Subgroups — #13129322

Order 1664.

910 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#542	C₂	1	1	yes	maximal, characteristic
2	#11719427	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719426	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719406	C₂	1	2	yes	maximal, complemented
5	#11719406	C₂	1	2	yes	maximal, complemented
6	#11719377	C₂	1	2	yes	maximal, complemented
7	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719376	C₂	1	2	yes	maximal, complemented
10	#11719356	C₂	1	2	yes	maximal, complemented
11	#11719355	C₂	1	2	yes	maximal, complemented
12	#11719330	C₂	1	2	yes	maximal, complemented
13	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719328	C₂	1	2	yes	maximal, complemented
15	#11719327	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719308	C₂	1	1	yes	maximal, characteristic
17	#11719305	C₂	1	1	yes	maximal, characteristic
18	#11719274	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719272	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719223	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×#124	C₂²	1	1	yes	characteristic
27	C₁₃×#124	C₂²	1	2	yes	—
28	C₁₃×#123	C₂²	1	2	yes	—
29	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
30	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₁₃×#121	C₂²	1	1	yes	characteristic
32	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₁₃×#117	C₂²	1	1	yes	characteristic
35	Q₈×Dic₁₃	C₂²	1	2	yes	—
36	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
37	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic
38	#88198	C₂²	1	2	yes	—
39	#88198	C₂²	1	2	yes	—
40	#88198	C₂²	1	2	yes	—
41	#88198	C₂²	1	1	yes	characteristic
42	#88198	C₂²	1	1	yes	characteristic
43	#88190	C₂²	1	1	yes	characteristic
44	#88190	C₂²	1	1	yes	characteristic
45	#88190	C₂²	1	2	yes	—
46	#88189	C₂²	1	2	yes	—
47	#88189	C₂²	1	2	yes	—
48	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
49	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
50	D₄×Dic₁₃	C₂²	1	2	yes	—
51	#88180	C₂²	1	1	yes	characteristic
52	#88180	C₂²	1	2	yes	—
53	#88178	C₂²	1	1	yes	characteristic
54	#88178	C₂²	1	1	yes	characteristic
55	#88178	C₂²	1	2	yes	—
56	#88178	C₂²	1	2	yes	—
57	C₂×#6101	C₂²	1	2	yes	—
58	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
59	#88144	C₂²	1	1	yes	characteristic
60	#88144	C₂²	1	1	yes	characteristic
61	#88144	C₂²	1	1	yes	characteristic
62	#88144	C₂²	1	1	yes	characteristic
63	#88144	C₂²	1	2	yes	—
64	#88144	C₂²	1	2	yes	—
65	#88143	C₂²	1	2	yes	—
66	#88143	C₂²	1	2	yes	—
67	#88143	C₂²	1	2	yes	—
68	#88143	C₂²	1	2	yes	—
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	#88142	C₂²	1	1	yes	characteristic
74	#88142	C₂²	1	1	yes	characteristic
75	#88142	C₂²	1	2	yes	—
76	#88142	C₂²	1	1	yes	characteristic
77	#88142	C₂²	1	1	yes	characteristic
78	#88142	C₂²	1	2	yes	—
79	#88141	C₂²	1	1	yes	characteristic
80	#88141	C₂²	1	1	yes	characteristic
81	#88141	C₂²	1	1	yes	characteristic
82	#88141	C₂²	1	1	yes	characteristic
83	#88141	C₂²	1	2	yes	—
84	#88141	C₂²	1	2	yes	—
85	#88133	C₂²	1	2	yes	—
86	#88133	C₂²	1	2	yes	—
87	#88133	C₂²	1	2	yes	—
88	#88133	C₂²	1	2	yes	—
89	#88133	C₂²	1	2	yes	—
90	#88133	C₂²	1	2	yes	—
91	#88133	C₂²	1	2	yes	—
92	#88133	C₂²	1	2	yes	—
93	#88133	C₂²	1	2	yes	—
94	#88133	C₂²	1	2	yes	—
95	#88133	C₂²	1	2	yes	—
96	#88133	C₂²	1	2	yes	—
97	#88132	C₂²	1	1	yes	characteristic
98	#88132	C₂²	1	1	yes	characteristic
99	#88132	C₂²	1	1	yes	characteristic
100	#88132	C₂²	1	1	yes	characteristic
101	#88132	C₂²	1	2	yes	—
102	#88132	C₂²	1	2	yes	—
103	#88132	C₂²	1	2	yes	—
104	#88132	C₂²	1	2	yes	—
105	#88132	C₂²	1	2	yes	—
106	#88132	C₂²	1	2	yes	—
107	#88131	C₂²	1	2	yes	—
108	#88131	C₂²	1	2	yes	—
109	#88131	C₂²	1	2	yes	—
110	#88131	C₂²	1	2	yes	—
111	#88124	C₂²	1	1	yes	characteristic
112	#88124	C₂²	1	2	yes	—
113	#88124	C₂²	1	2	yes	—
114	#88123	C₂²	1	1	yes	characteristic
115	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
116	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
117	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
118	C₄×Dic₂₆	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	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	C₂×D₄×C₁₃	C₂³	1	2	yes	—
127	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
128	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
129	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
130	C₂²×Dic₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
133	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
134	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
135	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
136	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
137	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
138	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
139	C₂×Dic₂₆	C₂³	1	2	yes	—
140	C₂×Dic₂₆	C₂³	1	2	yes	—
141	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
142	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
143	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
144	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
145	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
146	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
148	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
149	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
150	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
151	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
152	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
153	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
154	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
155	C₄²×C₁₃	C₂³	1	1	yes	characteristic
156	C₄²×C₁₃	C₂³	1	1	yes	characteristic
157	C₄²×C₁₃	C₂³	1	2	yes	—
158	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
159	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
160	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
161	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
162	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
163	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
164	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
165	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
166	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
167	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
168	C₄⋊Dic₁₃	C₂³	1	2	yes	—
169	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
170	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
171	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
172	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
173	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
174	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
175	C₄⋊Dic₁₃	C₂³	1	2	yes	—
176	C₄⋊Dic₁₃	C₂³	1	2	yes	—
177	C₄⋊Dic₁₃	C₂³	1	2	yes	—
178	C₄⋊Dic₁₃	C₂³	1	2	yes	—
179	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	#6101	C₂³	1	1	yes	characteristic
183	#6101	C₂³	1	2	yes	—
184	#6101	C₂³	1	1	yes	characteristic
185	#6101	C₂³	1	1	yes	characteristic
186	#6101	C₂³	1	1	yes	characteristic
187	#6101	C₂³	1	2	yes	—
188	#6101	C₂³	1	1	yes	characteristic
189	#6101	C₂³	1	2	yes	—
190	#6101	C₂³	1	2	yes	—
191	#6101	C₂³	1	1	yes	characteristic
192	#6101	C₂³	1	1	yes	characteristic
193	#6101	C₂³	1	1	yes	characteristic
194	#6101	C₂³	1	2	yes	—
195	#6101	C₂³	1	2	yes	—
196	#6101	C₂³	1	2	yes	—
197	#6101	C₂³	1	2	yes	—
198	#6101	C₂³	1	2	yes	—
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	2	yes	—
208	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
209	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
210	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
211	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
212	C₄×Dic₁₃	C₂³	1	2	yes	—
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	2	yes	—
220	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	#3555	—	13	1	no	maximal, Sylow
223	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
224	C₂³×C₁₃	C₂⁴	1	2	yes	—
225	Q₈×C₁₃	—	2	2	no	—
226	Q₈×C₁₃	—	4	2	no	—
227	D₄×C₁₃	—	2	2	no	—
228	D₄×C₁₃	—	4	2	no	—
229	C₂×C₄×C₁₃	—	2	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
232	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
235	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
236	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
237	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×Dic₁₃	—	2	2	no	—
241	C₂×Dic₁₃	—	2	4	no	—
242	C₂×Dic₁₃	—	4	1	no	—
243	C₂×Dic₁₃	—	4	2	no	—
244	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	2	yes	—
251	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₁₃	C₂⁴	1	2	yes	—
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
256	Dic₂₆	—	2	2	no	—
257	Dic₂₆	—	2	2	no	—
258	Dic₂₆	—	2	2	no	—
259	Dic₂₆	—	2	2	no	—
260	Dic₂₆	—	4	1	no	—
261	Dic₂₆	—	4	2	no	—
262	Dic₂₆	—	4	2	no	—
263	Dic₂₆	—	4	1	no	—
264	#563	—	13	2	no	—
265	#563	—	13	2	no	—
266	Q₈²	—	13	1	no	—
267	#557	—	13	1	no	—
268	#557	—	13	1	no	—
269	#557	—	13	1	no	—
270	#556	—	13	2	no	—
271	#556	—	13	1	no	—
272	#556	—	13	1	no	—
273	#556	—	13	1	no	—
274	#554	—	13	1	no	—
275	#552	—	13	2	no	—
276	#544	—	13	2	no	—
277	#542	—	13	1	no	—
278	#542	D₁₃	1	1	yes	characteristic
279	#541	—	13	2	no	—
280	#541	—	13	2	no	—
281	#541	—	13	1	no	—
282	#541	—	13	2	no	—
283	#541	—	13	1	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	2	no	—
289	C₂²×C₁₃	—	2	1	no	—
290	C₂²×C₁₃	—	2	2	no	—
291	C₂²×C₁₃	—	2	2	no	—
292	C₂²×C₁₃	—	2	1	no	—
293	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
294	C₄×C₁₃	—	2	1	no	—
295	C₄×C₁₃	—	2	1	no	—
296	C₄×C₁₃	—	2	1	no	—
297	C₄×C₁₃	—	2	2	no	—
298	C₄×C₁₃	—	2	1	no	—
299	C₄×C₁₃	—	2	2	no	—
300	C₄×C₁₃	—	2	2	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
303	Dic₁₃	—	2	2	no	—
304	Dic₁₃	—	2	2	no	—
305	Dic₁₃	—	2	1	no	—
306	Dic₁₃	—	2	1	no	—
307	Dic₁₃	—	2	1	no	—
308	Dic₁₃	—	2	2	no	—
309	Dic₁₃	—	2	1	no	—
310	Dic₁₃	—	2	1	no	—
311	Dic₁₃	—	2	2	no	—
312	Dic₁₃	—	2	1	no	—
313	Dic₁₃	—	2	1	no	—
314	Dic₁₃	2₋¹⁺⁴	1	2	yes	—
315	C₄⋊Q₈	—	13	1	no	—
316	C₄⋊Q₈	—	13	1	no	—
317	C₄⋊Q₈	—	13	2	no	—
318	C₄⋊Q₈	—	13	2	no	—
319	C₄⋊Q₈	—	13	2	no	—
320	C₄⋊Q₈	—	13	1	no	—
321	C₄⋊Q₈	—	13	1	no	—
322	C₄⋊Q₈	—	13	1	no	—
323	C₄⋊Q₈	—	13	2	no	—
324	C₄⋊Q₈	—	13	1	no	—
325	C₄⋊Q₈	—	13	2	no	—
326	C₄⋊Q₈	—	13	1	no	—
327	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
328	#126	—	13	2	no	—
329	#126	—	13	2	no	—
330	#126	—	13	2	no	—
331	#126	—	13	2	no	—
332	#126	—	13	2	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	C₂×D₁₃	1	2	yes	—
341	#125	—	13	1	no	—
342	#125	—	13	1	no	—
343	#125	—	13	1	no	—
344	#125	—	13	2	no	—
345	#125	—	13	2	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	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	2	no	—
355	#125	—	13	1	no	—
356	#125	—	13	2	no	—
357	#125	—	13	2	no	—
358	#124	—	13	1	no	—
359	#124	—	13	1	no	—
360	#124	—	13	2	no	—
361	#124	C₂×D₁₃	1	1	yes	characteristic
362	#124	C₂×D₁₃	1	2	yes	—
363	#123	—	13	2	no	—
364	#123	—	13	2	no	—
365	#123	C₂×D₁₃	1	2	yes	—
366	C₂²⋊Q₈	—	13	1	no	—
367	C₂²⋊Q₈	—	13	1	no	—
368	C₂²⋊Q₈	—	13	2	no	—
369	C₂²⋊Q₈	—	13	2	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	1	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	C₂²⋊Q₈	—	13	2	no	—
380	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
381	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
382	#121	C₂×D₁₃	1	1	yes	characteristic
383	C₄×Q₈	—	13	1	no	—
384	C₄×Q₈	—	13	2	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	2	no	—
390	C₄×Q₈	—	13	1	no	—
391	C₄×Q₈	—	13	1	no	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	—	13	1	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	2	no	—
397	C₄×Q₈	—	13	2	no	—
398	C₄×Q₈	—	13	1	no	—
399	C₄×Q₈	—	13	1	no	—
400	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
401	C₄×D₄	—	13	2	no	—
402	C₄×D₄	—	13	1	no	—
403	C₄×D₄	—	13	1	no	—
404	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
405	#117	—	13	1	no	—
406	#117	—	13	2	no	—
407	#117	—	13	2	no	—
408	#117	—	13	2	no	—
409	#117	—	13	2	no	—
410	#117	—	13	2	no	—
411	#117	C₂×D₁₃	1	1	yes	characteristic
412	C₂×C₄⋊C₄	—	13	2	no	—
413	C₂×C₄²	—	13	1	no	—
414	C₂×C₁₃	—	4	1	no	—
415	C₂×C₁₃	—	4	2	no	—
416	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
417	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
418	C₂×C₁₃	#585	1	1	yes	characteristic
419	C₂×Q₈	—	13	1	no	—
420	C₂×Q₈	—	13	1	no	—
421	C₂×Q₈	—	13	1	no	—
422	C₂×Q₈	—	13	1	no	—
423	C₂×Q₈	—	13	1	no	—
424	C₂×Q₈	—	13	2	no	—
425	C₂×Q₈	—	13	1	no	—
426	C₂×Q₈	—	13	2	no	—
427	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
428	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
429	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
430	C₂×D₄	C₂²×D₁₃	1	2	yes	—
431	C₂²×C₄	—	13	1	no	—
432	C₂²×C₄	—	13	2	no	—
433	C₂²×C₄	—	13	1	no	—
434	C₂²×C₄	—	13	2	no	—
435	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
436	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
437	C₄⋊C₄	—	13	1	no	—
438	C₄⋊C₄	—	13	2	no	—
439	C₄⋊C₄	—	13	2	no	—
440	C₄⋊C₄	—	13	2	no	—
441	C₄⋊C₄	—	13	1	no	—
442	C₄⋊C₄	—	13	1	no	—
443	C₄⋊C₄	—	13	2	no	—
444	C₄⋊C₄	—	13	1	no	—
445	C₄⋊C₄	—	13	1	no	—
446	C₄⋊C₄	—	13	2	no	—
447	C₄⋊C₄	—	13	2	no	—
448	C₄⋊C₄	—	13	2	no	—
449	C₄⋊C₄	—	13	2	no	—
450	C₄⋊C₄	—	13	1	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	1	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	1	no	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	2	no	—
470	C₄⋊C₄	—	13	1	no	—
471	C₄⋊C₄	—	13	2	no	—
472	C₄⋊C₄	—	13	1	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	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	C₂²⋊C₄	—	13	2	no	—
485	C₂²⋊C₄	—	13	1	no	—
486	C₂²⋊C₄	—	13	2	no	—
487	C₂²⋊C₄	—	13	2	no	—
488	C₂²⋊C₄	—	13	1	no	—
489	C₂²⋊C₄	—	13	2	no	—
490	C₂²⋊C₄	—	13	2	no	—
491	C₂²⋊C₄	—	13	2	no	—
492	C₂²⋊C₄	—	13	2	no	—
493	C₂²⋊C₄	—	13	2	no	—
494	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
495	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
496	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
497	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
498	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
500	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
501	C₄²	—	13	1	no	—
502	C₄²	—	13	1	no	—
503	C₄²	—	13	1	no	—
504	C₄²	—	13	1	no	—
505	C₄²	—	13	2	no	—
506	C₄²	—	13	2	no	—
507	C₄²	—	13	2	no	—
508	C₄²	—	13	1	no	—
509	C₄²	—	13	1	no	—
510	C₄²	—	13	2	no	—
511	C₄²	—	13	2	no	—
512	C₄²	—	13	2	no	—
513	C₄²	—	13	2	no	—
514	C₄²	—	13	2	no	—
515	C₄²	C₂²×D₁₃	1	1	yes	characteristic
516	C₄²	C₂²×D₁₃	1	1	yes	characteristic
517	C₄²	C₂²×D₁₃	1	2	yes	—
518	C₁₃	#3555	1	1	yes	characteristic, complemented, Sylow
519	C₂³	C₂³×D₁₃	1	1	yes	characteristic
520	C₂³	C₂³×D₁₃	1	2	yes	—
521	Q₈	—	2	2	no	—
522	Q₈	—	4	2	no	—
523	Q₈	—	26	2	no	—
524	Q₈	—	26	2	no	—
525	Q₈	—	26	2	no	—
526	Q₈	—	26	2	no	—
527	Q₈	—	52	1	no	—
528	Q₈	—	52	2	no	—
529	Q₈	—	52	2	no	—
530	Q₈	—	52	1	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	13	1	no	—
536	C₂×C₄	—	13	1	no	—
537	C₂×C₄	—	13	2	no	—
538	C₂×C₄	—	13	2	no	—
539	C₂×C₄	—	13	1	no	—
540	C₂×C₄	—	13	1	no	—
541	C₂×C₄	—	13	1	no	—
542	C₂×C₄	—	13	2	no	—
543	C₂×C₄	—	13	1	no	—
544	C₂×C₄	—	13	1	no	—
545	C₂×C₄	—	13	2	no	—
546	C₂×C₄	—	13	1	no	—
547	C₂×C₄	—	26	2	no	—
548	C₂×C₄	—	26	4	no	—
549	C₂×C₄	—	52	2	no	—
550	C₂×C₄	—	52	1	no	—
551	C₂×C₄	C₂³×D₁₃	1	2	yes	—
552	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
553	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
554	C₂×C₄	C₂³×D₁₃	1	2	yes	—
555	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
556	C₂×C₄	C₂³×D₁₃	1	2	yes	—
557	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
558	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
559	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	2	2	no	—
563	C₂²	—	2	1	no	—
564	C₂²	—	2	1	no	—
565	C₂²	—	2	2	no	—
566	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	1	no	—
573	C₄	—	2	1	no	—
574	C₄	—	2	1	no	—
575	C₄	—	13	2	no	—
576	C₄	—	26	2	no	—
577	C₄	—	26	2	no	—
578	C₄	—	26	1	no	—
579	C₄	—	26	1	no	—
580	C₄	—	26	1	no	—
581	C₄	—	26	2	no	—
582	C₄	—	26	1	no	—
583	C₄	—	26	1	no	—
584	C₄	—	26	2	no	—
585	C₄	—	26	1	no	—
586	C₄	—	26	1	no	—
587	C₄	#88257	1	2	yes	—
588	C₂	—	4	1	no	—
589	C₂	—	4	2	no	—
590	C₂	C₂×#88257	1	1	yes	characteristic
591	C₂	#11719650	1	1	yes	characteristic
592	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×#542	C₂
prime radical	C₁₃×#121	C₂²
hypercenter	#542	D₁₃
hypocenter	C₁₃	#3555
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #542

Complements

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

N	H ≅ G/N	type
2. #11719427	C₂	semidirect
3. #11719426	C₂	semidirect
4. #11719406	C₂	semidirect
5. #11719406	C₂	semidirect
6. #11719377	C₂	semidirect
7. #11719376	C₂	semidirect
8. #11719376	C₂	semidirect
9. #11719376	C₂	semidirect
10. #11719356	C₂	semidirect
11. #11719355	C₂	semidirect
12. #11719330	C₂	semidirect
13. #11719330	C₂	semidirect
14. #11719328	C₂	semidirect
15. #11719327	C₂	semidirect
18. #11719274	C₂	semidirect
19. #11719272	C₂	semidirect
20. #11719247	C₂	semidirect
21. #11719244	C₂	semidirect
22. #11719223	C₂	semidirect
23. #11719222	C₂	semidirect
518. 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×#542	2
#11719427	2
#11719426	2
#11719406	2
#11719377	2
#11719376	2
#11719356	2
#11719355	2
#11719330	2
#11719328	2
#11719327	2
#11719308	2
#11719305	2
#11719274	2
#11719272	2
#11719247	2
#11719244	2
#11719223	2
#11719222	2
#3555	13