Subgroups — #72259641

Order 16224.

988 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72259495	C₂	1	2	yes	maximal, complemented
2	#72259485	C₂	1	1	yes	maximal, characteristic, complemented
3	#72259389	C₂	1	1	yes	maximal, characteristic, complemented
4	#72259384	C₂	1	2	yes	maximal, complemented
5	D₄×#11759817	C₂	1	1	yes	maximal, characteristic, complemented
6	#72259375	C₂	1	1	yes	maximal, characteristic, complemented
7	#72259373	C₂	1	1	yes	maximal, characteristic, complemented
8	#72259284	C₃	1	1	yes	maximal, characteristic, complemented, Hall
9	#72259249	C₂×C₃	1	2	yes	complemented
10	#72259226	C₂×C₃	1	1	yes	characteristic, complemented
11	D₁₃×D₅₂	C₂×C₃	1	1	yes	characteristic, complemented
12	#72259220	C₂×C₃	1	1	yes	characteristic, complemented
13	D₁₃×C₂²⋊D₁₃	C₂×C₃	1	2	yes	complemented
14	D₄×C₁₃×D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
15	#72229419	C₂×C₃	1	1	yes	characteristic, complemented
16	#72229416	C₂	1	1	yes	maximal, characteristic, complemented
17	C₁₃×#6129	C₂×C₃	1	1	yes	characteristic, complemented
18	C₂×#72214094	C₂	1	2	yes	maximal, complemented
19	C₂×#13062579	C₂×C₃	1	2	yes	complemented
20	#72229261	C₂²	1	1	yes	characteristic, complemented
21	#72229258	C₂²	1	1	yes	characteristic, complemented
22	#72229237	C₂²	1	2	yes	complemented
23	C₄×#11759817	C₂²	1	1	yes	characteristic, complemented
24	C₄×#11759817	C₂²	1	1	yes	characteristic, complemented
25	C₂×#14523130	C₂²	1	2	yes	complemented
26	#72229203	C₂²	1	1	yes	characteristic, complemented
27	#72229196	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#11759817	C₂²	1	2	yes	complemented
29	D₄×#11759815	C₂	1	1	yes	maximal, characteristic, complemented
30	D₄×C₁₃⋊D₁₃	C₂×C₃	1	1	yes	characteristic, complemented
31	#72229020	C₂²	1	1	yes	characteristic, complemented
32	#72229013	C₂²	1	2	yes	complemented
33	D₄×#92788	C₂²	1	1	yes	characteristic, complemented
34	C₄×#11759815	C₂²	1	1	yes	characteristic, complemented
35	#72214127	C₂	1	2	yes	maximal, complemented
36	#72214115	C₂×C₃	1	2	yes	complemented
37	#72214094	C₂²	1	2	yes	complemented
38	#72214094	C₂²	1	1	yes	characteristic, complemented
39	#72214094	C₂²	1	1	yes	characteristic, complemented
40	#72214094	C₂²	1	2	yes	complemented
41	#72214094	C₂²	1	2	yes	complemented
42	#72214085	C₂²	1	2	yes	complemented
43	#72214085	C₂²	1	2	yes	complemented
44	C₂×#11759815⋊C₂	C₂²	1	2	yes	complemented
45	#72213995	C₂²	1	2	yes	complemented
46	C₂²×#11759815	C₂²	1	2	yes	complemented
47	C₂²×#92788	C₂³	1	2	yes	—
48	C₂×#11759817	—	4	2	no	—
49	C₂×#11759817	C₂³	1	1	yes	characteristic
50	C₂×#11759817	C₂³	1	2	yes	—
51	C₂×#11759817	C₂³	1	1	yes	characteristic
52	C₂×#11759815	—	4	2	no	—
53	C₂×#11759815	C₂³	1	1	yes	characteristic
54	C₂×#11759815	C₂³	1	2	yes	—
55	#11759815⋊C₂	—	4	2	no	—
56	C₄×#92788	C₂³	1	1	yes	characteristic
57	#14523130	C₂³	1	1	yes	characteristic
58	#14523130	C₂³	1	2	yes	—
59	#14523130	C₂³	1	1	yes	characteristic
60	#14523128	C₂³	1	1	yes	characteristic
61	C₂²×C₁₃⋊D₁₃	C₂²×C₃	1	2	yes	complemented
62	C₂²×C₁₃×D₁₃	C₂²×C₃	1	2	yes	complemented
63	C₂×D₁₃²	C₂²×C₃	1	2	yes	complemented
64	D₄×C₁₃²	C₂²×C₃	1	1	yes	characteristic, complemented
65	C₂²⋊(C₁₃⋊D₁₃)	C₂²×C₃	1	2	yes	complemented
66	C₄⋊(C₁₃⋊D₁₃)	C₂²×C₃	1	1	yes	characteristic, complemented
67	C₄×C₁₃⋊D₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
68	C₁₃×C₂²⋊D₁₃	C₂²×C₃	1	2	yes	complemented
69	C₁₃×C₂²⋊D₁₃	C₂²×C₃	1	2	yes	complemented
70	C₂×C₁₃×Dic₁₃	C₂²×C₃	1	2	yes	complemented
71	C₁₃×D₅₂	C₂²×C₃	1	1	yes	characteristic, complemented
72	C₄×C₁₃×D₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
73	C₄×C₁₃×D₁₃	C₂²×C₃	1	1	yes	characteristic, complemented
74	C₁₃×Dic₂₆	C₂²×C₃	1	1	yes	characteristic, complemented
75	#13062580	C₂²×C₃	1	1	yes	characteristic, complemented
76	#13062579	C₂²×C₃	1	2	yes	complemented
77	#13062579	C₂²×C₃	1	1	yes	characteristic, complemented
78	#13062579	C₂²×C₃	1	2	yes	complemented
79	#13062579	C₂²×C₃	1	2	yes	complemented
80	#13062579	C₂²×C₃	1	1	yes	characteristic, complemented
81	#13062578	C₂²×C₃	1	1	yes	characteristic, complemented
82	#13062577	C₂²×C₃	1	2	yes	complemented
83	D₁₃×Dic₁₃	C₂²×C₃	1	2	yes	complemented
84	#11929141	—	13	1	no	maximal
85	#88251⋊C₃	—	13	1	no	maximal
86	C₂×#92788	—	2	2	no	—
87	C₂×#92788	C₂⁴	1	1	yes	characteristic
88	#11759817	—	2	1	no	—
89	#11759817	—	2	2	no	—
90	#11759817	—	2	1	no	—
91	#11759815	—	2	1	no	—
92	#11759815	—	2	2	no	—
93	C₂²×C₁₃²	C₂³×C₃	1	2	yes	—
94	C₂×C₁₃⋊D₁₃	—	4	2	no	—
95	C₂×C₁₃⋊D₁₃	C₂³×C₃	1	2	yes	—
96	C₂×C₁₃⋊D₁₃	C₂³×C₃	1	1	yes	characteristic
97	C₂×C₁₃×D₁₃	—	4	2	no	—
98	C₂×C₁₃×D₁₃	C₂³×C₃	1	2	yes	—
99	C₂×C₁₃×D₁₃	C₂³×C₃	1	1	yes	characteristic
100	C₂×C₁₃×D₁₃	C₂³×C₃	1	1	yes	characteristic
101	D₁₃²	—	4	2	no	—
102	C₄×C₁₃²	C₂³×C₃	1	1	yes	characteristic
103	#10621725	C₂³×C₃	1	1	yes	characteristic
104	C₁₃×Dic₁₃	C₂³×C₃	1	2	yes	—
105	C₁₃×Dic₁₃	C₂³×C₃	1	1	yes	characteristic
106	C₁₃×Dic₁₃	C₂³×C₃	1	1	yes	characteristic
107	#41×C₁₃⋊C₃	—	13	1	no	—
108	C₂×D₄×C₁₃⋊C₃	—	13	1	no	—
109	C₂×(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
110	C₂×(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
111	#10597707	—	13	1	no	—
112	#10597707	—	13	1	no	—
113	#6129⋊C₃	—	13	1	no	—
114	#6129⋊C₃	—	13	2	no	—
115	#6129⋊C₃	—	13	1	no	—
116	D₄×D₁₃⋊C₃	—	13	1	no	—
117	D₄×D₁₃⋊C₃	—	13	2	no	—
118	D₄×D₁₃⋊C₃	—	13	1	no	—
119	D₄×D₁₃⋊C₃	—	13	2	no	—
120	D₄×D₁₃⋊C₃	—	13	2	no	—
121	D₄×D₁₃⋊C₃	—	13	1	no	—
122	D₄×D₁₃⋊C₃	—	13	1	no	—
123	D₄×D₁₃⋊C₃	—	26	6	no	—
124	#6127⋊C₃	—	13	1	no	—
125	#6127⋊C₃	—	13	1	no	—
126	#6127⋊C₃	—	13	1	no	—
127	#6127⋊C₃	—	13	2	no	—
128	C₂×C₄⋊(D₁₃⋊C₃)	—	13	1	no	—
129	C₂×C₄⋊(D₁₃⋊C₃)	—	13	2	no	—
130	#92788	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
131	#88256	—	13	1	no	—
132	#88251	—	13	1	no	—
133	C₂×C₁₃²	—	2	2	no	—
134	C₂×C₁₃²	C₂⁴×C₃	1	1	yes	characteristic
135	C₁₃⋊D₁₃	—	2	1	no	—
136	C₁₃⋊D₁₃	—	2	2	no	—
137	C₁₃×D₁₃	—	2	1	no	—
138	C₁₃×D₁₃	—	2	2	no	—
139	C₁₃×D₁₃	—	2	1	no	—
140	C₂³×C₁₃⋊C₃	—	13	2	no	—
141	C₂²×D₁₃⋊C₃	—	13	2	no	—
142	C₂²×D₁₃⋊C₃	—	13	2	no	—
143	C₂²×D₁₃⋊C₃	—	13	2	no	—
144	C₂²×D₁₃⋊C₃	—	13	2	no	—
145	C₂²×D₁₃⋊C₃	—	13	2	no	—
146	C₂²×D₁₃⋊C₃	—	26	12	no	—
147	Q₈×C₁₃⋊C₃	—	13	1	no	—
148	D₄×C₁₃⋊C₃	—	13	2	no	—
149	D₄×C₁₃⋊C₃	—	13	2	no	—
150	D₄×C₁₃⋊C₃	—	13	1	no	—
151	D₄×C₁₃⋊C₃	—	13	1	no	—
152	D₄×C₁₃⋊C₃	—	13	1	no	—
153	D₄×C₁₃⋊C₃	—	52	6	no	—
154	C₂×C₄×C₁₃⋊C₃	—	13	2	no	—
155	C₂×C₄×C₁₃⋊C₃	—	13	1	no	—
156	C₂×C₄×C₁₃⋊C₃	—	13	1	no	—
157	(C₂²⋊D₁₃)⋊C₃	—	13	1	no	—
158	(C₂²⋊D₁₃)⋊C₃	—	13	1	no	—
159	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
160	(C₂²⋊D₁₃)⋊C₃	—	13	1	no	—
161	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
162	(C₂²⋊D₁₃)⋊C₃	—	13	1	no	—
163	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
164	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
165	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
166	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
167	(C₂²⋊D₁₃)⋊C₃	—	13	2	no	—
168	(C₂²⋊D₁₃)⋊C₃	—	26	12	no	—
169	C₂×Dic₁₃⋊C₃	—	13	2	no	—
170	C₂×Dic₁₃⋊C₃	—	13	2	no	—
171	C₄⋊(D₁₃⋊C₃)	—	13	2	no	—
172	C₄⋊(D₁₃⋊C₃)	—	13	1	no	—
173	C₄⋊(D₁₃⋊C₃)	—	13	2	no	—
174	C₄⋊(D₁₃⋊C₃)	—	13	2	no	—
175	C₄⋊(D₁₃⋊C₃)	—	13	1	no	—
176	C₄⋊(D₁₃⋊C₃)	—	13	1	no	—
177	C₄⋊(D₁₃⋊C₃)	—	13	1	no	—
178	C₄⋊(D₁₃⋊C₃)	—	13	1	no	—
179	C₄⋊(D₁₃⋊C₃)	—	26	6	no	—
180	C₄×D₁₃⋊C₃	—	13	1	no	—
181	C₄×D₁₃⋊C₃	—	13	2	no	—
182	C₄×D₁₃⋊C₃	—	13	1	no	—
183	C₄×D₁₃⋊C₃	—	13	2	no	—
184	C₄×D₁₃⋊C₃	—	13	2	no	—
185	C₄×D₁₃⋊C₃	—	13	1	no	—
186	C₄×D₁₃⋊C₃	—	13	1	no	—
187	C₄×D₁₃⋊C₃	—	26	6	no	—
188	(C₁₃⋊C₃)⋊Q₈	—	13	1	no	—
189	(C₁₃⋊C₃)⋊Q₈	—	13	1	no	—
190	(C₁₃⋊C₃)⋊Q₈	—	13	1	no	—
191	C₁₃×#41	—	13	1	no	—
192	C₂×D₄×C₁₃	—	13	1	no	—
193	C₂×C₂²⋊D₁₃	—	13	2	no	—
194	C₂×C₂²⋊D₁₃	—	13	2	no	—
195	#6131	—	13	1	no	—
196	#6131	—	13	1	no	—
197	#6129	—	13	2	no	—
198	#6129	—	13	1	no	—
199	#6129	D₁₃⋊C₃	1	1	yes	characteristic, complemented
200	D₄×D₁₃	—	13	2	no	—
201	D₄×D₁₃	—	13	1	no	—
202	D₄×D₁₃	—	13	1	no	—
203	D₄×D₁₃	—	13	2	no	—
204	D₄×D₁₃	—	13	2	no	—
205	D₄×D₁₃	—	13	1	no	—
206	D₄×D₁₃	—	26	6	no	—
207	D₄×D₁₃	D₁₃⋊C₃	1	1	yes	characteristic, complemented
208	#6127	—	13	2	no	—
209	#6127	—	13	1	no	—
210	#6127	—	13	1	no	—
211	#6127	—	13	1	no	—
212	C₂×D₅₂	—	13	2	no	—
213	C₂×D₅₂	—	13	1	no	—
214	C₁₃²	C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
215	C₂²×C₁₃⋊C₃	—	13	2	no	—
216	C₂²×C₁₃⋊C₃	—	13	1	no	—
217	C₂²×C₁₃⋊C₃	—	13	1	no	—
218	C₂²×C₁₃⋊C₃	—	13	2	no	—
219	C₂²×C₁₃⋊C₃	—	13	2	no	—
220	C₂²×C₁₃⋊C₃	—	52	12	no	—
221	C₂²×C₁₃⋊C₃	—	52	2	no	—
222	C₂×D₁₃⋊C₃	—	13	1	no	—
223	C₂×D₁₃⋊C₃	—	13	2	no	—
224	C₂×D₁₃⋊C₃	—	13	1	no	—
225	C₂×D₁₃⋊C₃	—	13	2	no	—
226	C₂×D₁₃⋊C₃	—	13	2	no	—
227	C₂×D₁₃⋊C₃	—	13	1	no	—
228	C₂×D₁₃⋊C₃	—	13	1	no	—
229	C₂×D₁₃⋊C₃	—	26	6	no	—
230	C₂×D₁₃⋊C₃	—	26	12	no	—
231	C₂×D₁₃⋊C₃	—	52	2	no	—
232	C₂×D₁₃⋊C₃	—	52	2	no	—
233	C₂×D₁₃⋊C₃	—	52	2	no	—
234	C₂×D₁₃⋊C₃	—	52	2	no	—
235	C₂×D₁₃⋊C₃	—	52	2	no	—
236	C₂×D₁₃⋊C₃	—	52	24	no	—
237	C₄×C₁₃⋊C₃	—	13	1	no	—
238	C₄×C₁₃⋊C₃	—	13	1	no	—
239	C₄×C₁₃⋊C₃	—	13	2	no	—
240	C₄×C₁₃⋊C₃	—	13	1	no	—
241	C₄×C₁₃⋊C₃	—	13	1	no	—
242	C₄×C₁₃⋊C₃	—	52	6	no	—
243	Dic₁₃⋊C₃	—	13	1	no	—
244	Dic₁₃⋊C₃	—	13	1	no	—
245	Dic₁₃⋊C₃	—	13	1	no	—
246	Dic₁₃⋊C₃	—	13	1	no	—
247	Dic₁₃⋊C₃	—	13	2	no	—
248	Dic₁₃⋊C₃	—	26	6	no	—
249	C₂³×C₁₃	—	13	2	no	—
250	C₂²×D₁₃	—	13	2	no	—
251	C₂²×D₁₃	—	13	2	no	—
252	C₂²×D₁₃	—	13	2	no	—
253	C₂²×D₁₃	—	13	2	no	—
254	C₂²×D₁₃	—	26	12	no	—
255	C₂²×D₁₃	C₂×D₁₃⋊C₃	1	2	yes	complemented
256	Q₈×C₁₃	—	13	1	no	—
257	D₄×C₁₃	—	2	6	no	—
258	D₄×C₁₃	—	13	2	no	—
259	D₄×C₁₃	—	13	2	no	—
260	D₄×C₁₃	—	13	1	no	—
261	D₄×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
262	D₄×C₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
263	C₂×C₄×C₁₃	—	13	2	no	—
264	C₂×C₄×C₁₃	—	13	1	no	—
265	C₂×C₄×C₁₃	—	13	1	no	—
266	C₂²⋊D₁₃	—	13	2	no	—
267	C₂²⋊D₁₃	—	13	2	no	—
268	C₂²⋊D₁₃	—	13	1	no	—
269	C₂²⋊D₁₃	—	13	1	no	—
270	C₂²⋊D₁₃	—	13	1	no	—
271	C₂²⋊D₁₃	—	13	1	no	—
272	C₂²⋊D₁₃	—	13	2	no	—
273	C₂²⋊D₁₃	—	13	2	no	—
274	C₂²⋊D₁₃	—	13	2	no	—
275	C₂²⋊D₁₃	—	26	12	no	—
276	C₂²⋊D₁₃	C₂×D₁₃⋊C₃	1	2	yes	complemented
277	C₂²⋊D₁₃	C₂×D₁₃⋊C₃	1	2	yes	complemented
278	C₂×Dic₁₃	—	13	2	no	—
279	C₂×Dic₁₃	C₂×D₁₃⋊C₃	1	2	yes	complemented
280	D₅₂	—	13	2	no	—
281	D₅₂	—	13	1	no	—
282	D₅₂	—	13	2	no	—
283	D₅₂	—	13	2	no	—
284	D₅₂	—	13	1	no	—
285	D₅₂	—	13	1	no	—
286	D₅₂	—	13	1	no	—
287	D₅₂	—	26	6	no	—
288	D₅₂	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
289	C₄×D₁₃	—	13	2	no	—
290	C₄×D₁₃	—	13	1	no	—
291	C₄×D₁₃	—	13	1	no	—
292	C₄×D₁₃	—	13	2	no	—
293	C₄×D₁₃	—	13	2	no	—
294	C₄×D₁₃	—	26	6	no	—
295	C₄×D₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
296	C₄×D₁₃	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
297	Dic₂₆	—	13	1	no	—
298	Dic₂₆	—	13	1	no	—
299	Dic₂₆	C₂×D₁₃⋊C₃	1	1	yes	characteristic, complemented
300	C₃×H(5,𝔽₂)	—	169	1	no	Hall
301	C₂×C₁₃⋊C₃	—	13	1	no	—
302	C₂×C₁₃⋊C₃	—	13	1	no	—
303	C₂×C₁₃⋊C₃	—	26	2	no	—
304	C₂×C₁₃⋊C₃	—	26	2	no	—
305	C₂×C₁₃⋊C₃	—	26	1	no	—
306	C₂×C₁₃⋊C₃	—	26	1	no	—
307	C₂×C₁₃⋊C₃	—	26	2	no	—
308	C₂×C₁₃⋊C₃	—	52	6	no	—
309	C₂×C₁₃⋊C₃	—	104	12	no	—
310	D₁₃⋊C₃	—	26	1	no	—
311	D₁₃⋊C₃	—	26	1	no	—
312	D₁₃⋊C₃	—	26	1	no	—
313	D₁₃⋊C₃	—	26	2	no	—
314	D₁₃⋊C₃	—	26	2	no	—
315	D₁₃⋊C₃	—	26	12	no	—
316	D₁₃⋊C₃	—	26	2	no	—
317	D₁₃⋊C₃	—	26	1	no	—
318	D₁₃⋊C₃	—	52	12	no	—
319	C₂²×C₁₃	—	2	12	no	—
320	C₂²×C₁₃	—	13	2	no	—
321	C₂²×C₁₃	—	13	1	no	—
322	C₂²×C₁₃	—	13	1	no	—
323	C₂²×C₁₃	—	52	2	no	—
324	C₂²×C₁₃	C₂²×D₁₃⋊C₃	1	2	yes	—
325	C₂²×C₁₃	C₂²×D₁₃⋊C₃	1	2	yes	—
326	C₂×D₁₃	—	4	2	no	—
327	C₂×D₁₃	—	13	1	no	—
328	C₂×D₁₃	—	13	2	no	—
329	C₂×D₁₃	—	13	1	no	—
330	C₂×D₁₃	—	13	2	no	—
331	C₂×D₁₃	—	26	6	no	—
332	C₂×D₁₃	—	26	12	no	—
333	C₂×D₁₃	—	52	2	no	—
334	C₂×D₁₃	—	52	2	no	—
335	C₂×D₁₃	—	52	2	no	—
336	C₂×D₁₃	—	52	2	no	—
337	C₂×D₁₃	—	52	24	no	—
338	C₂×D₁₃	C₂²×D₁₃⋊C₃	1	2	yes	—
339	C₂×D₁₃	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
340	C₂×D₁₃	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
341	C₄×C₁₃	—	2	6	no	—
342	C₄×C₁₃	—	13	1	no	—
343	C₄×C₁₃	—	13	1	no	—
344	C₄×C₁₃	—	13	2	no	—
345	C₄×C₁₃	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
346	C₄×C₁₃	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
347	Dic₁₃	—	13	1	no	—
348	Dic₁₃	—	13	1	no	—
349	Dic₁₃	—	26	6	no	—
350	Dic₁₃	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
351	Dic₁₃	C₂²×D₁₃⋊C₃	1	1	yes	characteristic
352	Dic₁₃	C₂²×D₁₃⋊C₃	1	2	yes	—
353	C₃×#41	—	338	1	no	—
354	C₃×#41	—	169	1	no	—
355	C₃×#41	—	169	2	no	—
356	C₃×#41	—	169	1	no	—
357	C₃×#41	—	169	1	no	—
358	C₂×C₃×D₄	—	338	1	no	—
359	C₂×C₃×D₄	—	169	1	no	—
360	C₂×C₃×D₄	—	169	2	no	—
361	C₂×C₃×D₄	—	169	2	no	—
362	C₂×C₃×D₄	—	169	2	no	—
363	C₂×C₃×D₄	—	169	1	no	—
364	C₁₃⋊C₃	—	13	1	no	—
365	C₁₃⋊C₃	—	13	1	no	—
366	C₁₃⋊C₃	—	52	6	no	—
367	H(5,𝔽₂)	—	169	1	no	Sylow
368	C₂×C₁₃	—	2	2	no	—
369	C₂×C₁₃	—	2	2	no	—
370	C₂×C₁₃	—	2	6	no	—
371	C₂×C₁₃	—	4	12	no	—
372	C₂×C₁₃	—	26	1	no	—
373	C₂×C₁₃	—	26	2	no	—
374	C₂×C₁₃	—	26	1	no	—
375	C₂×C₁₃	C₂³×D₁₃⋊C₃	1	1	yes	characteristic
376	C₂×C₁₃	C₂³×D₁₃⋊C₃	1	1	yes	characteristic
377	D₁₃	—	2	1	no	—
378	D₁₃	—	2	2	no	—
379	D₁₃	—	2	1	no	—
380	D₁₃	—	26	12	no	—
381	D₁₃	—	26	1	no	—
382	D₁₃	—	26	2	no	—
383	D₁₃	—	26	1	no	—
384	D₁₃	—	26	2	no	—
385	D₁₃	—	52	12	no	—
386	C₂³×C₃	—	338	2	no	—
387	C₂³×C₃	—	169	2	no	—
388	C₂³×C₃	—	169	2	no	—
389	C₃×Q₈	—	338	1	no	—
390	C₃×Q₈	—	169	1	no	—
391	C₃×D₄	—	338	2	no	—
392	C₃×D₄	—	338	2	no	—
393	C₃×D₄	—	338	1	no	—
394	C₃×D₄	—	676	1	no	—
395	C₃×D₄	—	169	1	no	—
396	C₃×D₄	—	169	2	no	—
397	C₃×D₄	—	169	1	no	—
398	C₃×D₄	—	169	2	no	—
399	C₃×D₄	—	169	2	no	—
400	C₃×D₄	—	169	1	no	—
401	C₃×D₄	—	169	1	no	—
402	C₃×D₄	—	169	2	no	—
403	C₂×C₃×C₄	—	338	2	no	—
404	C₂×C₃×C₄	—	338	1	no	—
405	C₂×C₃×C₄	—	338	1	no	—
406	C₂×C₃×C₄	—	169	2	no	—
407	C₂×C₃×C₄	—	169	2	no	—
408	C₂×C₃×C₄	—	169	1	no	—
409	#41	—	13	1	no	—
410	#41	—	169	1	no	—
411	#41	—	169	2	no	—
412	#41	—	169	1	no	—
413	#41	—	169	1	no	—
414	C₂×D₄	—	13	1	no	—
415	C₂×D₄	—	169	1	no	—
416	C₂×D₄	—	169	2	no	—
417	C₂×D₄	—	169	2	no	—
418	C₂×D₄	—	169	2	no	—
419	C₂×D₄	—	169	1	no	—
420	C₁₃	—	2	6	no	—
421	C₁₃	#88251⋊C₃	1	1	yes	characteristic, complemented
422	C₁₃	#11929141	1	1	yes	characteristic, complemented
423	C₂²×C₃	—	338	1	no	—
424	C₂²×C₃	—	338	1	no	—
425	C₂²×C₃	—	338	2	no	—
426	C₂²×C₃	—	676	2	no	—
427	C₂²×C₃	—	676	2	no	—
428	C₂²×C₃	—	676	2	no	—
429	C₂²×C₃	—	676	2	no	—
430	C₂²×C₃	—	169	1	no	—
431	C₂²×C₃	—	169	2	no	—
432	C₃×C₄	—	338	1	no	—
433	C₃×C₄	—	338	1	no	—
434	C₃×C₄	—	338	2	no	—
435	C₃×C₄	—	676	1	no	—
436	C₃×C₄	—	169	1	no	—
437	C₂³	—	13	2	no	—
438	C₂³	—	169	2	no	—
439	C₂³	—	169	2	no	—
440	Q₈	—	13	1	no	—
441	Q₈	—	169	1	no	—
442	D₄	—	13	2	no	—
443	D₄	—	13	2	no	—
444	D₄	—	13	1	no	—
445	D₄	—	169	1	no	—
446	D₄	—	169	2	no	—
447	D₄	—	169	1	no	—
448	D₄	—	169	2	no	—
449	D₄	—	169	2	no	—
450	D₄	—	169	1	no	—
451	D₄	—	169	2	no	—
452	D₄	—	169	1	no	—
453	D₄	#11759815⋊C₂	1	1	yes	characteristic, complemented
454	C₂×C₄	—	13	2	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	169	2	no	—
458	C₂×C₄	—	169	2	no	—
459	C₂×C₄	—	169	1	no	—
460	C₂×C₃	—	1352	2	no	—
461	C₂×C₃	—	338	1	no	—
462	C₂×C₃	—	338	1	no	—
463	C₂×C₃	—	338	2	no	—
464	C₂×C₃	—	676	2	no	—
465	C₂×C₃	—	676	1	no	—
466	C₂×C₃	—	676	1	no	—
467	C₂²	—	13	1	no	—
468	C₂²	—	13	1	no	—
469	C₂²	—	13	2	no	—
470	C₂²	—	52	2	no	—
471	C₂²	—	676	2	no	—
472	C₂²	—	676	2	no	—
473	C₂²	—	169	1	no	—
474	C₂²	—	169	2	no	—
475	C₂²	C₂×#11759815⋊C₂	1	2	yes	—
476	C₄	—	13	1	no	—
477	C₄	—	13	1	no	—
478	C₄	—	13	2	no	—
479	C₄	—	169	1	no	—
480	C₄	C₂×#11759815⋊C₂	1	1	yes	characteristic
481	C₃	—	676	1	no	Sylow
482	C₂	—	2	2	no	—
483	C₂	—	26	1	no	—
484	C₂	—	26	2	no	—
485	C₂	—	26	1	no	—
486	C₂	—	338	1	no	—
487	C₂	—	338	2	no	—
488	C₂	C₂²×#11759815⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#11759815⋊C₂
commutator, socle, cosocle	C₂×C₁₃²	C₂⁴×C₃
Fitting	D₄×C₁₃²	C₂²×C₃
hypercenter	D₄	#11759815⋊C₂
hypocenter	C₁₃²	C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₃² ▷ C₁₃²
UCS	C₁ ◁ C₂ ◁ D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #72259495	C₂	semidirect
2. #72259485	C₂	semidirect
3. #72259389	C₂	semidirect
4. #72259384	C₂	semidirect
5. D₄×#11759817	C₂	semidirect
6. #72259375	C₂	semidirect
7. #72259373	C₂	semidirect
8. #72259284	C₃	semidirect
9. #72259249	C₂×C₃	semidirect
10. #72259226	C₂×C₃	semidirect
11. D₁₃×D₅₂	C₂×C₃	semidirect
12. #72259220	C₂×C₃	semidirect
13. D₁₃×C₂²⋊D₁₃	C₂×C₃	semidirect
14. D₄×C₁₃×D₁₃	C₂×C₃	semidirect
15. #72229419	C₂×C₃	semidirect
16. #72229416	C₂	semidirect
17. C₁₃×#6129	C₂×C₃	semidirect
18. C₂×#72214094	C₂	semidirect
19. C₂×#13062579	C₂×C₃	semidirect
20. #72229261	C₂²	semidirect
21. #72229258	C₂²	semidirect
22. #72229237	C₂²	semidirect
23. C₄×#11759817	C₂²	semidirect
24. C₄×#11759817	C₂²	semidirect
25. C₂×#14523130	C₂²	semidirect
26. #72229203	C₂²	semidirect
27. #72229196	C₂²	semidirect
28. C₂²×#11759817	C₂²	semidirect
29. D₄×#11759815	C₂	semidirect
30. D₄×C₁₃⋊D₁₃	C₂×C₃	semidirect
31. #72229020	C₂²	semidirect
32. #72229013	C₂²	semidirect
33. D₄×#92788	C₂²	semidirect
34. C₄×#11759815	C₂²	semidirect
35. #72214127	C₂	semidirect
36. #72214115	C₂×C₃	semidirect
37. #72214094	C₂²	semidirect
38. #72214094	C₂²	semidirect
39. #72214094	C₂²	semidirect
40. #72214094	C₂²	semidirect
41. #72214094	C₂²	semidirect
42. #72214085	C₂²	semidirect
43. #72214085	C₂²	semidirect
44. C₂×#11759815⋊C₂	C₂²	semidirect
45. #72213995	C₂²	semidirect
46. C₂²×#11759815	C₂²	semidirect
61. C₂²×C₁₃⋊D₁₃	C₂²×C₃	semidirect
62. C₂²×C₁₃×D₁₃	C₂²×C₃	semidirect
63. C₂×D₁₃²	C₂²×C₃	semidirect
64. D₄×C₁₃²	C₂²×C₃	semidirect
65. C₂²⋊(C₁₃⋊D₁₃)	C₂²×C₃	semidirect
66. C₄⋊(C₁₃⋊D₁₃)	C₂²×C₃	semidirect
67. C₄×C₁₃⋊D₁₃	C₂²×C₃	semidirect
68. C₁₃×C₂²⋊D₁₃	C₂²×C₃	semidirect
69. C₁₃×C₂²⋊D₁₃	C₂²×C₃	semidirect
70. C₂×C₁₃×Dic₁₃	C₂²×C₃	semidirect
71. C₁₃×D₅₂	C₂²×C₃	semidirect
72. C₄×C₁₃×D₁₃	C₂²×C₃	semidirect
73. C₄×C₁₃×D₁₃	C₂²×C₃	semidirect
74. C₁₃×Dic₂₆	C₂²×C₃	semidirect
75. #13062580	C₂²×C₃	semidirect
76. #13062579	C₂²×C₃	semidirect
77. #13062579	C₂²×C₃	semidirect
78. #13062579	C₂²×C₃	semidirect
79. #13062579	C₂²×C₃	semidirect
80. #13062579	C₂²×C₃	semidirect
81. #13062578	C₂²×C₃	semidirect
82. #13062577	C₂²×C₃	semidirect
83. D₁₃×Dic₁₃	C₂²×C₃	semidirect
130. #92788	H(5,𝔽₂)	semidirect
199. #6129	D₁₃⋊C₃	semidirect
207. D₄×D₁₃	D₁₃⋊C₃	semidirect
214. C₁₃²	C₃×H(5,𝔽₂)	semidirect
255. C₂²×D₁₃	C₂×D₁₃⋊C₃	semidirect
261. D₄×C₁₃	C₂×D₁₃⋊C₃	semidirect
262. D₄×C₁₃	C₂×D₁₃⋊C₃	semidirect
276. C₂²⋊D₁₃	C₂×D₁₃⋊C₃	semidirect
277. C₂²⋊D₁₃	C₂×D₁₃⋊C₃	semidirect
279. C₂×Dic₁₃	C₂×D₁₃⋊C₃	semidirect
288. D₅₂	C₂×D₁₃⋊C₃	semidirect
295. C₄×D₁₃	C₂×D₁₃⋊C₃	semidirect
296. C₄×D₁₃	C₂×D₁₃⋊C₃	semidirect
299. Dic₂₆	C₂×D₁₃⋊C₃	semidirect
421. C₁₃	#88251⋊C₃	semidirect
422. C₁₃	#11929141	semidirect
453. D₄	#11759815⋊C₂	semidirect

Maximal subgroups

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

subgroup	index
#72259495	2
#72259485	2
#72259389	2
#72259384	2
D₄×#11759817	2
#72259375	2
#72259373	2
#72259284	3
#72229416	2
C₂×#72214094	2
D₄×#11759815	2
#72214127	2
#11929141	13
#88251⋊C₃	13