Group #15780294 — subgroups

Subgroups — #15780294

Order 3328.

506 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 506 conjugacy classes of subgroups — too many to draw. Only its 143 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	C₂²×#88052	C₂	1	1	yes	maximal, characteristic
2	C₂×#11718777	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718084	C₂	1	2	yes	maximal, complemented
4	#13112927	C₂	1	2	yes	maximal, complemented
5	C₁₃×#1808	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88178	—	2	1	no	—
8	C₂²×Dic₅₂	C₂²	1	1	yes	characteristic
9	C₂×C₁₃×#107	C₂²	1	2	yes	—
10	C₁₃×#380	—	2	1	no	—
11	#11718777	—	2	2	no	—
12	#11718777	C₄	1	4	yes	complemented
13	C₂×#88058	C₂²	1	1	yes	characteristic
14	C₂×#88056	—	2	1	no	—
15	C₂×#88052	—	2	4	no	—
16	C₂×#88052	—	2	2	no	—
17	C₂²×#6090	C₂²	1	2	yes	—
18	C₁₃×#340	—	2	1	no	—
19	#11718084	—	2	4	no	—
20	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
21	C₂²×Dic₂₆	—	2	1	no	—
22	C₂²×C₈×C₁₃	—	2	2	no	—
23	C₂²×C₈×C₁₃	—	2	2	no	—
24	C₂²×C₈×C₁₃	C₂×C₄	1	2	yes	—
25	C₂²×C₈×C₁₃	D₄	1	2	yes	—
26	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
27	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₄	—	2	2	no	—
29	C₂×C₁₃×C₂²⋊C₄	—	4	1	no	—
30	C₂×C₂²⋊Dic₁₃	—	4	1	no	—
31	C₂×C₄⋊Dic₁₃	—	2	1	no	—
32	#88178	—	2	4	no	—
33	#88178	—	4	2	no	—
34	C₂×#6101	—	4	1	no	—
35	C₂×Dic₅₂	—	2	2	no	—
36	C₂×Dic₅₂	—	2	2	no	—
37	C₂×Dic₅₂	—	2	1	no	—
38	C₂×Dic₅₂	C₂×C₄	1	2	yes	—
39	C₁₃×#107	—	2	2	no	—
40	C₁₃×#107	—	2	2	no	—
41	C₁₃×#95	—	4	1	no	—
42	#88058	—	2	1	no	—
43	#88058	C₂×C₄	1	2	yes	—
44	#88056	—	2	4	no	—
45	#88052	—	2	8	no	—
46	C₂×#6090	—	2	2	no	—
47	C₂×#6090	—	2	2	no	—
48	C₂×#6090	D₄	1	4	yes	—
49	#13062	—	13	1	no	maximal, Sylow
50	C₂⁴×C₁₃	D₈	1	1	yes	characteristic
51	C₂²×C₄×C₁₃	—	2	2	no	—
52	C₂²×C₄×C₁₃	—	2	2	no	—
53	C₂²×C₄×C₁₃	—	4	2	no	—
54	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
55	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
56	C₂²×C₄×C₁₃	SD₁₆	1	2	yes	—
57	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
58	C₂²×Dic₁₃	—	4	1	no	—
59	C₂²×Dic₁₃	—	4	1	no	—
60	C₂×Dic₂₆	—	2	2	no	—
61	C₂×Dic₂₆	—	4	2	no	—
62	C₂×Dic₂₆	—	4	2	no	—
63	C₂×Dic₂₆	—	4	1	no	—
64	C₂×C₈×C₁₃	—	2	2	no	—
65	C₂×C₈×C₁₃	—	2	4	no	—
66	C₂×C₈×C₁₃	—	2	2	no	—
67	C₂×C₈×C₁₃	—	2	2	no	—
68	C₂×C₈×C₁₃	C₂²⋊C₄	1	2	yes	—
69	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
70	C₂×C₈×C₁₃	C₂×D₄	1	2	yes	—
71	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
72	C₂×C₈×C₁₃	#41	1	2	yes	—
73	C₁₃×C₄⋊C₄	—	4	2	no	—
74	C₁₃×C₄⋊C₄	—	4	2	no	—
75	C₁₃×C₂²⋊C₄	—	8	2	no	—
76	C₂²⋊Dic₁₃	—	4	4	no	—
77	C₄⋊Dic₁₃	—	2	2	no	—
78	C₄⋊Dic₁₃	—	4	1	no	—
79	#6101	—	4	4	no	—
80	Dic₅₂	—	2	4	no	—
81	Dic₅₂	—	4	1	no	—
82	Dic₅₂	—	4	1	no	—
83	#6090	—	2	4	no	—
84	C₂²×M₃₂	—	13	1	no	—
85	C₂×#467	—	13	1	no	—
86	C₂×#358	—	13	2	no	—
87	#1808	D₁₃	1	1	yes	characteristic
88	#1380	—	13	2	no	—
89	C₂³×C₁₃	—	2	2	no	—
90	C₂³×C₁₃	—	2	1	no	—
91	C₂³×C₁₃	—	2	1	no	—
92	C₂³×C₁₃	—	2	2	no	—
93	C₂³×C₁₃	#102	1	2	yes	—
94	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
95	C₂×C₄×C₁₃	—	2	2	no	—
96	C₂×C₄×C₁₃	—	2	2	no	—
97	C₂×C₄×C₁₃	—	2	2	no	—
98	C₂×C₄×C₁₃	—	2	4	no	—
99	C₂×C₄×C₁₃	—	8	2	no	—
100	C₂×C₄×C₁₃	—	8	2	no	—
101	C₂×C₄×C₁₃	—	8	2	no	—
102	C₂×C₄×C₁₃	#102	1	2	yes	—
103	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
104	C₂×C₄×C₁₃	#121	1	2	yes	—
105	C₂×C₄×C₁₃	C₂×SD₁₆	1	1	yes	characteristic
106	C₂×C₄×C₁₃	#135	1	2	yes	—
107	C₂×Dic₁₃	—	4	2	no	—
108	C₂×Dic₁₃	—	4	2	no	—
109	C₂×Dic₁₃	—	8	2	no	—
110	C₂×Dic₁₃	—	8	1	no	—
111	C₂×Dic₁₃	—	8	1	no	—
112	Dic₂₆	—	4	2	no	—
113	Dic₂₆	—	4	2	no	—
114	Dic₂₆	—	8	2	no	—
115	C₈×C₁₃	—	2	2	no	—
116	C₈×C₁₃	C₄×D₄	1	2	yes	—
117	C₈×C₁₃	#120	1	1	yes	characteristic
118	C₈×C₁₃	#123	1	1	yes	characteristic
119	C₂²×Q₁₆	—	13	1	no	—
120	C₂³×C₈	C₂×D₁₃	1	1	yes	characteristic
121	C₂×C₂²⋊Q₈	—	26	1	no	—
122	C₂×M₃₂	—	26	4	no	—
123	C₂×M₃₂	—	26	2	no	—
124	C₂²×C₁₆	—	13	2	no	—
125	#467	—	13	4	no	—
126	#467	—	26	2	no	—
127	C₂×#107	—	13	1	no	—
128	C₂×#107	C₂×D₁₃	1	2	yes	—
129	C₂×#103	—	26	1	no	—
130	#380	—	2	1	no	—
131	#358	—	26	4	no	—
132	#340	—	2	1	no	—
133	C₂²×C₁₃	—	2	2	no	—
134	C₂²×C₁₃	—	2	2	no	—
135	C₂²×C₁₃	—	2	2	no	—
136	C₂²×C₁₃	—	4	2	no	—
137	C₂²×C₁₃	—	4	2	no	—
138	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
139	C₂²×C₁₃	#466	1	2	yes	—
140	C₂²×C₁₃	#509	1	1	yes	characteristic
141	C₂²×C₁₃	#510	1	1	yes	characteristic
142	C₂²×C₁₃	#510	1	2	yes	—
143	C₄×C₁₃	—	2	2	no	—
144	C₄×C₁₃	—	16	2	no	—
145	C₄×C₁₃	#386	1	1	yes	characteristic
146	C₄×C₁₃	#416	1	1	yes	characteristic
147	C₄×C₁₃	#465	1	2	yes	—
148	Dic₁₃	—	8	2	no	—
149	Dic₁₃	—	8	2	no	—
150	C₂²×Q₈	—	26	1	no	—
151	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
152	C₂×Q₁₆	—	13	2	no	—
153	C₂×Q₁₆	—	26	1	no	—
154	C₂×Q₁₆	—	26	2	no	—
155	C₂×Q₁₆	—	26	2	no	—
156	C₂²×C₈	—	2	2	no	—
157	C₂²×C₈	—	2	2	no	—
158	C₂²×C₈	C₄×D₁₃	1	2	yes	—
159	C₂²×C₈	D₅₂	1	2	yes	—
160	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
161	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
162	C₂²⋊Q₈	—	26	4	no	—
163	C₂²⋊Q₈	—	52	2	no	—
164	C₂×C₄⋊C₄	—	2	2	no	—
165	C₂×C₄⋊C₄	—	26	1	no	—
166	C₂×C₄⋊C₄	—	52	1	no	—
167	C₂×C₂²⋊C₄	—	4	1	no	—
168	C₂×C₂²⋊C₄	—	52	1	no	—
169	M₃₂	—	26	8	no	—
170	C₂×C₁₆	—	13	4	no	—
171	C₂×C₁₆	—	26	2	no	—
172	C₂×C₁₆	—	26	2	no	—
173	#107	—	2	2	no	—
174	#107	—	2	2	no	—
175	#107	—	13	2	no	—
176	#107	—	26	1	no	—
177	#103	—	26	4	no	—
178	#95	—	4	1	no	—
179	C₂×C₁₃	—	4	2	no	—
180	C₂×C₁₃	#1893	1	1	yes	characteristic
181	C₂×C₁₃	#2139	1	1	yes	characteristic
182	C₂×C₁₃	#2141	1	1	yes	characteristic
183	C₂×C₁₃	#2219	1	2	yes	—
184	C₂×C₁₃	#2220	1	2	yes	—
185	C₂⁴	#6104	1	1	yes	characteristic
186	C₂×Q₈	—	26	2	no	—
187	C₂×Q₈	—	52	1	no	—
188	C₂×Q₈	—	52	2	no	—
189	C₂×Q₈	—	52	2	no	—
190	C₂²×C₄	—	2	2	no	—
191	C₂²×C₄	—	2	2	no	—
192	C₂²×C₄	—	4	2	no	—
193	C₂²×C₄	—	52	1	no	—
194	C₂²×C₄	—	52	1	no	—
195	C₂²×C₄	#6103	1	2	yes	—
196	C₂²×C₄	#6104	1	1	yes	characteristic
197	C₂²×C₄	#6106	1	2	yes	—
198	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
199	Q₁₆	—	26	4	no	—
200	Q₁₆	—	52	1	no	—
201	Q₁₆	—	52	1	no	—
202	C₂×C₈	—	2	2	no	—
203	C₂×C₈	—	2	4	no	—
204	C₂×C₈	—	2	2	no	—
205	C₂×C₈	—	2	2	no	—
206	C₂×C₈	#6103	1	2	yes	—
207	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
208	C₂×C₈	C₂×D₅₂	1	1	yes	characteristic
209	C₂×C₈	D₄×D₁₃	1	2	yes	—
210	C₂×C₈	#6129	1	2	yes	—
211	C₄⋊C₄	—	4	2	no	—
212	C₄⋊C₄	—	4	2	no	—
213	C₄⋊C₄	—	26	2	no	—
214	C₄⋊C₄	—	52	1	no	—
215	C₄⋊C₄	—	52	4	no	—
216	C₂²⋊C₄	—	8	2	no	—
217	C₂²⋊C₄	—	52	4	no	—
218	C₁₆	—	26	4	no	—
219	C₁₃	#13062	1	1	yes	characteristic, complemented, Sylow
220	C₂³	—	2	2	no	—
221	C₂³	—	2	1	no	—
222	C₂³	—	2	1	no	—
223	C₂³	—	2	2	no	—
224	C₂³	#88049	1	2	yes	—
225	C₂³	C₂×#6104	1	1	yes	characteristic
226	Q₈	—	52	2	no	—
227	Q₈	—	52	2	no	—
228	Q₈	—	104	2	no	—
229	C₂×C₄	—	2	2	no	—
230	C₂×C₄	—	2	2	no	—
231	C₂×C₄	—	2	4	no	—
232	C₂×C₄	—	2	2	no	—
233	C₂×C₄	—	8	2	no	—
234	C₂×C₄	—	8	2	no	—
235	C₂×C₄	—	8	2	no	—
236	C₂×C₄	—	52	2	no	—
237	C₂×C₄	—	52	2	no	—
238	C₂×C₄	—	104	2	no	—
239	C₂×C₄	—	104	1	no	—
240	C₂×C₄	—	104	1	no	—
241	C₂×C₄	#88049	1	2	yes	—
242	C₂×C₄	C₂×#6103	1	1	yes	characteristic
243	C₂×C₄	#88193	1	2	yes	—
244	C₂×C₄	C₂×#6106	1	1	yes	characteristic
245	C₂×C₄	#88204	1	2	yes	—
246	C₈	—	2	2	no	—
247	C₈	#88135	1	2	yes	—
248	C₈	#88136	1	1	yes	characteristic
249	C₈	#88140	1	1	yes	characteristic
250	C₂²	—	2	2	no	—
251	C₂²	—	2	2	no	—
252	C₂²	—	2	2	no	—
253	C₂²	—	4	2	no	—
254	C₂²	—	4	2	no	—
255	C₂²	C₂×#88049	1	1	yes	characteristic
256	C₂²	#11718699	1	2	yes	—
257	C₂²	#11718808	1	1	yes	characteristic
258	C₂²	#11718840	1	1	yes	characteristic
259	C₂²	#11718856	1	2	yes	—
260	C₄	—	2	2	no	—
261	C₄	—	16	2	no	—
262	C₄	—	104	2	no	—
263	C₄	—	104	2	no	—
264	C₄	#11718619	1	1	yes	characteristic
265	C₄	#11718663	1	1	yes	characteristic
266	C₄	#11718709	1	2	yes	—
267	C₂	—	4	2	no	—
268	C₂	#13115262	1	1	yes	characteristic
269	C₂	#13116546	1	1	yes	characteristic
270	C₂	#13116555	1	1	yes	characteristic
271	C₂	#13116942	1	2	yes	—
272	C₂	#13116947	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#88052

C₂

yes

maximal, characteristic

C₂×#11718777

C₂

yes

maximal, characteristic

C₂×#11718084

C₂

yes

maximal, complemented

#13112927

C₂

yes

maximal, complemented

C₁₃×#1808

C₂

yes

maximal, characteristic

C₂³×C₈×C₁₃

C₂²

yes

characteristic

C₂×#88178

—

C₂²×Dic₅₂

C₂²

yes

characteristic

C₂×C₁₃×#107

C₂²

yes

—

C₁₃×#380

—

#11718777

—

#11718777

C₄

yes

complemented

C₂×#88058

C₂²

yes

—

—

—

C₂²×#6090

C₂²

yes

—

C₁₃×#340

—

#11718084

—

C₂³×C₄×C₁₃

D₄

yes

characteristic

C₂²×Dic₂₆

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

—

C₂²×C₈×C₁₃

C₂×C₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

—

C₂²×C₈×C₁₃

D₄

yes

characteristic

C₂²×C₈×C₁₃

C₂³

yes

characteristic

C₂×C₁₃×C₄⋊C₄

—

C₂×C₁₃×C₂²⋊C₄

—

C₂×C₂²⋊Dic₁₃

—

C₂×C₄⋊Dic₁₃

—

#88178

—

#88178

—

C₂×#6101

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

—

C₂×Dic₅₂

C₂×C₄

yes

—

C₁₃×#107

—

C₁₃×#107

—

C₁₃×#95

—

#88058

—

#88058

C₂×C₄

yes

—

—

—

—

—

D₄

yes

—

#13062

—

maximal, Sylow

C₂⁴×C₁₃

D₈

yes

characteristic

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

—

C₂²×C₄×C₁₃

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₃

D₈

yes

characteristic

C₂²×C₄×C₁₃

SD₁₆

yes

—

C₂²×C₄×C₁₃

C₂×D₄

yes

characteristic

C₂²×Dic₁₃

—

C₂²×Dic₁₃

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×Dic₂₆

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

—

C₂×C₈×C₁₃

C₂²⋊C₄

yes

—

C₂×C₈×C₁₃

C₂²×C₄

yes

characteristic

C₂×C₈×C₁₃

C₂×D₄

yes

—

C₂×C₈×C₁₃

C₂×D₄

yes

characteristic

C₂×C₈×C₁₃

#41

yes

—

C₁₃×C₄⋊C₄

—

C₁₃×C₄⋊C₄

—

C₁₃×C₂²⋊C₄

—

C₂²⋊Dic₁₃

—

C₄⋊Dic₁₃

—

C₄⋊Dic₁₃

—

#6101

—

Dic₅₂

—

Dic₅₂

—

Dic₅₂

—

#6090

—

C₂²×M₃₂

—

C₂×#467

—

C₂×#358

—

#1808

D₁₃

yes

characteristic

#1380

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

—

C₂³×C₁₃

#102

yes

—

C₂³×C₁₃

C₂×D₈

yes

characteristic

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

C₂×C₄×C₁₃

—

100

C₂×C₄×C₁₃

—

101

C₂×C₄×C₁₃

—

102

C₂×C₄×C₁₃

#102

yes

—

103

C₂×C₄×C₁₃

C₂×C₂²⋊C₄

yes

characteristic

104

C₂×C₄×C₁₃

#121

yes

—

105

C₂×C₄×C₁₃

C₂×SD₁₆

yes

characteristic

106

C₂×C₄×C₁₃

#135

yes

—

107

C₂×Dic₁₃

—

108

C₂×Dic₁₃

—

109

C₂×Dic₁₃

—

110

C₂×Dic₁₃

—

111

C₂×Dic₁₃

—

112

Dic₂₆

—

113

Dic₂₆

—

114

Dic₂₆

—

115

C₈×C₁₃

—

116

C₈×C₁₃

C₄×D₄

yes

—

117

C₈×C₁₃

#120

yes

characteristic

118

C₈×C₁₃

#123

yes

characteristic

119

C₂²×Q₁₆

—

120

C₂³×C₈

C₂×D₁₃

yes

characteristic

121

C₂×C₂²⋊Q₈

—

122

C₂×M₃₂

—

123

C₂×M₃₂

—

124

C₂²×C₁₆

—

125

#467

—

126

#467

—

127

C₂×#107

—

128

C₂×#107

C₂×D₁₃

yes

—

129

C₂×#103

—

130

#380

—

131

#358

—

132

#340

—

133

C₂²×C₁₃

—

134

C₂²×C₁₃

—

135

C₂²×C₁₃

—

136

C₂²×C₁₃

—

137

C₂²×C₁₃

—

138

C₂²×C₁₃

C₂×#102

yes

characteristic

139

C₂²×C₁₃

#466

yes

—

140

C₂²×C₁₃

#509

yes

characteristic

141

C₂²×C₁₃

#510

yes

characteristic

142

C₂²×C₁₃

#510

yes

—

143

C₄×C₁₃

—

144

C₄×C₁₃

—

145

C₄×C₁₃

#386

yes

characteristic

146

C₄×C₁₃

#416

yes

characteristic

147

C₄×C₁₃

#465

yes

—

148

Dic₁₃

—

149

Dic₁₃

—

150

C₂²×Q₈

—

151

C₂³×C₄

C₂²⋊D₁₃

yes

characteristic

152

C₂×Q₁₆

—

153

C₂×Q₁₆

—

154

C₂×Q₁₆

—

155

C₂×Q₁₆

—

156

C₂²×C₈

—

157

C₂²×C₈

—

158

C₂²×C₈

C₄×D₁₃

yes

—

159

C₂²×C₈

D₅₂

yes

—

160

C₂²×C₈

C₂²⋊D₁₃

yes

characteristic

161

C₂²×C₈

C₂²×D₁₃

yes

characteristic

162

C₂²⋊Q₈

—

163

C₂²⋊Q₈

—

164

C₂×C₄⋊C₄

—

165

C₂×C₄⋊C₄

—

166

C₂×C₄⋊C₄

—

167

C₂×C₂²⋊C₄

—

168

C₂×C₂²⋊C₄

—

169

M₃₂

—

170

C₂×C₁₆

—

171

C₂×C₁₆

—

172

C₂×C₁₆

—

173

#107

—

174

#107

—

175

#107

—

176

#107

—

177

#103

—

178

#95

—

179

C₂×C₁₃

—

180

C₂×C₁₃

#1893

yes

characteristic

181

C₂×C₁₃

#2139

yes

characteristic

182

C₂×C₁₃

#2141

yes

characteristic

183

C₂×C₁₃

#2219

yes

—

184

C₂×C₁₃

#2220

yes

—

185

C₂⁴

#6104

yes

characteristic

186

C₂×Q₈

—

187

C₂×Q₈

—

188

C₂×Q₈

—

189

C₂×Q₈

—

190

C₂²×C₄

—

191

C₂²×C₄

—

192

C₂²×C₄

—

193

C₂²×C₄

—

194

C₂²×C₄

—

195

C₂²×C₄

#6103

yes

—

196

C₂²×C₄

#6104

yes

characteristic

197

C₂²×C₄

#6106

yes

—

198

C₂²×C₄

C₂×C₂²⋊D₁₃

yes

characteristic

199

Q₁₆

—

200

Q₁₆

—

201

Q₁₆

—

202

C₂×C₈

—

203

C₂×C₈

—

204

C₂×C₈

—

205

C₂×C₈

—

206

C₂×C₈

#6103

yes

—

207

C₂×C₈

C₂×C₄×D₁₃

yes

characteristic

208

C₂×C₈

C₂×D₅₂

yes

characteristic

209

C₂×C₈

D₄×D₁₃

yes

—

210

C₂×C₈

#6129

yes

—

211

C₄⋊C₄

—

212

C₄⋊C₄

—

213

C₄⋊C₄

—

214

C₄⋊C₄

—

215

C₄⋊C₄

—

216

C₂²⋊C₄

—

217

C₂²⋊C₄

—

218

C₁₆

—

219

C₁₃

#13062

yes

characteristic, complemented, Sylow

220

C₂³

—

221

C₂³

—

222

C₂³

—

223

C₂³

—

224

C₂³

#88049

yes

—

225

C₂³

C₂×#6104

yes

characteristic

226

Q₈

—

227

Q₈

—

228

Q₈

—

104

—

229

C₂×C₄

—

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

—

104

—

239

C₂×C₄

—

104

—

240

C₂×C₄

—

104

—

241

C₂×C₄

#88049

yes

—

242

C₂×C₄

C₂×#6103

yes

characteristic

243

C₂×C₄

#88193

yes

—

244

C₂×C₄

C₂×#6106

yes

characteristic

245

C₂×C₄

#88204

yes

—

246

C₈

—

247

C₈

#88135

yes

—

248

C₈

#88136

yes

characteristic

249

C₈

#88140

yes

characteristic

250

C₂²

—

251

C₂²

—

252

C₂²

—

253

C₂²

—

254

C₂²

—

255

C₂²

C₂×#88049

yes

characteristic

256

C₂²

#11718699

yes

—

257

C₂²

#11718808

yes

characteristic

258

C₂²

#11718840

yes

characteristic

259

C₂²

#11718856

yes

—

260

C₄

—

261

C₄

—

262

C₄

—

104

—

263

C₄

—

104

—

264

C₄

#11718619

yes

characteristic

265

C₄

#11718663

yes

characteristic

266

C₄

#11718709

yes

—

267

C₂

—

268

C₂

#13115262

yes

characteristic

269

C₂

#13116546

yes

characteristic

270

C₂

#13116555

yes

characteristic

271

C₂

#13116942

yes

—

272

C₂

#13116947

yes

—

	subgroup	G/H
center	C₂³	C₂×#6104
commutator	C₂×C₈×C₁₃	C₂²×C₄
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₁₃×#1808	C₂
socle	C₂³×C₁₃	C₂×D₈
prime radical	C₂⁴×C₁₃	D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	#1808	D₁₃
hypocenter	C₁₃	#13062
LCS	G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

subgroup

G/H

center

C₂³

C₂×#6104

commutator

C₂×C₈×C₁₃

C₂²×C₄

Frattini

C₂²×C₈

C₂²×D₁₃

Fitting

C₁₃×#1808

C₂

socle

C₂³×C₁₃

C₂×D₈

prime radical

C₂⁴×C₁₃

D₈

cosocle

C₂²×C₈×C₁₃

C₂³

D₁₃

C₁₃

G ▷ C₂×C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃

UCS

C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ #1808

N	H ≅ G/N	type
3. C₂×#11718084	C₂	semidirect
4. #13112927	C₂	semidirect
12. #11718777	C₄	semidirect
219. C₁₃	#13062	semidirect

H ≅ G/N

type

3. C₂×#11718084

C₂

semidirect

4. #13112927

C₂

semidirect

12. #11718777

C₄

semidirect

219. C₁₃

#13062

semidirect

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

subgroup	index
C₂²×#88052	2
C₂×#11718777	2
C₂×#11718084	2
#13112927	2
C₁₃×#1808	2
#13062	13

subgroup

index

C₂²×#88052

C₁₃×#1808

Subgroups — #15780294

Conjugacy classes of subgroups

Complements

Maximal subgroups