Subgroups — #13128656

Order 1664.

988 conjugacy classes of subgroups.

The subgroup lattice has 606 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	#11719434	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719426	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719394	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×#125	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719390	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719341	C₂	1	2	yes	maximal, complemented
9	#11719341	C₂	1	2	yes	maximal, complemented
10	#11719340	C₂	1	2	yes	maximal, complemented
11	#11719328	C₂	1	2	yes	maximal, complemented
12	#11719328	C₂	1	2	yes	maximal, complemented
13	#11719327	C₂	1	2	yes	maximal, complemented
14	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719272	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719251	C₂	1	1	yes	maximal, characteristic
17	#11719251	C₂	1	1	yes	maximal, characteristic
18	#11719248	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719244	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#6129	C₂	1	1	yes	maximal, characteristic
22	#11719216	C₂	1	2	yes	maximal, complemented
23	C₂×#88143	C₂	1	2	yes	maximal, complemented
24	C₂×#6129	C₂²	1	1	yes	characteristic
25	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
26	C₁₃×#125	C₂²	1	1	yes	characteristic
27	C₁₃×#125	C₂²	1	1	yes	characteristic
28	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
30	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
31	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic
32	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
33	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
34	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
35	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
36	#88200	C₂²	1	2	yes	—
37	#88200	C₂²	1	1	yes	characteristic
38	Q₈×Dic₁₃	C₂²	1	2	yes	—
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	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
44	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
45	D₄×Dic₁₃	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	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	—
50	#88178	C₂²	1	2	yes	—
51	#88178	C₂²	1	2	yes	—
52	#88178	C₂²	1	2	yes	—
53	C₂×#6101	C₂²	1	2	yes	—
54	C₂×#6101	C₂²	1	2	yes	—
55	C₂×#6101	C₂²	1	2	yes	—
56	C₂×#6101	C₂²	1	2	yes	—
57	C₂×C₄×Dic₁₃	C₂²	1	2	yes	—
58	#88151	C₂²	1	2	yes	—
59	#88151	C₂²	1	1	yes	characteristic
60	#88150	C₂²	1	2	yes	—
61	#88150	C₂²	1	1	yes	characteristic
62	#88150	C₂²	1	1	yes	characteristic
63	#88150	C₂²	1	2	yes	—
64	#88146	C₂²	1	1	yes	characteristic
65	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
66	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
67	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
68	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
69	#88144	C₂²	1	1	yes	characteristic
70	#88144	C₂²	1	1	yes	characteristic
71	#88144	C₂²	1	1	yes	characteristic
72	#88144	C₂²	1	1	yes	characteristic
73	#88143	C₂²	1	2	yes	—
74	#88143	C₂²	1	2	yes	—
75	#88143	C₂²	1	2	yes	—
76	#88143	C₂²	1	1	yes	characteristic
77	#88143	C₂²	1	2	yes	—
78	#88143	C₂²	1	2	yes	—
79	#88143	C₂²	1	2	yes	—
80	#88143	C₂²	1	2	yes	—
81	#88143	C₂²	1	2	yes	—
82	#88143	C₂²	1	2	yes	—
83	#88143	C₂²	1	1	yes	characteristic
84	#88143	C₂²	1	2	yes	—
85	#88143	C₂²	1	2	yes	—
86	#88143	C₂²	1	2	yes	—
87	#88142	C₂²	1	1	yes	characteristic
88	#88142	C₂²	1	2	yes	—
89	#88142	C₂²	1	1	yes	characteristic
90	#88142	C₂²	1	1	yes	characteristic
91	#88142	C₂²	1	2	yes	—
92	#88142	C₂²	1	2	yes	—
93	#88141	C₂²	1	1	yes	characteristic
94	#88141	C₂²	1	1	yes	characteristic
95	#88141	C₂²	1	2	yes	—
96	#88141	C₂²	1	1	yes	characteristic
97	#88141	C₂²	1	2	yes	—
98	#88141	C₂²	1	2	yes	—
99	#88135	C₂²	1	2	yes	—
100	#88135	C₂²	1	2	yes	—
101	#88135	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	#88132	C₂²	1	2	yes	—
108	#88131	C₂²	1	2	yes	—
109	#88131	C₂²	1	2	yes	—
110	#88131	C₂²	1	2	yes	—
111	#88126	C₂²	1	1	yes	characteristic
112	#88126	C₂²	1	1	yes	characteristic
113	C₄²×D₁₃	C₂²	1	1	yes	characteristic
114	#88124	C₂²	1	1	yes	characteristic
115	#88124	C₂²	1	1	yes	characteristic
116	#88123	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	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	C₂²×Dic₁₃	C₂³	1	2	yes	—
131	C₂²×Dic₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	2	yes	—
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	#6129	Q₈	1	8	yes	complemented
135	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
136	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
137	C₂×C₄×D₁₃	C₂³	1	2	yes	—
138	C₂×C₄×D₁₃	C₂³	1	2	yes	—
139	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
140	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
141	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
142	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
143	C₂×Dic₂₆	C₂³	1	2	yes	—
144	C₂×Dic₂₆	C₂³	1	2	yes	—
145	C₂×Dic₂₆	C₂³	1	2	yes	—
146	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
147	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
148	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
149	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
150	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
151	C₁₃×C₄⋊C₄	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	2	yes	—
155	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
160	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
161	C₄²×C₁₃	C₂³	1	1	yes	characteristic
162	C₄²×C₁₃	C₂³	1	1	yes	characteristic
163	C₄²×C₁₃	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	#6103	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
176	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
177	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₄⋊Dic₁₃	C₂³	1	2	yes	—
179	C₄⋊Dic₁₃	C₂³	1	2	yes	—
180	C₄⋊Dic₁₃	C₂³	1	2	yes	—
181	C₄⋊Dic₁₃	C₂³	1	2	yes	—
182	C₄⋊Dic₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
190	#6101	C₂³	1	2	yes	—
191	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
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	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	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	#6101	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	1	yes	characteristic
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	1	yes	characteristic
218	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
219	C₄×Dic₁₃	C₂³	1	2	yes	—
220	C₄×Dic₁₃	C₂³	1	2	yes	—
221	C₄×Dic₁₃	C₂³	1	2	yes	—
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	#3504	—	13	1	no	maximal, Sylow
224	C₂³×C₁₃	C₂⁴	1	2	yes	—
225	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
226	Q₈×C₁₃	—	4	1	no	—
227	Q₈×C₁₃	—	4	2	no	—
228	D₄×C₁₃	C₂×Q₈	1	4	yes	—
229	C₂×C₄×C₁₃	—	4	2	no	—
230	C₂×C₄×C₁₃	—	4	2	no	—
231	C₂×C₄×C₁₃	—	4	2	no	—
232	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
233	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
235	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
242	C₂²⋊D₁₃	C₂×Q₈	1	8	yes	—
243	C₂×Dic₁₃	—	4	2	no	—
244	C₂×Dic₁₃	—	4	2	no	—
245	C₂×Dic₁₃	—	4	2	no	—
246	C₂×Dic₁₃	C₂×Q₈	1	8	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	2	yes	—
254	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₁₃	C₂⁴	1	2	yes	—
256	C₂×Dic₁₃	C₂⁴	1	2	yes	—
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₄×D₁₃	—	4	1	no	—
259	C₄×D₁₃	—	4	2	no	—
260	C₄×D₁₃	—	4	2	no	—
261	C₄×D₁₃	—	4	1	no	—
262	C₄×D₁₃	C₂×Q₈	1	4	yes	—
263	Dic₂₆	—	4	1	no	—
264	Dic₂₆	—	4	2	no	—
265	Dic₂₆	—	4	2	no	—
266	Dic₂₆	—	4	1	no	—
267	Dic₂₆	—	4	1	no	—
268	Dic₂₆	—	4	2	no	—
269	Dic₂₆	C₂×Q₈	1	4	yes	—
270	#557	—	13	1	no	—
271	#557	—	13	1	no	—
272	#557	—	13	1	no	—
273	#557	—	13	1	no	—
274	#554	—	13	2	no	—
275	#554	—	13	2	no	—
276	#554	—	13	2	no	—
277	#554	—	13	1	no	—
278	#554	—	13	1	no	—
279	#554	—	13	1	no	—
280	#554	—	13	2	no	—
281	#554	D₁₃	1	1	yes	characteristic, complemented
282	#544	—	13	1	no	—
283	#544	—	13	1	no	—
284	#544	—	13	2	no	—
285	#544	—	13	2	no	—
286	#533	—	13	2	no	—
287	#533	—	13	1	no	—
288	C₂×#125	—	13	1	no	—
289	C₂×#125	—	13	2	no	—
290	#520	—	13	1	no	—
291	#520	—	13	1	no	—
292	C₄×#41	—	13	1	no	—
293	C₂²×C₁₃	—	2	2	no	—
294	C₂²×C₁₃	—	2	2	no	—
295	C₂²×C₁₃	C₂²×Q₈	1	4	yes	—
296	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
297	C₂×D₁₃	—	2	1	no	—
298	C₂×D₁₃	—	2	1	no	—
299	C₂×D₁₃	C₂²×Q₈	1	2	yes	—
300	C₄×C₁₃	—	2	1	no	—
301	C₄×C₁₃	—	2	2	no	—
302	C₄×C₁₃	—	2	1	no	—
303	C₄×C₁₃	—	2	1	no	—
304	C₄×C₁₃	—	2	2	no	—
305	C₄×C₁₃	—	2	1	no	—
306	C₄×C₁₃	—	2	1	no	—
307	C₄×C₁₃	—	2	2	no	—
308	C₄×C₁₃	—	2	1	no	—
309	C₄×C₁₃	C₂²×Q₈	1	2	yes	—
310	Dic₁₃	—	2	1	no	—
311	Dic₁₃	—	2	1	no	—
312	Dic₁₃	—	2	1	no	—
313	Dic₁₃	—	2	2	no	—
314	Dic₁₃	—	2	2	no	—
315	Dic₁₃	—	2	2	no	—
316	Dic₁₃	—	2	1	no	—
317	Dic₁₃	—	2	1	no	—
318	Dic₁₃	—	2	1	no	—
319	Dic₁₃	C₂²×Q₈	1	4	yes	—
320	Dic₁₃	C₂²×Q₈	1	2	yes	—
321	C₂×#41	—	13	1	no	—
322	C₄⋊Q₈	—	13	2	no	—
323	C₄⋊Q₈	—	13	1	no	—
324	C₄⋊Q₈	—	13	2	no	—
325	C₄⋊Q₈	—	13	2	no	—
326	C₄⋊Q₈	—	13	2	no	—
327	C₄⋊Q₈	—	13	1	no	—
328	C₄⋊Q₈	—	13	2	no	—
329	C₄⋊Q₈	—	13	2	no	—
330	C₄⋊Q₈	—	13	1	no	—
331	C₄⋊Q₈	—	13	1	no	—
332	C₄⋊Q₈	—	13	1	no	—
333	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
334	#125	—	13	2	no	—
335	#125	—	13	1	no	—
336	#125	—	13	2	no	—
337	#125	—	13	2	no	—
338	#125	—	13	2	no	—
339	#125	—	13	2	no	—
340	#125	—	13	2	no	—
341	#125	—	13	2	no	—
342	#125	—	13	2	no	—
343	#125	—	13	1	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	1	no	—
351	#125	—	13	1	no	—
352	#125	—	13	1	no	—
353	#125	—	13	1	no	—
354	#125	C₂×D₁₃	1	1	yes	characteristic
355	#125	C₂×D₁₃	1	1	yes	characteristic
356	C₂²⋊Q₈	—	13	1	no	—
357	C₂²⋊Q₈	—	13	2	no	—
358	C₂²⋊Q₈	—	13	2	no	—
359	C₂²⋊Q₈	—	13	2	no	—
360	C₂²⋊Q₈	—	13	2	no	—
361	C₂²⋊Q₈	—	13	1	no	—
362	C₂²⋊Q₈	—	13	1	no	—
363	C₂²⋊Q₈	—	13	1	no	—
364	C₂²⋊Q₈	—	13	2	no	—
365	C₂²⋊Q₈	—	13	2	no	—
366	C₂²⋊Q₈	—	13	2	no	—
367	C₂²⋊Q₈	—	13	2	no	—
368	C₂²⋊Q₈	—	13	2	no	—
369	C₂²⋊Q₈	—	13	2	no	—
370	C₂²⋊Q₈	—	13	2	no	—
371	C₂²⋊Q₈	—	13	2	no	—
372	C₂²⋊Q₈	—	13	2	no	—
373	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
374	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
375	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
376	C₄×Q₈	—	13	2	no	—
377	C₄×Q₈	—	13	1	no	—
378	C₄×Q₈	—	13	1	no	—
379	C₄×Q₈	—	13	1	no	—
380	C₄×Q₈	—	13	2	no	—
381	C₄×Q₈	—	13	2	no	—
382	C₄×Q₈	—	13	2	no	—
383	C₄×Q₈	—	13	1	no	—
384	C₄×Q₈	—	13	1	no	—
385	C₄×Q₈	—	13	1	no	—
386	C₄×Q₈	—	13	1	no	—
387	C₄×Q₈	—	13	1	no	—
388	C₄×Q₈	—	13	1	no	—
389	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic
390	C₄×D₄	—	13	1	no	—
391	C₄×D₄	—	13	1	no	—
392	C₄×D₄	—	13	1	no	—
393	C₄×D₄	—	13	2	no	—
394	C₄×D₄	—	13	2	no	—
395	C₄×D₄	—	13	2	no	—
396	C₄×D₄	—	13	2	no	—
397	C₄×D₄	—	13	2	no	—
398	C₄×D₄	—	13	2	no	—
399	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
400	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
401	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
402	#117	—	13	1	no	—
403	#117	—	13	2	no	—
404	#117	—	13	2	no	—
405	#117	—	13	2	no	—
406	#117	—	13	1	no	—
407	#117	—	13	1	no	—
408	C₂×C₄⋊C₄	—	13	2	no	—
409	C₂×C₄⋊C₄	—	13	2	no	—
410	C₂×C₄⋊C₄	—	13	2	no	—
411	C₂×C₄⋊C₄	—	13	2	no	—
412	C₂×C₄⋊C₄	—	13	2	no	—
413	C₂×C₄⋊C₄	—	13	1	no	—
414	C₂×C₄⋊C₄	—	13	1	no	—
415	C₂×C₄⋊C₄	—	13	2	no	—
416	C₂×C₄⋊C₄	—	13	2	no	—
417	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
418	C₂×C₄²	—	13	2	no	—
419	C₂×C₄²	—	13	1	no	—
420	C₂×C₁₃	—	2	4	no	—
421	C₂×C₁₃	C₂³×Q₈	1	1	yes	characteristic
422	C₂×C₁₃	#585	1	1	yes	characteristic
423	C₂×C₁₃	#585	1	1	yes	characteristic
424	D₁₃	—	2	2	no	—
425	#41	—	13	8	no	—
426	C₂×Q₈	—	13	1	no	—
427	C₂×Q₈	—	13	2	no	—
428	C₂×Q₈	—	13	1	no	—
429	C₂×Q₈	—	13	2	no	—
430	C₂×Q₈	—	13	1	no	—
431	C₂×Q₈	—	13	1	no	—
432	C₂×Q₈	—	13	2	no	—
433	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
434	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
435	C₂×D₄	—	13	2	no	—
436	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
437	C₂²×C₄	—	13	2	no	—
438	C₂²×C₄	—	13	1	no	—
439	C₂²×C₄	—	13	2	no	—
440	C₂²×C₄	—	13	2	no	—
441	C₂²×C₄	—	13	2	no	—
442	C₂²×C₄	—	13	1	no	—
443	C₂²×C₄	—	13	1	no	—
444	C₂²×C₄	—	13	2	no	—
445	C₂²×C₄	—	13	2	no	—
446	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
447	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
448	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
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	1	no	—
456	C₄⋊C₄	—	13	2	no	—
457	C₄⋊C₄	—	13	2	no	—
458	C₄⋊C₄	—	13	1	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	1	no	—
464	C₄⋊C₄	—	13	1	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	2	no	—
474	C₄⋊C₄	—	13	1	no	—
475	C₄⋊C₄	—	13	1	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	2	no	—
483	C₄⋊C₄	—	13	1	no	—
484	C₄⋊C₄	—	13	2	no	—
485	C₄⋊C₄	—	13	1	no	—
486	C₄⋊C₄	—	13	2	no	—
487	C₄⋊C₄	—	13	1	no	—
488	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
489	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
491	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
492	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
493	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
494	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
495	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
498	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₂²⋊C₄	—	13	2	no	—
500	C₂²⋊C₄	—	13	2	no	—
501	C₂²⋊C₄	—	13	2	no	—
502	C₂²⋊C₄	—	13	1	no	—
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	C₂²×D₁₃	1	2	yes	—
508	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
509	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
510	C₄²	—	13	1	no	—
511	C₄²	—	13	2	no	—
512	C₄²	—	13	1	no	—
513	C₄²	—	13	2	no	—
514	C₄²	—	13	2	no	—
515	C₄²	—	13	1	no	—
516	C₄²	—	13	2	no	—
517	C₄²	—	13	2	no	—
518	C₄²	—	13	2	no	—
519	C₄²	—	13	2	no	—
520	C₄²	—	13	1	no	—
521	C₄²	—	13	1	no	—
522	C₄²	C₂²×D₁₃	1	1	yes	characteristic
523	C₄²	C₂²×D₁₃	1	1	yes	characteristic
524	C₄²	C₂²×D₁₃	1	1	yes	characteristic
525	C₁₃	#3504	1	1	yes	characteristic, complemented, Sylow
526	C₂³	—	13	1	no	—
527	C₂³	C₂³×D₁₃	1	2	yes	—
528	Q₈	—	4	1	no	—
529	Q₈	—	4	2	no	—
530	Q₈	—	13	4	no	—
531	Q₈	—	52	2	no	—
532	Q₈	—	52	1	no	—
533	Q₈	—	52	2	no	—
534	Q₈	—	52	1	no	—
535	Q₈	—	52	2	no	—
536	Q₈	—	52	1	no	—
537	D₄	—	13	8	no	—
538	D₄	Q₈×D₁₃	1	4	yes	—
539	C₂×C₄	—	4	2	no	—
540	C₂×C₄	—	4	2	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	13	8	no	—
543	C₂×C₄	—	13	2	no	—
544	C₂×C₄	—	13	1	no	—
545	C₂×C₄	—	13	4	no	—
546	C₂×C₄	—	13	1	no	—
547	C₂×C₄	—	13	1	no	—
548	C₂×C₄	—	13	1	no	—
549	C₂×C₄	—	13	2	no	—
550	C₂×C₄	—	13	1	no	—
551	C₂×C₄	—	13	2	no	—
552	C₂×C₄	—	13	1	no	—
553	C₂×C₄	—	13	2	no	—
554	C₂×C₄	—	13	1	no	—
555	C₂×C₄	—	52	2	no	—
556	C₂×C₄	—	52	1	no	—
557	C₂×C₄	—	52	1	no	—
558	C₂×C₄	—	52	2	no	—
559	C₂×C₄	—	52	2	no	—
560	C₂×C₄	—	52	2	no	—
561	C₂×C₄	—	52	2	no	—
562	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
563	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
564	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
565	C₂×C₄	C₂³×D₁₃	1	2	yes	—
566	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
567	C₂×C₄	C₂³×D₁₃	1	2	yes	—
568	C₂×C₄	C₂³×D₁₃	1	2	yes	—
569	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
570	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
571	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
572	C₂²	—	2	2	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	13	2	no	—
575	C₂²	—	26	1	no	—
576	C₂²	—	26	1	no	—
577	C₂²	C₂×Q₈×D₁₃	1	4	yes	—
578	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	2	1	no	—
582	C₄	—	2	1	no	—
583	C₄	—	2	1	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	2	no	—
587	C₄	—	2	1	no	—
588	C₄	—	13	2	no	—
589	C₄	—	13	4	no	—
590	C₄	—	26	1	no	—
591	C₄	—	26	2	no	—
592	C₄	—	26	1	no	—
593	C₄	—	26	2	no	—
594	C₄	—	26	1	no	—
595	C₄	—	26	2	no	—
596	C₄	—	26	1	no	—
597	C₄	—	26	1	no	—
598	C₄	—	26	1	no	—
599	C₄	C₂×Q₈×D₁₃	1	2	yes	—
600	C₂	—	2	4	no	—
601	C₂	—	26	2	no	—
602	C₂	C₂²×Q₈×D₁₃	1	1	yes	characteristic
603	C₂	#11719648	1	1	yes	characteristic
604	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
prime radical	C₂×#6129	C₂²
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3504
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. #11719434	C₂	semidirect
3. #11719426	C₂	semidirect
4. #11719394	C₂	semidirect
5. D₁₃×#125	C₂	semidirect
6. #11719390	C₂	semidirect
7. #11719390	C₂	semidirect
8. #11719341	C₂	semidirect
9. #11719341	C₂	semidirect
10. #11719340	C₂	semidirect
11. #11719328	C₂	semidirect
12. #11719328	C₂	semidirect
13. #11719327	C₂	semidirect
14. #11719283	C₂	semidirect
15. #11719272	C₂	semidirect
18. #11719248	C₂	semidirect
19. #11719244	C₂	semidirect
20. #11719244	C₂	semidirect
22. #11719216	C₂	semidirect
23. C₂×#88143	C₂	semidirect
134. #6129	Q₈	semidirect
281. #554	D₁₃	semidirect
525. C₁₃	#3504	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
#11719434	2
#11719426	2
#11719394	2
D₁₃×#125	2
#11719390	2
#11719341	2
#11719340	2
#11719328	2
#11719327	2
#11719283	2
#11719272	2
#11719251	2
#11719248	2
#11719244	2
C₄×#6129	2
#11719216	2
C₂×#88143	2
#3504	13