Subgroups — #13129405

Order 1664.

1032 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719429	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719417	C₂	1	2	yes	maximal, complemented
5	#11719415	C₂	1	2	yes	maximal, complemented
6	#11719410	C₂	1	2	yes	maximal, complemented
7	#11719409	C₂	1	2	yes	maximal, complemented
8	#11719382	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719381	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719380	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719352	C₂	1	2	yes	maximal, complemented
13	#11719339	C₂	1	2	yes	maximal, complemented
14	#11719289	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719287	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719281	C₂	1	1	yes	maximal, characteristic, complemented
19	Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719259	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719239	C₂	1	2	yes	maximal, complemented
23	#11719232	C₂	1	2	yes	maximal, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
26	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₂×#6129	C₂²	1	1	yes	characteristic
29	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#126	C₂²	1	2	yes	complemented
32	C₁₃×#126	C₂²	1	2	yes	complemented
33	C₁₃×#124	C₂²	1	1	yes	characteristic
34	C₁₃×#124	C₂²	1	1	yes	characteristic
35	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₄×Q₈×C₁₃	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	#88201	C₂²	1	1	yes	characteristic
42	#88201	C₂²	1	1	yes	characteristic, complemented
43	#88200	C₂²	1	1	yes	characteristic
44	#88200	C₂²	1	1	yes	characteristic
45	#88200	C₂²	1	1	yes	characteristic, complemented
46	#88200	C₂²	1	2	yes	complemented
47	#88198	C₂²	1	1	yes	characteristic, complemented
48	#88192	C₂²	1	1	yes	characteristic
49	#88190	C₂²	1	1	yes	characteristic
50	#88184	C₂²	1	2	yes	—
51	#88183	C₂²	1	2	yes	complemented
52	C₂×#6103	C₂²	1	2	yes	—
53	#88178	C₂²	1	2	yes	complemented
54	#88152	C₂²	1	2	yes	complemented
55	#88152	C₂²	1	1	yes	characteristic, complemented
56	#88152	C₂²	1	1	yes	characteristic, complemented
57	#88152	C₂²	1	2	yes	complemented
58	#88151	C₂²	1	1	yes	characteristic
59	#88151	C₂²	1	2	yes	—
60	#88151	C₂²	1	1	yes	characteristic, complemented
61	#88151	C₂²	1	2	yes	complemented
62	#88151	C₂²	1	2	yes	complemented
63	#88150	C₂²	1	2	yes	—
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	complemented
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	1	yes	characteristic
71	#88149	C₂²	1	2	yes	complemented
72	#88148	C₂²	1	1	yes	characteristic
73	#88148	C₂²	1	1	yes	characteristic
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	2	yes	—
78	#88146	C₂²	1	2	yes	complemented
79	#88144	C₂²	1	1	yes	characteristic, complemented
80	#88143	C₂²	1	2	yes	complemented
81	#88142	C₂²	1	2	yes	complemented
82	#88142	C₂²	1	1	yes	characteristic, complemented
83	#88140	C₂²	1	2	yes	—
84	#88139	C₂²	1	2	yes	—
85	#88139	C₂²	1	2	yes	—
86	#88139	C₂²	1	2	yes	complemented
87	#88139	C₂²	1	2	yes	complemented
88	#88138	C₂²	1	2	yes	—
89	#88138	C₂²	1	2	yes	complemented
90	#88137	C₂²	1	2	yes	—
91	#88137	C₂²	1	2	yes	complemented
92	#88137	C₂²	1	2	yes	complemented
93	#88136	C₂²	1	2	yes	—
94	#88136	C₂²	1	2	yes	—
95	#88135	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
97	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
98	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
99	#88133	C₂²	1	2	yes	complemented
100	#88132	C₂²	1	2	yes	complemented
101	#88132	C₂²	1	2	yes	complemented
102	#88132	C₂²	1	2	yes	complemented
103	#88130	C₂²	1	2	yes	complemented
104	#88129	C₂²	1	1	yes	characteristic
105	#88129	C₂²	1	1	yes	characteristic
106	#88129	C₂²	1	2	yes	complemented
107	#88129	C₂²	1	2	yes	complemented
108	C₄×D₅₂	C₂²	1	1	yes	characteristic
109	C₄×D₅₂	C₂²	1	2	yes	—
110	C₄×D₅₂	C₂²	1	1	yes	characteristic
111	C₄×D₅₂	C₂²	1	1	yes	characteristic
112	C₄×D₅₂	C₂²	1	2	yes	complemented
113	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
114	#88126	C₂²	1	2	yes	—
115	#88126	C₂²	1	1	yes	characteristic, complemented
116	#88126	C₂²	1	1	yes	characteristic, complemented
117	C₄²×D₁₃	C₂²	1	1	yes	characteristic
118	#88123	C₂²	1	2	yes	complemented
119	#88123	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	2	yes	—
133	#6131	—	4	2	no	—
134	Q₈×D₁₃	—	4	2	no	—
135	Q₈×D₁₃	—	4	2	no	—
136	Q₈×D₁₃	—	4	2	no	—
137	#6129	—	4	2	no	—
138	D₄×D₁₃	—	4	2	no	—
139	C₂×D₅₂	C₂³	1	1	yes	characteristic
140	C₂×D₅₂	C₂³	1	1	yes	characteristic
141	C₂×D₅₂	C₂³	1	1	yes	characteristic
142	C₂×D₅₂	C₂³	1	2	yes	—
143	C₂×D₅₂	C₂³	1	1	yes	characteristic
144	C₂×D₅₂	C₂³	1	2	yes	—
145	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
156	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
157	C₂×Dic₂₆	C₂³	1	2	yes	—
158	C₂×Dic₂₆	C₂³	1	2	yes	—
159	C₂×Dic₂₆	C₂³	1	2	yes	—
160	C₂×Dic₂₆	C₂³	1	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊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	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₄²×C₁₃	C₂³	1	2	yes	—
176	C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	C₂³	1	1	yes	characteristic
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	1	yes	characteristic
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	1	yes	characteristic
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	2	yes	—
199	#6103	C₂³	1	2	yes	—
200	#6103	C₂³	1	2	yes	—
201	#6103	C₂³	1	2	yes	—
202	#6103	C₂³	1	2	yes	—
203	#6103	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	2	yes	—
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₁₃	C₂³	1	2	yes	—
209	C₄⋊Dic₁₃	C₂³	1	2	yes	—
210	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	1	yes	characteristic
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	1	yes	characteristic
221	#6101	C₂³	1	1	yes	characteristic
222	#6101	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	#3561	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	2	yes	—
230	C₂²×D₁₃	—	2	4	no	—
231	C₂²×D₁₃	—	4	2	no	—
232	C₂²×D₁₃	—	4	2	no	—
233	C₂²×D₁₃	C₂⁴	1	2	yes	—
234	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	4	1	no	—
240	D₄×C₁₃	—	2	2	no	—
241	C₂×C₄×C₁₃	—	4	2	no	—
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
249	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₁₃	—	4	2	no	—
253	C₂²⋊D₁₃	—	4	2	no	—
254	C₂²⋊D₁₃	—	4	2	no	—
255	C₂×Dic₁₃	—	4	2	no	—
256	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
257	C₂×Dic₁₃	C₂⁴	1	2	yes	—
258	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₃	C₂⁴	1	2	yes	—
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
264	D₅₂	—	2	2	no	—
265	D₅₂	—	2	2	no	—
266	D₅₂	—	2	2	no	—
267	D₅₂	—	4	2	no	—
268	D₅₂	—	4	1	no	—
269	D₅₂	—	4	2	no	—
270	C₄×D₁₃	—	2	2	no	—
271	C₄×D₁₃	—	2	2	no	—
272	C₄×D₁₃	—	2	2	no	—
273	C₄×D₁₃	—	2	2	no	—
274	C₄×D₁₃	—	4	1	no	—
275	C₄×D₁₃	—	4	2	no	—
276	C₄×D₁₃	—	4	2	no	—
277	C₄×D₁₃	—	4	2	no	—
278	C₄×D₁₃	—	4	2	no	—
279	C₄×D₁₃	—	4	2	no	—
280	Dic₂₆	—	2	2	no	—
281	Dic₂₆	—	2	2	no	—
282	Dic₂₆	—	4	2	no	—
283	Dic₂₆	—	4	2	no	—
284	Dic₂₆	—	4	2	no	—
285	Dic₂₆	—	4	2	no	—
286	#563	—	13	2	no	—
287	#562	—	13	2	no	—
288	#556	—	13	1	no	—
289	#556	D₁₃	1	1	yes	characteristic, complemented
290	#551	—	13	2	no	—
291	#551	—	13	2	no	—
292	D₄×Q₈	—	13	1	no	—
293	D₄×Q₈	—	13	1	no	—
294	#548	—	13	1	no	—
295	#548	—	13	1	no	—
296	#546	—	13	1	no	—
297	#546	—	13	1	no	—
298	#543	—	13	2	no	—
299	#542	—	13	2	no	—
300	#542	—	13	1	no	—
301	#542	—	13	1	no	—
302	#542	—	13	2	no	—
303	#538	—	13	2	no	—
304	#536	—	13	1	no	—
305	#536	—	13	1	no	—
306	#533	—	13	1	no	—
307	#529	—	13	1	no	—
308	C₂×#124	—	13	1	no	—
309	C₂²×C₁₃	—	2	2	no	—
310	C₂²×C₁₃	—	2	2	no	—
311	C₂²×C₁₃	—	2	2	no	—
312	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
313	C₂×D₁₃	—	2	1	no	—
314	C₂×D₁₃	—	2	1	no	—
315	C₂×D₁₃	—	2	1	no	—
316	C₂×D₁₃	—	2	1	no	—
317	C₂×D₁₃	—	2	2	no	—
318	C₂×D₁₃	—	2	1	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	2	no	—
321	C₂×D₁₃	—	2	2	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	8	4	no	—
325	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
326	C₄×C₁₃	—	2	2	no	—
327	C₄×C₁₃	—	2	2	no	—
328	C₄×C₁₃	—	2	1	no	—
329	C₄×C₁₃	—	2	1	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	2	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	1	no	—
341	Dic₁₃	—	2	1	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	2	no	—
344	C₂×#41	—	13	1	no	—
345	C₂×#41	—	13	1	no	—
346	C₂²×Q₈	—	13	1	no	—
347	C₂²×Q₈	—	13	1	no	—
348	C₂²×Q₈	—	13	1	no	—
349	C₂²×D₄	—	13	1	no	—
350	C₄⋊Q₈	—	13	1	no	—
351	C₄⋊Q₈	—	13	1	no	—
352	C₄⋊Q₈	—	13	2	no	—
353	C₄⋊Q₈	—	13	1	no	—
354	C₄⋊Q₈	—	13	2	no	—
355	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
356	#126	—	13	1	no	—
357	#126	—	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	C₂×D₁₃	1	2	yes	complemented
363	#126	C₂×D₁₃	1	2	yes	complemented
364	#125	—	13	1	no	—
365	#125	—	13	2	no	—
366	#124	—	13	1	no	—
367	#124	—	13	1	no	—
368	#124	—	13	1	no	—
369	#124	—	13	2	no	—
370	#124	—	13	2	no	—
371	#124	—	13	2	no	—
372	#124	—	13	2	no	—
373	#124	—	13	1	no	—
374	#124	—	13	1	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#124	C₂×D₁₃	1	1	yes	characteristic
378	#124	C₂×D₁₃	1	1	yes	characteristic
379	#123	—	13	2	no	—
380	#123	—	13	1	no	—
381	#123	—	13	1	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	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	1	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	—	13	1	no	—
396	C₂²⋊Q₈	—	13	2	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	—	13	2	no	—
408	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
409	#121	—	13	1	no	—
410	#121	—	13	2	no	—
411	#121	—	13	1	no	—
412	#121	—	13	2	no	—
413	#121	—	13	1	no	—
414	#121	—	13	2	no	—
415	#121	—	13	2	no	—
416	#120	—	13	2	no	—
417	#120	—	13	2	no	—
418	C₄×Q₈	—	13	2	no	—
419	C₄×Q₈	—	13	1	no	—
420	C₄×Q₈	—	13	1	no	—
421	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
422	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
423	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
424	C₄×D₄	—	13	2	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	—	13	1	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	2	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	2	no	—
432	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
433	#117	—	13	2	no	—
434	#117	—	13	1	no	—
435	#117	—	13	1	no	—
436	#117	—	13	2	no	—
437	#117	C₂×D₁₃	1	2	yes	complemented
438	C₂×C₂²⋊C₄	—	13	2	no	—
439	C₂×C₂²⋊C₄	—	13	2	no	—
440	C₂×C₂²⋊C₄	—	13	2	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₄²	—	13	1	no	—
443	C₂×C₁₃	—	4	2	no	—
444	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
446	C₂×C₁₃	#585	1	1	yes	characteristic
447	D₁₃	—	2	2	no	—
448	D₁₃	—	4	1	no	—
449	D₁₃	—	4	1	no	—
450	D₁₃	—	4	2	no	—
451	C₂⁴	—	13	2	no	—
452	#41	—	52	2	no	—
453	#41	—	52	2	no	—
454	C₂×Q₈	—	13	1	no	—
455	C₂×Q₈	—	13	1	no	—
456	C₂×Q₈	—	13	2	no	—
457	C₂×Q₈	—	13	2	no	—
458	C₂×Q₈	—	13	2	no	—
459	C₂×Q₈	—	13	2	no	—
460	C₂×Q₈	—	52	2	no	—
461	C₂×Q₈	—	52	2	no	—
462	C₂×Q₈	—	52	2	no	—
463	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
464	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
465	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
466	C₂×D₄	—	13	2	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	2	no	—
469	C₂×D₄	—	13	1	no	—
470	C₂×D₄	—	13	1	no	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	2	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	52	2	no	—
476	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
477	C₂²×C₄	—	13	2	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	1	no	—
480	C₂²×C₄	—	13	1	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	2	no	—
487	C₂²×C₄	—	13	2	no	—
488	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	1	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	—	13	1	no	—
497	C₄⋊C₄	—	13	1	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	1	no	—
502	C₄⋊C₄	—	13	1	no	—
503	C₄⋊C₄	—	13	2	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	C₂²×D₁₃	1	1	yes	characteristic
509	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
511	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
512	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
513	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
514	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
516	C₂²⋊C₄	—	13	2	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	1	no	—
520	C₂²⋊C₄	—	13	1	no	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	2	no	—
526	C₂²⋊C₄	—	13	2	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	1	no	—
534	C₂²⋊C₄	—	13	1	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	2	no	—
537	C₂²⋊C₄	—	13	1	no	—
538	C₂²⋊C₄	—	13	1	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	2	no	—
541	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
545	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
546	C₄²	—	13	1	no	—
547	C₄²	—	13	1	no	—
548	C₄²	—	13	1	no	—
549	C₄²	—	13	2	no	—
550	C₄²	—	13	2	no	—
551	C₄²	C₂²×D₁₃	1	1	yes	characteristic
552	C₄²	C₂²×D₁₃	1	2	yes	—
553	C₄²	C₂²×D₁₃	1	1	yes	characteristic
554	C₄²	C₂²×D₁₃	1	1	yes	characteristic
555	C₄²	C₂²×D₁₃	1	2	yes	—
556	C₁₃	#3561	1	1	yes	characteristic, complemented, Sylow
557	C₂³	—	13	1	no	—
558	C₂³	—	13	2	no	—
559	C₂³	—	13	1	no	—
560	C₂³	—	13	1	no	—
561	C₂³	—	26	4	no	—
562	C₂³	—	52	2	no	—
563	C₂³	—	52	2	no	—
564	C₂³	C₂³×D₁₃	1	2	yes	—
565	Q₈	—	2	2	no	—
566	Q₈	—	2	2	no	—
567	Q₈	—	4	1	no	—
568	Q₈	—	26	2	no	—
569	Q₈	—	26	2	no	—
570	Q₈	—	52	2	no	—
571	Q₈	—	52	2	no	—
572	Q₈	—	52	2	no	—
573	Q₈	—	52	2	no	—
574	D₄	—	2	2	no	—
575	D₄	—	26	2	no	—
576	D₄	—	26	2	no	—
577	D₄	—	26	2	no	—
578	D₄	—	52	2	no	—
579	D₄	—	52	1	no	—
580	D₄	—	52	2	no	—
581	D₄	—	52	2	no	—
582	D₄	—	52	2	no	—
583	D₄	—	52	2	no	—
584	C₂×C₄	—	4	2	no	—
585	C₂×C₄	—	13	1	no	—
586	C₂×C₄	—	13	1	no	—
587	C₂×C₄	—	13	2	no	—
588	C₂×C₄	—	13	1	no	—
589	C₂×C₄	—	13	2	no	—
590	C₂×C₄	—	13	2	no	—
591	C₂×C₄	—	13	1	no	—
592	C₂×C₄	—	13	1	no	—
593	C₂×C₄	—	26	2	no	—
594	C₂×C₄	—	26	2	no	—
595	C₂×C₄	—	26	2	no	—
596	C₂×C₄	—	26	2	no	—
597	C₂×C₄	—	52	2	no	—
598	C₂×C₄	—	52	1	no	—
599	C₂×C₄	—	52	2	no	—
600	C₂×C₄	—	52	2	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
607	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₃	1	2	yes	—
609	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
610	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₃	1	2	yes	—
612	C₂×C₄	C₂³×D₁₃	1	2	yes	—
613	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
614	C₂²	—	2	2	no	—
615	C₂²	—	2	2	no	—
616	C₂²	—	2	2	no	—
617	C₂²	—	13	2	no	—
618	C₂²	—	26	1	no	—
619	C₂²	—	26	1	no	—
620	C₂²	—	26	1	no	—
621	C₂²	—	26	1	no	—
622	C₂²	—	26	2	no	—
623	C₂²	—	26	2	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	1	no	—
626	C₂²	—	26	1	no	—
627	C₂²	—	26	1	no	—
628	C₂²	—	26	2	no	—
629	C₂²	—	104	4	no	—
630	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
631	C₄	—	2	2	no	—
632	C₄	—	2	2	no	—
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	1	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	26	1	no	—
641	C₄	—	26	1	no	—
642	C₄	—	26	1	no	—
643	C₄	—	26	2	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	2	no	—
646	C₄	—	26	1	no	—
647	C₄	—	26	1	no	—
648	C₄	#88256	1	2	yes	—
649	C₂	—	4	2	no	—
650	C₂	—	26	2	no	—
651	C₂	—	52	2	no	—
652	C₂	—	52	1	no	—
653	C₂	—	52	1	no	—
654	C₂	C₂×#88256	1	1	yes	characteristic
655	C₂	#11719648	1	1	yes	characteristic
656	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×#556	C₂
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3561
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719432	C₂	semidirect
3. #11719429	C₂	semidirect
4. #11719417	C₂	semidirect
5. #11719415	C₂	semidirect
6. #11719410	C₂	semidirect
7. #11719409	C₂	semidirect
8. #11719382	C₂	semidirect
9. #11719381	C₂	semidirect
10. #11719380	C₂	semidirect
11. D₁₃×#124	C₂	semidirect
12. #11719352	C₂	semidirect
13. #11719339	C₂	semidirect
14. #11719289	C₂	semidirect
15. #11719287	C₂	semidirect
16. #11719285	C₂	semidirect
17. #11719283	C₂	semidirect
18. #11719281	C₂	semidirect
19. Q₈×D₅₂	C₂	semidirect
20. #11719266	C₂	semidirect
21. #11719259	C₂	semidirect
22. #11719239	C₂	semidirect
23. #11719232	C₂	semidirect
26. C₂×Q₈×D₁₃	C₂²	semidirect
27. C₂×Q₈×D₁₃	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×#126	C₂²	semidirect
32. C₁₃×#126	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₄×Q₈×C₁₃	C₂²	semidirect
37. C₄×Q₈×C₁₃	C₂²	semidirect
38. C₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
42. #88201	C₂²	semidirect
45. #88200	C₂²	semidirect
46. #88200	C₂²	semidirect
47. #88198	C₂²	semidirect
51. #88183	C₂²	semidirect
53. #88178	C₂²	semidirect
54. #88152	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88152	C₂²	semidirect
57. #88152	C₂²	semidirect
60. #88151	C₂²	semidirect
61. #88151	C₂²	semidirect
62. #88151	C₂²	semidirect
65. #88150	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
78. #88146	C₂²	semidirect
79. #88144	C₂²	semidirect
80. #88143	C₂²	semidirect
81. #88142	C₂²	semidirect
82. #88142	C₂²	semidirect
86. #88139	C₂²	semidirect
87. #88139	C₂²	semidirect
89. #88138	C₂²	semidirect
91. #88137	C₂²	semidirect
92. #88137	C₂²	semidirect
95. #88135	C₂²	semidirect
99. #88133	C₂²	semidirect
100. #88132	C₂²	semidirect
101. #88132	C₂²	semidirect
102. #88132	C₂²	semidirect
103. #88130	C₂²	semidirect
106. #88129	C₂²	semidirect
107. #88129	C₂²	semidirect
112. C₄×D₅₂	C₂²	semidirect
113. C₄×D₅₂	C₂²	semidirect
115. #88126	C₂²	semidirect
116. #88126	C₂²	semidirect
118. #88123	C₂²	semidirect
119. #88123	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
289. #556	D₁₃	semidirect
355. C₄⋊Q₈	C₂×D₁₃	semidirect
362. #126	C₂×D₁₃	semidirect
363. #126	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
421. C₄×Q₈	C₂×D₁₃	semidirect
422. C₄×Q₈	C₂×D₁₃	semidirect
423. C₄×Q₈	C₂×D₁₃	semidirect
437. #117	C₂×D₁₃	semidirect
556. C₁₃	#3561	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#556	2
#11719432	2
#11719429	2
#11719417	2
#11719415	2
#11719410	2
#11719409	2
#11719382	2
#11719381	2
#11719380	2
D₁₃×#124	2
#11719352	2
#11719339	2
#11719289	2
#11719287	2
#11719285	2
#11719283	2
#11719281	2
Q₈×D₅₂	2
#11719266	2
#11719259	2
#11719239	2
#11719232	2
#3561	13