Subgroups — #13128808

Order 1664.

1014 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719401	C₂	1	2	yes	maximal, complemented
3	#11719400	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719399	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719398	C₂	1	2	yes	maximal, complemented
6	#11719398	C₂	1	2	yes	maximal, complemented
7	#11719397	C₂	1	2	yes	maximal, complemented
8	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719396	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719395	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719393	C₂	1	1	yes	maximal, characteristic, complemented
12	D₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719220	C₂	1	2	yes	maximal, complemented
15	#11719219	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719218	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719218	C₂	1	2	yes	maximal, complemented
18	#11719216	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719212	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719212	C₂	1	2	yes	maximal, complemented
21	#11719209	C₂	1	2	yes	maximal, complemented
22	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄×#6127	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6127	C₂²	1	1	yes	characteristic
25	C₂×#6127	C₂²	1	2	yes	—
26	C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₁₃×#125	C₂²	1	1	yes	characteristic
29	C₁₃×#125	C₂²	1	1	yes	characteristic
30	C₁₃×#125	C₂²	1	2	yes	—
31	C₁₃×#125	C₂²	1	2	yes	—
32	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
33	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
35	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
37	#88184	C₂²	1	1	yes	characteristic
38	#88184	C₂²	1	2	yes	—
39	#88183	C₂²	1	2	yes	—
40	#88183	C₂²	1	2	yes	—
41	#88183	C₂²	1	2	yes	—
42	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
44	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
48	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
49	#88180	C₂²	1	1	yes	characteristic
50	#88180	C₂²	1	2	yes	—
51	#88178	C₂²	1	1	yes	characteristic
52	#88178	C₂²	1	2	yes	—
53	#88152	C₂²	1	2	yes	—
54	#88152	C₂²	1	2	yes	—
55	#88152	C₂²	1	2	yes	—
56	#88152	C₂²	1	2	yes	—
57	#88152	C₂²	1	2	yes	—
58	#88152	C₂²	1	2	yes	—
59	#88151	C₂²	1	1	yes	characteristic
60	#88151	C₂²	1	2	yes	—
61	#88151	C₂²	1	1	yes	characteristic
62	#88150	C₂²	1	2	yes	—
63	#88150	C₂²	1	2	yes	—
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	—
66	#88150	C₂²	1	2	yes	—
67	#88150	C₂²	1	2	yes	—
68	#88149	C₂²	1	1	yes	characteristic
69	#88149	C₂²	1	2	yes	—
70	#88149	C₂²	1	1	yes	characteristic
71	#88148	C₂²	1	2	yes	—
72	#88148	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	#88147	C₂²	1	2	yes	—
78	#88147	C₂²	1	2	yes	—
79	#88147	C₂²	1	1	yes	characteristic
80	#88147	C₂²	1	2	yes	—
81	#88147	C₂²	1	1	yes	characteristic
82	#88146	C₂²	1	2	yes	—
83	#88146	C₂²	1	2	yes	—
84	#88146	C₂²	1	1	yes	characteristic
85	#88146	C₂²	1	2	yes	—
86	#88146	C₂²	1	1	yes	characteristic
87	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
88	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
90	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
92	#88144	C₂²	1	1	yes	characteristic
93	#88144	C₂²	1	2	yes	—
94	#88144	C₂²	1	1	yes	characteristic
95	#88143	C₂²	1	2	yes	—
96	#88143	C₂²	1	2	yes	—
97	#88143	C₂²	1	2	yes	—
98	#88143	C₂²	1	2	yes	—
99	#88143	C₂²	1	2	yes	—
100	#88143	C₂²	1	2	yes	—
101	#88142	C₂²	1	1	yes	characteristic
102	#88142	C₂²	1	2	yes	—
103	#88142	C₂²	1	1	yes	characteristic
104	#88141	C₂²	1	2	yes	—
105	#88141	C₂²	1	2	yes	—
106	#88141	C₂²	1	1	yes	characteristic
107	#88141	C₂²	1	1	yes	characteristic
108	#88141	C₂²	1	2	yes	—
109	#88130	C₂²	1	2	yes	—
110	#88129	C₂²	1	1	yes	characteristic
111	C₄×D₅₂	C₂²	1	1	yes	characteristic
112	C₄×D₅₂	C₂²	1	1	yes	characteristic
113	C₄×D₅₂	C₂²	1	1	yes	characteristic
114	#88126	C₂²	1	1	yes	characteristic
115	#88126	C₂²	1	1	yes	characteristic
116	#88126	C₂²	1	2	yes	—
117	C₄²×D₁₃	C₂²	1	1	yes	characteristic
118	C₄²×D₁₃	C₂²	1	1	yes	characteristic
119	#88124	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	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
126	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
131	#6127	—	2	4	no	—
132	#6127	—	2	8	no	—
133	C₂×D₅₂	C₂³	1	1	yes	characteristic
134	C₂×D₅₂	C₂³	1	1	yes	characteristic
135	C₂×D₅₂	C₂³	1	2	yes	—
136	C₂×D₅₂	C₂³	1	2	yes	—
137	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
140	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
141	C₂×C₄×D₁₃	C₂³	1	2	yes	—
142	C₂×C₄×D₁₃	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	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	2	yes	—
148	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
149	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
150	C₂×Dic₂₆	C₂³	1	2	yes	—
151	C₂×Dic₂₆	C₂³	1	2	yes	—
152	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
155	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
156	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
157	C₁₃×C₄⋊C₄	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	2	yes	—
161	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
164	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
166	C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₄²×C₁₃	C₂³	1	1	yes	characteristic
168	C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₄²×C₁₃	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
171	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
173	#6103	C₂³	1	1	yes	characteristic
174	#6103	C₂³	1	1	yes	characteristic
175	#6103	C₂³	1	1	yes	characteristic
176	#6103	C₂³	1	1	yes	characteristic
177	#6103	C₂³	1	2	yes	—
178	#6103	C₂³	1	2	yes	—
179	#6103	C₂³	1	2	yes	—
180	#6103	C₂³	1	2	yes	—
181	#6103	C₂³	1	2	yes	—
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
190	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
192	C₄⋊Dic₁₃	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	#6101	C₂³	1	1	yes	characteristic
198	#6101	C₂³	1	1	yes	characteristic
199	#6101	C₂³	1	1	yes	characteristic
200	#6101	C₂³	1	1	yes	characteristic
201	#6101	C₂³	1	2	yes	—
202	#6101	C₂³	1	2	yes	—
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	2	yes	—
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
214	C₄×Dic₁₃	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	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
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	#3515	—	13	1	no	maximal, Sylow
225	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
226	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
227	C₂²×D₁₃	C₂⁴	1	2	yes	—
228	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	4	no	—
231	C₂×C₄×C₁₃	—	2	2	no	—
232	C₂×C₄×C₁₃	—	4	2	no	—
233	C₂×C₄×C₁₃	—	4	1	no	—
234	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
238	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂²⋊D₁₃	—	2	2	no	—
245	C₂²⋊D₁₃	—	2	4	no	—
246	C₂²⋊D₁₃	#41	1	4	yes	—
247	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂⁴	1	2	yes	—
250	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
251	C₂×Dic₁₃	C₂⁴	1	2	yes	—
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₁₃	C₂⁴	1	2	yes	—
255	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
256	D₅₂	—	2	2	no	—
257	D₅₂	—	2	4	no	—
258	D₅₂	—	2	2	no	—
259	D₅₂	—	4	2	no	—
260	C₄×D₁₃	—	2	2	no	—
261	C₄×D₁₃	—	2	4	no	—
262	C₄×D₁₃	—	2	2	no	—
263	C₄×D₁₃	—	2	2	no	—
264	C₄×D₁₃	—	2	2	no	—
265	C₄×D₁₃	—	2	4	no	—
266	C₄×D₁₃	—	4	1	no	—
267	C₄×D₁₃	—	4	2	no	—
268	C₄×D₁₃	—	4	2	no	—
269	C₄×D₁₃	—	4	2	no	—
270	C₄×D₁₃	—	4	1	no	—
271	Dic₂₆	—	2	2	no	—
272	Dic₂₆	—	2	2	no	—
273	Dic₂₆	—	2	4	no	—
274	Dic₂₆	—	4	2	no	—
275	#557	—	13	1	no	—
276	#554	—	13	1	no	—
277	#554	—	13	1	no	—
278	#553	—	13	1	no	—
279	#553	—	13	1	no	—
280	#552	—	13	2	no	—
281	#552	—	13	2	no	—
282	#552	—	13	1	no	—
283	#552	—	13	2	no	—
284	#552	—	13	1	no	—
285	#547	—	13	1	no	—
286	#547	—	13	2	no	—
287	#541	—	13	2	no	—
288	#539	—	13	2	no	—
289	#539	—	13	2	no	—
290	#533	—	13	1	no	—
291	#529	—	13	1	no	—
292	#529	—	13	1	no	—
293	#529	—	13	1	no	—
294	C₂×#125	—	13	1	no	—
295	C₂×#125	D₁₃	1	1	yes	characteristic, complemented
296	#520	—	13	2	no	—
297	C₄×#41	—	13	1	no	—
298	C₂²×C₁₃	—	2	1	no	—
299	C₂²×C₁₃	—	2	1	no	—
300	C₂²×C₁₃	C₂×#41	1	2	yes	—
301	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
302	C₂×D₁₃	—	2	1	no	—
303	C₂×D₁₃	—	2	1	no	—
304	C₂×D₁₃	—	2	1	no	—
305	C₂×D₁₃	—	2	2	no	—
306	C₂×D₁₃	—	2	1	no	—
307	C₂×D₁₃	—	2	2	no	—
308	C₂×D₁₃	—	2	2	no	—
309	C₂×D₁₃	—	2	1	no	—
310	C₂×D₁₃	C₂×#41	1	2	yes	—
311	C₄×C₁₃	—	2	2	no	—
312	C₄×C₁₃	—	2	1	no	—
313	C₄×C₁₃	—	2	1	no	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	1	no	—
316	C₄×C₁₃	—	2	2	no	—
317	C₄×C₁₃	—	2	1	no	—
318	C₄×C₁₃	—	2	1	no	—
319	C₄×C₁₃	—	2	2	no	—
320	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
321	Dic₁₃	—	2	1	no	—
322	Dic₁₃	—	2	2	no	—
323	Dic₁₃	—	2	2	no	—
324	Dic₁₃	—	2	1	no	—
325	Dic₁₃	—	2	1	no	—
326	Dic₁₃	—	2	1	no	—
327	Dic₁₃	—	2	2	no	—
328	Dic₁₃	—	2	1	no	—
329	Dic₁₃	C₂×#41	1	2	yes	—
330	C₂×#41	—	13	1	no	—
331	C₂×#41	—	13	2	no	—
332	C₄⋊Q₈	—	13	1	no	—
333	C₄⋊Q₈	—	13	1	no	—
334	C₄⋊Q₈	—	13	2	no	—
335	#126	—	13	2	no	—
336	#126	—	13	2	no	—
337	#126	—	13	2	no	—
338	#126	—	13	2	no	—
339	#126	—	13	2	no	—
340	#126	—	13	2	no	—
341	#126	—	13	2	no	—
342	#125	—	13	2	no	—
343	#125	—	13	2	no	—
344	#125	—	13	1	no	—
345	#125	—	13	1	no	—
346	#125	—	13	2	no	—
347	#125	—	13	2	no	—
348	#125	—	13	2	no	—
349	#125	—	13	2	no	—
350	#125	—	13	2	no	—
351	#125	—	13	1	no	—
352	#125	C₂×D₁₃	1	1	yes	characteristic
353	#125	C₂×D₁₃	1	1	yes	characteristic
354	#125	C₂×D₁₃	1	2	yes	—
355	#125	C₂×D₁₃	1	2	yes	—
356	#125	C₂×D₁₃	1	1	yes	characteristic
357	#125	C₂×D₁₃	1	1	yes	characteristic
358	#124	—	13	1	no	—
359	#123	—	13	2	no	—
360	#123	—	13	2	no	—
361	#123	—	13	2	no	—
362	#123	—	13	2	no	—
363	#123	—	13	2	no	—
364	#123	—	13	2	no	—
365	#123	—	13	2	no	—
366	#123	—	13	2	no	—
367	#123	—	13	2	no	—
368	C₂²⋊Q₈	—	13	1	no	—
369	C₂²⋊Q₈	—	13	2	no	—
370	C₂²⋊Q₈	—	13	1	no	—
371	C₂²⋊Q₈	—	13	1	no	—
372	C₂²⋊Q₈	—	13	2	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	2	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	2	no	—
379	#121	—	13	1	no	—
380	#121	—	13	2	no	—
381	#121	—	13	1	no	—
382	#121	—	13	1	no	—
383	#121	—	13	2	no	—
384	C₄×Q₈	—	13	2	no	—
385	C₄×Q₈	—	13	2	no	—
386	C₄×Q₈	—	13	1	no	—
387	C₄×Q₈	—	13	1	no	—
388	C₄×Q₈	—	13	2	no	—
389	C₄×Q₈	—	13	1	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	1	no	—
392	C₄×D₄	—	13	1	no	—
393	C₄×D₄	—	13	1	no	—
394	C₄×D₄	—	13	1	no	—
395	C₄×D₄	—	13	1	no	—
396	C₄×D₄	—	13	2	no	—
397	C₄×D₄	—	13	2	no	—
398	C₄×D₄	—	13	2	no	—
399	C₄×D₄	—	13	2	no	—
400	C₄×D₄	—	13	2	no	—
401	C₄×D₄	—	13	2	no	—
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	—	13	1	no	—
405	C₄×D₄	—	13	1	no	—
406	C₄×D₄	—	13	1	no	—
407	#117	—	13	1	no	—
408	#117	—	13	2	no	—
409	#117	—	13	2	no	—
410	#117	—	13	2	no	—
411	#117	—	13	2	no	—
412	#117	—	13	1	no	—
413	#117	—	13	1	no	—
414	#117	—	13	1	no	—
415	#117	—	13	1	no	—
416	#117	—	13	2	no	—
417	C₂×C₄⋊C₄	—	13	2	no	—
418	C₂×C₄⋊C₄	—	13	2	no	—
419	C₂×C₄⋊C₄	—	13	1	no	—
420	C₂×C₄⋊C₄	—	13	2	no	—
421	C₂×C₄⋊C₄	—	13	1	no	—
422	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
423	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
424	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
425	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
426	C₂×C₄²	—	13	1	no	—
427	C₂×C₄²	—	13	1	no	—
428	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
429	C₂×C₁₃	—	2	2	no	—
430	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
431	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂×C₁₃	#585	1	1	yes	characteristic
433	D₁₃	—	2	2	no	—
434	D₁₃	—	4	1	no	—
435	D₁₃	—	4	2	no	—
436	#41	—	26	4	no	—
437	#41	—	26	8	no	—
438	C₂×Q₈	—	13	1	no	—
439	C₂×Q₈	—	13	2	no	—
440	C₂×Q₈	—	13	1	no	—
441	C₂×Q₈	—	13	2	no	—
442	C₂×D₄	—	13	1	no	—
443	C₂×D₄	—	13	1	no	—
444	C₂×D₄	—	13	2	no	—
445	C₂×D₄	—	13	1	no	—
446	C₂×D₄	—	13	2	no	—
447	C₂×D₄	—	13	1	no	—
448	C₂×D₄	—	13	2	no	—
449	C₂²×C₄	—	13	1	no	—
450	C₂²×C₄	—	13	1	no	—
451	C₂²×C₄	—	13	1	no	—
452	C₂²×C₄	—	13	1	no	—
453	C₂²×C₄	—	13	2	no	—
454	C₂²×C₄	—	13	2	no	—
455	C₂²×C₄	—	13	1	no	—
456	C₂²×C₄	—	13	1	no	—
457	C₂²×C₄	—	13	2	no	—
458	C₂²×C₄	—	13	2	no	—
459	C₂²×C₄	—	13	2	no	—
460	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
461	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
462	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
463	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
465	C₄⋊C₄	—	13	1	no	—
466	C₄⋊C₄	—	13	2	no	—
467	C₄⋊C₄	—	13	1	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	2	no	—
470	C₄⋊C₄	—	13	2	no	—
471	C₄⋊C₄	—	13	2	no	—
472	C₄⋊C₄	—	13	2	no	—
473	C₄⋊C₄	—	13	2	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	2	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	—	13	2	no	—
478	C₄⋊C₄	—	13	1	no	—
479	C₄⋊C₄	—	13	1	no	—
480	C₄⋊C₄	—	13	1	no	—
481	C₄⋊C₄	—	13	1	no	—
482	C₄⋊C₄	—	13	1	no	—
483	C₄⋊C₄	—	13	2	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	2	no	—
486	C₄⋊C₄	—	13	2	no	—
487	C₄⋊C₄	—	13	2	no	—
488	C₄⋊C₄	—	13	2	no	—
489	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
490	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
491	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
492	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
493	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
494	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
495	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
497	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
499	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
500	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
501	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
502	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
503	C₂²⋊C₄	—	13	1	no	—
504	C₂²⋊C₄	—	13	2	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	—	13	1	no	—
511	C₂²⋊C₄	—	13	1	no	—
512	C₂²⋊C₄	—	13	1	no	—
513	C₂²⋊C₄	—	13	2	no	—
514	C₂²⋊C₄	—	13	2	no	—
515	C₂²⋊C₄	—	13	2	no	—
516	C₂²⋊C₄	—	13	2	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	C₄²	—	13	1	no	—
523	C₄²	—	13	1	no	—
524	C₄²	—	13	1	no	—
525	C₄²	—	13	1	no	—
526	C₄²	—	13	1	no	—
527	C₄²	—	13	1	no	—
528	C₄²	—	13	2	no	—
529	C₄²	—	13	2	no	—
530	C₄²	—	13	2	no	—
531	C₄²	—	13	2	no	—
532	C₄²	—	13	2	no	—
533	C₄²	C₂²×D₁₃	1	1	yes	characteristic
534	C₄²	C₂²×D₁₃	1	1	yes	characteristic
535	C₄²	C₂²×D₁₃	1	1	yes	characteristic
536	C₄²	C₂²×D₁₃	1	1	yes	characteristic
537	C₁₃	#3515	1	1	yes	characteristic, complemented, Sylow
538	C₂³	—	13	1	no	—
539	C₂³	—	13	1	no	—
540	C₂³	—	13	2	no	—
541	C₂³	C₂³×D₁₃	1	1	yes	characteristic
542	Q₈	—	26	4	no	—
543	Q₈	—	26	2	no	—
544	Q₈	—	26	2	no	—
545	Q₈	—	52	2	no	—
546	D₄	—	13	4	no	—
547	D₄	—	26	4	no	—
548	D₄	—	26	2	no	—
549	D₄	—	26	2	no	—
550	D₄	—	26	4	no	—
551	D₄	—	26	2	no	—
552	D₄	—	52	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	13	1	no	—
559	C₂×C₄	—	13	1	no	—
560	C₂×C₄	—	13	1	no	—
561	C₂×C₄	—	13	2	no	—
562	C₂×C₄	—	13	1	no	—
563	C₂×C₄	—	13	1	no	—
564	C₂×C₄	—	13	1	no	—
565	C₂×C₄	—	13	2	no	—
566	C₂×C₄	—	13	2	no	—
567	C₂×C₄	—	26	2	no	—
568	C₂×C₄	—	26	4	no	—
569	C₂×C₄	—	26	2	no	—
570	C₂×C₄	—	26	4	no	—
571	C₂×C₄	—	26	2	no	—
572	C₂×C₄	—	26	2	no	—
573	C₂×C₄	—	52	1	no	—
574	C₂×C₄	—	52	2	no	—
575	C₂×C₄	—	52	1	no	—
576	C₂×C₄	—	52	2	no	—
577	C₂×C₄	—	52	2	no	—
578	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
579	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
581	C₂×C₄	C₂³×D₁₃	1	2	yes	—
582	C₂×C₄	C₂³×D₁₃	1	2	yes	—
583	C₂×C₄	C₂³×D₁₃	1	2	yes	—
584	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₁₃	1	2	yes	—
587	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	13	2	no	—
591	C₂²	—	26	1	no	—
592	C₂²	—	26	1	no	—
593	C₂²	—	26	1	no	—
594	C₂²	—	26	2	no	—
595	C₂²	—	26	1	no	—
596	C₂²	—	26	2	no	—
597	C₂²	—	26	2	no	—
598	C₂²	—	26	1	no	—
599	C₂²	#41×D₁₃	1	2	yes	—
600	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
601	C₄	—	2	1	no	—
602	C₄	—	2	1	no	—
603	C₄	—	2	2	no	—
604	C₄	—	2	2	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	1	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	2	no	—
610	C₄	—	13	2	no	—
611	C₄	—	26	1	no	—
612	C₄	—	26	1	no	—
613	C₄	—	26	2	no	—
614	C₄	—	26	1	no	—
615	C₄	—	26	2	no	—
616	C₄	—	26	1	no	—
617	C₄	—	26	2	no	—
618	C₄	—	26	1	no	—
619	C₄	#88254	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	26	2	no	—
622	C₂	—	52	1	no	—
623	C₂	—	52	2	no	—
624	C₂	C₂×#88254	1	1	yes	characteristic
625	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
626	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₂×C₁₃×#125	C₂
hypercenter	C₂×#125	D₁₃
hypocenter	C₁₃	#3515
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#125	C₂	semidirect
2. #11719401	C₂	semidirect
3. #11719400	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719398	C₂	semidirect
6. #11719398	C₂	semidirect
7. #11719397	C₂	semidirect
8. #11719396	C₂	semidirect
9. #11719396	C₂	semidirect
10. #11719395	C₂	semidirect
11. #11719393	C₂	semidirect
12. D₁₃×#125	C₂	semidirect
13. #11719390	C₂	semidirect
14. #11719220	C₂	semidirect
15. #11719219	C₂	semidirect
16. #11719218	C₂	semidirect
17. #11719218	C₂	semidirect
18. #11719216	C₂	semidirect
19. #11719212	C₂	semidirect
20. #11719212	C₂	semidirect
21. #11719209	C₂	semidirect
22. #11719184	C₂	semidirect
23. C₄×#6127	C₂	semidirect
295. C₂×#125	D₁₃	semidirect
537. C₁₃	#3515	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#125	2
#11719401	2
#11719400	2
#11719399	2
#11719398	2
#11719397	2
#11719396	2
#11719395	2
#11719393	2
D₁₃×#125	2
#11719390	2
#11719220	2
#11719219	2
#11719218	2
#11719216	2
#11719212	2
#11719209	2
#11719184	2
C₄×#6127	2
#3515	13