Subgroups — #16797623

Order 3328.

870 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₃⋊#424	C₂	1	1	yes	maximal, characteristic
2	#13131298	C₂	1	1	yes	maximal, characteristic
3	#13130634	C₂	1	1	yes	maximal, characteristic, complemented
4	#13130634	C₂	1	1	yes	maximal, characteristic, complemented
5	#13130630	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×C₄⋊#261	C₂	1	1	yes	maximal, characteristic, complemented
7	#13130625	C₂	1	1	yes	maximal, characteristic, complemented
8	#13130625	C₂	1	1	yes	maximal, characteristic, complemented
9	#13130623	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄⋊C₈×#261	C₂	1	1	yes	maximal, characteristic, complemented
11	#13130579	C₂	1	1	yes	maximal, characteristic
12	#13130579	C₂	1	1	yes	maximal, characteristic
13	#13130575	C₂	1	1	yes	maximal, characteristic
14	#13130571	C₂	1	1	yes	maximal, characteristic
15	D₁₃×#433	C₂	1	1	yes	maximal, characteristic
16	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
17	C₂²×D₁₃⋊C₈	C₂²	1	1	yes	characteristic
18	D₁₃×#117	C₂²	1	1	yes	characteristic
19	C₄×C₂²⋊#261	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊#261	C₂²	1	1	yes	characteristic
21	C₂×#88100	C₂²	1	1	yes	characteristic
22	C₂×#88100	C₂²	1	1	yes	characteristic
23	C₂×#88100	C₂²	1	1	yes	characteristic
24	C₂×#88100	C₂²	1	1	yes	characteristic
25	C₂×C₈×#261	C₂²	1	1	yes	characteristic
26	C₂×C₈×#261	C₂²	1	1	yes	characteristic
27	C₂×C₈×#261	C₂²	1	1	yes	characteristic
28	C₂×C₈×#261	C₂²	1	1	yes	characteristic
29	#11719082	C₄	1	2	yes	—
30	#11719082	C₄	1	2	yes	—
31	#11719079	C₄	1	2	yes	complemented
32	#11719079	C₄	1	2	yes	complemented
33	#11719071	C₄	1	2	yes	—
34	#11719071	C₄	1	2	yes	—
35	#11719067	C₄	1	2	yes	complemented
36	#11719067	C₄	1	2	yes	complemented
37	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
39	#11719057	C₂²	1	1	yes	characteristic
40	C₄²×#261	C₂²	1	1	yes	characteristic
41	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
42	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
43	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
44	D₁₃⋊(C₄⋊C₈)	C₂²	1	1	yes	characteristic
45	C₁₃×#433	C₄	1	1	yes	characteristic, complemented
46	#11718661	C₄	1	1	yes	characteristic, complemented
47	#11718501	C₄	1	1	yes	characteristic, complemented
48	#11718501	C₄	1	1	yes	characteristic, complemented
49	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
50	D₁₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
51	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
52	D₁₃×C₂²⋊C₈	C₂²	1	1	yes	characteristic
53	#11718381	C₄	1	1	yes	characteristic, complemented
54	#11718381	C₄	1	1	yes	characteristic, complemented
55	#11718370	C₄	1	1	yes	characteristic, complemented
56	D₁₃×#97	C₂²	1	1	yes	characteristic
57	#11718351	C₄	1	1	yes	characteristic, complemented
58	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
59	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
60	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
61	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
62	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
63	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
64	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
65	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
66	(C₂×#261)⋊C₈	C₂²	1	1	yes	characteristic
67	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
68	C₂×C₂²⋊#261	C₂×C₄	1	2	yes	—
69	C₂×C₂²⋊#261	C₂×C₄	1	2	yes	—
70	C₂×#6122	C₂×C₄	1	2	yes	—
71	C₂²×#1057	C₂×C₄	1	2	yes	—
72	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
73	C₂×C₄⋊#261	C₂×C₄	1	2	yes	—
74	C₂×C₄×#261	C₂×C₄	1	2	yes	—
75	C₂×C₄×#261	C₂×C₄	1	2	yes	—
76	C₂×C₄×#261	C₂³	1	1	yes	characteristic
77	C₂×C₄×#261	C₂³	1	1	yes	characteristic
78	C₂×C₄×#261	C₂³	1	1	yes	characteristic
79	C₂×C₄×#261	C₂³	1	1	yes	characteristic
80	D₁₃⋊M₁₆	—	4	1	no	—
81	D₁₃⋊M₁₆	—	4	1	no	—
82	C₂×#6118	C₂×C₄	1	2	yes	—
83	C₂×D₁₃⋊C₈	—	4	1	no	—
84	C₂×D₁₃⋊C₈	—	4	1	no	—
85	C₂×D₁₃⋊C₈	C₂×C₄	1	2	yes	—
86	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
87	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
88	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
89	C₂×D₁₃⋊C₈	C₂³	1	1	yes	characteristic
90	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
91	#88180	C₂×C₄	1	1	yes	characteristic
92	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
93	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
94	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
95	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
96	#88146	C₂×C₄	1	1	yes	characteristic
97	#88146	C₂×C₄	1	1	yes	characteristic
98	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
99	C₄⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
100	C₂²⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
101	C₂²⋊C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
102	#88131	C₂×C₄	1	1	yes	characteristic
103	#88131	C₂×C₄	1	1	yes	characteristic
104	#88126	C₂×C₄	1	1	yes	characteristic
105	#88126	C₂×C₄	1	1	yes	characteristic
106	C₄²×D₁₃	C₂³	1	1	yes	characteristic
107	C₄²×D₁₃	C₂³	1	1	yes	characteristic
108	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
109	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
110	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
111	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
112	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
113	(C₂×#261)⋊C₄	C₂×C₄	1	2	yes	—
114	#88112	C₂×C₄	1	2	yes	—
115	#88112	C₂×C₄	1	2	yes	—
116	#88112	C₂×C₄	1	2	yes	—
117	#88112	C₂×C₄	1	2	yes	—
118	C₄⋊#1057	C₂×C₄	1	2	yes	—
119	C₄⋊#1057	C₂×C₄	1	2	yes	—
120	C₄⋊#1057	C₂×C₄	1	2	yes	—
121	C₄⋊#1057	C₂×C₄	1	2	yes	—
122	#88100	—	4	1	no	—
123	#88100	—	4	1	no	—
124	#88100	—	4	1	no	—
125	#88100	—	4	1	no	—
126	C₈×#261	—	4	1	no	—
127	C₈×#261	—	4	1	no	—
128	C₈×#261	—	4	1	no	—
129	C₈×#261	—	4	1	no	—
130	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
131	C₁₃×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
132	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
133	C₁₃×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
134	C₁₃×#97	C₂×C₄	1	1	yes	characteristic
135	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
136	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
137	C₂²⋊#1055	C₂×C₄	1	1	yes	characteristic
138	#88060	C₂×C₄	1	1	yes	characteristic
139	#88060	C₂×C₄	1	1	yes	characteristic
140	#88060	C₂×C₄	1	1	yes	characteristic
141	#88060	C₂×C₄	1	1	yes	characteristic
142	#88055	C₂×C₄	1	1	yes	characteristic
143	#88055	C₂×C₄	1	1	yes	characteristic
144	#88054	C₂×C₄	1	1	yes	characteristic
145	#88054	C₂×C₄	1	1	yes	characteristic
146	#88054	C₂×C₄	1	1	yes	characteristic
147	#88054	C₂×C₄	1	1	yes	characteristic
148	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
149	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
150	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
151	C₄⋊#1055	C₂×C₄	1	1	yes	characteristic
152	#88043	C₂×C₄	1	1	yes	characteristic
153	C₄×#1055	C₂×C₄	1	1	yes	characteristic
154	#20553	—	13	1	no	maximal, Sylow
155	C₂³×D₁₃	C₂²×C₄	1	1	yes	characteristic
156	C₂²×#261	C₂²×C₄	1	2	yes	—
157	C₂²×#261	C₂²×C₄	1	2	yes	—
158	C₂²×#261	C₂²×C₄	1	2	yes	—
159	C₂²×#261	C₂²×C₄	1	2	yes	—
160	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₄×D₁₃	—	2	1	no	—
163	C₂×C₄×D₁₃	—	2	1	no	—
164	C₂×C₄×D₁₃	—	2	1	no	—
165	C₂×C₄×D₁₃	—	2	1	no	—
166	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊#261	—	2	4	no	—
175	C₂²⋊#261	—	4	2	no	—
176	#6122	—	4	2	no	—
177	C₂×#1057	—	4	2	no	—
178	C₂×#1057	C₂²×C₄	1	2	yes	—
179	C₂×#1057	C₂²×C₄	1	2	yes	—
180	C₂×#1057	C₂²×C₄	1	2	yes	—
181	C₂×#1057	C₂²×C₄	1	2	yes	—
182	C₄⋊#261	—	2	4	no	—
183	C₄⋊#261	—	4	2	no	—
184	C₄×#261	—	2	4	no	—
185	C₄×#261	—	2	1	no	—
186	C₄×#261	—	2	1	no	—
187	C₄×#261	—	2	1	no	—
188	C₄×#261	—	2	1	no	—
189	C₄×#261	—	2	1	no	—
190	C₄×#261	—	2	1	no	—
191	C₄×#261	—	2	1	no	—
192	C₄×#261	—	2	1	no	—
193	C₄×#261	—	4	2	no	—
194	#6118	—	4	2	no	—
195	D₁₃⋊C₈	—	2	1	no	—
196	D₁₃⋊C₈	—	2	1	no	—
197	D₁₃⋊C₈	—	2	1	no	—
198	D₁₃⋊C₈	—	2	1	no	—
199	D₁₃⋊C₈	—	2	1	no	—
200	D₁₃⋊C₈	—	2	1	no	—
201	D₁₃⋊C₈	—	2	1	no	—
202	D₁₃⋊C₈	—	2	1	no	—
203	D₁₃⋊C₈	—	4	2	no	—
204	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
205	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
206	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
207	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
208	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
209	C₁₃×C₄⋊C₄	C₄²	1	1	yes	characteristic
210	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
211	C₁₃×C₂²⋊C₄	C₄²	1	1	yes	characteristic
212	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
213	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
214	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
215	C₂²⋊Dic₁₃	C₄²	1	1	yes	characteristic
216	#6103	C₄²	1	1	yes	characteristic
217	#6103	C₄²	1	1	yes	characteristic
218	#6103	C₄²	1	1	yes	characteristic
219	#6103	C₄²	1	1	yes	characteristic
220	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
221	C₄⋊Dic₁₃	C₄²	1	1	yes	characteristic
222	#6101	C₄²	1	1	yes	characteristic
223	#6101	C₄²	1	1	yes	characteristic
224	#6101	C₄²	1	1	yes	characteristic
225	#6101	C₄²	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
228	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
230	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
231	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
232	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
233	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
234	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
235	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
236	C₈×D₁₃	—	2	1	no	—
237	C₈×D₁₃	—	2	1	no	—
238	C₈×D₁₃	—	2	1	no	—
239	C₈×D₁₃	—	2	1	no	—
240	C₈×D₁₃	—	2	1	no	—
241	C₈×D₁₃	—	2	1	no	—
242	C₈×D₁₃	—	2	1	no	—
243	C₈×D₁₃	—	2	1	no	—
244	C₂×#433	—	13	1	no	—
245	C₂×#424	—	13	1	no	—
246	#2298	—	13	1	no	—
247	#1771	—	13	1	no	—
248	#1771	—	13	1	no	—
249	#1770	—	13	1	no	—
250	C₈×C₄⋊C₄	—	13	1	no	—
251	#1768	—	13	1	no	—
252	#1768	—	13	1	no	—
253	#1767	—	13	1	no	—
254	C₄×C₄⋊C₈	—	13	1	no	—
255	#1753	—	13	1	no	—
256	#1753	—	13	1	no	—
257	#1752	—	13	1	no	—
258	C₈×C₂²⋊C₄	—	13	1	no	—
259	C₂³×C₁₃	C₂×C₄²	1	1	yes	characteristic
260	C₂²×D₁₃	—	2	1	no	—
261	C₂²×D₁₃	—	2	1	no	—
262	C₂²×D₁₃	—	2	2	no	—
263	C₂²×D₁₃	—	2	2	no	—
264	C₂²×D₁₃	C₂×C₄²	1	1	yes	characteristic
265	C₂²×D₁₃	C₂³×C₄	1	1	yes	characteristic
266	C₂×#261	—	2	2	no	—
267	C₂×#261	—	2	2	no	—
268	C₂×#261	—	2	2	no	—
269	C₂×#261	—	2	2	no	—
270	C₂×#261	—	2	2	no	—
271	C₂×#261	—	2	2	no	—
272	C₂×#261	—	2	2	no	—
273	C₂×#261	—	2	2	no	—
274	C₂×#261	—	2	2	no	—
275	C₂×#261	—	2	2	no	—
276	C₂×#261	—	2	2	no	—
277	C₂×#261	#131	1	4	yes	—
278	C₂×C₄×C₁₃	—	2	1	no	—
279	C₂×C₄×C₁₃	—	2	1	no	—
280	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
281	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
282	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
283	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
284	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
285	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
286	C₂×Dic₁₃	—	2	1	no	—
287	C₂×Dic₁₃	—	2	1	no	—
288	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
289	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
290	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
291	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
292	C₂×Dic₁₃	C₂×C₄²	1	1	yes	characteristic
293	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
294	C₄×D₁₃	—	2	1	no	—
295	C₄×D₁₃	—	2	1	no	—
296	C₄×D₁₃	—	2	2	no	—
297	C₄×D₁₃	—	2	2	no	—
298	C₄×D₁₃	—	2	2	no	—
299	C₄×D₁₃	—	2	2	no	—
300	C₄×D₁₃	—	2	1	no	—
301	C₄×D₁₃	—	2	1	no	—
302	C₄×D₁₃	—	2	1	no	—
303	C₄×D₁₃	—	2	1	no	—
304	C₄×D₁₃	H(5,𝔽₂)	1	1	yes	characteristic
305	C₄×D₁₃	H(5,𝔽₂)	1	1	yes	characteristic
306	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
307	C₄×D₁₃	2₋¹⁺⁴	1	1	yes	characteristic
308	#1057	—	2	2	no	—
309	#1057	—	2	2	no	—
310	#1057	—	2	2	no	—
311	#1057	—	2	2	no	—
312	C₈×C₁₃	—	2	1	no	—
313	C₈×C₁₃	—	2	1	no	—
314	C₈×C₁₃	—	2	1	no	—
315	C₈×C₁₃	—	2	1	no	—
316	#1055	—	2	1	no	—
317	#1055	—	2	1	no	—
318	#1055	—	2	1	no	—
319	#1055	—	2	1	no	—
320	C₂²×M₁₆	—	13	1	no	—
321	C₂³×C₈	—	13	1	no	—
322	C₂×#117	—	13	1	no	—
323	#433	—	13	1	no	—
324	#433	—	13	1	no	—
325	#433	—	13	1	no	—
326	#433	—	13	1	no	—
327	#433	—	13	1	no	—
328	#433	—	13	1	no	—
329	#433	—	13	1	no	—
330	#433	#261	1	1	yes	characteristic, complemented
331	#424	—	13	2	no	—
332	#424	—	13	2	no	—
333	#424	—	13	2	no	—
334	#424	—	13	2	no	—
335	C₂×C₄⋊C₈	—	13	1	no	—
336	C₂×C₄⋊C₈	—	13	1	no	—
337	C₂×C₄⋊C₈	—	13	1	no	—
338	C₂×C₄⋊C₈	—	13	1	no	—
339	C₂×C₄⋊C₈	—	13	1	no	—
340	C₂×C₄⋊C₈	—	13	1	no	—
341	C₂×C₂²⋊C₈	—	13	1	no	—
342	C₂×C₂²⋊C₈	—	13	1	no	—
343	C₂×#97	—	13	1	no	—
344	C₂×#97	—	13	1	no	—
345	C₂×#97	—	13	1	no	—
346	C₂×#97	—	13	1	no	—
347	C₂×#97	—	13	1	no	—
348	C₂×C₄×C₈	—	13	1	no	—
349	C₂×C₄×C₈	—	13	1	no	—
350	C₂×C₄×C₈	—	13	1	no	—
351	C₂×C₄×C₈	—	13	1	no	—
352	C₂×C₄×C₈	—	13	1	no	—
353	#388	—	13	2	no	—
354	#388	—	13	2	no	—
355	#387	—	13	2	no	—
356	#387	—	13	2	no	—
357	C₄×C₄⋊C₄	—	13	1	no	—
358	C₄×C₄⋊C₄	—	13	1	no	—
359	C₄×C₂²⋊C₄	—	13	1	no	—
360	C₄×C₂²⋊C₄	—	13	1	no	—
361	#376	—	13	1	no	—
362	C₄³	—	13	1	no	—
363	#336	—	13	1	no	—
364	#336	—	13	1	no	—
365	#336	—	13	1	no	—
366	#336	—	13	1	no	—
367	#336	—	13	1	no	—
368	#336	—	13	1	no	—
369	#336	—	13	1	no	—
370	#336	—	13	1	no	—
371	C₂²×C₁₃	—	2	1	no	—
372	C₂²×C₁₃	—	2	1	no	—
373	C₂²×C₁₃	—	2	1	no	—
374	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
375	C₂×D₁₃	—	2	1	no	—
376	C₂×D₁₃	—	2	1	no	—
377	C₂×D₁₃	—	2	1	no	—
378	C₂×D₁₃	—	4	2	no	—
379	C₂×D₁₃	—	4	2	no	—
380	C₂×D₁₃	#520	1	1	yes	characteristic
381	C₂×D₁₃	#520	1	1	yes	characteristic
382	C₂×D₁₃	C₂×#131	1	2	yes	—
383	C₂×D₁₃	#568	1	2	yes	—
384	#261	—	2	4	no	—
385	#261	—	4	2	no	—
386	#261	—	4	2	no	—
387	#261	—	4	2	no	—
388	C₄×C₁₃	—	2	1	no	—
389	C₄×C₁₃	—	2	1	no	—
390	C₄×C₁₃	—	2	1	no	—
391	C₄×C₁₃	—	2	1	no	—
392	C₄×C₁₃	—	2	1	no	—
393	C₄×C₁₃	#520	1	1	yes	characteristic
394	C₄×C₁₃	#520	1	1	yes	characteristic
395	Dic₁₃	—	2	1	no	—
396	Dic₁₃	—	2	1	no	—
397	Dic₁₃	—	2	1	no	—
398	Dic₁₃	—	2	1	no	—
399	Dic₁₃	—	2	1	no	—
400	Dic₁₃	#518	1	1	yes	characteristic
401	Dic₁₃	#519	1	1	yes	characteristic
402	C₂³×C₄	—	13	1	no	—
403	C₂×M₁₆	—	13	2	no	—
404	C₂×M₁₆	—	13	2	no	—
405	C₂×M₁₆	—	52	1	no	—
406	C₂×M₁₆	—	52	1	no	—
407	C₂²×C₈	—	13	1	no	—
408	C₂²×C₈	—	13	1	no	—
409	C₂²×C₈	—	13	1	no	—
410	C₂²×C₈	—	13	1	no	—
411	C₂²×C₈	—	13	2	no	—
412	C₂²×C₈	—	13	2	no	—
413	C₂²×C₈	—	13	1	no	—
414	C₂²×C₈	—	13	1	no	—
415	C₂²×C₈	—	13	1	no	—
416	C₂²×C₈	—	13	1	no	—
417	C₂²×C₈	—	52	1	no	—
418	C₂²×C₈	—	52	1	no	—
419	#117	—	13	1	no	—
420	#117	—	13	1	no	—
421	#117	—	13	1	no	—
422	#117	—	13	1	no	—
423	#117	—	13	1	no	—
424	#117	—	13	1	no	—
425	#117	—	13	1	no	—
426	#117	C₂×#261	1	1	yes	characteristic
427	C₂×C₄⋊C₄	—	13	1	no	—
428	C₂×C₄⋊C₄	—	13	1	no	—
429	C₂×C₄⋊C₄	—	13	2	no	—
430	C₂×C₄⋊C₄	—	13	2	no	—
431	C₂×C₂²⋊C₄	—	13	1	no	—
432	C₂×C₂²⋊C₄	—	13	1	no	—
433	C₂×C₂²⋊C₄	—	13	2	no	—
434	C₂×C₂²⋊C₄	—	13	2	no	—
435	C₂×C₄²	—	13	1	no	—
436	C₂×C₄²	—	13	1	no	—
437	C₂×C₄²	—	13	1	no	—
438	C₂×C₄²	—	13	1	no	—
439	C₂×C₄²	—	13	1	no	—
440	C₂×C₄²	—	13	1	no	—
441	C₂×C₄²	—	13	2	no	—
442	C₂×C₄²	—	13	2	no	—
443	C₄⋊C₈	—	13	2	no	—
444	C₄⋊C₈	—	13	2	no	—
445	C₄⋊C₈	—	13	2	no	—
446	C₄⋊C₈	—	13	2	no	—
447	C₄⋊C₈	—	13	2	no	—
448	C₄⋊C₈	—	13	2	no	—
449	C₄⋊C₈	—	13	2	no	—
450	C₄⋊C₈	—	13	2	no	—
451	C₄⋊C₈	—	13	1	no	—
452	C₄⋊C₈	—	13	1	no	—
453	C₄⋊C₈	—	13	1	no	—
454	C₄⋊C₈	—	13	1	no	—
455	C₄⋊C₈	—	13	1	no	—
456	C₄⋊C₈	—	13	1	no	—
457	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
458	C₄⋊C₈	C₂×#261	1	1	yes	characteristic
459	C₂²⋊C₈	—	13	1	no	—
460	C₂²⋊C₈	—	13	1	no	—
461	C₂²⋊C₈	—	13	1	no	—
462	C₂²⋊C₈	—	13	1	no	—
463	C₂²⋊C₈	—	13	1	no	—
464	C₂²⋊C₈	—	13	1	no	—
465	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
466	C₂²⋊C₈	C₂×#261	1	1	yes	characteristic
467	#97	—	13	1	no	—
468	#97	—	13	1	no	—
469	#97	—	13	1	no	—
470	#97	—	52	1	no	—
471	#97	—	52	1	no	—
472	#97	—	52	1	no	—
473	#97	—	52	1	no	—
474	#97	C₂×#261	1	1	yes	characteristic
475	C₄×C₈	—	13	1	no	—
476	C₄×C₈	—	13	1	no	—
477	C₄×C₈	—	13	1	no	—
478	C₄×C₈	—	52	1	no	—
479	C₄×C₈	—	52	1	no	—
480	C₄×C₈	—	52	1	no	—
481	C₄×C₈	—	52	1	no	—
482	C₄×C₈	C₂×#261	1	1	yes	characteristic
483	#95	—	13	2	no	—
484	#95	—	13	2	no	—
485	#95	—	13	2	no	—
486	#95	—	13	2	no	—
487	#95	—	13	2	no	—
488	#95	—	13	2	no	—
489	C₂×C₁₃	—	4	1	no	—
490	C₂×C₁₃	#2274	1	1	yes	characteristic
491	C₂×C₁₃	C₄×#131	1	1	yes	characteristic
492	C₂×C₁₃	#2875	1	1	yes	characteristic
493	D₁₃	—	4	1	no	—
494	D₁₃	#2992	1	2	yes	—
495	D₁₃	#2993	1	2	yes	—
496	C₂⁴	—	13	1	no	—
497	C₂²×C₄	—	13	1	no	—
498	C₂²×C₄	—	13	2	no	—
499	C₂²×C₄	—	13	1	no	—
500	C₂²×C₄	—	13	1	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	1	no	—
503	C₂²×C₄	—	13	1	no	—
504	C₂²×C₄	—	13	1	no	—
505	C₂²×C₄	—	13	1	no	—
506	C₂²×C₄	—	13	1	no	—
507	C₂²×C₄	—	13	2	no	—
508	C₂²×C₄	—	13	2	no	—
509	C₂²×C₄	—	13	2	no	—
510	C₂²×C₄	—	26	1	no	—
511	C₂²×C₄	—	26	1	no	—
512	C₂²×C₄	—	26	1	no	—
513	C₂²×C₄	—	26	1	no	—
514	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
515	M₁₆	—	52	2	no	—
516	M₁₆	—	52	2	no	—
517	C₂×C₈	—	13	2	no	—
518	C₂×C₈	—	13	2	no	—
519	C₂×C₈	—	13	2	no	—
520	C₂×C₈	—	13	2	no	—
521	C₂×C₈	—	13	1	no	—
522	C₂×C₈	—	13	1	no	—
523	C₂×C₈	—	13	1	no	—
524	C₂×C₈	—	13	1	no	—
525	C₂×C₈	—	26	1	no	—
526	C₂×C₈	—	26	1	no	—
527	C₂×C₈	—	26	1	no	—
528	C₂×C₈	—	26	1	no	—
529	C₂×C₈	—	26	1	no	—
530	C₂×C₈	—	26	1	no	—
531	C₂×C₈	—	26	1	no	—
532	C₂×C₈	—	26	1	no	—
533	C₂×C₈	—	26	1	no	—
534	C₂×C₈	—	26	1	no	—
535	C₂×C₈	—	26	1	no	—
536	C₂×C₈	—	26	1	no	—
537	C₂×C₈	—	26	1	no	—
538	C₂×C₈	—	26	1	no	—
539	C₂×C₈	—	26	1	no	—
540	C₂×C₈	—	26	1	no	—
541	C₂×C₈	—	52	2	no	—
542	C₂×C₈	—	52	2	no	—
543	C₂×C₈	C₂²×#261	1	1	yes	characteristic
544	C₂×C₈	C₂²×#261	1	1	yes	characteristic
545	C₂×C₈	C₂²×#261	1	1	yes	characteristic
546	C₂×C₈	C₂²×#261	1	1	yes	characteristic
547	C₄⋊C₄	—	13	1	no	—
548	C₄⋊C₄	—	13	1	no	—
549	C₄⋊C₄	—	13	1	no	—
550	C₄⋊C₄	—	13	1	no	—
551	C₄⋊C₄	—	13	1	no	—
552	C₄⋊C₄	—	13	1	no	—
553	C₄⋊C₄	—	26	4	no	—
554	C₄⋊C₄	—	52	2	no	—
555	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
556	C₄⋊C₄	C₄×#261	1	1	yes	characteristic
557	C₂²⋊C₄	—	13	1	no	—
558	C₂²⋊C₄	—	13	1	no	—
559	C₂²⋊C₄	—	13	1	no	—
560	C₂²⋊C₄	—	13	1	no	—
561	C₂²⋊C₄	—	13	1	no	—
562	C₂²⋊C₄	—	13	1	no	—
563	C₂²⋊C₄	—	26	4	no	—
564	C₂²⋊C₄	—	52	2	no	—
565	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
566	C₂²⋊C₄	C₄×#261	1	1	yes	characteristic
567	C₄²	—	13	1	no	—
568	C₄²	—	13	1	no	—
569	C₄²	—	13	1	no	—
570	C₄²	—	13	1	no	—
571	C₄²	—	13	1	no	—
572	C₄²	—	13	1	no	—
573	C₄²	—	26	1	no	—
574	C₄²	—	26	1	no	—
575	C₄²	—	26	1	no	—
576	C₄²	—	26	1	no	—
577	C₄²	—	26	1	no	—
578	C₄²	—	26	1	no	—
579	C₄²	—	26	1	no	—
580	C₄²	—	26	1	no	—
581	C₄²	—	26	4	no	—
582	C₄²	—	52	2	no	—
583	C₄²	C₂²×#261	1	1	yes	characteristic
584	C₄²	C₂²×#261	1	1	yes	characteristic
585	C₁₃	#20553	1	1	yes	characteristic, complemented, Sylow
586	C₂³	—	13	1	no	—
587	C₂³	—	13	1	no	—
588	C₂³	—	26	2	no	—
589	C₂³	—	26	2	no	—
590	C₂³	—	26	1	no	—
591	C₂³	—	26	1	no	—
592	C₂³	C₂×C₄×#261	1	1	yes	characteristic
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	13	1	no	—
596	C₂×C₄	—	13	1	no	—
597	C₂×C₄	—	13	1	no	—
598	C₂×C₄	—	13	1	no	—
599	C₂×C₄	—	13	1	no	—
600	C₂×C₄	—	13	4	no	—
601	C₂×C₄	—	13	1	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	26	1	no	—
607	C₂×C₄	—	26	1	no	—
608	C₂×C₄	—	26	2	no	—
609	C₂×C₄	—	26	2	no	—
610	C₂×C₄	—	26	2	no	—
611	C₂×C₄	—	26	2	no	—
612	C₂×C₄	—	26	1	no	—
613	C₂×C₄	—	26	1	no	—
614	C₂×C₄	—	26	1	no	—
615	C₂×C₄	—	26	1	no	—
616	C₂×C₄	—	26	2	no	—
617	C₂×C₄	—	26	2	no	—
618	C₂×C₄	—	26	1	no	—
619	C₂×C₄	—	26	1	no	—
620	C₂×C₄	—	26	2	no	—
621	C₂×C₄	—	26	2	no	—
622	C₂×C₄	—	26	2	no	—
623	C₂×C₄	—	26	2	no	—
624	C₂×C₄	—	26	2	no	—
625	C₂×C₄	—	26	2	no	—
626	C₂×C₄	—	26	2	no	—
627	C₂×C₄	—	26	2	no	—
628	C₂×C₄	—	26	2	no	—
629	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
630	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
631	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
632	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
633	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
634	C₂×C₄	C₂³×#261	1	1	yes	characteristic
635	C₈	—	2	1	no	—
636	C₈	—	2	1	no	—
637	C₈	—	2	1	no	—
638	C₈	—	2	1	no	—
639	C₈	—	26	2	no	—
640	C₈	—	26	2	no	—
641	C₈	—	26	2	no	—
642	C₈	—	26	2	no	—
643	C₈	—	26	1	no	—
644	C₈	—	26	1	no	—
645	C₈	—	26	1	no	—
646	C₈	—	26	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	1	no	—
649	C₂²	—	2	1	no	—
650	C₂²	—	13	1	no	—
651	C₂²	—	13	1	no	—
652	C₂²	—	13	2	no	—
653	C₂²	—	13	2	no	—
654	C₂²	—	26	1	no	—
655	C₂²	—	26	1	no	—
656	C₂²	—	26	1	no	—
657	C₂²	—	52	2	no	—
658	C₂²	—	52	2	no	—
659	C₂²	C₂²×C₄×#261	1	1	yes	characteristic
660	C₄	—	2	1	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	13	1	no	—
666	C₄	—	13	1	no	—
667	C₄	—	26	4	no	—
668	C₄	—	26	1	no	—
669	C₄	—	26	1	no	—
670	C₄	—	26	1	no	—
671	C₄	—	26	1	no	—
672	C₄	—	26	1	no	—
673	C₄	—	52	2	no	—
674	C₄	—	52	2	no	—
675	C₄	—	52	2	no	—
676	C₄	#11719631	1	1	yes	characteristic
677	C₄	#11719631	1	1	yes	characteristic
678	C₂	—	4	1	no	—
679	C₂	—	13	2	no	—
680	C₂	—	13	2	no	—
681	C₂	—	52	1	no	—
682	C₂	#13131273	1	1	yes	characteristic
683	C₂	#131×#261	1	1	yes	characteristic
684	C₂	#13131406	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#261
commutator, socle	C₂²×C₁₃	C₂²×C₄²
Fitting	C₁₃×#433	C₄
prime radical	C₂³×D₁₃	C₂²×C₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#433	#261
hypocenter	C₁₃	#20553
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #433

Complements

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

N	H ≅ G/N	type
3. #13130634	C₂	semidirect
4. #13130634	C₂	semidirect
5. #13130630	C₂	semidirect
6. C₈×C₄⋊#261	C₂	semidirect
7. #13130625	C₂	semidirect
8. #13130625	C₂	semidirect
9. #13130623	C₂	semidirect
10. C₄⋊C₈×#261	C₂	semidirect
31. #11719079	C₄	semidirect
32. #11719079	C₄	semidirect
35. #11719067	C₄	semidirect
36. #11719067	C₄	semidirect
45. C₁₃×#433	C₄	semidirect
46. #11718661	C₄	semidirect
47. #11718501	C₄	semidirect
48. #11718501	C₄	semidirect
53. #11718381	C₄	semidirect
54. #11718381	C₄	semidirect
55. #11718370	C₄	semidirect
57. #11718351	C₄	semidirect
330. #433	#261	semidirect
585. C₁₃	#20553	semidirect

Maximal subgroups

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

subgroup	index
D₁₃⋊#424	2
#13131298	2
#13130634	2
#13130630	2
C₈×C₄⋊#261	2
#13130625	2
#13130623	2
C₄⋊C₈×#261	2
#13130579	2
#13130575	2
#13130571	2
D₁₃×#433	2
#20553	13