Subgroups — #13128396

Order 1664.

1132 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
3	#41×Dic₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#88180	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719363	C₂	1	2	yes	maximal, complemented
7	#11719355	C₂	1	2	yes	maximal, complemented
8	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719344	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719340	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719323	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719321	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719319	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719296	C₂	1	2	yes	maximal, complemented
17	#11719292	C₂	1	2	yes	maximal, complemented
18	#11719262	C₂	1	2	yes	maximal, complemented
19	#11719243	C₂	1	2	yes	maximal, complemented
20	#11719243	C₂	1	2	yes	maximal, complemented
21	C₄×#6129	C₂	1	2	yes	maximal, complemented
22	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
26	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#6129	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
29	C₁₃×#123	C₂²	1	2	yes	—
30	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
33	C₁₃×#121	C₂²	1	1	yes	characteristic, complemented
34	C₁₃×#120	C₂²	1	2	yes	—
35	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
36	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
37	C₁₃×#117	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
39	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
40	#88200	C₂²	1	1	yes	characteristic, complemented
41	#88200	C₂²	1	1	yes	characteristic, complemented
42	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
43	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
44	#88193	C₂²	1	2	yes	—
45	#88193	C₂²	1	2	yes	—
46	#88192	C₂²	1	2	yes	—
47	#88192	C₂²	1	1	yes	characteristic, complemented
48	#88192	C₂²	1	1	yes	characteristic, complemented
49	#88191	C₂²	1	2	yes	—
50	#88190	C₂²	1	2	yes	complemented
51	#88189	C₂²	1	2	yes	—
52	#88189	C₂²	1	2	yes	complemented
53	#88189	C₂²	1	2	yes	complemented
54	D₄×Dic₁₃	C₂²	1	2	yes	—
55	D₄×Dic₁₃	C₂²	1	2	yes	—
56	D₄×Dic₁₃	C₂²	1	2	yes	complemented
57	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
58	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
61	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
62	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
68	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
69	C₂×#6103	C₂²	1	1	yes	characteristic
70	#88180	C₂²	1	1	yes	characteristic
71	#88180	C₂²	1	1	yes	characteristic
72	#88180	C₂²	1	2	yes	—
73	#88180	C₂²	1	2	yes	complemented
74	#88180	C₂²	1	1	yes	characteristic, complemented
75	#88180	C₂²	1	1	yes	characteristic, complemented
76	#88180	C₂²	1	2	yes	complemented
77	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
78	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
79	C₂×#6101	C₂²	1	1	yes	characteristic
80	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
81	C₂×C₄×Dic₁₃	C₂²	1	2	yes	complemented
82	C₂×C₄×Dic₁₃	C₂²	1	2	yes	complemented
83	#88152	C₂²	1	2	yes	complemented
84	#88152	C₂²	1	2	yes	complemented
85	#88151	C₂²	1	2	yes	complemented
86	#88146	C₂²	1	1	yes	characteristic, complemented
87	#88146	C₂²	1	1	yes	characteristic, complemented
88	#88146	C₂²	1	2	yes	complemented
89	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
90	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
91	#88144	C₂²	1	1	yes	characteristic, complemented
92	#88144	C₂²	1	1	yes	characteristic, complemented
93	#88144	C₂²	1	2	yes	complemented
94	#88143	C₂²	1	2	yes	complemented
95	#88143	C₂²	1	2	yes	complemented
96	#88142	C₂²	1	1	yes	characteristic, complemented
97	#88142	C₂²	1	1	yes	characteristic, complemented
98	#88141	C₂²	1	2	yes	complemented
99	#88140	C₂²	1	2	yes	—
100	#88140	C₂²	1	2	yes	complemented
101	#88139	C₂²	1	2	yes	—
102	#88139	C₂²	1	2	yes	complemented
103	#88137	C₂²	1	2	yes	—
104	#88137	C₂²	1	2	yes	complemented
105	#88135	C₂²	1	2	yes	—
106	#88135	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
108	#88133	C₂²	1	2	yes	complemented
109	#88133	C₂²	1	2	yes	complemented
110	#88133	C₂²	1	2	yes	complemented
111	#88133	C₂²	1	2	yes	complemented
112	#88132	C₂²	1	2	yes	—
113	#88132	C₂²	1	2	yes	—
114	#88132	C₂²	1	2	yes	complemented
115	#88132	C₂²	1	2	yes	complemented
116	#88131	C₂²	1	2	yes	—
117	#88131	C₂²	1	2	yes	complemented
118	#88131	C₂²	1	2	yes	complemented
119	#88126	C₂²	1	2	yes	complemented
120	C₄²×D₁₃	C₂²	1	2	yes	complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	1	yes	characteristic
125	C₁₃×#41	—	2	4	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂×D₄×C₁₃	C₂³	1	2	yes	—
130	C₂×D₄×C₁₃	C₂³	1	2	yes	—
131	C₂²×C₄×C₁₃	—	2	4	no	—
132	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
134	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
137	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	—	2	4	no	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
145	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
146	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
147	C₂²×Dic₁₃	C₂³	1	2	yes	—
148	C₂²×Dic₁₃	C₂³	1	2	yes	—
149	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
150	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
151	C₂²×Dic₁₃	C₂³	1	2	yes	—
152	C₂²×Dic₁₃	C₂³	1	2	yes	—
153	#6129	—	2	8	no	—
154	C₂×C₄×D₁₃	—	2	4	no	—
155	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
156	C₂×C₄×D₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×Dic₂₆	C₂³	1	2	yes	—
162	C₂×Dic₂₆	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
167	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₄²×C₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₄⋊Dic₁₃	C₂³	1	2	yes	—
195	C₄⋊Dic₁₃	C₂³	1	2	yes	—
196	C₄⋊Dic₁₃	C₂³	1	2	yes	—
197	C₄⋊Dic₁₃	C₂³	1	2	yes	—
198	C₄⋊Dic₁₃	C₂³	1	2	yes	—
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
202	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	2	yes	—
205	#6101	C₂³	1	2	yes	—
206	#6101	C₂³	1	2	yes	—
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	1	yes	characteristic
214	#6101	C₂³	1	1	yes	characteristic
215	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
216	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
217	C₄×Dic₁₃	C₂³	1	2	yes	—
218	C₄×Dic₁₃	C₂³	1	2	yes	—
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	#3475	—	13	1	no	maximal, Sylow
228	C₂³×C₁₃	—	2	2	no	—
229	C₂³×C₁₃	—	2	2	no	—
230	C₂³×C₁₃	—	4	1	no	—
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₃	C₂⁴	1	2	yes	—
233	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	—	2	2	no	—
236	C₂²×D₁₃	—	2	2	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
239	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
240	Q₈×C₁₃	—	2	2	no	—
241	D₄×C₁₃	—	2	4	no	—
242	D₄×C₁₃	—	2	4	no	—
243	D₄×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	4	2	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	2	2	no	—
249	C₂×C₄×C₁₃	—	2	2	no	—
250	C₂×C₄×C₁₃	—	2	4	no	—
251	C₂×C₄×C₁₃	#41	1	4	yes	complemented
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
259	C₂²⋊D₁₃	—	2	2	no	—
260	C₂²⋊D₁₃	—	2	4	no	—
261	C₂²⋊D₁₃	—	2	2	no	—
262	C₂²⋊D₁₃	—	2	2	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂²⋊D₁₃	#41	1	4	yes	complemented
265	C₂×Dic₁₃	—	2	2	no	—
266	C₂×Dic₁₃	—	2	4	no	—
267	C₂×Dic₁₃	—	2	4	no	—
268	C₂×Dic₁₃	—	2	2	no	—
269	C₂×Dic₁₃	—	4	1	no	—
270	C₂×Dic₁₃	—	4	2	no	—
271	C₂×Dic₁₃	—	4	2	no	—
272	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	2	yes	—
275	C₂×Dic₁₃	C₂⁴	1	2	yes	—
276	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
277	C₂×Dic₁₃	C₂⁴	1	2	yes	—
278	C₂×Dic₁₃	C₂⁴	1	2	yes	—
279	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
280	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
281	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
282	C₄×D₁₃	—	2	4	no	—
283	C₄×D₁₃	—	2	2	no	—
284	C₄×D₁₃	—	2	2	no	—
285	C₄×D₁₃	—	2	2	no	—
286	C₄×D₁₃	—	2	2	no	—
287	C₄×D₁₃	—	4	2	no	—
288	Dic₂₆	—	2	4	no	—
289	Dic₂₆	—	4	2	no	—
290	#556	—	13	1	no	—
291	#555	—	13	1	no	—
292	#554	—	13	1	no	—
293	#553	—	13	1	no	—
294	#553	—	13	1	no	—
295	#552	—	13	2	no	—
296	#552	—	13	1	no	—
297	#552	—	13	1	no	—
298	#551	—	13	2	no	—
299	#551	—	13	2	no	—
300	#547	—	13	1	no	—
301	#546	—	13	2	no	—
302	#533	—	13	1	no	—
303	#529	—	13	2	no	—
304	#529	—	13	2	no	—
305	#529	—	13	2	no	—
306	#525	—	13	1	no	—
307	#525	D₁₃	1	1	yes	characteristic, complemented
308	C₄×#41	—	13	1	no	—
309	C₄×#41	—	13	2	no	—
310	C₂×C₄×D₄	—	13	1	no	—
311	C₂×#117	—	13	1	no	—
312	C₂×#117	—	13	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	2	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	2	no	—
321	C₂²×C₁₃	—	2	2	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	4	4	no	—
324	C₂²×C₁₃	C₂×#41	1	2	yes	—
325	C₂²×C₁₃	C₂×#41	1	2	yes	—
326	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	4	4	no	—
333	C₂×D₁₃	C₂×#41	1	2	yes	—
334	C₄×C₁₃	—	2	2	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	1	no	—
337	C₄×C₁₃	—	2	2	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	C₂×#41	1	2	yes	—
340	C₄×C₁₃	C₂×#41	1	2	yes	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	2	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	2	no	—
348	Dic₁₃	—	2	2	no	—
349	Dic₁₃	—	2	1	no	—
350	Dic₁₃	C₂×#41	1	2	yes	—
351	C₂×#41	—	13	2	no	—
352	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
353	C₂²×D₄	—	13	1	no	—
354	C₂³×C₄	—	13	1	no	—
355	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
356	C₄⋊Q₈	—	13	1	no	—
357	C₄⋊Q₈	—	13	1	no	—
358	#126	—	13	2	no	—
359	#126	—	13	2	no	—
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#125	—	13	2	no	—
365	#125	—	13	2	no	—
366	#125	—	13	2	no	—
367	#125	—	13	1	no	—
368	#125	—	13	1	no	—
369	#124	—	13	2	no	—
370	#124	—	13	2	no	—
371	#124	—	13	2	no	—
372	#123	—	13	2	no	—
373	#123	—	13	2	no	—
374	#123	—	13	2	no	—
375	#123	—	13	2	no	—
376	#123	—	13	2	no	—
377	#123	—	13	2	no	—
378	#123	—	13	2	no	—
379	#123	C₂×D₁₃	1	2	yes	—
380	C₂²⋊Q₈	—	13	1	no	—
381	C₂²⋊Q₈	—	13	1	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	—	13	2	no	—
386	C₂²⋊Q₈	—	13	2	no	—
387	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
388	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
389	#121	—	13	1	no	—
390	#121	—	13	1	no	—
391	#121	—	13	2	no	—
392	#121	—	13	2	no	—
393	#121	—	13	2	no	—
394	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
395	#121	C₂×D₁₃	1	1	yes	characteristic, complemented
396	#120	—	13	2	no	—
397	#120	C₂×D₁₃	1	2	yes	—
398	C₄×Q₈	—	13	1	no	—
399	C₄×Q₈	—	13	1	no	—
400	C₄×Q₈	—	13	2	no	—
401	C₄×Q₈	—	13	2	no	—
402	C₄×Q₈	—	13	2	no	—
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	—	13	1	no	—
405	C₄×D₄	—	13	2	no	—
406	C₄×D₄	—	13	2	no	—
407	C₄×D₄	—	13	1	no	—
408	C₄×D₄	—	13	1	no	—
409	C₄×D₄	—	13	1	no	—
410	C₄×D₄	—	13	1	no	—
411	C₄×D₄	—	13	1	no	—
412	C₄×D₄	—	13	1	no	—
413	C₄×D₄	—	13	1	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	—	13	1	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	2	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
421	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
422	#117	—	13	1	no	—
423	#117	—	13	1	no	—
424	#117	—	13	2	no	—
425	#117	—	13	2	no	—
426	#117	—	13	1	no	—
427	#117	—	13	1	no	—
428	#117	—	13	2	no	—
429	#117	—	13	1	no	—
430	#117	—	13	1	no	—
431	#117	—	13	2	no	—
432	#117	—	13	2	no	—
433	#117	—	13	2	no	—
434	#117	—	13	2	no	—
435	#117	—	13	2	no	—
436	#117	C₂×D₁₃	1	1	yes	characteristic
437	C₂×C₄⋊C₄	—	13	1	no	—
438	C₂×C₄⋊C₄	—	13	1	no	—
439	C₂×C₄⋊C₄	—	13	1	no	—
440	C₂×C₄⋊C₄	—	13	1	no	—
441	C₂×C₄⋊C₄	—	13	1	no	—
442	C₂×C₂²⋊C₄	—	13	2	no	—
443	C₂×C₂²⋊C₄	—	13	1	no	—
444	C₂×C₂²⋊C₄	—	13	1	no	—
445	C₂×C₂²⋊C₄	—	13	2	no	—
446	C₂×C₄²	—	13	2	no	—
447	C₂×C₄²	—	13	1	no	—
448	C₂×C₄²	—	13	2	no	—
449	C₂×C₄²	—	13	2	no	—
450	C₂×C₁₃	—	2	2	no	—
451	C₂×C₁₃	—	2	2	no	—
452	C₂×C₁₃	—	4	2	no	—
453	C₂×C₁₃	—	4	1	no	—
454	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
455	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
456	C₂×C₁₃	#585	1	1	yes	characteristic
457	D₁₃	—	2	2	no	—
458	D₁₃	—	4	1	no	—
459	C₂⁴	—	13	1	no	—
460	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
461	#41	—	2	4	no	—
462	#41	—	26	8	no	—
463	C₂×Q₈	—	13	2	no	—
464	C₂×Q₈	—	13	2	no	—
465	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	1	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	2	no	—
472	C₂×D₄	—	26	4	no	—
473	C₂×D₄	C₂²×D₁₃	1	2	yes	—
474	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
475	C₂×D₄	C₂²×D₁₃	1	2	yes	—
476	C₂×D₄	C₂²×D₁₃	1	2	yes	—
477	C₂²×C₄	—	2	4	no	—
478	C₂²×C₄	—	13	2	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	1	no	—
482	C₂²×C₄	—	13	1	no	—
483	C₂²×C₄	—	13	2	no	—
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	13	2	no	—
486	C₂²×C₄	—	13	1	no	—
487	C₂²×C₄	—	13	1	no	—
488	C₂²×C₄	—	13	1	no	—
489	C₂²×C₄	—	13	1	no	—
490	C₂²×C₄	—	13	2	no	—
491	C₂²×C₄	—	26	4	no	—
492	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
493	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
494	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
496	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
497	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₄⋊C₄	—	13	1	no	—
500	C₄⋊C₄	—	13	1	no	—
501	C₄⋊C₄	—	13	1	no	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	1	no	—
504	C₄⋊C₄	—	13	2	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	2	no	—
514	C₄⋊C₄	—	13	2	no	—
515	C₄⋊C₄	—	13	2	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
522	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
523	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
524	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	1	no	—
527	C₂²⋊C₄	—	13	2	no	—
528	C₂²⋊C₄	—	13	2	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	1	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	2	no	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	1	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	1	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
548	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
549	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	2	no	—
552	C₄²	—	13	2	no	—
553	C₄²	—	13	2	no	—
554	C₄²	—	13	2	no	—
555	C₄²	—	13	1	no	—
556	C₄²	—	13	1	no	—
557	C₄²	—	13	2	no	—
558	C₄²	—	13	2	no	—
559	C₄²	—	13	1	no	—
560	C₄²	—	13	1	no	—
561	C₄²	—	13	2	no	—
562	C₄²	C₂²×D₁₃	1	2	yes	—
563	C₁₃	#3475	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	2	2	no	—
565	C₂³	—	2	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	13	1	no	—
568	C₂³	—	13	1	no	—
569	C₂³	—	26	2	no	—
570	C₂³	—	26	2	no	—
571	C₂³	—	52	1	no	—
572	C₂³	C₂³×D₁₃	1	1	yes	characteristic
573	C₂³	C₂³×D₁₃	1	2	yes	—
574	C₂³	C₂³×D₁₃	1	1	yes	characteristic
575	C₂³	C₂³×D₁₃	1	1	yes	characteristic
576	Q₈	—	2	2	no	—
577	Q₈	—	26	4	no	—
578	Q₈	—	52	2	no	—
579	D₄	—	2	4	no	—
580	D₄	—	2	4	no	—
581	D₄	—	2	2	no	—
582	D₄	—	4	2	no	—
583	D₄	—	13	4	no	—
584	D₄	—	26	2	no	—
585	D₄	—	26	2	no	—
586	D₄	—	26	4	no	—
587	D₄	—	26	2	no	—
588	D₄	—	52	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	2	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	13	1	no	—
596	C₂×C₄	—	13	1	no	—
597	C₂×C₄	—	13	2	no	—
598	C₂×C₄	—	13	1	no	—
599	C₂×C₄	—	13	2	no	—
600	C₂×C₄	—	13	1	no	—
601	C₂×C₄	—	13	2	no	—
602	C₂×C₄	—	13	2	no	—
603	C₂×C₄	—	13	1	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	26	4	no	—
606	C₂×C₄	—	26	2	no	—
607	C₂×C₄	—	26	4	no	—
608	C₂×C₄	—	26	2	no	—
609	C₂×C₄	—	26	4	no	—
610	C₂×C₄	—	26	2	no	—
611	C₂×C₄	—	26	2	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	26	2	no	—
614	C₂×C₄	—	52	2	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	—	52	2	no	—
617	C₂×C₄	—	52	1	no	—
618	C₂×C₄	#6129	1	4	yes	complemented
619	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
620	C₂×C₄	C₂³×D₁₃	1	2	yes	—
621	C₂×C₄	C₂³×D₁₃	1	2	yes	—
622	C₂×C₄	C₂³×D₁₃	1	2	yes	—
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	2	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	2	2	no	—
635	C₂²	—	2	1	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	13	2	no	—
638	C₂²	—	26	1	no	—
639	C₂²	—	26	1	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	1	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	52	4	no	—
644	C₂²	C₂×#6129	1	2	yes	—
645	C₂²	#41×D₁₃	1	2	yes	—
646	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	13	2	no	—
653	C₄	—	26	1	no	—
654	C₄	—	26	1	no	—
655	C₄	—	26	2	no	—
656	C₄	—	26	1	no	—
657	C₄	—	26	2	no	—
658	C₄	—	26	2	no	—
659	C₄	—	26	1	no	—
660	C₄	—	26	2	no	—
661	C₄	—	26	1	no	—
662	C₄	C₂×#6129	1	2	yes	—
663	C₄	C₂×#6129	1	2	yes	—
664	C₂	—	2	2	no	—
665	C₂	—	2	2	no	—
666	C₂	—	4	1	no	—
667	C₂	—	4	2	no	—
668	C₂	—	26	2	no	—
669	C₂	—	52	1	no	—
670	C₂	C₂²×#6129	1	1	yes	characteristic
671	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
672	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₁₃×#525	C₂
hypercenter	#525	D₁₃
hypocenter	C₁₃	#3475
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ #525

Complements

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

N	H ≅ G/N	type
1. C₁₃×#525	C₂	semidirect
2. #11719533	C₂	semidirect
3. #41×Dic₁₃	C₂	semidirect
4. C₂×C₄×C₂²⋊D₁₃	C₂	semidirect
5. C₂×#88180	C₂	semidirect
6. #11719363	C₂	semidirect
7. #11719355	C₂	semidirect
8. #11719347	C₂	semidirect
9. #11719346	C₂	semidirect
10. #11719344	C₂	semidirect
11. #11719340	C₂	semidirect
12. #11719323	C₂	semidirect
13. #11719321	C₂	semidirect
14. #11719319	C₂	semidirect
15. #11719316	C₂	semidirect
16. #11719296	C₂	semidirect
17. #11719292	C₂	semidirect
18. #11719262	C₂	semidirect
19. #11719243	C₂	semidirect
20. #11719243	C₂	semidirect
21. C₄×#6129	C₂	semidirect
22. D₁₃×#117	C₂	semidirect
23. #11719222	C₂	semidirect
30. C₁₃×C₂²⋊Q₈	C₂²	semidirect
31. C₁₃×C₂²⋊Q₈	C₂²	semidirect
32. C₁₃×#121	C₂²	semidirect
33. C₁₃×#121	C₂²	semidirect
35. C₄×D₄×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
40. #88200	C₂²	semidirect
41. #88200	C₂²	semidirect
42. Q₈×Dic₁₃	C₂²	semidirect
43. Q₈×Dic₁₃	C₂²	semidirect
47. #88192	C₂²	semidirect
48. #88192	C₂²	semidirect
50. #88190	C₂²	semidirect
52. #88189	C₂²	semidirect
53. #88189	C₂²	semidirect
56. D₄×Dic₁₃	C₂²	semidirect
57. D₄×Dic₁₃	C₂²	semidirect
58. D₄×Dic₁₃	C₂²	semidirect
67. C₄×C₂²⋊D₁₃	C₂²	semidirect
68. C₄×C₂²⋊D₁₃	C₂²	semidirect
73. #88180	C₂²	semidirect
74. #88180	C₂²	semidirect
75. #88180	C₂²	semidirect
76. #88180	C₂²	semidirect
77. C₂×C₄⋊Dic₁₃	C₂²	semidirect
78. C₂×C₄⋊Dic₁₃	C₂²	semidirect
81. C₂×C₄×Dic₁₃	C₂²	semidirect
82. C₂×C₄×Dic₁₃	C₂²	semidirect
83. #88152	C₂²	semidirect
84. #88152	C₂²	semidirect
85. #88151	C₂²	semidirect
86. #88146	C₂²	semidirect
87. #88146	C₂²	semidirect
88. #88146	C₂²	semidirect
89. C₄⋊C₄×D₁₃	C₂²	semidirect
90. C₄⋊C₄×D₁₃	C₂²	semidirect
91. #88144	C₂²	semidirect
92. #88144	C₂²	semidirect
93. #88144	C₂²	semidirect
94. #88143	C₂²	semidirect
95. #88143	C₂²	semidirect
96. #88142	C₂²	semidirect
97. #88142	C₂²	semidirect
98. #88141	C₂²	semidirect
100. #88140	C₂²	semidirect
102. #88139	C₂²	semidirect
104. #88137	C₂²	semidirect
106. #88135	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88133	C₂²	semidirect
110. #88133	C₂²	semidirect
111. #88133	C₂²	semidirect
114. #88132	C₂²	semidirect
115. #88132	C₂²	semidirect
117. #88131	C₂²	semidirect
118. #88131	C₂²	semidirect
119. #88126	C₂²	semidirect
120. C₄²×D₁₃	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
251. C₂×C₄×C₁₃	#41	semidirect
264. C₂²⋊D₁₃	#41	semidirect
307. #525	D₁₃	semidirect
387. C₂²⋊Q₈	C₂×D₁₃	semidirect
388. C₂²⋊Q₈	C₂×D₁₃	semidirect
394. #121	C₂×D₁₃	semidirect
395. #121	C₂×D₁₃	semidirect
420. C₄×D₄	C₂×D₁₃	semidirect
421. C₄×D₄	C₂×D₁₃	semidirect
563. C₁₃	#3475	semidirect
618. C₂×C₄	#6129	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#525	2
#11719533	2
#41×Dic₁₃	2
C₂×C₄×C₂²⋊D₁₃	2
C₂×#88180	2
#11719363	2
#11719355	2
#11719347	2
#11719346	2
#11719344	2
#11719340	2
#11719323	2
#11719321	2
#11719319	2
#11719316	2
#11719296	2
#11719292	2
#11719262	2
#11719243	2
C₄×#6129	2
D₁₃×#117	2
#11719222	2
#3475	13