Group #15762038 — subgroups

Subgroups — #15762038

Order 3328.

590 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 590 conjugacy classes of subgroups — too many to draw. Only its 151 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	#13114953	C₂	1	1	yes	maximal, characteristic, complemented
2	#13114689	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#11718139	C₂	1	2	yes	maximal, complemented
4	C₂×#11718136	C₂	1	2	yes	maximal
5	C₁₃×#2858	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
7	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
8	C₂×C₁₃×#124	—	2	2	no	—
9	C₁₃×#390	—	2	1	no	—
10	C₁₃×#390	—	2	1	no	—
11	C₁₃×#390	C₄	1	4	yes	—
12	C₄³×C₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊#1055	C₂²	1	2	yes	—
14	C₂×C₄⋊#1055	C₂²	1	2	yes	—
15	C₂×#88043	—	2	1	no	—
16	#11718139	—	2	4	no	—
17	#11718136	—	2	4	no	—
18	#11718116	—	2	1	no	—
19	#11718116	—	2	2	no	—
20	C₂²×Q₈×C₁₃	—	2	1	no	—
21	C₂²×D₄×C₁₃	—	2	1	no	—
22	C₂²×D₄×C₁₃	—	2	1	no	—
23	C₂²×D₄×C₁₃	C₂×C₄	1	2	yes	—
24	C₁₃×C₄⋊Q₈	—	2	2	no	—
25	C₁₃×C₄⋊Q₈	—	2	2	no	—
26	C₁₃×#127	—	2	2	no	—
27	C₁₃×#127	—	2	2	no	—
28	C₁₃×#124	—	4	8	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	1	no	—
30	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
31	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
32	C₂×C₁₃×C₂²⋊C₄	—	2	4	no	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	D₄	1	2	yes	—
37	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
38	C₂²×#1055	—	2	2	no	—
39	C₂²×#1055	—	2	2	no	—
40	C₄⋊#1055	—	2	2	no	—
41	C₄⋊#1055	—	2	2	no	—
42	C₄⋊#1055	—	2	2	no	—
43	C₄⋊#1055	D₄	1	4	yes	—
44	#88043	—	4	2	no	—
45	#9710	—	13	1	no	maximal, Sylow
46	C₂⁴×C₁₃	—	2	2	no	—
47	C₂×Q₈×C₁₃	—	4	1	no	—
48	C₂×Q₈×C₁₃	—	4	1	no	—
49	C₂×Q₈×C₁₃	—	4	4	no	—
50	C₂×D₄×C₁₃	—	2	4	no	—
51	C₂×D₄×C₁₃	—	4	4	no	—
52	C₂×D₄×C₁₃	—	4	2	no	—
53	C₂×D₄×C₁₃	—	4	1	no	—
54	C₂×D₄×C₁₃	—	4	1	no	—
55	C₂×D₄×C₁₃	—	4	2	no	—
56	C₂×D₄×C₁₃	—	4	4	no	—
57	C₂×D₄×C₁₃	—	4	1	no	—
58	C₂×D₄×C₁₃	—	4	1	no	—
59	C₂²×C₄×C₁₃	—	2	2	no	—
60	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
61	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
62	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
65	C₁₃×C₄⋊C₄	—	2	4	no	—
66	C₁₃×C₄⋊C₄	—	4	2	no	—
67	C₁₃×C₂²⋊C₄	—	4	8	no	—
68	C₁₃×C₂²⋊C₄	—	4	8	no	—
69	C₄²×C₁₃	—	2	2	no	—
70	C₄²×C₁₃	—	2	4	no	—
71	C₄²×C₁₃	—	2	1	no	—
72	C₄²×C₁₃	—	2	1	no	—
73	C₄²×C₁₃	—	4	2	no	—
74	C₄²×C₁₃	C₂×D₄	1	2	yes	—
75	C₄²×C₁₃	#41	1	2	yes	—
76	C₂×#1055	—	2	4	no	—
77	C₂×#1055	—	4	2	no	—
78	C₂×#1055	—	4	2	no	—
79	C₂×#1055	—	4	2	no	—
80	C₂×#1055	—	4	4	no	—
81	#2858	D₁₃	1	1	yes	characteristic
82	#1831	—	13	1	no	—
83	#1767	—	13	1	no	—
84	C₂×#332	—	13	2	no	—
85	C₂×#331	—	13	2	no	—
86	C₂³×C₁₃	—	4	2	no	—
87	C₂³×C₁₃	—	4	4	no	—
88	C₂³×C₁₃	—	4	2	no	—
89	C₂³×C₁₃	—	4	2	no	—
90	C₂³×C₁₃	—	4	4	no	—
91	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
92	Q₈×C₁₃	—	8	2	no	—
93	Q₈×C₁₃	—	8	2	no	—
94	D₄×C₁₃	—	8	4	no	—
95	D₄×C₁₃	—	8	2	no	—
96	D₄×C₁₃	—	8	2	no	—
97	D₄×C₁₃	—	8	2	no	—
98	D₄×C₁₃	—	8	2	no	—
99	C₂×C₄×C₁₃	—	2	2	no	—
100	C₂×C₄×C₁₃	—	2	2	no	—
101	C₂×C₄×C₁₃	—	2	2	no	—
102	C₂×C₄×C₁₃	—	2	2	no	—
103	C₂×C₄×C₁₃	—	2	2	no	—
104	C₂×C₄×C₁₃	—	2	2	no	—
105	C₂×C₄×C₁₃	—	2	2	no	—
106	C₂×C₄×C₁₃	—	4	2	no	—
107	C₂×C₄×C₁₃	—	4	4	no	—
108	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
109	C₂×C₄×C₁₃	#121	1	2	yes	—
110	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
111	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
112	C₂×C₄×C₁₃	#135	1	2	yes	—
113	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	1	yes	characteristic
114	C₂×C₄×C₁₃	AGL(1,ℤ/8)	1	4	yes	—
115	C₂×C₄×C₁₃	#137	1	1	yes	characteristic
116	#1055	—	4	4	no	—
117	#1055	—	8	2	no	—
118	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
119	C₂×#127	C₂×D₁₃	1	1	yes	characteristic
120	C₂×#124	—	2	2	no	—
121	C₂×C₄⋊C₈	—	13	2	no	—
122	C₂×C₄⋊C₈	—	13	2	no	—
123	C₂×#97	—	26	1	no	—
124	#390	—	2	1	no	—
125	#390	—	2	1	no	—
126	#390	Dic₁₃	1	4	yes	—
127	C₄³	C₂×D₁₃	1	1	yes	characteristic
128	#336	—	26	2	no	—
129	#336	—	26	1	no	—
130	#332	—	26	4	no	—
131	#331	—	26	4	no	—
132	C₂²×C₁₃	—	8	4	no	—
133	C₂²×C₁₃	—	8	4	no	—
134	C₂²×C₁₃	—	8	2	no	—
135	C₂²×C₁₃	—	8	2	no	—
136	C₂²×C₁₃	—	8	2	no	—
137	C₂²×C₁₃	#390	1	1	yes	characteristic
138	C₂²×C₁₃	#413	1	2	yes	—
139	C₂²×C₁₃	#416	1	1	yes	characteristic
140	C₂²×C₁₃	#417	1	1	yes	characteristic
141	C₂²×C₁₃	#418	1	2	yes	—
142	C₄×C₁₃	—	2	2	no	—
143	C₄×C₁₃	—	4	2	no	—
144	C₄×C₁₃	—	4	2	no	—
145	C₄×C₁₃	—	8	2	no	—
146	C₄×C₁₃	#463	1	2	yes	—
147	C₄×C₁₃	#464	1	2	yes	—
148	C₄×C₁₃	#490	1	2	yes	—
149	C₄×C₁₃	#496	1	2	yes	—
150	C₂²×Q₈	—	2	1	no	—
151	C₂²×D₄	—	2	1	no	—
152	C₂²×D₄	—	2	1	no	—
153	C₂²×D₄	C₂×Dic₁₃	1	2	yes	—
154	C₂²×C₈	—	26	2	no	—
155	C₂²×C₈	—	26	2	no	—
156	C₄⋊Q₈	—	2	2	no	—
157	C₄⋊Q₈	—	2	2	no	—
158	#127	—	2	2	no	—
159	#127	—	2	2	no	—
160	#124	—	4	8	no	—
161	C₂×C₄⋊C₄	—	2	1	no	—
162	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
163	C₂×C₂²⋊C₄	—	2	4	no	—
164	C₂×C₂²⋊C₄	—	2	4	no	—
165	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
166	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
167	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
168	C₂×C₄²	C₂²⋊D₁₃	1	1	yes	characteristic
169	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
170	C₄⋊C₈	—	13	4	no	—
171	C₄⋊C₈	—	26	2	no	—
172	C₄⋊C₈	—	26	2	no	—
173	C₄⋊C₈	—	26	2	no	—
174	#97	—	52	2	no	—
175	C₂×C₁₃	—	16	2	no	—
176	C₂×C₁₃	#1553	1	2	yes	—
177	C₂×C₁₃	#1557	1	2	yes	—
178	C₂×C₁₃	#1961	1	1	yes	characteristic
179	C₂×C₁₃	#1967	1	1	yes	characteristic
180	C₂×C₁₃	#1983	1	1	yes	characteristic
181	C₂⁴	—	2	2	no	—
182	C₂×Q₈	—	4	4	no	—
183	C₂×Q₈	—	4	1	no	—
184	C₂×Q₈	—	4	1	no	—
185	C₂×D₄	—	2	4	no	—
186	C₂×D₄	—	4	4	no	—
187	C₂×D₄	—	4	4	no	—
188	C₂×D₄	—	4	1	no	—
189	C₂×D₄	—	4	2	no	—
190	C₂×D₄	—	4	1	no	—
191	C₂×D₄	—	4	1	no	—
192	C₂×D₄	—	4	2	no	—
193	C₂×D₄	—	4	1	no	—
194	C₂²×C₄	—	2	2	no	—
195	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
196	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
197	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
198	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
199	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
200	C₂×C₈	—	26	4	no	—
201	C₂×C₈	—	52	2	no	—
202	C₂×C₈	—	52	2	no	—
203	C₂×C₈	—	52	4	no	—
204	C₂×C₈	—	52	2	no	—
205	C₄⋊C₄	—	2	4	no	—
206	C₄⋊C₄	—	4	2	no	—
207	C₂²⋊C₄	—	4	8	no	—
208	C₂²⋊C₄	—	4	8	no	—
209	C₄²	—	2	4	no	—
210	C₄²	—	2	1	no	—
211	C₄²	—	2	2	no	—
212	C₄²	—	2	1	no	—
213	C₄²	—	4	2	no	—
214	C₄²	D₄×D₁₃	1	2	yes	—
215	C₄²	#6129	1	2	yes	—
216	C₁₃	#9710	1	1	yes	characteristic, complemented, Sylow
217	C₂³	—	4	4	no	—
218	C₂³	—	4	2	no	—
219	C₂³	—	4	2	no	—
220	C₂³	—	4	2	no	—
221	C₂³	—	4	4	no	—
222	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
223	Q₈	—	8	2	no	—
224	Q₈	—	8	2	no	—
225	D₄	—	8	4	no	—
226	D₄	—	8	2	no	—
227	D₄	—	8	2	no	—
228	D₄	—	8	2	no	—
229	D₄	—	8	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	2	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	2	2	no	—
234	C₂×C₄	—	2	2	no	—
235	C₂×C₄	—	2	2	no	—
236	C₂×C₄	—	2	2	no	—
237	C₂×C₄	—	4	4	no	—
238	C₂×C₄	—	4	2	no	—
239	C₂×C₄	#88186	1	4	yes	—
240	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
241	C₂×C₄	#88190	1	1	yes	characteristic
242	C₂×C₄	#88192	1	2	yes	—
243	C₂×C₄	#88194	1	1	yes	characteristic
244	C₂×C₄	#88203	1	1	yes	characteristic
245	C₂×C₄	#88204	1	2	yes	—
246	C₂×C₄	#88205	1	1	yes	characteristic
247	C₈	—	52	4	no	—
248	C₈	—	104	2	no	—
249	C₂²	—	8	2	no	—
250	C₂²	—	8	2	no	—
251	C₂²	—	8	2	no	—
252	C₂²	—	8	4	no	—
253	C₂²	—	8	4	no	—
254	C₂²	#11718876	1	2	yes	—
255	C₂²	#11718882	1	1	yes	characteristic
256	C₂²	#11718893	1	1	yes	characteristic
257	C₂²	#11718894	1	1	yes	characteristic
258	C₂²	#11718898	1	2	yes	—
259	C₄	—	2	2	no	—
260	C₄	—	4	2	no	—
261	C₄	—	4	2	no	—
262	C₄	—	8	2	no	—
263	C₄	#11718715	1	2	yes	—
264	C₄	#11718718	1	2	yes	—
265	C₄	#11718732	1	2	yes	—
266	C₄	#11718735	1	2	yes	—
267	C₂	—	16	2	no	—
268	C₂	#13113541	1	2	yes	—
269	C₂	#13113558	1	2	yes	—
270	C₂	#13115661	1	1	yes	characteristic
271	C₂	#13115686	1	1	yes	characteristic
272	C₂	#13115769	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#13114953

C₂

yes

maximal, characteristic, complemented

#13114689

C₂

yes

maximal, characteristic, complemented

C₂×#11718139

C₂

yes

maximal, complemented

C₂×#11718136

C₂

yes

maximal

C₁₃×#2858

C₂

yes

maximal, characteristic

C₂×C₁₃×C₄⋊Q₈

C₂²

yes

characteristic

C₂×C₁₃×#127

C₂²

yes

characteristic

C₂×C₁₃×#124

—

C₁₃×#390

—

C₁₃×#390

—

C₁₃×#390

C₄

yes

—

C₄³×C₁₃

C₂²

yes

characteristic

C₂×C₄⋊#1055

C₂²

yes

—

C₂×C₄⋊#1055

C₂²

yes

—

—

—

—

—

—

C₂²×Q₈×C₁₃

—

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

—

C₂²×D₄×C₁₃

C₂×C₄

yes

—

C₁₃×C₄⋊Q₈

—

C₁₃×C₄⋊Q₈

—

C₁₃×#127

—

C₁₃×#127

—

C₁₃×#124

—

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₄⋊C₄

C₂×C₄

yes

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₄²×C₁₃

C₂×C₄

yes

—

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

characteristic

C₂×C₄²×C₁₃

D₄

yes

—

C₂×C₄²×C₁₃

C₂³

yes

characteristic

C₂²×#1055

—

C₂²×#1055

—

—

—

—

D₄

yes

—

#88043

—

#9710

—

maximal, Sylow

C₂⁴×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×Q₈×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂×D₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

—

C₄²×C₁₃

C₂×D₄

yes

—

C₄²×C₁₃

#41

yes

—

—

—

—

—

—

D₁₃

yes

—

—

—

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₃

—

Q₈×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

D₄×C₁₃

—

C₂×C₄×C₁₃

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

—

103

C₂×C₄×C₁₃

—

104

C₂×C₄×C₁₃

—

105

C₂×C₄×C₁₃

—

106

C₂×C₄×C₁₃

—

107

C₂×C₄×C₁₃

—

108

C₂×C₄×C₁₃

C₄×D₄

yes

—

109

C₂×C₄×C₁₃

#121

yes

—

110

C₂×C₄×C₁₃

#124

yes

characteristic

111

C₂×C₄×C₁₃

#127

yes

characteristic

112

C₂×C₄×C₁₃

#135

yes

—

113

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

characteristic

114

C₂×C₄×C₁₃

AGL(1,ℤ/8)

yes

—

115

C₂×C₄×C₁₃

#137

yes

characteristic

116

#1055

—

117

#1055

—

118

C₂×C₄⋊Q₈

C₂×D₁₃

yes

characteristic

119

C₂×#127

C₂×D₁₃

yes

characteristic

120

C₂×#124

—

121

C₂×C₄⋊C₈

—

122

C₂×C₄⋊C₈

—

123

C₂×#97

—

124

#390

—

125

#390

—

126

#390

Dic₁₃

yes

—

127

C₄³

C₂×D₁₃

yes

characteristic

128

#336

—

129

#336

—

130

#332

—

131

#331

—

132

C₂²×C₁₃

—

133

C₂²×C₁₃

—

134

C₂²×C₁₃

—

135

C₂²×C₁₃

—

136

C₂²×C₁₃

—

137

C₂²×C₁₃

#390

yes

characteristic

138

C₂²×C₁₃

#413

yes

—

139

C₂²×C₁₃

#416

yes

characteristic

140

C₂²×C₁₃

#417

yes

characteristic

141

C₂²×C₁₃

#418

yes

—

142

C₄×C₁₃

—

143

C₄×C₁₃

—

144

C₄×C₁₃

—

145

C₄×C₁₃

—

146

C₄×C₁₃

#463

yes

—

147

C₄×C₁₃

#464

yes

—

148

C₄×C₁₃

#490

yes

—

149

C₄×C₁₃

#496

yes

—

150

C₂²×Q₈

—

151

C₂²×D₄

—

152

C₂²×D₄

—

153

C₂²×D₄

C₂×Dic₁₃

yes

—

154

C₂²×C₈

—

155

C₂²×C₈

—

156

C₄⋊Q₈

—

157

C₄⋊Q₈

—

158

#127

—

159

#127

—

160

#124

—

161

C₂×C₄⋊C₄

—

162

C₂×C₄⋊C₄

C₂×Dic₁₃

yes

—

163

C₂×C₂²⋊C₄

—

164

C₂×C₂²⋊C₄

—

165

C₂×C₄²

C₂×Dic₁₃

yes

—

166

C₂×C₄²

C₂²⋊D₁₃

yes

—

167

C₂×C₄²

C₂²⋊D₁₃

yes

characteristic

168

C₂×C₄²

C₂²⋊D₁₃

yes

characteristic

169

C₂×C₄²

C₂²×D₁₃

yes

characteristic

170

C₄⋊C₈

—

171

C₄⋊C₈

—

172

C₄⋊C₈

—

173

C₄⋊C₈

—

174

#97

—

175

C₂×C₁₃

—

176

C₂×C₁₃

#1553

yes

—

177

C₂×C₁₃

#1557

yes

—

178

C₂×C₁₃

#1961

yes

characteristic

179

C₂×C₁₃

#1967

yes

characteristic

180

C₂×C₁₃

#1983

yes

characteristic

181

C₂⁴

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×D₄

—

186

C₂×D₄

—

187

C₂×D₄

—

188

C₂×D₄

—

189

C₂×D₄

—

190

C₂×D₄

—

191

C₂×D₄

—

192

C₂×D₄

—

193

C₂×D₄

—

194

C₂²×C₄

—

195

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

196

C₂²×C₄

C₂²⋊Dic₁₃

yes

—

197

C₂²×C₄

C₂²×Dic₁₃

yes

characteristic

198

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

199

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

200

C₂×C₈

—

201

C₂×C₈

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

207

C₂²⋊C₄

—

208

C₂²⋊C₄

—

209

C₄²

—

210

C₄²

—

211

C₄²

—

212

C₄²

—

213

C₄²

—

214

C₄²

D₄×D₁₃

yes

—

215

C₄²

#6129

yes

—

216

C₁₃

#9710

yes

characteristic, complemented, Sylow

217

C₂³

—

218

C₂³

—

219

C₂³

—

220

C₂³

—

221

C₂³

—

222

C₂³

C₂×C₂²⋊Dic₁₃

yes

characteristic

223

Q₈

—

224

Q₈

—

225

D₄

—

226

D₄

—

227

D₄

—

228

D₄

—

229

D₄

—

230

C₂×C₄

—

231

C₂×C₄

—

232

C₂×C₄

—

233

C₂×C₄

—

234

C₂×C₄

—

235

C₂×C₄

—

236

C₂×C₄

—

237

C₂×C₄

—

238

C₂×C₄

—

239

C₂×C₄

#88186

yes

—

240

C₂×C₄

D₄×Dic₁₃

yes

—

241

C₂×C₄

#88190

yes

characteristic

242

C₂×C₄

#88192

yes

—

243

C₂×C₄

#88194

yes

characteristic

244

C₂×C₄

#88203

yes

characteristic

245

C₂×C₄

#88204

yes

—

246

C₂×C₄

#88205

yes

characteristic

247

C₈

—

248

C₈

—

104

—

249

C₂²

—

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

#11718876

yes

—

255

C₂²

#11718882

yes

characteristic

256

C₂²

#11718893

yes

characteristic

257

C₂²

#11718894

yes

characteristic

258

C₂²

#11718898

yes

—

259

C₄

—

260

C₄

—

261

C₄

—

262

C₄

—

263

C₄

#11718715

yes

—

264

C₄

#11718718

yes

—

265

C₄

#11718732

yes

—

266

C₄

#11718735

yes

—

267

C₂

—

268

C₂

#13113541

yes

—

269

C₂

#13113558

yes

—

270

C₂

#13115661

yes

characteristic

271

C₂

#13115686

yes

characteristic

272

C₂

#13115769

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₁₃
commutator	C₂²×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₁₃
Fitting	C₁₃×#2858	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂×C₁₃×#127	C₂²
cosocle	C₂×C₄²×C₁₃	C₂³
hypercenter	#2858	D₁₃
hypocenter	C₁₃	#9710
LCS	G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ #2858

subgroup

G/H

center

C₂³

C₂×C₂²⋊Dic₁₃

commutator

C₂²×C₄×C₁₃

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₁₃

Fitting

C₁₃×#2858

C₂

socle

C₂³×C₁₃

C₂×C₂²⋊C₄

prime radical

C₂×C₁₃×#127

C₂²

cosocle

C₂×C₄²×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂²×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₄³ ◁ #2858

N	H ≅ G/N	type
1. #13114953	C₂	semidirect
2. #13114689	C₂	semidirect
3. C₂×#11718139	C₂	semidirect
216. C₁₃	#9710	semidirect

H ≅ G/N

type

1. #13114953

C₂

semidirect

2. #13114689

C₂

semidirect

3. C₂×#11718139

C₂

semidirect

216. C₁₃

#9710

semidirect

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

subgroup	index
#13114953	2
#13114689	2
C₂×#11718139	2
C₂×#11718136	2
C₁₃×#2858	2
#9710	13

subgroup

index

C₁₃×#2858

Subgroups — #15762038

Conjugacy classes of subgroups

Complements

Maximal subgroups