Group #18069749 — subgroups

Subgroups — #18069749

Order 4864.

388 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 75 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	#14563933	C₂	1	1	yes	maximal, characteristic
2	C₄×#10597290	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₉×#99	C₂	1	1	yes	maximal, characteristic
4	C₂²×#64520	C₄	1	1	yes	characteristic, complemented
5	C₂×#10597290	—	2	1	no	—
6	C₂×C₂²⋊(C₁₉⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₁₉⋊C₈)	C₄	1	1	yes	characteristic, complemented
8	C₄×#64520	—	2	1	no	—
9	#11926313	C₄	1	2	yes	complemented
10	#11926299	—	2	1	no	—
11	C₂×C₄×D₄×C₁₉	C₂²	1	1	yes	characteristic
12	C₂×C₁₉×#99	—	2	1	no	—
13	C₄×C₂²⋊C₄×C₁₉	—	2	1	no	—
14	C₁₉×#342	C₄	1	2	yes	—
15	C₂²×D₄×C₁₉	D₄	1	1	yes	characteristic
16	C₂³×C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
17	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
18	C₄×D₄×C₁₉	—	4	1	no	—
19	C₄×D₄×C₁₉	—	4	1	no	—
20	C₂×C₄⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
21	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
22	C₂×C₂²⋊C₄×C₁₉	C₂×C₄	1	1	yes	characteristic
23	C₂×C₂²⋊C₄×C₁₉	Q₈	1	1	yes	characteristic
24	C₂×C₄²×C₁₉	—	4	1	no	—
25	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
26	C₂×#64520	—	2	2	no	—
27	C₂×#64520	—	4	2	no	—
28	C₂×#64520	—	4	1	no	—
29	C₂²×C₁₉⋊C₈	—	2	1	no	—
30	C₂²×C₁₉⋊C₈	—	2	1	no	—
31	C₁₉×#99	—	2	4	no	—
32	C₁₉×#95	—	4	1	no	—
33	#10597290	—	2	4	no	—
34	C₂²⋊(C₁₉⋊C₈)	—	4	2	no	—
35	C₂²⋊(C₁₉⋊C₈)	—	4	1	no	—
36	#10597260	—	4	1	no	—
37	C₄×C₁₉⋊C₈	—	4	1	no	—
38	C₂⁴×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
39	C₂⁴×C₁₉	C₄⋊C₄	1	1	yes	characteristic
40	C₂×D₄×C₁₉	—	2	2	no	—
41	C₂×D₄×C₁₉	—	2	2	no	—
42	C₂×D₄×C₁₉	—	4	1	no	—
43	C₂²×C₄×C₁₉	—	2	1	no	—
44	C₂²×C₄×C₁₉	—	2	1	no	—
45	C₂²×C₄×C₁₉	—	2	1	no	—
46	C₂²×C₄×C₁₉	—	2	1	no	—
47	C₂²×C₄×C₁₉	—	4	1	no	—
48	C₂²×C₄×C₁₉	—	4	1	no	—
49	C₂²×C₄×C₁₉	—	4	1	no	—
50	C₂²×C₄×C₁₉	—	4	1	no	—
51	C₂²×C₄×C₁₉	—	4	2	no	—
52	C₂²×C₄×C₁₉	C₄²	1	1	yes	characteristic
53	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
54	C₂²×C₄×C₁₉	C₂²⋊C₄	1	1	yes	characteristic
55	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
56	C₂²×C₄×C₁₉	C₄⋊C₄	1	1	yes	characteristic
57	C₄⋊C₄×C₁₉	—	4	1	no	—
58	C₂²⋊C₄×C₁₉	—	2	4	no	—
59	C₂²⋊C₄×C₁₉	—	4	1	no	—
60	C₂²⋊C₄×C₁₉	—	4	1	no	—
61	C₂²⋊C₄×C₁₉	—	4	2	no	—
62	C₄²×C₁₉	—	2	1	no	—
63	C₄²×C₁₉	—	2	1	no	—
64	C₄²×C₁₉	—	8	1	no	—
65	C₄²×C₁₉	—	8	1	no	—
66	#64520	—	2	4	no	—
67	#64520	—	4	2	no	—
68	#64520	—	4	2	no	—
69	#64520	—	4	2	no	—
70	C₂×C₁₉⋊C₈	—	2	2	no	—
71	C₂×C₁₉⋊C₈	—	4	2	no	—
72	C₂×C₁₉⋊C₈	—	4	1	no	—
73	C₂×C₁₉⋊C₈	—	4	1	no	—
74	C₂×C₁₉⋊C₈	—	4	1	no	—
75	C₂×C₁₉⋊C₈	—	4	1	no	—
76	C₂×C₁₉⋊C₈	—	4	1	no	—
77	#7282	—	19	1	no	maximal, Sylow
78	C₂³×C₁₉	—	2	1	no	—
79	C₂³×C₁₉	—	2	1	no	—
80	C₂³×C₁₉	—	2	1	no	—
81	C₂³×C₁₉	—	2	1	no	—
82	C₂³×C₁₉	—	2	1	no	—
83	C₂³×C₁₉	—	4	1	no	—
84	C₂³×C₁₉	—	4	1	no	—
85	C₂³×C₁₉	—	4	1	no	—
86	C₂³×C₁₉	—	4	1	no	—
87	C₂³×C₁₉	#95	1	1	yes	characteristic
88	C₂³×C₁₉	#104	1	2	yes	—
89	D₄×C₁₉	—	4	4	no	—
90	C₂×C₄×C₁₉	—	2	1	no	—
91	C₂×C₄×C₁₉	—	2	1	no	—
92	C₂×C₄×C₁₉	—	2	1	no	—
93	C₂×C₄×C₁₉	—	2	1	no	—
94	C₂×C₄×C₁₉	—	2	1	no	—
95	C₂×C₄×C₁₉	—	2	1	no	—
96	C₂×C₄×C₁₉	—	2	1	no	—
97	C₂×C₄×C₁₉	—	4	2	no	—
98	C₂×C₄×C₁₉	—	4	1	no	—
99	C₂×C₄×C₁₉	—	4	1	no	—
100	C₂×C₄×C₁₉	—	4	1	no	—
101	C₂×C₄×C₁₉	—	4	1	no	—
102	C₂×C₄×C₁₉	—	4	1	no	—
103	C₂×C₄×C₁₉	—	4	1	no	—
104	C₂×C₄×C₁₉	—	4	1	no	—
105	C₂×C₄×C₁₉	—	4	4	no	—
106	C₂×C₄×C₁₉	—	8	1	no	—
107	C₂×C₄×C₁₉	—	8	2	no	—
108	C₂×C₄×C₁₉	—	8	2	no	—
109	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
110	C₂×C₄×C₁₉	#99	1	1	yes	characteristic
111	C₂×C₄×C₁₉	#104	1	2	yes	—
112	C₁₉⋊C₈	—	4	4	no	—
113	C₁₉⋊C₈	—	4	2	no	—
114	C₁₉⋊C₈	—	8	1	no	—
115	#1870	—	19	1	no	—
116	C₄×#100	—	19	1	no	—
117	C₄×#99	D₁₉	1	1	yes	characteristic
118	C₂²×C₁₉	—	2	1	no	—
119	C₂²×C₁₉	—	2	1	no	—
120	C₂²×C₁₉	—	2	2	no	—
121	C₂²×C₁₉	—	4	2	no	—
122	C₂²×C₁₉	—	4	1	no	—
123	C₂²×C₁₉	—	4	1	no	—
124	C₂²×C₁₉	—	4	1	no	—
125	C₂²×C₁₉	—	4	1	no	—
126	C₂²×C₁₉	—	4	1	no	—
127	C₂²×C₁₉	—	8	1	no	—
128	C₂²×C₁₉	—	8	1	no	—
129	C₂²×C₁₉	—	8	1	no	—
130	C₂²×C₁₉	#339	1	1	yes	characteristic
131	C₂²×C₁₉	#339	1	1	yes	characteristic
132	C₂²×C₁₉	#342	1	1	yes	characteristic
133	C₄×C₁₉	—	2	2	no	—
134	C₄×C₁₉	—	2	1	no	—
135	C₄×C₁₉	—	4	1	no	—
136	C₄×C₁₉	—	4	1	no	—
137	C₄×C₁₉	—	4	1	no	—
138	C₄×C₁₉	—	8	4	no	—
139	C₄×C₁₉	AΣL(1,𝔽₁₆)	1	1	yes	characteristic
140	C₄×C₁₉	#352	1	1	yes	characteristic
141	C₂²×M₁₆	—	19	1	no	—
142	C₂×C₄×D₄	C₂×D₁₉	1	1	yes	characteristic
143	C₂×#100	—	38	1	no	—
144	C₂×#99	—	2	1	no	—
145	C₂×C₂²⋊C₈	—	19	1	no	—
146	C₂×C₂²⋊C₈	—	38	1	no	—
147	C₄×M₁₆	—	38	1	no	—
148	C₄×C₂²⋊C₄	—	2	1	no	—
149	#343	—	19	2	no	—
150	#342	Dic₁₉	1	2	yes	—
151	#336	—	38	1	no	—
152	C₂×C₁₉	—	2	1	no	—
153	C₂×C₁₉	—	2	1	no	—
154	C₂×C₁₉	—	4	2	no	—
155	C₂×C₁₉	—	8	1	no	—
156	C₂×C₁₉	#1297	1	1	yes	characteristic
157	C₂×C₁₉	#1390	1	1	yes	characteristic
158	C₂×C₁₉	#1395	1	1	yes	characteristic
159	C₂²×D₄	C₂²⋊D₁₉	1	1	yes	characteristic
160	C₂³×C₄	C₄×D₁₉	1	1	yes	characteristic
161	C₂³×C₄	C₂²⋊D₁₉	1	1	yes	characteristic
162	C₂×M₁₆	—	38	2	no	—
163	C₂×M₁₆	—	76	2	no	—
164	C₂×M₁₆	—	76	1	no	—
165	C₂²×C₈	—	38	1	no	—
166	C₂²×C₈	—	38	1	no	—
167	C₄×D₄	—	4	1	no	—
168	C₄×D₄	—	4	1	no	—
169	C₂×C₄⋊C₄	C₄×D₁₉	1	1	yes	characteristic
170	C₂×C₂²⋊C₄	—	2	2	no	—
171	C₂×C₂²⋊C₄	Dic₃₈	1	1	yes	characteristic
172	C₂×C₂²⋊C₄	C₂×Dic₁₉	1	1	yes	characteristic
173	C₂×C₄²	—	4	1	no	—
174	C₂×C₄²	D₇₆	1	1	yes	characteristic
175	#100	—	38	4	no	—
176	#99	—	2	4	no	—
177	C₂²⋊C₈	—	76	2	no	—
178	C₂²⋊C₈	—	76	1	no	—
179	#97	—	76	1	no	—
180	C₄×C₈	—	76	1	no	—
181	#95	—	4	1	no	—
182	C₁₉	#7282	1	1	yes	characteristic, complemented, Sylow
183	C₂⁴	Dic₁₉⋊C₄	1	1	yes	characteristic
184	C₂⁴	C₂²⋊Dic₁₉	1	1	yes	characteristic
185	C₂×D₄	—	2	2	no	—
186	C₂×D₄	—	2	2	no	—
187	C₂×D₄	—	4	1	no	—
188	C₂²×C₄	—	2	1	no	—
189	C₂²×C₄	—	2	1	no	—
190	C₂²×C₄	—	2	1	no	—
191	C₂²×C₄	—	2	1	no	—
192	C₂²×C₄	—	4	1	no	—
193	C₂²×C₄	—	4	1	no	—
194	C₂²×C₄	—	4	1	no	—
195	C₂²×C₄	—	4	1	no	—
196	C₂²×C₄	—	4	2	no	—
197	C₂²×C₄	C₄×Dic₁₉	1	1	yes	characteristic
198	C₂²×C₄	Dic₁₉⋊C₄	1	1	yes	characteristic
199	C₂²×C₄	C₄⋊Dic₁₉	1	1	yes	characteristic
200	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
201	C₂²×C₄	(C₂×D₁₉)⋊C₄	1	1	yes	characteristic
202	M₁₆	—	38	4	no	—
203	M₁₆	—	76	2	no	—
204	M₁₆	—	76	2	no	—
205	M₁₆	—	76	2	no	—
206	C₂×C₈	—	38	2	no	—
207	C₂×C₈	—	76	2	no	—
208	C₂×C₈	—	76	1	no	—
209	C₂×C₈	—	76	1	no	—
210	C₂×C₈	—	76	1	no	—
211	C₂×C₈	—	76	1	no	—
212	C₂×C₈	—	76	1	no	—
213	C₄⋊C₄	—	4	1	no	—
214	C₂²⋊C₄	—	2	4	no	—
215	C₂²⋊C₄	—	4	1	no	—
216	C₂²⋊C₄	—	4	1	no	—
217	C₂²⋊C₄	—	4	2	no	—
218	C₄²	—	2	1	no	—
219	C₄²	—	2	1	no	—
220	C₄²	—	8	1	no	—
221	C₄²	—	8	1	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	2	1	no	—
224	C₂³	—	2	1	no	—
225	C₂³	—	2	1	no	—
226	C₂³	—	2	1	no	—
227	C₂³	—	4	1	no	—
228	C₂³	—	4	1	no	—
229	C₂³	—	4	1	no	—
230	C₂³	—	4	1	no	—
231	C₂³	C₁₉⋊#95	1	1	yes	characteristic
232	C₂³	#10597294	1	2	yes	—
233	D₄	—	4	4	no	—
234	C₂×C₄	—	2	1	no	—
235	C₂×C₄	—	2	1	no	—
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	1	no	—
239	C₂×C₄	—	2	1	no	—
240	C₂×C₄	—	2	1	no	—
241	C₂×C₄	—	4	2	no	—
242	C₂×C₄	—	4	1	no	—
243	C₂×C₄	—	4	1	no	—
244	C₂×C₄	—	4	1	no	—
245	C₂×C₄	—	4	1	no	—
246	C₂×C₄	—	4	1	no	—
247	C₂×C₄	—	4	1	no	—
248	C₂×C₄	—	4	1	no	—
249	C₂×C₄	—	4	4	no	—
250	C₂×C₄	—	8	1	no	—
251	C₂×C₄	—	8	2	no	—
252	C₂×C₄	—	8	2	no	—
253	C₂×C₄	#10597262	1	2	yes	—
254	C₂×C₄	#10597263	1	1	yes	characteristic
255	C₂×C₄	#10597263	1	1	yes	characteristic
256	C₈	—	76	4	no	—
257	C₈	—	76	2	no	—
258	C₈	—	152	1	no	—
259	C₂²	—	2	1	no	—
260	C₂²	—	2	1	no	—
261	C₂²	—	2	2	no	—
262	C₂²	—	4	2	no	—
263	C₂²	—	4	1	no	—
264	C₂²	—	4	1	no	—
265	C₂²	—	4	1	no	—
266	C₂²	—	4	1	no	—
267	C₂²	—	4	1	no	—
268	C₂²	—	8	1	no	—
269	C₂²	—	8	1	no	—
270	C₂²	—	8	1	no	—
271	C₂²	#11926303	1	1	yes	characteristic
272	C₂²	#11926304	1	1	yes	characteristic
273	C₂²	#11926310	1	1	yes	characteristic
274	C₄	—	2	1	no	—
275	C₄	—	2	2	no	—
276	C₄	—	4	1	no	—
277	C₄	—	4	1	no	—
278	C₄	—	4	1	no	—
279	C₄	—	8	4	no	—
280	C₄	#11926330	1	1	yes	characteristic
281	C₄	#11926333	1	1	yes	characteristic
282	C₂	—	2	1	no	—
283	C₂	—	2	1	no	—
284	C₂	—	4	2	no	—
285	C₂	—	8	1	no	—
286	C₂	#14561521	1	1	yes	characteristic
287	C₂	#14561752	1	1	yes	characteristic
288	C₂	#14561763	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#14563933

C₂

yes

maximal, characteristic

C₄×#10597290

C₂

yes

maximal, characteristic

C₄×C₁₉×#99

C₂

yes

maximal, characteristic

C₂²×#64520

C₄

yes

characteristic, complemented

C₂×#10597290

—

C₂×C₂²⋊(C₁₉⋊C₈)

—

C₂×C₂²⋊(C₁₉⋊C₈)

C₄

yes

characteristic, complemented

C₄×#64520

—

#11926313

C₄

yes

complemented

#11926299

—

C₂×C₄×D₄×C₁₉

C₂²

yes

characteristic

C₂×C₁₉×#99

—

C₄×C₂²⋊C₄×C₁₉

—

C₁₉×#342

C₄

yes

—

C₂²×D₄×C₁₉

D₄

yes

characteristic

C₂³×C₄×C₁₉

C₂×C₄

yes

characteristic

C₂³×C₄×C₁₉

D₄

yes

characteristic

C₄×D₄×C₁₉

—

C₄×D₄×C₁₉

—

C₂×C₄⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

—

C₂×C₂²⋊C₄×C₁₉

C₂×C₄

yes

characteristic

C₂×C₂²⋊C₄×C₁₉

Q₈

yes

characteristic

C₂×C₄²×C₁₉

—

C₂×C₄²×C₁₉

D₄

yes

—

—

—

C₂²×C₁₉⋊C₈

—

C₂²×C₁₉⋊C₈

—

C₁₉×#99

—

C₁₉×#95

—

#10597290

—

C₂²⋊(C₁₉⋊C₈)

—

C₂²⋊(C₁₉⋊C₈)

—

#10597260

—

C₄×C₁₉⋊C₈

—

C₂⁴×C₁₉

C₂²⋊C₄

yes

characteristic

C₂⁴×C₁₉

C₄⋊C₄

yes

characteristic

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂×D₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

—

C₂²×C₄×C₁₉

C₄²

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₂²⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₂²×C₄×C₁₉

C₄⋊C₄

yes

characteristic

C₄⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₂²⋊C₄×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

C₄²×C₁₉

—

—

—

—

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

C₂×C₁₉⋊C₈

—

#7282

—

maximal, Sylow

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

—

C₂³×C₁₉

#95

yes

characteristic

C₂³×C₁₉

#104

yes

—

D₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

C₂×C₄×C₁₉

—

100

C₂×C₄×C₁₉

—

101

C₂×C₄×C₁₉

—

102

C₂×C₄×C₁₉

—

103

C₂×C₄×C₁₉

—

104

C₂×C₄×C₁₉

—

105

C₂×C₄×C₁₉

—

106

C₂×C₄×C₁₉

—

107

C₂×C₄×C₁₉

—

108

C₂×C₄×C₁₉

—

109

C₂×C₄×C₁₉

#99

yes

characteristic

110

C₂×C₄×C₁₉

#99

yes

characteristic

111

C₂×C₄×C₁₉

#104

yes

—

112

C₁₉⋊C₈

—

113

C₁₉⋊C₈

—

114

C₁₉⋊C₈

—

115

#1870

—

116

C₄×#100

—

117

C₄×#99

D₁₉

yes

characteristic

118

C₂²×C₁₉

—

119

C₂²×C₁₉

—

120

C₂²×C₁₉

—

121

C₂²×C₁₉

—

122

C₂²×C₁₉

—

123

C₂²×C₁₉

—

124

C₂²×C₁₉

—

125

C₂²×C₁₉

—

126

C₂²×C₁₉

—

127

C₂²×C₁₉

—

128

C₂²×C₁₉

—

129

C₂²×C₁₉

—

130

C₂²×C₁₉

#339

yes

characteristic

131

C₂²×C₁₉

#339

yes

characteristic

132

C₂²×C₁₉

#342

yes

characteristic

133

C₄×C₁₉

—

134

C₄×C₁₉

—

135

C₄×C₁₉

—

136

C₄×C₁₉

—

137

C₄×C₁₉

—

138

C₄×C₁₉

—

139

C₄×C₁₉

AΣL(1,𝔽₁₆)

yes

characteristic

140

C₄×C₁₉

#352

yes

characteristic

141

C₂²×M₁₆

—

142

C₂×C₄×D₄

C₂×D₁₉

yes

characteristic

143

C₂×#100

—

144

C₂×#99

—

145

C₂×C₂²⋊C₈

—

146

C₂×C₂²⋊C₈

—

147

C₄×M₁₆

—

148

C₄×C₂²⋊C₄

—

149

#343

—

150

#342

Dic₁₉

yes

—

151

#336

—

152

C₂×C₁₉

—

153

C₂×C₁₉

—

154

C₂×C₁₉

—

155

C₂×C₁₉

—

156

C₂×C₁₉

#1297

yes

characteristic

157

C₂×C₁₉

#1390

yes

characteristic

158

C₂×C₁₉

#1395

yes

characteristic

159

C₂²×D₄

C₂²⋊D₁₉

yes

characteristic

160

C₂³×C₄

C₄×D₁₉

yes

characteristic

161

C₂³×C₄

C₂²⋊D₁₉

yes

characteristic

162

C₂×M₁₆

—

163

C₂×M₁₆

—

164

C₂×M₁₆

—

165

C₂²×C₈

—

166

C₂²×C₈

—

167

C₄×D₄

—

168

C₄×D₄

—

169

C₂×C₄⋊C₄

C₄×D₁₉

yes

characteristic

170

C₂×C₂²⋊C₄

—

171

C₂×C₂²⋊C₄

Dic₃₈

yes

characteristic

172

C₂×C₂²⋊C₄

C₂×Dic₁₉

yes

characteristic

173

C₂×C₄²

—

174

C₂×C₄²

D₇₆

yes

characteristic

175

#100

—

176

#99

—

177

C₂²⋊C₈

—

178

C₂²⋊C₈

—

179

#97

—

180

C₄×C₈

—

181

#95

—

182

C₁₉

#7282

yes

characteristic, complemented, Sylow

183

C₂⁴

Dic₁₉⋊C₄

yes

characteristic

184

C₂⁴

C₂²⋊Dic₁₉

yes

characteristic

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

—

196

C₂²×C₄

—

197

C₂²×C₄

C₄×Dic₁₉

yes

characteristic

198

C₂²×C₄

Dic₁₉⋊C₄

yes

characteristic

199

C₂²×C₄

C₄⋊Dic₁₉

yes

characteristic

200

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

201

C₂²×C₄

(C₂×D₁₉)⋊C₄

yes

characteristic

202

M₁₆

—

203

M₁₆

—

204

M₁₆

—

205

M₁₆

—

206

C₂×C₈

—

207

C₂×C₈

—

208

C₂×C₈

—

209

C₂×C₈

—

210

C₂×C₈

—

211

C₂×C₈

—

212

C₂×C₈

—

213

C₄⋊C₄

—

214

C₂²⋊C₄

—

215

C₂²⋊C₄

—

216

C₂²⋊C₄

—

217

C₂²⋊C₄

—

218

C₄²

—

219

C₄²

—

220

C₄²

—

221

C₄²

—

222

C₂³

—

223

C₂³

—

224

C₂³

—

225

C₂³

—

226

C₂³

—

227

C₂³

—

228

C₂³

—

229

C₂³

—

230

C₂³

—

231

C₂³

C₁₉⋊#95

yes

characteristic

232

C₂³

#10597294

yes

—

233

D₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

—

240

C₂×C₄

—

241

C₂×C₄

—

242

C₂×C₄

—

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

253

C₂×C₄

#10597262

yes

—

254

C₂×C₄

#10597263

yes

characteristic

255

C₂×C₄

#10597263

yes

characteristic

256

C₈

—

257

C₈

—

258

C₈

—

152

—

259

C₂²

—

260

C₂²

—

261

C₂²

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

—

268

C₂²

—

269

C₂²

—

270

C₂²

—

271

C₂²

#11926303

yes

characteristic

272

C₂²

#11926304

yes

characteristic

273

C₂²

#11926310

yes

characteristic

274

C₄

—

275

C₄

—

276

C₄

—

277

C₄

—

278

C₄

—

279

C₄

—

280

C₄

#11926330

yes

characteristic

281

C₄

#11926333

yes

characteristic

282

C₂

—

283

C₂

—

284

C₂

—

285

C₂

—

286

C₂

#14561521

yes

characteristic

287

C₂

#14561752

yes

characteristic

288

C₂

#14561763

yes

characteristic

	subgroup	G/H
center	C₂×C₄	#10597263
commutator	C₂²×C₄×C₁₉	C₄²
Frattini	C₂×C₄×D₄	C₂×D₁₉
Fitting	C₄×C₁₉×#99	C₂
socle	C₂²×C₁₉	#342
prime radical	C₂²×D₄×C₁₉	D₄
cosocle	C₂×C₄×D₄×C₁₉	C₂²
hypercenter	C₄×#99	D₁₉
hypocenter	C₁₉	#7282
LCS	G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ C₄×#99

subgroup

G/H

center

C₂×C₄

#10597263

commutator

C₂²×C₄×C₁₉

C₄²

Frattini

C₂×C₄×D₄

C₂×D₁₉

Fitting

C₄×C₁₉×#99

C₂

socle

C₂²×C₁₉

#342

prime radical

C₂²×D₄×C₁₉

D₄

cosocle

C₂×C₄×D₄×C₁₉

C₂²

hypercenter

C₄×#99

D₁₉

hypocenter

C₁₉

#7282

LCS

G ▷ C₂²×C₄×C₁₉ ▷ C₂³×C₁₉ ▷ C₂×C₁₉ ▷ C₁₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄×D₄ ◁ C₄×#99

N	H ≅ G/N	type
4. C₂²×#64520	C₄	semidirect
7. C₂×C₂²⋊(C₁₉⋊C₈)	C₄	semidirect
9. #11926313	C₄	semidirect
182. C₁₉	#7282	semidirect

H ≅ G/N

type

4. C₂²×#64520

C₄

semidirect

7. C₂×C₂²⋊(C₁₉⋊C₈)

C₄

semidirect

9. #11926313

C₄

semidirect

182. C₁₉

#7282

semidirect

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

subgroup	index
#14563933	2
C₄×#10597290	2
C₄×C₁₉×#99	2
#7282	19

subgroup

index

#14563933

C₄×#10597290

C₄×C₁₉×#99

#7282

Subgroups — #18069749

Conjugacy classes of subgroups

Complements

Maximal subgroups