Subgroups — #13129319

Order 1664.

910 conjugacy classes of subgroups.

The subgroup lattice has 600 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	#11719434	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719427	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719417	C₂	1	2	yes	maximal, complemented
5	#11719407	C₂	1	2	yes	maximal, complemented
6	#11719406	C₂	1	2	yes	maximal, complemented
7	#11719406	C₂	1	2	yes	maximal, complemented
8	#11719377	C₂	1	2	yes	maximal, complemented
9	#11719374	C₂	1	2	yes	maximal
10	#11719346	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719340	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719288	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719288	C₂	1	2	yes	maximal, complemented
16	#11719274	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719272	C₂	1	2	yes	maximal, complemented
18	#11719246	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719243	C₂	1	1	yes	maximal, characteristic
20	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719234	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719224	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719222	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₃×#126	C₂²	1	2	yes	—
26	C₁₃×#126	C₂²	1	2	yes	—
27	C₁₃×#124	C₂²	1	2	yes	—
28	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
29	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
31	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₁₃×#117	C₂²	1	1	yes	characteristic
34	C₁₃×#117	C₂²	1	1	yes	characteristic
35	#88200	C₂²	1	2	yes	—
36	#88200	C₂²	1	1	yes	characteristic
37	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
38	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
39	#88198	C₂²	1	2	yes	—
40	#88198	C₂²	1	2	yes	—
41	#88198	C₂²	1	2	yes	—
42	#88198	C₂²	1	1	yes	characteristic
43	#88193	C₂²	1	1	yes	characteristic
44	#88189	C₂²	1	1	yes	characteristic
45	#88189	C₂²	1	2	yes	—
46	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
48	#88180	C₂²	1	1	yes	characteristic
49	#88180	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
51	#88178	C₂²	1	1	yes	characteristic
52	#88178	C₂²	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
54	#88152	C₂²	1	1	yes	characteristic
55	#88152	C₂²	1	2	yes	—
56	#88152	C₂²	1	2	yes	—
57	#88151	C₂²	1	1	yes	characteristic
58	#88151	C₂²	1	2	yes	—
59	#88150	C₂²	1	2	yes	—
60	#88146	C₂²	1	1	yes	characteristic
61	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
62	#88144	C₂²	1	1	yes	characteristic
63	#88144	C₂²	1	1	yes	characteristic
64	#88144	C₂²	1	1	yes	characteristic
65	#88144	C₂²	1	2	yes	—
66	#88144	C₂²	1	2	yes	—
67	#88143	C₂²	1	2	yes	—
68	#88143	C₂²	1	1	yes	characteristic
69	#88143	C₂²	1	2	yes	—
70	#88143	C₂²	1	2	yes	—
71	#88143	C₂²	1	2	yes	—
72	#88143	C₂²	1	2	yes	—
73	#88143	C₂²	1	2	yes	—
74	#88142	C₂²	1	1	yes	characteristic
75	#88142	C₂²	1	1	yes	characteristic
76	#88142	C₂²	1	2	yes	—
77	#88142	C₂²	1	1	yes	characteristic
78	#88142	C₂²	1	1	yes	characteristic
79	#88142	C₂²	1	2	yes	—
80	#88141	C₂²	1	1	yes	characteristic
81	#88141	C₂²	1	1	yes	characteristic
82	#88141	C₂²	1	2	yes	—
83	#88141	C₂²	1	2	yes	—
84	#88141	C₂²	1	2	yes	—
85	#88140	C₂²	1	1	yes	characteristic
86	#88139	C₂²	1	2	yes	—
87	#88139	C₂²	1	1	yes	characteristic
88	#88139	C₂²	1	2	yes	—
89	#88137	C₂²	1	2	yes	—
90	#88135	C₂²	1	2	yes	—
91	#88133	C₂²	1	2	yes	—
92	#88133	C₂²	1	2	yes	—
93	#88133	C₂²	1	1	yes	characteristic
94	#88133	C₂²	1	2	yes	—
95	#88133	C₂²	1	2	yes	—
96	#88133	C₂²	1	2	yes	—
97	#88133	C₂²	1	2	yes	—
98	#88132	C₂²	1	2	yes	—
99	#88132	C₂²	1	2	yes	—
100	#88132	C₂²	1	2	yes	—
101	#88132	C₂²	1	2	yes	—
102	#88132	C₂²	1	1	yes	characteristic
103	#88132	C₂²	1	2	yes	—
104	#88132	C₂²	1	2	yes	—
105	#88131	C₂²	1	2	yes	—
106	#88131	C₂²	1	2	yes	—
107	#88130	C₂²	1	2	yes	—
108	#88130	C₂²	1	2	yes	—
109	#88126	C₂²	1	1	yes	characteristic
110	#88126	C₂²	1	2	yes	—
111	#88124	C₂²	1	1	yes	characteristic
112	#88124	C₂²	1	2	yes	—
113	#88124	C₂²	1	2	yes	—
114	#88124	C₂²	1	2	yes	—
115	#88124	C₂²	1	2	yes	—
116	#88123	C₂²	1	2	yes	—
117	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
118	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
119	C₄×Dic₂₆	C₂²	1	2	yes	—
120	C₄×Dic₂₆	C₂²	1	2	yes	—
121	C₄×Dic₂₆	C₂²	1	2	yes	—
122	C₄×Dic₂₆	C₂²	1	2	yes	—
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	1	yes	characteristic
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
129	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
131	C₂²×Dic₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
133	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₄×D₁₃	C₂³	1	2	yes	—
135	C₂×Dic₂₆	C₂³	1	2	yes	—
136	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
138	C₂×Dic₂₆	C₂³	1	2	yes	—
139	C₂×Dic₂₆	C₂³	1	2	yes	—
140	C₂×Dic₂₆	C₂³	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
142	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
145	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
146	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
150	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
153	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
154	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
155	C₄²×C₁₃	C₂³	1	2	yes	—
156	C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₄²×C₁₃	C₂³	1	2	yes	—
158	C₄²×C₁₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
162	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
163	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
164	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
165	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
166	#6103	C₂³	1	1	yes	characteristic
167	#6103	C₂³	1	2	yes	—
168	#6103	C₂³	1	1	yes	characteristic
169	#6103	C₂³	1	1	yes	characteristic
170	#6103	C₂³	1	1	yes	characteristic
171	#6103	C₂³	1	2	yes	—
172	#6103	C₂³	1	2	yes	—
173	C₄⋊Dic₁₃	C₂³	1	2	yes	—
174	C₄⋊Dic₁₃	C₂³	1	2	yes	—
175	C₄⋊Dic₁₃	C₂³	1	2	yes	—
176	C₄⋊Dic₁₃	C₂³	1	2	yes	—
177	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
179	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₄⋊Dic₁₃	C₂³	1	2	yes	—
183	C₄⋊Dic₁₃	C₂³	1	2	yes	—
184	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	#6101	C₂³	1	1	yes	characteristic
187	#6101	C₂³	1	1	yes	characteristic
188	#6101	C₂³	1	2	yes	—
189	#6101	C₂³	1	1	yes	characteristic
190	#6101	C₂³	1	2	yes	—
191	#6101	C₂³	1	2	yes	—
192	#6101	C₂³	1	2	yes	—
193	#6101	C₂³	1	2	yes	—
194	#6101	C₂³	1	2	yes	—
195	#6101	C₂³	1	2	yes	—
196	#6101	C₂³	1	2	yes	—
197	#6101	C₂³	1	1	yes	characteristic
198	#6101	C₂³	1	1	yes	characteristic
199	#6101	C₂³	1	2	yes	—
200	#6101	C₂³	1	2	yes	—
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	1	yes	characteristic
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	C₄×Dic₁₃	C₂³	1	2	yes	—
211	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
213	C₄×Dic₁₃	C₂³	1	2	yes	—
214	C₄×Dic₁₃	C₂³	1	2	yes	—
215	C₄×Dic₁₃	C₂³	1	2	yes	—
216	C₄×Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
222	#3555	—	13	1	no	maximal, Sylow
223	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
225	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
226	Q₈×C₁₃	—	2	2	no	—
227	Q₈×C₁₃	—	4	2	no	—
228	D₄×C₁₃	—	4	1	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	2	2	no	—
231	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
233	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂²⋊D₁₃	—	2	2	no	—
241	C₂²⋊D₁₃	—	4	1	no	—
242	C₂×Dic₁₃	—	2	2	no	—
243	C₂×Dic₁₃	—	4	1	no	—
244	C₂×Dic₁₃	—	4	2	no	—
245	C₂×Dic₁₃	C₂⁴	1	2	yes	—
246	C₂×Dic₁₃	C₂⁴	1	2	yes	—
247	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
248	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	C₄×D₁₃	—	2	2	no	—
257	C₄×D₁₃	—	4	2	no	—
258	Dic₂₆	—	2	2	no	—
259	Dic₂₆	—	2	4	no	—
260	Dic₂₆	—	2	2	no	—
261	Dic₂₆	—	4	2	no	—
262	Dic₂₆	—	4	2	no	—
263	Dic₂₆	—	4	2	no	—
264	#563	—	13	2	no	—
265	#563	—	13	2	no	—
266	Q₈²	—	13	1	no	—
267	#557	—	13	2	no	—
268	#557	—	13	1	no	—
269	#556	—	13	2	no	—
270	#556	—	13	1	no	—
271	#556	—	13	1	no	—
272	#556	D₁₃	1	1	yes	characteristic, complemented
273	#554	—	13	1	no	—
274	#552	—	13	1	no	—
275	#552	—	13	1	no	—
276	#544	—	13	1	no	—
277	#544	—	13	1	no	—
278	#542	—	13	2	no	—
279	#541	—	13	2	no	—
280	#541	—	13	2	no	—
281	#541	—	13	1	no	—
282	#541	—	13	1	no	—
283	#541	—	13	2	no	—
284	#533	—	13	1	no	—
285	#533	—	13	1	no	—
286	#529	—	13	1	no	—
287	C₂²×C₁₃	—	2	1	no	—
288	C₂²×C₁₃	—	2	1	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	1	no	—
291	C₂²×C₁₃	—	2	1	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
294	C₂×D₁₃	—	2	1	no	—
295	C₂×D₁₃	—	2	1	no	—
296	C₂×D₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	1	no	—
298	C₄×C₁₃	—	2	2	no	—
299	C₄×C₁₃	—	2	1	no	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	2	no	—
303	C₄×C₁₃	—	2	2	no	—
304	C₄×C₁₃	—	2	1	no	—
305	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
306	Dic₁₃	—	2	2	no	—
307	Dic₁₃	—	2	2	no	—
308	Dic₁₃	—	2	1	no	—
309	Dic₁₃	—	2	1	no	—
310	Dic₁₃	—	2	1	no	—
311	Dic₁₃	—	2	1	no	—
312	Dic₁₃	—	2	2	no	—
313	Dic₁₃	—	2	1	no	—
314	Dic₁₃	—	2	1	no	—
315	Dic₁₃	—	2	2	no	—
316	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
317	C₄⋊Q₈	—	13	1	no	—
318	C₄⋊Q₈	—	13	2	no	—
319	C₄⋊Q₈	—	13	2	no	—
320	C₄⋊Q₈	—	13	2	no	—
321	C₄⋊Q₈	—	13	1	no	—
322	C₄⋊Q₈	—	13	1	no	—
323	C₄⋊Q₈	—	13	1	no	—
324	C₄⋊Q₈	—	13	2	no	—
325	C₄⋊Q₈	—	13	2	no	—
326	C₄⋊Q₈	—	13	1	no	—
327	C₄⋊Q₈	—	13	2	no	—
328	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
329	#126	—	13	1	no	—
330	#126	—	13	2	no	—
331	#126	—	13	2	no	—
332	#126	—	13	1	no	—
333	#126	—	13	2	no	—
334	#126	—	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	C₂×D₁₃	1	2	yes	—
342	#126	C₂×D₁₃	1	2	yes	—
343	#125	—	13	1	no	—
344	#125	—	13	2	no	—
345	#125	—	13	1	no	—
346	#125	—	13	1	no	—
347	#125	—	13	2	no	—
348	#125	—	13	2	no	—
349	#125	—	13	2	no	—
350	#125	—	13	2	no	—
351	#125	—	13	2	no	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	1	no	—
355	#125	—	13	2	no	—
356	#125	—	13	2	no	—
357	#125	—	13	2	no	—
358	#125	—	13	2	no	—
359	#125	—	13	1	no	—
360	#124	—	13	1	no	—
361	#124	—	13	2	no	—
362	#124	—	13	2	no	—
363	#124	C₂×D₁₃	1	2	yes	—
364	#123	—	13	1	no	—
365	#123	—	13	2	no	—
366	#123	—	13	1	no	—
367	#123	—	13	2	no	—
368	C₂²⋊Q₈	—	13	2	no	—
369	C₂²⋊Q₈	—	13	1	no	—
370	C₂²⋊Q₈	—	13	1	no	—
371	C₂²⋊Q₈	—	13	1	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	2	no	—
374	C₂²⋊Q₈	—	13	2	no	—
375	C₂²⋊Q₈	—	13	1	no	—
376	C₂²⋊Q₈	—	13	2	no	—
377	C₂²⋊Q₈	—	13	2	no	—
378	C₂²⋊Q₈	—	13	2	no	—
379	C₂²⋊Q₈	—	13	2	no	—
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	2	no	—
382	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
383	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
384	#121	—	13	1	no	—
385	C₄×Q₈	—	13	1	no	—
386	C₄×Q₈	—	13	1	no	—
387	C₄×Q₈	—	13	2	no	—
388	C₄×Q₈	—	13	1	no	—
389	C₄×Q₈	—	13	1	no	—
390	C₄×Q₈	—	13	2	no	—
391	C₄×Q₈	—	13	2	no	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	2	no	—
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	2	no	—
397	C₄×Q₈	—	13	2	no	—
398	C₄×Q₈	C₂×D₁₃	1	2	yes	—
399	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
400	C₄×D₄	—	13	1	no	—
401	C₄×D₄	—	13	1	no	—
402	C₄×D₄	—	13	2	no	—
403	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
404	#117	—	13	1	no	—
405	#117	—	13	1	no	—
406	#117	—	13	1	no	—
407	#117	—	13	2	no	—
408	#117	—	13	2	no	—
409	#117	—	13	1	no	—
410	#117	—	13	2	no	—
411	#117	C₂×D₁₃	1	1	yes	characteristic
412	#117	C₂×D₁₃	1	1	yes	characteristic
413	C₂×C₄⋊C₄	—	13	1	no	—
414	C₂×C₄⋊C₄	—	13	1	no	—
415	C₂×C₄²	—	13	1	no	—
416	C₂×C₁₃	—	4	1	no	—
417	C₂×C₁₃	—	4	1	no	—
418	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
419	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
420	C₂×C₁₃	#585	1	1	yes	characteristic
421	D₁₃	—	4	1	no	—
422	C₂×Q₈	—	13	1	no	—
423	C₂×Q₈	—	13	1	no	—
424	C₂×Q₈	—	13	2	no	—
425	C₂×Q₈	—	13	2	no	—
426	C₂×Q₈	—	13	2	no	—
427	C₂×Q₈	—	13	2	no	—
428	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
429	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
430	C₂×D₄	—	13	1	no	—
431	C₂×D₄	—	13	1	no	—
432	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
433	C₂²×C₄	—	13	1	no	—
434	C₂²×C₄	—	13	1	no	—
435	C₂²×C₄	—	13	2	no	—
436	C₂²×C₄	—	13	1	no	—
437	C₂²×C₄	—	13	2	no	—
438	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
440	C₄⋊C₄	—	13	1	no	—
441	C₄⋊C₄	—	13	1	no	—
442	C₄⋊C₄	—	13	2	no	—
443	C₄⋊C₄	—	13	2	no	—
444	C₄⋊C₄	—	13	2	no	—
445	C₄⋊C₄	—	13	1	no	—
446	C₄⋊C₄	—	13	2	no	—
447	C₄⋊C₄	—	13	1	no	—
448	C₄⋊C₄	—	13	1	no	—
449	C₄⋊C₄	—	13	2	no	—
450	C₄⋊C₄	—	13	2	no	—
451	C₄⋊C₄	—	13	1	no	—
452	C₄⋊C₄	—	13	1	no	—
453	C₄⋊C₄	—	13	2	no	—
454	C₄⋊C₄	—	13	1	no	—
455	C₄⋊C₄	—	13	2	no	—
456	C₄⋊C₄	—	13	1	no	—
457	C₄⋊C₄	—	13	1	no	—
458	C₄⋊C₄	—	13	2	no	—
459	C₄⋊C₄	—	13	2	no	—
460	C₄⋊C₄	—	13	2	no	—
461	C₄⋊C₄	—	13	2	no	—
462	C₄⋊C₄	—	13	2	no	—
463	C₄⋊C₄	—	13	2	no	—
464	C₄⋊C₄	—	13	2	no	—
465	C₄⋊C₄	—	13	2	no	—
466	C₄⋊C₄	—	13	2	no	—
467	C₄⋊C₄	—	13	2	no	—
468	C₄⋊C₄	—	13	2	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	1	no	—
474	C₄⋊C₄	—	13	2	no	—
475	C₄⋊C₄	—	13	1	no	—
476	C₄⋊C₄	—	13	2	no	—
477	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
478	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
479	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
480	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
481	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
482	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
483	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
484	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
485	C₂²⋊C₄	—	13	1	no	—
486	C₂²⋊C₄	—	13	2	no	—
487	C₂²⋊C₄	—	13	1	no	—
488	C₂²⋊C₄	—	13	2	no	—
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	2	no	—
499	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
500	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
501	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
502	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
503	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
504	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
505	C₄²	—	13	1	no	—
506	C₄²	—	13	1	no	—
507	C₄²	—	13	1	no	—
508	C₄²	—	13	1	no	—
509	C₄²	—	13	2	no	—
510	C₄²	—	13	2	no	—
511	C₄²	—	13	1	no	—
512	C₄²	—	13	2	no	—
513	C₄²	—	13	2	no	—
514	C₄²	—	13	2	no	—
515	C₄²	—	13	2	no	—
516	C₄²	—	13	2	no	—
517	C₄²	C₂²×D₁₃	1	2	yes	—
518	C₄²	C₂²×D₁₃	1	1	yes	characteristic
519	C₄²	C₂²×D₁₃	1	2	yes	—
520	C₄²	C₂²×D₁₃	1	2	yes	—
521	C₁₃	#3555	1	1	yes	characteristic, complemented, Sylow
522	C₂³	—	13	1	no	—
523	C₂³	C₂³×D₁₃	1	1	yes	characteristic
524	C₂³	C₂³×D₁₃	1	1	yes	characteristic
525	Q₈	—	2	2	no	—
526	Q₈	—	4	2	no	—
527	Q₈	—	26	2	no	—
528	Q₈	—	26	4	no	—
529	Q₈	—	26	2	no	—
530	Q₈	—	52	2	no	—
531	Q₈	—	52	2	no	—
532	Q₈	—	52	2	no	—
533	D₄	—	4	1	no	—
534	D₄	—	26	2	no	—
535	D₄	—	52	1	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	13	1	no	—
539	C₂×C₄	—	13	2	no	—
540	C₂×C₄	—	13	2	no	—
541	C₂×C₄	—	13	1	no	—
542	C₂×C₄	—	13	1	no	—
543	C₂×C₄	—	13	1	no	—
544	C₂×C₄	—	13	1	no	—
545	C₂×C₄	—	13	1	no	—
546	C₂×C₄	—	13	1	no	—
547	C₂×C₄	—	13	2	no	—
548	C₂×C₄	—	13	2	no	—
549	C₂×C₄	—	26	2	no	—
550	C₂×C₄	—	26	2	no	—
551	C₂×C₄	—	52	2	no	—
552	C₂×C₄	—	52	2	no	—
553	C₂×C₄	—	52	1	no	—
554	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
555	C₂×C₄	C₂³×D₁₃	1	2	yes	—
556	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
557	C₂×C₄	C₂³×D₁₃	1	2	yes	—
558	C₂×C₄	C₂³×D₁₃	1	2	yes	—
559	C₂×C₄	C₂³×D₁₃	1	2	yes	—
560	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
561	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
562	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	1	no	—
566	C₂²	—	2	1	no	—
567	C₂²	—	2	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	26	1	no	—
570	C₂²	—	26	1	no	—
571	C₂²	—	26	1	no	—
572	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	2	2	no	—
576	C₄	—	2	2	no	—
577	C₄	—	2	1	no	—
578	C₄	—	2	2	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	13	2	no	—
582	C₄	—	26	1	no	—
583	C₄	—	26	2	no	—
584	C₄	—	26	2	no	—
585	C₄	—	26	1	no	—
586	C₄	—	26	1	no	—
587	C₄	—	26	2	no	—
588	C₄	—	26	1	no	—
589	C₄	—	26	1	no	—
590	C₄	—	26	2	no	—
591	C₄	—	26	1	no	—
592	C₄	#88257	1	2	yes	—
593	C₂	—	4	1	no	—
594	C₂	—	4	1	no	—
595	C₂	—	52	1	no	—
596	C₂	C₂×#88257	1	1	yes	characteristic
597	C₂	#11719648	1	1	yes	characteristic
598	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
prime radical	#88193	C₂²
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3555
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. #11719434	C₂	semidirect
3. #11719427	C₂	semidirect
4. #11719417	C₂	semidirect
5. #11719407	C₂	semidirect
6. #11719406	C₂	semidirect
7. #11719406	C₂	semidirect
8. #11719377	C₂	semidirect
10. #11719346	C₂	semidirect
11. #11719340	C₂	semidirect
12. #11719330	C₂	semidirect
13. #11719327	C₂	semidirect
14. #11719288	C₂	semidirect
15. #11719288	C₂	semidirect
16. #11719274	C₂	semidirect
17. #11719272	C₂	semidirect
18. #11719246	C₂	semidirect
20. #11719238	C₂	semidirect
21. #11719234	C₂	semidirect
22. #11719224	C₂	semidirect
23. #11719222	C₂	semidirect
272. #556	D₁₃	semidirect
521. C₁₃	#3555	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
#11719434	2
#11719427	2
#11719417	2
#11719407	2
#11719406	2
#11719377	2
#11719374	2
#11719346	2
#11719340	2
#11719330	2
#11719327	2
#11719288	2
#11719274	2
#11719272	2
#11719246	2
#11719243	2
#11719238	2
#11719234	2
#11719224	2
#11719222	2
#3555	13