Subgroups — #13129299

Order 1664.

1022 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719438	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719403	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719352	C₂	1	2	yes	maximal, complemented
9	#11719352	C₂	1	2	yes	maximal, complemented
10	#11719345	C₂	1	2	yes	maximal, complemented
11	#11719343	C₂	1	2	yes	maximal, complemented
12	#11719338	C₂	1	2	yes	maximal, complemented
13	#11719333	C₂	1	2	yes	maximal, complemented
14	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719267	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719264	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719253	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719220	C₂	1	2	yes	maximal, complemented
23	#11719212	C₂	1	2	yes	maximal, complemented
24	C₂×Q₈×D₁₃	C₂²	1	2	yes	—
25	C₂×#6127	C₂²	1	2	yes	—
26	C₂×#6127	C₂²	1	2	yes	—
27	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
28	C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
33	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
37	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
38	#88201	C₂²	1	2	yes	—
39	#88201	C₂²	1	2	yes	—
40	#88200	C₂²	1	2	yes	—
41	#88200	C₂²	1	2	yes	—
42	#88200	C₂²	1	1	yes	characteristic
43	#88198	C₂²	1	1	yes	characteristic
44	#88194	C₂²	1	1	yes	characteristic
45	#88194	C₂²	1	1	yes	characteristic
46	#88192	C₂²	1	1	yes	characteristic
47	#88190	C₂²	1	1	yes	characteristic
48	#88184	C₂²	1	2	yes	—
49	#88184	C₂²	1	2	yes	—
50	#88183	C₂²	1	2	yes	—
51	#88183	C₂²	1	2	yes	—
52	#88183	C₂²	1	2	yes	—
53	#88183	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
57	#88178	C₂²	1	2	yes	—
58	#88152	C₂²	1	2	yes	—
59	#88152	C₂²	1	2	yes	—
60	#88151	C₂²	1	1	yes	characteristic
61	#88151	C₂²	1	1	yes	characteristic
62	#88151	C₂²	1	2	yes	—
63	#88150	C₂²	1	2	yes	—
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	1	yes	characteristic
66	#88150	C₂²	1	2	yes	—
67	#88150	C₂²	1	1	yes	characteristic
68	#88150	C₂²	1	2	yes	—
69	#88149	C₂²	1	1	yes	characteristic
70	#88149	C₂²	1	2	yes	—
71	#88149	C₂²	1	1	yes	characteristic
72	#88149	C₂²	1	2	yes	—
73	#88148	C₂²	1	2	yes	—
74	#88148	C₂²	1	2	yes	—
75	#88148	C₂²	1	2	yes	—
76	#88148	C₂²	1	2	yes	—
77	#88148	C₂²	1	2	yes	—
78	#88148	C₂²	1	2	yes	—
79	#88147	C₂²	1	1	yes	characteristic
80	#88147	C₂²	1	1	yes	characteristic
81	#88147	C₂²	1	1	yes	characteristic
82	#88147	C₂²	1	2	yes	—
83	#88147	C₂²	1	1	yes	characteristic
84	#88147	C₂²	1	2	yes	—
85	#88146	C₂²	1	2	yes	—
86	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
87	#88144	C₂²	1	1	yes	characteristic
88	#88143	C₂²	1	1	yes	characteristic
89	#88143	C₂²	1	2	yes	—
90	#88143	C₂²	1	1	yes	characteristic
91	#88143	C₂²	1	2	yes	—
92	#88142	C₂²	1	1	yes	characteristic
93	#88142	C₂²	1	1	yes	characteristic
94	#88142	C₂²	1	2	yes	—
95	#88142	C₂²	1	1	yes	characteristic
96	#88141	C₂²	1	1	yes	characteristic
97	#88141	C₂²	1	1	yes	characteristic
98	#88141	C₂²	1	2	yes	—
99	#88139	C₂²	1	2	yes	—
100	#88139	C₂²	1	2	yes	—
101	#88139	C₂²	1	2	yes	—
102	#88139	C₂²	1	2	yes	—
103	#88138	C₂²	1	2	yes	—
104	#88138	C₂²	1	2	yes	—
105	#88138	C₂²	1	2	yes	—
106	#88138	C₂²	1	2	yes	—
107	#88137	C₂²	1	2	yes	—
108	#88137	C₂²	1	2	yes	—
109	#88137	C₂²	1	2	yes	—
110	#88133	C₂²	1	2	yes	—
111	#88129	C₂²	1	1	yes	characteristic
112	#88129	C₂²	1	1	yes	characteristic
113	#88128	C₂²	1	1	yes	characteristic
114	C₄×D₅₂	C₂²	1	1	yes	characteristic
115	C₄×D₅₂	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	1	yes	characteristic
117	#88126	C₂²	1	1	yes	characteristic
118	C₄²×D₁₃	C₂²	1	1	yes	characteristic
119	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
122	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
125	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
126	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
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	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
134	Q₈×D₁₃	—	4	4	no	—
135	#6127	—	4	4	no	—
136	#6127	—	4	4	no	—
137	C₂×D₅₂	C₂³	1	1	yes	characteristic
138	C₂×D₅₂	C₂³	1	1	yes	characteristic
139	C₂×D₅₂	C₂³	1	2	yes	—
140	C₂×D₅₂	C₂³	1	2	yes	—
141	C₂×D₅₂	C₂³	1	2	yes	—
142	C₂×D₅₂	C₂³	1	2	yes	—
143	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂³	1	2	yes	—
146	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂³	1	2	yes	—
148	C₂×C₄×D₁₃	C₂³	1	2	yes	—
149	C₂×C₄×D₁₃	C₂³	1	2	yes	—
150	C₂×C₄×D₁₃	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃	C₂³	1	2	yes	—
152	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
153	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
154	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
155	C₂×Dic₂₆	C₂³	1	2	yes	—
156	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
157	C₂×Dic₂₆	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
159	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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×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	C₄²×C₁₃	C₂³	1	1	yes	characteristic
173	C₄²×C₁₃	C₂³	1	1	yes	characteristic
174	C₄²×C₁₃	C₂³	1	1	yes	characteristic
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
178	#6103	C₂³	1	1	yes	characteristic
179	#6103	C₂³	1	1	yes	characteristic
180	#6103	C₂³	1	1	yes	characteristic
181	#6103	C₂³	1	1	yes	characteristic
182	#6103	C₂³	1	2	yes	—
183	#6103	C₂³	1	2	yes	—
184	#6103	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	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
196	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
197	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
201	#6101	C₂³	1	1	yes	characteristic
202	#6101	C₂³	1	1	yes	characteristic
203	#6101	C₂³	1	2	yes	—
204	#6101	C₂³	1	1	yes	characteristic
205	#6101	C₂³	1	1	yes	characteristic
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	1	yes	characteristic
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	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	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
218	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	#3554	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	2	yes	—
227	C₂²×D₁₃	C₂⁴	1	2	yes	—
228	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
229	C₂²×D₁₃	C₂⁴	1	2	yes	—
230	Q₈×C₁₃	—	4	2	no	—
231	Q₈×C₁₃	—	4	1	no	—
232	D₄×C₁₃	—	2	2	no	—
233	C₂×C₄×C₁₃	—	4	2	no	—
234	C₂×C₄×C₁₃	—	4	2	no	—
235	C₂×C₄×C₁₃	—	4	2	no	—
236	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
245	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
246	C₂²⋊D₁₃	—	2	4	no	—
247	C₂²⋊D₁₃	—	4	2	no	—
248	C₂²⋊D₁₃	—	4	2	no	—
249	C₂²⋊D₁₃	—	4	2	no	—
250	C₂²⋊D₁₃	—	4	2	no	—
251	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₃	C₂⁴	1	2	yes	—
253	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	D₅₂	—	2	2	no	—
261	D₅₂	—	2	2	no	—
262	D₅₂	—	4	2	no	—
263	D₅₂	—	4	2	no	—
264	D₅₂	—	4	2	no	—
265	D₅₂	—	4	2	no	—
266	C₄×D₁₃	—	2	2	no	—
267	C₄×D₁₃	—	2	2	no	—
268	C₄×D₁₃	—	2	4	no	—
269	C₄×D₁₃	—	4	2	no	—
270	C₄×D₁₃	—	4	1	no	—
271	C₄×D₁₃	—	4	2	no	—
272	C₄×D₁₃	—	4	2	no	—
273	C₄×D₁₃	—	4	2	no	—
274	C₄×D₁₃	—	4	2	no	—
275	Dic₂₆	—	2	2	no	—
276	Dic₂₆	—	2	2	no	—
277	Dic₂₆	—	2	4	no	—
278	Dic₂₆	—	2	2	no	—
279	Dic₂₆	—	4	1	no	—
280	Dic₂₆	—	4	2	no	—
281	#562	—	13	2	no	—
282	#562	—	13	2	no	—
283	#559	—	13	1	no	—
284	#559	—	13	1	no	—
285	#559	—	13	1	no	—
286	#557	—	13	1	no	—
287	#554	—	13	1	no	—
288	#554	D₁₃	1	1	yes	characteristic, complemented
289	#550	—	13	1	no	—
290	D₄×Q₈	—	13	1	no	—
291	#548	—	13	2	no	—
292	#547	—	13	2	no	—
293	#542	—	13	1	no	—
294	#542	—	13	2	no	—
295	#542	—	13	1	no	—
296	#540	—	13	1	no	—
297	#540	—	13	1	no	—
298	#539	—	13	2	no	—
299	#539	—	13	2	no	—
300	#536	—	13	2	no	—
301	#533	—	13	1	no	—
302	#532	—	13	1	no	—
303	#529	—	13	1	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	2	no	—
306	C₂²×C₁₃	—	2	2	no	—
307	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
308	C₂×D₁₃	—	2	2	no	—
309	C₂×D₁₃	—	2	1	no	—
310	C₂×D₁₃	—	2	2	no	—
311	C₂×D₁₃	—	2	1	no	—
312	C₂×D₁₃	—	2	2	no	—
313	C₂×D₁₃	—	2	2	no	—
314	C₂×D₁₃	—	2	1	no	—
315	C₂×D₁₃	—	2	2	no	—
316	C₂×D₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	2	no	—
319	C₄×C₁₃	—	2	1	no	—
320	C₄×C₁₃	—	2	2	no	—
321	C₄×C₁₃	—	2	1	no	—
322	C₄×C₁₃	—	2	1	no	—
323	C₄×C₁₃	—	2	2	no	—
324	C₄×C₁₃	—	2	1	no	—
325	C₄×C₁₃	—	2	1	no	—
326	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
327	Dic₁₃	—	2	1	no	—
328	Dic₁₃	—	2	2	no	—
329	Dic₁₃	—	2	1	no	—
330	Dic₁₃	—	2	2	no	—
331	Dic₁₃	—	2	1	no	—
332	Dic₁₃	—	2	1	no	—
333	Dic₁₃	—	2	1	no	—
334	Dic₁₃	—	2	1	no	—
335	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
336	C₂×#41	—	13	2	no	—
337	C₂×#41	—	13	2	no	—
338	C₂²×Q₈	—	13	2	no	—
339	C₄⋊Q₈	—	13	1	no	—
340	C₄⋊Q₈	—	13	1	no	—
341	C₄⋊Q₈	—	13	1	no	—
342	C₄⋊Q₈	—	13	2	no	—
343	C₄⋊Q₈	—	13	1	no	—
344	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
345	#127	—	13	1	no	—
346	#127	—	13	1	no	—
347	#127	—	13	1	no	—
348	#126	—	13	2	no	—
349	#126	—	13	2	no	—
350	#126	—	13	2	no	—
351	#125	—	13	1	no	—
352	#125	—	13	1	no	—
353	#125	—	13	2	no	—
354	#125	—	13	2	no	—
355	#125	—	13	1	no	—
356	#125	C₂×D₁₃	1	1	yes	characteristic
357	#125	C₂×D₁₃	1	1	yes	characteristic
358	#124	—	13	2	no	—
359	#124	—	13	2	no	—
360	#124	—	13	1	no	—
361	#124	—	13	2	no	—
362	#124	—	13	2	no	—
363	#124	—	13	2	no	—
364	#124	—	13	2	no	—
365	#124	—	13	1	no	—
366	#124	—	13	1	no	—
367	#123	—	13	2	no	—
368	#123	—	13	2	no	—
369	#123	—	13	2	no	—
370	#123	—	13	2	no	—
371	#123	—	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	—	13	2	no	—
380	C₂²⋊Q₈	—	13	1	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	1	no	—
385	C₂²⋊Q₈	—	13	1	no	—
386	C₂²⋊Q₈	—	13	1	no	—
387	C₂²⋊Q₈	—	13	1	no	—
388	C₂²⋊Q₈	—	13	2	no	—
389	C₂²⋊Q₈	—	13	2	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	2	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
394	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
395	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
396	#121	—	13	1	no	—
397	#121	—	13	2	no	—
398	#121	—	13	2	no	—
399	#121	—	13	1	no	—
400	#121	—	13	1	no	—
401	#121	—	13	2	no	—
402	#121	—	13	2	no	—
403	#121	—	13	2	no	—
404	#121	—	13	2	no	—
405	#121	—	13	2	no	—
406	#121	—	13	2	no	—
407	C₄×Q₈	—	13	1	no	—
408	C₄×Q₈	—	13	2	no	—
409	C₄×Q₈	—	13	1	no	—
410	C₄×Q₈	—	13	1	no	—
411	C₄×Q₈	—	13	1	no	—
412	C₄×Q₈	—	13	1	no	—
413	C₄×Q₈	—	13	1	no	—
414	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
415	C₄×D₄	—	13	2	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	2	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	—	13	1	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	1	no	—
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	C₂×D₁₃	1	1	yes	characteristic
427	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
428	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
429	#117	—	13	2	no	—
430	#117	—	13	1	no	—
431	#117	—	13	1	no	—
432	C₂×C₄⋊C₄	—	13	2	no	—
433	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
434	C₂×C₄²	—	13	1	no	—
435	C₂×C₁₃	—	4	2	no	—
436	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
437	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
438	C₂×C₁₃	#585	1	1	yes	characteristic
439	D₁₃	—	4	2	no	—
440	D₁₃	—	4	1	no	—
441	D₁₃	—	4	2	no	—
442	#41	—	52	4	no	—
443	#41	—	52	4	no	—
444	C₂×Q₈	—	13	1	no	—
445	C₂×Q₈	—	13	1	no	—
446	C₂×Q₈	—	13	2	no	—
447	C₂×Q₈	—	13	1	no	—
448	C₂×Q₈	—	13	1	no	—
449	C₂×Q₈	—	13	2	no	—
450	C₂×Q₈	—	52	4	no	—
451	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
452	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
453	C₂×D₄	—	13	2	no	—
454	C₂×D₄	—	13	2	no	—
455	C₂×D₄	—	13	2	no	—
456	C₂×D₄	—	13	2	no	—
457	C₂×D₄	—	13	2	no	—
458	C₂×D₄	—	13	1	no	—
459	C₂×D₄	—	13	1	no	—
460	C₂×D₄	—	13	2	no	—
461	C₂×D₄	—	13	2	no	—
462	C₂×D₄	—	13	2	no	—
463	C₂×D₄	—	13	2	no	—
464	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
465	C₂²×C₄	—	13	1	no	—
466	C₂²×C₄	—	13	1	no	—
467	C₂²×C₄	—	13	2	no	—
468	C₂²×C₄	—	13	1	no	—
469	C₂²×C₄	—	13	2	no	—
470	C₂²×C₄	—	13	2	no	—
471	C₂²×C₄	—	13	2	no	—
472	C₂²×C₄	—	13	2	no	—
473	C₂²×C₄	—	13	2	no	—
474	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
475	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
476	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
477	C₄⋊C₄	—	13	1	no	—
478	C₄⋊C₄	—	13	2	no	—
479	C₄⋊C₄	—	13	2	no	—
480	C₄⋊C₄	—	13	2	no	—
481	C₄⋊C₄	—	13	1	no	—
482	C₄⋊C₄	—	13	1	no	—
483	C₄⋊C₄	—	13	1	no	—
484	C₄⋊C₄	—	13	1	no	—
485	C₄⋊C₄	—	13	1	no	—
486	C₄⋊C₄	—	13	1	no	—
487	C₄⋊C₄	—	13	1	no	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	—	13	1	no	—
490	C₄⋊C₄	—	13	1	no	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	1	no	—
494	C₄⋊C₄	—	13	1	no	—
495	C₄⋊C₄	—	13	1	no	—
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	—	13	2	no	—
498	C₄⋊C₄	—	13	2	no	—
499	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
503	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
504	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
506	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
507	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
509	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
510	C₂²⋊C₄	—	13	2	no	—
511	C₂²⋊C₄	—	13	2	no	—
512	C₂²⋊C₄	—	13	2	no	—
513	C₂²⋊C₄	—	13	1	no	—
514	C₂²⋊C₄	—	13	1	no	—
515	C₂²⋊C₄	—	13	1	no	—
516	C₂²⋊C₄	—	13	1	no	—
517	C₂²⋊C₄	—	13	2	no	—
518	C₂²⋊C₄	—	13	2	no	—
519	C₂²⋊C₄	—	13	2	no	—
520	C₂²⋊C₄	—	13	2	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	C₂²×D₁₃	1	2	yes	—
531	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
532	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
533	C₄²	—	13	1	no	—
534	C₄²	—	13	1	no	—
535	C₄²	—	13	1	no	—
536	C₄²	—	13	2	no	—
537	C₄²	—	13	1	no	—
538	C₄²	—	13	1	no	—
539	C₄²	—	13	2	no	—
540	C₄²	—	13	2	no	—
541	C₄²	C₂²×D₁₃	1	1	yes	characteristic
542	C₄²	C₂²×D₁₃	1	1	yes	characteristic
543	C₄²	C₂²×D₁₃	1	1	yes	characteristic
544	C₁₃	#3554	1	1	yes	characteristic, complemented, Sylow
545	C₂³	—	13	1	no	—
546	C₂³	—	13	2	no	—
547	C₂³	—	13	2	no	—
548	C₂³	C₂³×D₁₃	1	2	yes	—
549	Q₈	—	4	2	no	—
550	Q₈	—	4	1	no	—
551	Q₈	—	26	2	no	—
552	Q₈	—	26	4	no	—
553	Q₈	—	26	2	no	—
554	Q₈	—	26	2	no	—
555	Q₈	—	52	1	no	—
556	Q₈	—	52	2	no	—
557	D₄	—	2	2	no	—
558	D₄	—	26	4	no	—
559	D₄	—	26	2	no	—
560	D₄	—	26	2	no	—
561	D₄	—	52	2	no	—
562	D₄	—	52	2	no	—
563	D₄	—	52	2	no	—
564	D₄	—	52	2	no	—
565	D₄	—	52	2	no	—
566	D₄	—	52	2	no	—
567	D₄	—	52	2	no	—
568	D₄	—	52	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	13	1	no	—
573	C₂×C₄	—	13	2	no	—
574	C₂×C₄	—	13	1	no	—
575	C₂×C₄	—	13	1	no	—
576	C₂×C₄	—	13	1	no	—
577	C₂×C₄	—	13	1	no	—
578	C₂×C₄	—	13	1	no	—
579	C₂×C₄	—	13	2	no	—
580	C₂×C₄	—	13	1	no	—
581	C₂×C₄	—	26	4	no	—
582	C₂×C₄	—	26	2	no	—
583	C₂×C₄	—	26	2	no	—
584	C₂×C₄	—	52	2	no	—
585	C₂×C₄	—	52	1	no	—
586	C₂×C₄	—	52	2	no	—
587	C₂×C₄	—	52	2	no	—
588	C₂×C₄	—	52	2	no	—
589	C₂×C₄	—	52	2	no	—
590	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₁₃	1	2	yes	—
594	C₂×C₄	C₂³×D₁₃	1	2	yes	—
595	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
596	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
597	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
598	C₂×C₄	C₂³×D₁₃	1	2	yes	—
599	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
600	C₂²	—	2	2	no	—
601	C₂²	—	2	2	no	—
602	C₂²	—	2	2	no	—
603	C₂²	—	26	1	no	—
604	C₂²	—	26	2	no	—
605	C₂²	—	26	2	no	—
606	C₂²	—	26	1	no	—
607	C₂²	—	26	2	no	—
608	C₂²	—	26	2	no	—
609	C₂²	—	26	2	no	—
610	C₂²	—	26	1	no	—
611	C₂²	—	26	2	no	—
612	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
613	C₄	—	2	1	no	—
614	C₄	—	2	2	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	1	no	—
619	C₄	—	2	2	no	—
620	C₄	—	2	2	no	—
621	C₄	—	2	1	no	—
622	C₄	—	13	2	no	—
623	C₄	—	26	1	no	—
624	C₄	—	26	2	no	—
625	C₄	—	26	1	no	—
626	C₄	—	26	1	no	—
627	C₄	—	26	1	no	—
628	C₄	—	26	1	no	—
629	C₄	—	26	2	no	—
630	C₄	—	26	1	no	—
631	C₄	#88254	1	2	yes	—
632	C₂	—	4	2	no	—
633	C₂	—	52	1	no	—
634	C₂	—	52	2	no	—
635	C₂	—	52	2	no	—
636	C₂	C₂×#88254	1	1	yes	characteristic
637	C₂	#11719648	1	1	yes	characteristic
638	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3554
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. #11719438	C₂	semidirect
3. #11719432	C₂	semidirect
4. #11719403	C₂	semidirect
5. #11719396	C₂	semidirect
6. #11719395	C₂	semidirect
7. #11719390	C₂	semidirect
8. #11719352	C₂	semidirect
9. #11719352	C₂	semidirect
10. #11719345	C₂	semidirect
11. #11719343	C₂	semidirect
12. #11719338	C₂	semidirect
13. #11719333	C₂	semidirect
14. #11719290	C₂	semidirect
15. #11719283	C₂	semidirect
16. #11719267	C₂	semidirect
17. #11719266	C₂	semidirect
18. #11719264	C₂	semidirect
19. #11719264	C₂	semidirect
20. #11719258	C₂	semidirect
21. #11719253	C₂	semidirect
22. #11719220	C₂	semidirect
23. #11719212	C₂	semidirect
288. #554	D₁₃	semidirect
544. C₁₃	#3554	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#554	2
#11719438	2
#11719432	2
#11719403	2
#11719396	2
#11719395	2
#11719390	2
#11719352	2
#11719345	2
#11719343	2
#11719338	2
#11719333	2
#11719290	2
#11719283	2
#11719267	2
#11719266	2
#11719264	2
#11719258	2
#11719253	2
#11719220	2
#11719212	2
#3554	13