. #14562373

C₂

semidirect

15. C₁₉×#563

C₄

semidirect

152. #563

Dic₁₉

semidirect

210. C₁₉

#8531

semidirect

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

subgroup	index
#14564613	2
#14564464	2
#14562373	2
#14562370	2
C₁₉×#3550	2
#8531	19

subgroup

index

C₁₉×#3550

Subgroups — #18075098

Conjugacy classes of subgroups

Complements

Maximal subgroups