Subgroups — #13128882

Order 1664.

1124 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	C₁₃×#552	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719415	C₂	1	2	yes	maximal, complemented
3	#11719410	C₂	1	2	yes	maximal, complemented
4	#11719399	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719397	C₂	1	2	yes	maximal, complemented
6	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719395	C₂	1	2	yes	maximal, complemented
8	#11719370	C₂	1	2	yes	maximal, complemented
9	#11719359	C₂	1	2	yes	maximal, complemented
10	#11719337	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
13	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719257	C₂	1	1	yes	maximal, characteristic, complemented
17	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719232	C₂	1	2	yes	maximal, complemented
20	#11719229	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719228	C₂	1	2	yes	maximal, complemented
22	C₂×#88151	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic, complemented
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₂×#6127	C₂²	1	2	yes	—
28	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
31	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
32	C₁₃×#126	C₂²	1	2	yes	complemented
33	C₁₃×#125	C₂²	1	2	yes	complemented
34	C₁₃×#125	C₂²	1	1	yes	characteristic, complemented
35	C₁₃×#123	C₂²	1	2	yes	—
36	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#117	C₂²	1	2	yes	complemented
41	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
42	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
43	#88200	C₂²	1	1	yes	characteristic
44	#88198	C₂²	1	1	yes	characteristic, complemented
45	#88193	C₂²	1	2	yes	—
46	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
47	#88184	C₂²	1	1	yes	characteristic, complemented
48	#88183	C₂²	1	2	yes	complemented
49	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
51	C₂×#6103	C₂²	1	2	yes	—
52	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
53	#88178	C₂²	1	1	yes	characteristic, complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	2	yes	complemented
56	#88151	C₂²	1	1	yes	characteristic
57	#88151	C₂²	1	1	yes	characteristic
58	#88151	C₂²	1	2	yes	—
59	#88151	C₂²	1	1	yes	characteristic, complemented
60	#88151	C₂²	1	1	yes	characteristic, complemented
61	#88151	C₂²	1	2	yes	complemented
62	#88151	C₂²	1	1	yes	characteristic, complemented
63	#88151	C₂²	1	2	yes	complemented
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	—
66	#88150	C₂²	1	2	yes	complemented
67	#88150	C₂²	1	2	yes	complemented
68	#88150	C₂²	1	2	yes	complemented
69	#88149	C₂²	1	1	yes	characteristic
70	#88149	C₂²	1	2	yes	—
71	#88149	C₂²	1	1	yes	characteristic, complemented
72	#88148	C₂²	1	2	yes	—
73	#88148	C₂²	1	2	yes	—
74	#88148	C₂²	1	2	yes	complemented
75	#88148	C₂²	1	2	yes	complemented
76	#88148	C₂²	1	2	yes	complemented
77	#88147	C₂²	1	1	yes	characteristic
78	#88147	C₂²	1	2	yes	—
79	#88147	C₂²	1	2	yes	—
80	#88147	C₂²	1	1	yes	characteristic, complemented
81	#88146	C₂²	1	2	yes	complemented
82	#88146	C₂²	1	2	yes	complemented
83	#88146	C₂²	1	1	yes	characteristic, complemented
84	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
85	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
86	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
87	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
88	#88144	C₂²	1	2	yes	complemented
89	#88143	C₂²	1	2	yes	complemented
90	#88142	C₂²	1	1	yes	characteristic, complemented
91	#88142	C₂²	1	2	yes	complemented
92	#88141	C₂²	1	1	yes	characteristic, complemented
93	#88140	C₂²	1	2	yes	complemented
94	#88139	C₂²	1	2	yes	—
95	#88139	C₂²	1	2	yes	complemented
96	#88138	C₂²	1	2	yes	—
97	#88137	C₂²	1	2	yes	complemented
98	#88136	C₂²	1	2	yes	—
99	#88136	C₂²	1	2	yes	—
100	#88135	C₂²	1	1	yes	characteristic
101	#88135	C₂²	1	2	yes	—
102	#88135	C₂²	1	1	yes	characteristic
103	#88135	C₂²	1	2	yes	complemented
104	#88135	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
106	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
107	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
108	#88133	C₂²	1	2	yes	complemented
109	#88132	C₂²	1	2	yes	complemented
110	#88132	C₂²	1	2	yes	complemented
111	#88130	C₂²	1	2	yes	complemented
112	#88129	C₂²	1	2	yes	complemented
113	#88129	C₂²	1	1	yes	characteristic, complemented
114	C₄×D₅₂	C₂²	1	2	yes	—
115	C₄×D₅₂	C₂²	1	1	yes	characteristic
116	C₄×D₅₂	C₂²	1	2	yes	complemented
117	C₄×D₅₂	C₂²	1	2	yes	complemented
118	#88126	C₂²	1	2	yes	—
119	C₄²×D₁₃	C₂²	1	1	yes	characteristic
120	C₄×Dic₂₆	C₂²	1	2	yes	complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂³×D₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
135	C₂²×Dic₁₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
137	#6131	—	4	2	no	—
138	Q₈×D₁₃	—	4	2	no	—
139	D₄×D₁₃	—	2	4	no	—
140	#6127	—	2	8	no	—
141	#6127	—	4	2	no	—
142	C₂×D₅₂	C₂³	1	2	yes	—
143	C₂×D₅₂	C₂³	1	1	yes	characteristic
144	C₂×D₅₂	C₂³	1	2	yes	—
145	C₂×D₅₂	C₂³	1	1	yes	characteristic
146	C₂×D₅₂	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	—	4	2	no	—
148	C₂×C₄×D₁₃	—	4	2	no	—
149	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
157	C₂×C₄×D₁₃	C₂³	1	2	yes	—
158	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₁₃	C₂³	1	2	yes	—
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₆	—	4	2	no	—
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
166	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
167	C₂×Dic₂₆	C₂³	1	2	yes	—
168	C₂×Dic₂₆	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
170	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
172	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
176	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
177	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
178	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
179	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
180	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
181	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
182	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
183	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
184	C₄²×C₁₃	C₂³	1	1	yes	characteristic
185	C₄²×C₁₃	C₂³	1	2	yes	—
186	C₄²×C₁₃	C₂³	1	2	yes	—
187	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
188	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
189	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	1	yes	characteristic
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	2	yes	—
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	1	yes	characteristic
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	1	yes	characteristic
204	#6103	C₂³	1	2	yes	—
205	#6103	C₂³	1	2	yes	—
206	#6103	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	2	yes	—
208	C₄⋊Dic₁₃	C₂³	1	2	yes	—
209	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₁₃	C₂³	1	2	yes	—
211	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄⋊Dic₁₃	C₂³	1	2	yes	—
213	C₄⋊Dic₁₃	C₂³	1	2	yes	—
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	2	yes	—
222	#6101	C₂³	1	2	yes	—
223	#6101	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	2	yes	—
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
229	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
230	#3520	—	13	1	no	maximal, Sylow
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂²×D₁₃	—	2	2	no	—
234	C₂²×D₁₃	—	2	2	no	—
235	C₂²×D₁₃	—	2	2	no	—
236	C₂²×D₁₃	—	2	2	no	—
237	C₂²×D₁₃	—	4	1	no	—
238	C₂²×D₁₃	—	4	1	no	—
239	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²×D₁₃	C₂⁴	1	2	yes	—
241	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
243	Q₈×C₁₃	—	2	2	no	—
244	D₄×C₁₃	—	2	2	no	—
245	C₂×C₄×C₁₃	—	2	4	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
253	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
254	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
255	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₃	—	2	4	no	—
258	C₂²⋊D₁₃	—	2	2	no	—
259	C₂²⋊D₁₃	—	4	2	no	—
260	C₂²⋊D₁₃	#41	1	4	yes	complemented
261	C₂×Dic₁₃	—	4	2	no	—
262	C₂×Dic₁₃	—	4	1	no	—
263	C₂×Dic₁₃	—	4	1	no	—
264	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
265	C₂×Dic₁₃	C₂⁴	1	2	yes	—
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	2	yes	—
269	C₂×Dic₁₃	C₂⁴	1	2	yes	—
270	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
271	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
272	D₅₂	—	2	4	no	—
273	D₅₂	—	2	2	no	—
274	D₅₂	—	2	4	no	—
275	D₅₂	—	2	2	no	—
276	D₅₂	—	4	2	no	—
277	C₄×D₁₃	—	2	4	no	—
278	C₄×D₁₃	—	2	2	no	—
279	C₄×D₁₃	—	2	2	no	—
280	C₄×D₁₃	—	2	2	no	—
281	C₄×D₁₃	—	2	2	no	—
282	C₄×D₁₃	—	2	4	no	—
283	C₄×D₁₃	—	2	2	no	—
284	C₄×D₁₃	—	4	1	no	—
285	C₄×D₁₃	—	4	1	no	—
286	C₄×D₁₃	—	4	1	no	—
287	C₄×D₁₃	—	4	1	no	—
288	C₄×D₁₃	—	4	2	no	—
289	C₄×D₁₃	—	4	2	no	—
290	C₄×D₁₃	—	4	2	no	—
291	Dic₂₆	—	2	2	no	—
292	Dic₂₆	—	2	2	no	—
293	Dic₂₆	—	2	4	no	—
294	Dic₂₆	—	4	2	no	—
295	Dic₂₆	—	4	2	no	—
296	#556	—	13	1	no	—
297	#554	—	13	2	no	—
298	#552	—	13	1	no	—
299	#552	D₁₃	1	1	yes	characteristic, complemented
300	#551	—	13	2	no	—
301	#551	—	13	2	no	—
302	D₄×Q₈	—	13	1	no	—
303	#548	—	13	1	no	—
304	#548	—	13	1	no	—
305	#547	—	13	1	no	—
306	#547	—	13	1	no	—
307	#546	—	13	2	no	—
308	#542	—	13	2	no	—
309	#539	—	13	2	no	—
310	#539	—	13	2	no	—
311	#533	—	13	1	no	—
312	#529	—	13	1	no	—
313	#525	—	13	1	no	—
314	#525	—	13	1	no	—
315	C₂×C₂²⋊Q₈	—	13	1	no	—
316	C₂×C₂²⋊Q₈	—	13	1	no	—
317	#520	—	13	2	no	—
318	C₂×C₄×D₄	—	13	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	—	2	1	no	—
323	C₂²×C₁₃	—	2	1	no	—
324	C₂²×C₁₃	C₂×#41	1	2	yes	—
325	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
326	C₂×D₁₃	—	2	1	no	—
327	C₂×D₁₃	—	2	1	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	1	no	—
330	C₂×D₁₃	—	2	2	no	—
331	C₂×D₁₃	—	2	1	no	—
332	C₂×D₁₃	—	2	1	no	—
333	C₂×D₁₃	—	2	2	no	—
334	C₂×D₁₃	—	2	2	no	—
335	C₂×D₁₃	—	2	1	no	—
336	C₂×D₁₃	—	4	4	no	—
337	C₂×D₁₃	—	4	4	no	—
338	C₂×D₁₃	C₂×#41	1	2	yes	—
339	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
340	C₄×C₁₃	—	2	2	no	—
341	C₄×C₁₃	—	2	2	no	—
342	C₄×C₁₃	—	2	1	no	—
343	C₄×C₁₃	—	2	1	no	—
344	C₄×C₁₃	—	2	2	no	—
345	C₄×C₁₃	—	2	1	no	—
346	C₄×C₁₃	—	2	1	no	—
347	C₄×C₁₃	—	2	2	no	—
348	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
349	Dic₁₃	—	2	2	no	—
350	Dic₁₃	—	2	2	no	—
351	Dic₁₃	—	2	2	no	—
352	Dic₁₃	—	2	1	no	—
353	Dic₁₃	—	2	1	no	—
354	Dic₁₃	—	2	1	no	—
355	Dic₁₃	—	2	1	no	—
356	Dic₁₃	C₂×#41	1	2	yes	—
357	C₂×#41	—	13	1	no	—
358	C₂×#41	—	13	2	no	—
359	C₂×#41	—	13	1	no	—
360	C₂²×Q₈	—	13	1	no	—
361	C₂²×Q₈	—	13	1	no	—
362	C₂²×D₄	—	13	1	no	—
363	C₂³×C₄	—	13	1	no	—
364	C₂³×C₄	—	13	1	no	—
365	C₄⋊Q₈	—	13	1	no	—
366	C₄⋊Q₈	—	13	1	no	—
367	C₄⋊Q₈	—	13	2	no	—
368	#126	—	13	2	no	—
369	#126	—	13	2	no	—
370	#126	—	13	2	no	—
371	#126	—	13	2	no	—
372	#126	C₂×D₁₃	1	2	yes	complemented
373	#125	—	13	2	no	—
374	#125	—	13	2	no	—
375	#125	C₂×D₁₃	1	1	yes	characteristic, complemented
376	#125	C₂×D₁₃	1	2	yes	complemented
377	#124	—	13	2	no	—
378	#124	—	13	2	no	—
379	#124	—	13	1	no	—
380	#124	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	—	13	2	no	—
387	#123	—	13	2	no	—
388	#123	—	13	2	no	—
389	#123	C₂×D₁₃	1	2	yes	—
390	C₂²⋊Q₈	—	13	1	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	1	no	—
393	C₂²⋊Q₈	—	13	1	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	1	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	2	no	—
399	C₂²⋊Q₈	—	13	1	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	—	13	2	no	—
406	C₂²⋊Q₈	—	13	2	no	—
407	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
408	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
409	#121	—	13	2	no	—
410	#121	—	13	1	no	—
411	#121	—	13	1	no	—
412	#121	—	13	1	no	—
413	#121	—	13	2	no	—
414	#121	—	13	2	no	—
415	#120	—	13	2	no	—
416	#120	—	13	2	no	—
417	C₄×Q₈	—	13	1	no	—
418	C₄×Q₈	—	13	2	no	—
419	C₄×Q₈	—	13	2	no	—
420	C₄×Q₈	—	13	1	no	—
421	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
422	C₄×D₄	—	13	1	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	—	13	1	no	—
425	C₄×D₄	—	13	1	no	—
426	C₄×D₄	—	13	2	no	—
427	C₄×D₄	—	13	2	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	1	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	2	no	—
437	C₄×D₄	—	13	2	no	—
438	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
439	#117	—	13	2	no	—
440	#117	—	13	2	no	—
441	#117	—	13	1	no	—
442	#117	—	13	2	no	—
443	#117	C₂×D₁₃	1	2	yes	complemented
444	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
445	C₂×C₄⋊C₄	—	13	2	no	—
446	C₂×C₄⋊C₄	—	13	1	no	—
447	C₂×C₄⋊C₄	—	13	2	no	—
448	C₂×C₄⋊C₄	—	13	2	no	—
449	C₂×C₄⋊C₄	—	13	1	no	—
450	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
451	C₂×C₂²⋊C₄	—	13	2	no	—
452	C₂×C₂²⋊C₄	—	13	1	no	—
453	C₂×C₂²⋊C₄	—	13	1	no	—
454	C₂×C₂²⋊C₄	—	13	2	no	—
455	C₂×C₄²	—	13	1	no	—
456	C₂×C₁₃	—	2	2	no	—
457	C₂×C₁₃	—	4	1	no	—
458	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
459	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
460	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
461	D₁₃	—	2	2	no	—
462	D₁₃	—	2	2	no	—
463	D₁₃	—	4	2	no	—
464	D₁₃	—	4	1	no	—
465	C₂⁴	—	13	1	no	—
466	C₂⁴	—	13	1	no	—
467	#41	—	26	8	no	—
468	#41	—	52	2	no	—
469	#41	—	52	2	no	—
470	C₂×Q₈	—	13	2	no	—
471	C₂×Q₈	—	13	1	no	—
472	C₂×Q₈	—	13	1	no	—
473	C₂×Q₈	—	13	2	no	—
474	C₂×Q₈	—	13	2	no	—
475	C₂×Q₈	—	52	2	no	—
476	C₂×Q₈	—	52	2	no	—
477	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
478	C₂×D₄	—	13	1	no	—
479	C₂×D₄	—	13	2	no	—
480	C₂×D₄	—	13	1	no	—
481	C₂×D₄	—	13	2	no	—
482	C₂×D₄	—	13	2	no	—
483	C₂×D₄	—	13	2	no	—
484	C₂×D₄	—	13	1	no	—
485	C₂×D₄	—	13	1	no	—
486	C₂×D₄	—	13	2	no	—
487	C₂×D₄	—	26	4	no	—
488	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
489	C₂²×C₄	—	13	2	no	—
490	C₂²×C₄	—	13	1	no	—
491	C₂²×C₄	—	13	1	no	—
492	C₂²×C₄	—	13	1	no	—
493	C₂²×C₄	—	13	1	no	—
494	C₂²×C₄	—	13	1	no	—
495	C₂²×C₄	—	13	2	no	—
496	C₂²×C₄	—	13	2	no	—
497	C₂²×C₄	—	13	1	no	—
498	C₂²×C₄	—	13	1	no	—
499	C₂²×C₄	—	13	2	no	—
500	C₂²×C₄	—	13	1	no	—
501	C₂²×C₄	—	13	1	no	—
502	C₂²×C₄	—	13	1	no	—
503	C₂²×C₄	—	13	2	no	—
504	C₂²×C₄	—	13	2	no	—
505	C₂²×C₄	—	13	1	no	—
506	C₂²×C₄	—	52	2	no	—
507	C₂²×C₄	—	52	2	no	—
508	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
509	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
511	C₄⋊C₄	—	13	1	no	—
512	C₄⋊C₄	—	13	2	no	—
513	C₄⋊C₄	—	13	2	no	—
514	C₄⋊C₄	—	13	1	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	1	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	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	—	13	2	no	—
524	C₄⋊C₄	—	13	2	no	—
525	C₄⋊C₄	—	13	2	no	—
526	C₄⋊C₄	—	13	2	no	—
527	C₄⋊C₄	—	13	2	no	—
528	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
529	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
530	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
533	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
534	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
535	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
536	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
537	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
538	C₂²⋊C₄	—	13	1	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	2	no	—
544	C₂²⋊C₄	—	13	2	no	—
545	C₂²⋊C₄	—	13	1	no	—
546	C₂²⋊C₄	—	13	1	no	—
547	C₂²⋊C₄	—	13	1	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	—	13	2	no	—
552	C₂²⋊C₄	—	13	2	no	—
553	C₂²⋊C₄	—	13	2	no	—
554	C₂²⋊C₄	—	13	2	no	—
555	C₂²⋊C₄	—	13	2	no	—
556	C₂²⋊C₄	—	13	2	no	—
557	C₂²⋊C₄	—	13	2	no	—
558	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
559	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
560	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
561	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
562	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
563	C₄²	—	13	1	no	—
564	C₄²	—	13	1	no	—
565	C₄²	—	13	1	no	—
566	C₄²	—	13	2	no	—
567	C₄²	—	13	2	no	—
568	C₄²	—	13	2	no	—
569	C₄²	C₂²×D₁₃	1	1	yes	characteristic
570	C₄²	C₂²×D₁₃	1	2	yes	—
571	C₄²	C₂²×D₁₃	1	2	yes	—
572	C₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
573	C₂³	—	13	1	no	—
574	C₂³	—	13	1	no	—
575	C₂³	—	13	1	no	—
576	C₂³	—	13	2	no	—
577	C₂³	—	26	2	no	—
578	C₂³	—	26	2	no	—
579	C₂³	—	26	2	no	—
580	C₂³	—	26	2	no	—
581	C₂³	—	52	1	no	—
582	C₂³	—	52	1	no	—
583	C₂³	C₂³×D₁₃	1	1	yes	characteristic
584	C₂³	C₂³×D₁₃	1	1	yes	characteristic
585	Q₈	—	2	2	no	—
586	Q₈	—	26	4	no	—
587	Q₈	—	26	2	no	—
588	Q₈	—	26	2	no	—
589	Q₈	—	52	2	no	—
590	Q₈	—	52	2	no	—
591	D₄	—	2	2	no	—
592	D₄	—	13	4	no	—
593	D₄	—	26	4	no	—
594	D₄	—	26	2	no	—
595	D₄	—	26	4	no	—
596	D₄	—	26	2	no	—
597	D₄	—	26	4	no	—
598	D₄	—	26	2	no	—
599	D₄	—	52	2	no	—
600	D₄	—	52	2	no	—
601	C₂×C₄	—	2	4	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	13	1	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	13	2	no	—
607	C₂×C₄	—	13	1	no	—
608	C₂×C₄	—	13	1	no	—
609	C₂×C₄	—	13	2	no	—
610	C₂×C₄	—	13	2	no	—
611	C₂×C₄	—	13	1	no	—
612	C₂×C₄	—	26	2	no	—
613	C₂×C₄	—	26	4	no	—
614	C₂×C₄	—	26	2	no	—
615	C₂×C₄	—	26	4	no	—
616	C₂×C₄	—	26	2	no	—
617	C₂×C₄	—	26	2	no	—
618	C₂×C₄	—	26	2	no	—
619	C₂×C₄	—	52	1	no	—
620	C₂×C₄	—	52	1	no	—
621	C₂×C₄	—	52	1	no	—
622	C₂×C₄	—	52	1	no	—
623	C₂×C₄	—	52	2	no	—
624	C₂×C₄	—	52	2	no	—
625	C₂×C₄	—	52	2	no	—
626	C₂×C₄	—	52	1	no	—
627	C₂×C₄	—	52	1	no	—
628	C₂×C₄	—	52	2	no	—
629	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
630	C₂×C₄	C₂³×D₁₃	1	2	yes	—
631	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
632	C₂×C₄	C₂³×D₁₃	1	2	yes	—
633	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₁₃	1	2	yes	—
635	C₂×C₄	C₂³×D₁₃	1	2	yes	—
636	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
637	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	1	no	—
643	C₂²	—	13	2	no	—
644	C₂²	—	13	2	no	—
645	C₂²	—	26	1	no	—
646	C₂²	—	26	1	no	—
647	C₂²	—	26	1	no	—
648	C₂²	—	26	1	no	—
649	C₂²	—	26	2	no	—
650	C₂²	—	26	1	no	—
651	C₂²	—	26	1	no	—
652	C₂²	—	26	2	no	—
653	C₂²	—	26	2	no	—
654	C₂²	—	26	1	no	—
655	C₂²	—	52	4	no	—
656	C₂²	—	52	4	no	—
657	C₂²	#41×D₁₃	1	2	yes	—
658	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	1	no	—
662	C₄	—	2	1	no	—
663	C₄	—	2	1	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	13	2	no	—
668	C₄	—	26	2	no	—
669	C₄	—	26	1	no	—
670	C₄	—	26	1	no	—
671	C₄	—	26	1	no	—
672	C₄	—	26	2	no	—
673	C₄	—	26	2	no	—
674	C₄	—	26	1	no	—
675	C₄	#88256	1	2	yes	—
676	C₂	—	2	2	no	—
677	C₂	—	4	1	no	—
678	C₂	—	26	2	no	—
679	C₂	—	26	2	no	—
680	C₂	—	52	1	no	—
681	C₂	—	52	2	no	—
682	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
683	C₂	C₂×#88256	1	1	yes	characteristic
684	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#552	C₂
hypercenter	#552	D₁₃
hypocenter	C₁₃	#3520
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. C₁₃×#552	C₂	semidirect
2. #11719415	C₂	semidirect
3. #11719410	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719397	C₂	semidirect
6. #11719396	C₂	semidirect
7. #11719395	C₂	semidirect
8. #11719370	C₂	semidirect
9. #11719359	C₂	semidirect
10. #11719337	C₂	semidirect
11. #11719336	C₂	semidirect
12. #11719332	C₂	semidirect
13. D₁₃×C₂²⋊Q₈	C₂	semidirect
14. #11719283	C₂	semidirect
15. #11719281	C₂	semidirect
16. #11719257	C₂	semidirect
17. C₄×D₄×D₁₃	C₂	semidirect
18. #11719238	C₂	semidirect
19. #11719232	C₂	semidirect
20. #11719229	C₂	semidirect
21. #11719228	C₂	semidirect
22. C₂×#88151	C₂	semidirect
23. #11719212	C₂	semidirect
24. C₂×#6131	C₂²	semidirect
25. C₂×Q₈×D₁₃	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
31. C₂²×Dic₂₆	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
33. C₁₃×#125	C₂²	semidirect
34. C₁₃×#125	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
41. C₁₃×#117	C₂²	semidirect
42. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
44. #88198	C₂²	semidirect
47. #88184	C₂²	semidirect
48. #88183	C₂²	semidirect
52. C₂×C₄⋊Dic₁₃	C₂²	semidirect
53. #88178	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
59. #88151	C₂²	semidirect
60. #88151	C₂²	semidirect
61. #88151	C₂²	semidirect
62. #88151	C₂²	semidirect
63. #88151	C₂²	semidirect
66. #88150	C₂²	semidirect
67. #88150	C₂²	semidirect
68. #88150	C₂²	semidirect
71. #88149	C₂²	semidirect
74. #88148	C₂²	semidirect
75. #88148	C₂²	semidirect
76. #88148	C₂²	semidirect
80. #88147	C₂²	semidirect
81. #88146	C₂²	semidirect
82. #88146	C₂²	semidirect
83. #88146	C₂²	semidirect
85. C₄⋊C₄×D₁₃	C₂²	semidirect
86. C₄⋊C₄×D₁₃	C₂²	semidirect
87. C₄⋊C₄×D₁₃	C₂²	semidirect
88. #88144	C₂²	semidirect
89. #88143	C₂²	semidirect
90. #88142	C₂²	semidirect
91. #88142	C₂²	semidirect
92. #88141	C₂²	semidirect
93. #88140	C₂²	semidirect
95. #88139	C₂²	semidirect
97. #88137	C₂²	semidirect
103. #88135	C₂²	semidirect
104. #88135	C₂²	semidirect
108. #88133	C₂²	semidirect
109. #88132	C₂²	semidirect
110. #88132	C₂²	semidirect
111. #88130	C₂²	semidirect
112. #88129	C₂²	semidirect
113. #88129	C₂²	semidirect
116. C₄×D₅₂	C₂²	semidirect
117. C₄×D₅₂	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
260. C₂²⋊D₁₃	#41	semidirect
299. #552	D₁₃	semidirect
372. #126	C₂×D₁₃	semidirect
375. #125	C₂×D₁₃	semidirect
376. #125	C₂×D₁₃	semidirect
407. C₂²⋊Q₈	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
421. C₄×Q₈	C₂×D₁₃	semidirect
443. #117	C₂×D₁₃	semidirect
444. #117	C₂×D₁₃	semidirect
450. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
572. C₁₃	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#552	2
#11719415	2
#11719410	2
#11719399	2
#11719397	2
#11719396	2
#11719395	2
#11719370	2
#11719359	2
#11719337	2
#11719336	2
#11719332	2
D₁₃×C₂²⋊Q₈	2
#11719283	2
#11719281	2
#11719257	2
C₄×D₄×D₁₃	2
#11719238	2
#11719232	2
#11719229	2
#11719228	2
C₂×#88151	2
#11719212	2
#3520	13