Subgroups — #13128586

Order 1664.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 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, complemented
2	#11719434	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719413	C₂	1	2	yes	maximal, complemented
5	#11719413	C₂	1	2	yes	maximal, complemented
6	#11719385	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719384	C₂	1	2	yes	maximal, complemented
8	#11719380	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719376	C₂	1	2	yes	maximal, complemented
10	#11719364	C₂	1	2	yes	maximal, complemented
11	#11719355	C₂	1	2	yes	maximal, complemented
12	#11719344	C₂	1	2	yes	maximal, complemented
13	#11719341	C₂	1	2	yes	maximal, complemented
14	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719311	C₂	1	1	yes	maximal, characteristic
17	#11719308	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719277	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719262	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719251	C₂	1	1	yes	maximal, characteristic, complemented
22	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719223	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
25	C₂×#6129	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
27	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
28	C₁₃×#126	C₂²	1	2	yes	complemented
29	C₁₃×#124	C₂²	1	2	yes	—
30	C₁₃×#124	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#123	C₂²	1	2	yes	—
32	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
33	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
34	C₁₃×#121	C₂²	1	1	yes	characteristic
35	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
36	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#117	C₂²	1	1	yes	characteristic
38	#88200	C₂²	1	2	yes	—
39	#88200	C₂²	1	2	yes	—
40	#88200	C₂²	1	1	yes	characteristic
41	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
42	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
43	#88198	C₂²	1	2	yes	complemented
44	#88198	C₂²	1	1	yes	characteristic, complemented
45	#88192	C₂²	1	1	yes	characteristic
46	#88191	C₂²	1	2	yes	—
47	#88190	C₂²	1	2	yes	—
48	#88190	C₂²	1	1	yes	characteristic, complemented
49	#88189	C₂²	1	2	yes	—
50	D₄×Dic₁₃	C₂²	1	2	yes	—
51	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
53	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
54	#88180	C₂²	1	1	yes	characteristic
55	#88180	C₂²	1	2	yes	complemented
56	#88178	C₂²	1	1	yes	characteristic
57	#88178	C₂²	1	1	yes	characteristic
58	C₂×#6101	C₂²	1	2	yes	complemented
59	#88151	C₂²	1	1	yes	characteristic
60	#88151	C₂²	1	1	yes	characteristic
61	#88150	C₂²	1	2	yes	—
62	#88150	C₂²	1	2	yes	—
63	#88150	C₂²	1	2	yes	—
64	#88146	C₂²	1	2	yes	—
65	#88146	C₂²	1	1	yes	characteristic
66	#88146	C₂²	1	1	yes	characteristic
67	#88146	C₂²	1	1	yes	characteristic
68	#88146	C₂²	1	2	yes	—
69	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
70	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
72	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
73	#88144	C₂²	1	2	yes	complemented
74	#88144	C₂²	1	1	yes	characteristic, complemented
75	#88144	C₂²	1	2	yes	complemented
76	#88143	C₂²	1	2	yes	complemented
77	#88143	C₂²	1	2	yes	complemented
78	#88143	C₂²	1	2	yes	complemented
79	#88143	C₂²	1	2	yes	complemented
80	#88143	C₂²	1	2	yes	complemented
81	#88142	C₂²	1	1	yes	characteristic, complemented
82	#88141	C₂²	1	1	yes	characteristic, complemented
83	#88141	C₂²	1	1	yes	characteristic, complemented
84	#88141	C₂²	1	2	yes	complemented
85	#88137	C₂²	1	2	yes	—
86	#88137	C₂²	1	2	yes	—
87	#88137	C₂²	1	2	yes	—
88	#88137	C₂²	1	2	yes	—
89	#88137	C₂²	1	2	yes	—
90	#88135	C₂²	1	2	yes	—
91	#88135	C₂²	1	2	yes	—
92	#88135	C₂²	1	2	yes	—
93	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
94	C₂²⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
95	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
96	#88133	C₂²	1	2	yes	—
97	#88133	C₂²	1	2	yes	—
98	#88133	C₂²	1	2	yes	—
99	#88133	C₂²	1	2	yes	—
100	#88133	C₂²	1	2	yes	complemented
101	#88133	C₂²	1	2	yes	complemented
102	#88133	C₂²	1	2	yes	complemented
103	#88132	C₂²	1	2	yes	—
104	#88132	C₂²	1	2	yes	complemented
105	#88132	C₂²	1	2	yes	complemented
106	#88132	C₂²	1	2	yes	complemented
107	#88131	C₂²	1	1	yes	characteristic
108	#88131	C₂²	1	1	yes	characteristic
109	#88131	C₂²	1	2	yes	complemented
110	#88131	C₂²	1	2	yes	complemented
111	#88126	C₂²	1	1	yes	characteristic
112	#88126	C₂²	1	1	yes	characteristic
113	#88126	C₂²	1	2	yes	—
114	#88126	C₂²	1	2	yes	—
115	C₄²×D₁₃	C₂²	1	1	yes	characteristic
116	C₄²×D₁₃	C₂²	1	1	yes	characteristic
117	#88124	C₂²	1	1	yes	characteristic, complemented
118	#88123	C₂²	1	1	yes	characteristic, complemented
119	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	2	yes	complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
125	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
126	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₁₃	C₂³	1	2	yes	—
128	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
133	C₂²×Dic₁₃	C₂³	1	2	yes	—
134	C₂²×Dic₁₃	C₂³	1	2	yes	—
135	Q₈×D₁₃	—	2	4	no	—
136	#6129	—	2	4	no	—
137	C₂×C₄×D₁₃	—	2	4	no	—
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	1	yes	characteristic
143	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
146	C₂×C₄×D₁₃	C₂³	1	2	yes	—
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
156	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
157	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
158	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
159	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
160	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
161	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
162	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
163	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
164	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
165	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
166	C₄²×C₁₃	C₂³	1	1	yes	characteristic
167	C₄²×C₁₃	C₂³	1	2	yes	—
168	C₄²×C₁₃	C₂³	1	1	yes	characteristic
169	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
172	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
173	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
174	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
175	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
176	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
177	#6103	C₂³	1	1	yes	characteristic
178	#6103	C₂³	1	2	yes	—
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	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
186	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₁₃	C₂³	1	2	yes	—
188	C₄⋊Dic₁₃	C₂³	1	2	yes	—
189	C₄⋊Dic₁₃	C₂³	1	2	yes	—
190	C₄⋊Dic₁₃	C₂³	1	2	yes	—
191	C₄⋊Dic₁₃	C₂³	1	2	yes	—
192	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
193	C₄⋊Dic₁₃	C₂³	1	2	yes	—
194	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
195	#6101	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
203	#6101	C₂³	1	1	yes	characteristic
204	#6101	C₂³	1	1	yes	characteristic
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	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	1	yes	characteristic
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	#3495	—	13	1	no	maximal, Sylow
226	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
227	C₂³×C₁₃	C₂⁴	1	2	yes	—
228	C₂²×D₁₃	—	2	2	no	—
229	C₂²×D₁₃	—	2	2	no	—
230	C₂²×D₁₃	—	4	1	no	—
231	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
233	Q₈×C₁₃	—	2	2	no	—
234	Q₈×C₁₃	—	4	2	no	—
235	D₄×C₁₃	—	2	2	no	—
236	D₄×C₁₃	—	4	2	no	—
237	C₂×C₄×C₁₃	—	2	2	no	—
238	C₂×C₄×C₁₃	—	4	2	no	—
239	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	2	yes	—
246	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₁₃	—	2	4	no	—
249	C₂²⋊D₁₃	—	2	4	no	—
250	C₂×Dic₁₃	—	2	2	no	—
251	C₂×Dic₁₃	—	2	4	no	—
252	C₂×Dic₁₃	—	4	2	no	—
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	2	yes	—
257	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₁₃	C₂⁴	1	2	yes	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	2	yes	—
261	C₂×Dic₁₃	C₂⁴	1	2	yes	—
262	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
263	C₄×D₁₃	—	2	2	no	—
264	C₄×D₁₃	—	2	4	no	—
265	C₄×D₁₃	—	2	2	no	—
266	C₄×D₁₃	—	2	2	no	—
267	C₄×D₁₃	—	2	2	no	—
268	C₄×D₁₃	—	2	2	no	—
269	C₄×D₁₃	—	4	1	no	—
270	C₄×D₁₃	—	4	2	no	—
271	C₄×D₁₃	—	4	1	no	—
272	C₄×D₁₃	#41	1	4	yes	—
273	Dic₂₆	—	2	2	no	—
274	Dic₂₆	—	2	2	no	—
275	Dic₂₆	—	2	4	no	—
276	Dic₂₆	—	4	2	no	—
277	#556	—	13	2	no	—
278	#554	—	13	2	no	—
279	#552	—	13	2	no	—
280	#552	—	13	2	no	—
281	#552	—	13	2	no	—
282	#552	—	13	2	no	—
283	#551	—	13	2	no	—
284	#551	—	13	2	no	—
285	#544	—	13	1	no	—
286	#542	—	13	1	no	—
287	#542	D₁₃	1	1	yes	characteristic, complemented
288	#541	—	13	1	no	—
289	#541	—	13	1	no	—
290	#536	—	13	1	no	—
291	#533	—	13	1	no	—
292	#533	—	13	1	no	—
293	#529	—	13	1	no	—
294	#529	—	13	1	no	—
295	#525	—	13	1	no	—
296	C₂×C₂²⋊Q₈	—	13	1	no	—
297	#520	—	13	1	no	—
298	#519	—	13	1	no	—
299	C₂×#117	—	13	1	no	—
300	C₂²×C₁₃	—	2	2	no	—
301	C₂²×C₁₃	—	2	1	no	—
302	C₂²×C₁₃	—	2	2	no	—
303	C₂²×C₁₃	—	2	1	no	—
304	C₂²×C₁₃	—	2	2	no	—
305	C₂²×C₁₃	—	2	1	no	—
306	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
307	C₂×D₁₃	—	2	1	no	—
308	C₂×D₁₃	—	2	1	no	—
309	C₂×D₁₃	—	2	1	no	—
310	C₂×D₁₃	—	2	1	no	—
311	C₂×D₁₃	—	4	4	no	—
312	C₂×D₁₃	C₂×#41	1	2	yes	—
313	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
314	C₄×C₁₃	—	2	2	no	—
315	C₄×C₁₃	—	2	1	no	—
316	C₄×C₁₃	—	2	1	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	C₂×#41	1	2	yes	—
323	Dic₁₃	—	2	2	no	—
324	Dic₁₃	—	2	2	no	—
325	Dic₁₃	—	2	1	no	—
326	Dic₁₃	—	2	1	no	—
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	C₂×#41	1	2	yes	—
333	C₂×#41	—	13	1	no	—
334	C₂²×Q₈	—	13	1	no	—
335	C₂³×C₄	—	13	1	no	—
336	C₄⋊Q₈	—	13	1	no	—
337	C₄⋊Q₈	—	13	2	no	—
338	C₄⋊Q₈	—	13	1	no	—
339	C₄⋊Q₈	—	13	1	no	—
340	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
341	#126	—	13	2	no	—
342	#126	—	13	2	no	—
343	#126	—	13	2	no	—
344	#126	—	13	2	no	—
345	#126	—	13	2	no	—
346	#126	—	13	2	no	—
347	#126	—	13	2	no	—
348	#126	C₂×D₁₃	1	2	yes	complemented
349	#125	—	13	1	no	—
350	#125	—	13	2	no	—
351	#125	—	13	2	no	—
352	#125	—	13	2	no	—
353	#125	—	13	2	no	—
354	#125	—	13	2	no	—
355	#125	—	13	2	no	—
356	#125	—	13	2	no	—
357	#125	—	13	1	no	—
358	#124	—	13	1	no	—
359	#124	—	13	2	no	—
360	#124	C₂×D₁₃	1	2	yes	—
361	#124	C₂×D₁₃	1	1	yes	characteristic, complemented
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	#123	C₂×D₁₃	1	2	yes	—
369	C₂²⋊Q₈	—	13	1	no	—
370	C₂²⋊Q₈	—	13	2	no	—
371	C₂²⋊Q₈	—	13	2	no	—
372	C₂²⋊Q₈	—	13	1	no	—
373	C₂²⋊Q₈	—	13	1	no	—
374	C₂²⋊Q₈	—	13	1	no	—
375	C₂²⋊Q₈	—	13	2	no	—
376	C₂²⋊Q₈	—	13	1	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	—	13	2	no	—
383	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
384	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
385	#121	—	13	1	no	—
386	#121	C₂×D₁₃	1	1	yes	characteristic
387	#120	—	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	2	no	—
392	C₄×Q₈	—	13	1	no	—
393	C₄×Q₈	—	13	1	no	—
394	C₄×Q₈	—	13	2	no	—
395	C₄×Q₈	—	13	1	no	—
396	C₄×Q₈	—	13	2	no	—
397	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
398	C₄×D₄	—	13	1	no	—
399	C₄×D₄	—	13	2	no	—
400	C₄×D₄	—	13	2	no	—
401	C₄×D₄	—	13	2	no	—
402	C₄×D₄	—	13	2	no	—
403	C₄×D₄	—	13	2	no	—
404	C₄×D₄	—	13	2	no	—
405	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
406	#117	—	13	1	no	—
407	#117	—	13	2	no	—
408	#117	—	13	1	no	—
409	#117	—	13	1	no	—
410	#117	—	13	1	no	—
411	#117	—	13	2	no	—
412	#117	—	13	2	no	—
413	#117	—	13	1	no	—
414	#117	—	13	1	no	—
415	#117	—	13	2	no	—
416	#117	—	13	2	no	—
417	#117	—	13	1	no	—
418	#117	—	13	1	no	—
419	#117	—	13	2	no	—
420	#117	—	13	2	no	—
421	#117	C₂×D₁₃	1	1	yes	characteristic
422	C₂×C₄⋊C₄	—	13	2	no	—
423	C₂×C₄⋊C₄	—	13	1	no	—
424	C₂×C₄⋊C₄	—	13	1	no	—
425	C₂×C₄⋊C₄	—	13	1	no	—
426	C₂×C₄⋊C₄	—	13	2	no	—
427	C₂×C₂²⋊C₄	—	13	1	no	—
428	C₂×C₂²⋊C₄	—	13	1	no	—
429	C₂×C₂²⋊C₄	—	13	2	no	—
430	C₂×C₄²	—	13	1	no	—
431	C₂×C₄²	—	13	1	no	—
432	C₂×C₁₃	—	4	1	no	—
433	C₂×C₁₃	—	4	2	no	—
434	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
435	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
436	C₂×C₁₃	#585	1	1	yes	characteristic
437	D₁₃	—	2	2	no	—
438	D₁₃	—	2	2	no	—
439	C₂⁴	—	13	1	no	—
440	#41	—	26	4	no	—
441	C₂×Q₈	—	13	2	no	—
442	C₂×Q₈	—	13	1	no	—
443	C₂×Q₈	—	13	1	no	—
444	C₂×Q₈	—	13	2	no	—
445	C₂×Q₈	—	26	4	no	—
446	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
447	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
448	C₂×D₄	—	13	2	no	—
449	C₂×D₄	—	13	2	no	—
450	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
451	C₂×D₄	C₂²×D₁₃	1	2	yes	—
452	C₂²×C₄	—	13	1	no	—
453	C₂²×C₄	—	13	2	no	—
454	C₂²×C₄	—	13	1	no	—
455	C₂²×C₄	—	13	2	no	—
456	C₂²×C₄	—	13	1	no	—
457	C₂²×C₄	—	13	1	no	—
458	C₂²×C₄	—	13	1	no	—
459	C₂²×C₄	—	13	2	no	—
460	C₂²×C₄	—	13	1	no	—
461	C₂²×C₄	—	13	1	no	—
462	C₂²×C₄	—	13	1	no	—
463	C₂²×C₄	—	13	1	no	—
464	C₂²×C₄	—	13	2	no	—
465	C₂²×C₄	—	26	4	no	—
466	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
468	C₄⋊C₄	—	13	1	no	—
469	C₄⋊C₄	—	13	2	no	—
470	C₄⋊C₄	—	13	1	no	—
471	C₄⋊C₄	—	13	1	no	—
472	C₄⋊C₄	—	13	1	no	—
473	C₄⋊C₄	—	13	1	no	—
474	C₄⋊C₄	—	13	1	no	—
475	C₄⋊C₄	—	13	2	no	—
476	C₄⋊C₄	—	13	2	no	—
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	2	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	—	13	2	no	—
490	C₄⋊C₄	—	13	2	no	—
491	C₄⋊C₄	—	13	2	no	—
492	C₄⋊C₄	—	13	2	no	—
493	C₄⋊C₄	—	13	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	2	no	—
496	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
498	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
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	C₂²⋊C₄	—	13	1	no	—
504	C₂²⋊C₄	—	13	1	no	—
505	C₂²⋊C₄	—	13	2	no	—
506	C₂²⋊C₄	—	13	2	no	—
507	C₂²⋊C₄	—	13	2	no	—
508	C₂²⋊C₄	—	13	2	no	—
509	C₂²⋊C₄	—	13	2	no	—
510	C₂²⋊C₄	—	13	2	no	—
511	C₂²⋊C₄	—	13	1	no	—
512	C₂²⋊C₄	—	13	1	no	—
513	C₂²⋊C₄	—	13	1	no	—
514	C₂²⋊C₄	—	13	1	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	C₂²×D₁₃	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
521	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
523	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₄²	—	13	1	no	—
527	C₄²	—	13	1	no	—
528	C₄²	—	13	1	no	—
529	C₄²	—	13	1	no	—
530	C₄²	—	13	1	no	—
531	C₄²	—	13	1	no	—
532	C₄²	—	13	2	no	—
533	C₄²	—	13	2	no	—
534	C₄²	—	13	2	no	—
535	C₄²	—	13	2	no	—
536	C₄²	—	13	2	no	—
537	C₄²	—	13	2	no	—
538	C₄²	C₂²×D₁₃	1	1	yes	characteristic
539	C₄²	C₂²×D₁₃	1	1	yes	characteristic
540	C₄²	C₂²×D₁₃	1	2	yes	—
541	C₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
542	C₂³	—	13	1	no	—
543	C₂³	—	13	1	no	—
544	C₂³	—	26	2	no	—
545	C₂³	—	26	2	no	—
546	C₂³	—	52	1	no	—
547	C₂³	C₂³×D₁₃	1	1	yes	characteristic
548	C₂³	C₂³×D₁₃	1	2	yes	—
549	Q₈	—	2	2	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	26	4	no	—
552	Q₈	—	26	2	no	—
553	Q₈	—	26	2	no	—
554	Q₈	—	52	2	no	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	D₄	—	26	4	no	—
558	D₄	—	26	4	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	13	1	no	—
562	C₂×C₄	—	13	4	no	—
563	C₂×C₄	—	13	1	no	—
564	C₂×C₄	—	13	1	no	—
565	C₂×C₄	—	13	1	no	—
566	C₂×C₄	—	13	2	no	—
567	C₂×C₄	—	13	1	no	—
568	C₂×C₄	—	13	2	no	—
569	C₂×C₄	—	13	1	no	—
570	C₂×C₄	—	13	2	no	—
571	C₂×C₄	—	13	2	no	—
572	C₂×C₄	—	26	2	no	—
573	C₂×C₄	—	26	2	no	—
574	C₂×C₄	—	26	2	no	—
575	C₂×C₄	—	26	2	no	—
576	C₂×C₄	—	26	4	no	—
577	C₂×C₄	—	26	2	no	—
578	C₂×C₄	—	26	4	no	—
579	C₂×C₄	—	26	2	no	—
580	C₂×C₄	—	52	1	no	—
581	C₂×C₄	—	52	2	no	—
582	C₂×C₄	—	52	1	no	—
583	C₂×C₄	—	52	2	no	—
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	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
589	C₂×C₄	C₂³×D₁₃	1	2	yes	—
590	C₂×C₄	C₂³×D₁₃	1	2	yes	—
591	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	2	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	1	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	2	1	no	—
599	C₂²	—	13	2	no	—
600	C₂²	—	13	2	no	—
601	C₂²	—	26	1	no	—
602	C₂²	—	26	1	no	—
603	C₂²	—	26	1	no	—
604	C₂²	—	26	1	no	—
605	C₂²	—	52	4	no	—
606	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	2	no	—
611	C₄	—	2	1	no	—
612	C₄	—	2	2	no	—
613	C₄	—	2	1	no	—
614	C₄	—	2	1	no	—
615	C₄	—	13	2	no	—
616	C₄	—	26	1	no	—
617	C₄	—	26	2	no	—
618	C₄	—	26	2	no	—
619	C₄	—	26	1	no	—
620	C₄	—	26	2	no	—
621	C₄	—	26	1	no	—
622	C₄	—	26	1	no	—
623	C₄	—	26	1	no	—
624	C₄	—	26	2	no	—
625	C₄	#41×D₁₃	1	2	yes	—
626	C₂	—	4	1	no	—
627	C₂	—	4	2	no	—
628	C₂	—	26	2	no	—
629	C₂	—	26	2	no	—
630	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
631	C₂	#11719650	1	1	yes	characteristic
632	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	#11719311	C₂
hypercenter	#542	D₁₃
hypocenter	C₁₃	#3495
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
1. C₁₃×#542	C₂	semidirect
2. #11719434	C₂	semidirect
3. #11719433	C₂	semidirect
4. #11719413	C₂	semidirect
5. #11719413	C₂	semidirect
6. #11719385	C₂	semidirect
7. #11719384	C₂	semidirect
8. #11719380	C₂	semidirect
9. #11719376	C₂	semidirect
10. #11719364	C₂	semidirect
11. #11719355	C₂	semidirect
12. #11719344	C₂	semidirect
13. #11719341	C₂	semidirect
14. D₁₃×C₂²⋊Q₈	C₂	semidirect
15. #11719330	C₂	semidirect
17. #11719308	C₂	semidirect
18. #11719283	C₂	semidirect
19. #11719277	C₂	semidirect
20. #11719262	C₂	semidirect
21. #11719251	C₂	semidirect
22. D₁₃×#117	C₂	semidirect
23. #11719223	C₂	semidirect
27. C₁₃×C₄⋊Q₈	C₂²	semidirect
28. C₁₃×#126	C₂²	semidirect
30. C₁₃×#124	C₂²	semidirect
33. C₁₃×C₂²⋊Q₈	C₂²	semidirect
35. C₄×Q₈×C₁₃	C₂²	semidirect
36. C₄×D₄×C₁₃	C₂²	semidirect
41. Q₈×Dic₁₃	C₂²	semidirect
42. Q₈×Dic₁₃	C₂²	semidirect
43. #88198	C₂²	semidirect
44. #88198	C₂²	semidirect
48. #88190	C₂²	semidirect
51. D₄×Dic₁₃	C₂²	semidirect
55. #88180	C₂²	semidirect
58. C₂×#6101	C₂²	semidirect
73. #88144	C₂²	semidirect
74. #88144	C₂²	semidirect
75. #88144	C₂²	semidirect
76. #88143	C₂²	semidirect
77. #88143	C₂²	semidirect
78. #88143	C₂²	semidirect
79. #88143	C₂²	semidirect
80. #88143	C₂²	semidirect
81. #88142	C₂²	semidirect
82. #88141	C₂²	semidirect
83. #88141	C₂²	semidirect
84. #88141	C₂²	semidirect
100. #88133	C₂²	semidirect
101. #88133	C₂²	semidirect
102. #88133	C₂²	semidirect
104. #88132	C₂²	semidirect
105. #88132	C₂²	semidirect
106. #88132	C₂²	semidirect
109. #88131	C₂²	semidirect
110. #88131	C₂²	semidirect
117. #88124	C₂²	semidirect
118. #88123	C₂²	semidirect
119. C₄×Dic₂₆	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
287. #542	D₁₃	semidirect
340. C₄⋊Q₈	C₂×D₁₃	semidirect
348. #126	C₂×D₁₃	semidirect
361. #124	C₂×D₁₃	semidirect
384. C₂²⋊Q₈	C₂×D₁₃	semidirect
397. C₄×Q₈	C₂×D₁₃	semidirect
405. C₄×D₄	C₂×D₁₃	semidirect
541. C₁₃	#3495	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
#11719434	2
#11719433	2
#11719413	2
#11719385	2
#11719384	2
#11719380	2
#11719376	2
#11719364	2
#11719355	2
#11719344	2
#11719341	2
D₁₃×C₂²⋊Q₈	2
#11719330	2
#11719311	2
#11719308	2
#11719283	2
#11719277	2
#11719262	2
#11719251	2
D₁₃×#117	2
#11719223	2
#3495	13