Subgroups — #13128883

Order 1664.

1124 conjugacy classes of subgroups.

The subgroup lattice has 660 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	#11719435	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719432	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719413	C₂	1	2	yes	maximal, complemented
5	#11719410	C₂	1	2	yes	maximal, complemented
6	#11719384	C₂	1	2	yes	maximal, complemented
7	#11719382	C₂	1	2	yes	maximal, complemented
8	#11719381	C₂	1	1	yes	maximal, characteristic, complemented
9	#11719376	C₂	1	1	yes	maximal, characteristic, complemented
10	#11719365	C₂	1	2	yes	maximal, complemented
11	#11719361	C₂	1	2	yes	maximal, complemented
12	#11719343	C₂	1	2	yes	maximal, complemented
13	#11719340	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
15	D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
16	#11719317	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719316	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719279	C₂	1	1	yes	maximal, characteristic, complemented
20	#11719266	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719233	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719228	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#6131	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₁₃	C₂²	1	2	yes	complemented
26	C₂×#6129	C₂²	1	2	yes	complemented
27	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
30	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
31	C₁₃×#126	C₂²	1	2	yes	complemented
32	C₁₃×#124	C₂²	1	1	yes	characteristic
33	C₁₃×#124	C₂²	1	2	yes	complemented
34	C₁₃×#123	C₂²	1	2	yes	complemented
35	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
36	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×#121	C₂²	1	1	yes	characteristic
38	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
40	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
41	#88200	C₂²	1	2	yes	—
42	#88200	C₂²	1	1	yes	characteristic
43	#88200	C₂²	1	2	yes	complemented
44	#88200	C₂²	1	2	yes	complemented
45	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
46	#88198	C₂²	1	1	yes	characteristic, complemented
47	#88192	C₂²	1	1	yes	characteristic
48	#88192	C₂²	1	2	yes	—
49	#88191	C₂²	1	2	yes	—
50	#88190	C₂²	1	1	yes	characteristic
51	#88189	C₂²	1	2	yes	complemented
52	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
53	#88183	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
58	#88178	C₂²	1	2	yes	complemented
59	#88152	C₂²	1	1	yes	characteristic, complemented
60	#88151	C₂²	1	1	yes	characteristic
61	#88151	C₂²	1	2	yes	—
62	#88151	C₂²	1	1	yes	characteristic, complemented
63	#88150	C₂²	1	1	yes	characteristic
64	#88150	C₂²	1	2	yes	—
65	#88150	C₂²	1	2	yes	complemented
66	#88150	C₂²	1	2	yes	complemented
67	#88148	C₂²	1	1	yes	characteristic
68	#88148	C₂²	1	2	yes	complemented
69	#88147	C₂²	1	1	yes	characteristic
70	#88147	C₂²	1	1	yes	characteristic
71	#88147	C₂²	1	2	yes	—
72	#88147	C₂²	1	2	yes	complemented
73	#88146	C₂²	1	2	yes	complemented
74	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
75	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
76	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
77	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
78	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
79	#88144	C₂²	1	2	yes	complemented
80	#88143	C₂²	1	1	yes	characteristic, complemented
81	#88143	C₂²	1	2	yes	complemented
82	#88143	C₂²	1	2	yes	complemented
83	#88142	C₂²	1	1	yes	characteristic, complemented
84	#88142	C₂²	1	1	yes	characteristic, complemented
85	#88139	C₂²	1	1	yes	characteristic, complemented
86	#88139	C₂²	1	2	yes	complemented
87	#88138	C₂²	1	1	yes	characteristic
88	#88138	C₂²	1	2	yes	—
89	#88138	C₂²	1	2	yes	complemented
90	#88137	C₂²	1	1	yes	characteristic
91	#88137	C₂²	1	2	yes	—
92	#88137	C₂²	1	2	yes	—
93	#88137	C₂²	1	2	yes	complemented
94	#88137	C₂²	1	2	yes	complemented
95	#88136	C₂²	1	2	yes	—
96	#88135	C₂²	1	2	yes	—
97	#88135	C₂²	1	2	yes	—
98	#88135	C₂²	1	2	yes	complemented
99	#88135	C₂²	1	2	yes	complemented
100	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
101	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
102	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
103	#88133	C₂²	1	1	yes	characteristic, complemented
104	#88133	C₂²	1	2	yes	complemented
105	#88133	C₂²	1	2	yes	complemented
106	#88133	C₂²	1	2	yes	complemented
107	#88132	C₂²	1	2	yes	complemented
108	#88132	C₂²	1	2	yes	complemented
109	#88132	C₂²	1	2	yes	complemented
110	#88131	C₂²	1	2	yes	complemented
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	C₄×D₅₂	C₂²	1	2	yes	complemented
115	#88126	C₂²	1	2	yes	—
116	#88126	C₂²	1	1	yes	characteristic, complemented
117	#88126	C₂²	1	2	yes	complemented
118	C₄²×D₁₃	C₂²	1	1	yes	characteristic
119	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
120	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
121	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	2	yes	—
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	1	yes	characteristic
131	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
133	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
134	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
135	C₂²×Dic₁₃	C₂³	1	2	yes	—
136	C₂²×Dic₁₃	C₂³	1	2	yes	—
137	#6131	—	2	4	no	—
138	Q₈×D₁₃	—	4	4	no	—
139	#6129	—	4	4	no	—
140	D₄×D₁₃	—	2	4	no	—
141	#6127	—	2	4	no	—
142	C₂×D₅₂	C₂³	1	1	yes	characteristic
143	C₂×D₅₂	C₂³	1	2	yes	—
144	C₂×D₅₂	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₁₃	—	4	4	no	—
146	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
147	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
148	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₁₃	C₂³	1	2	yes	—
151	C₂×C₄×D₁₃	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃	C₂³	1	2	yes	—
153	C₂×C₄×D₁₃	C₂³	1	2	yes	—
154	C₂×C₄×D₁₃	C₂³	1	2	yes	—
155	C₂×C₄×D₁₃	C₂³	1	2	yes	—
156	C₂×C₄×D₁₃	C₂³	1	2	yes	—
157	C₂×C₄×D₁₃	C₂³	1	2	yes	—
158	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
159	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
160	C₂×Dic₂₆	C₂³	1	2	yes	—
161	C₂×Dic₂₆	C₂³	1	2	yes	—
162	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
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	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
169	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
171	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
173	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
175	C₁₃×C₂²⋊C₄	C₂³	1	1	yes	characteristic
176	C₄²×C₁₃	C₂³	1	1	yes	characteristic
177	C₄²×C₁₃	C₂³	1	1	yes	characteristic
178	C₄²×C₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
182	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	#6103	C₂³	1	2	yes	—
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	2	yes	—
188	#6103	C₂³	1	1	yes	characteristic
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	1	yes	characteristic
191	#6103	C₂³	1	1	yes	characteristic
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	1	yes	characteristic
194	#6103	C₂³	1	1	yes	characteristic
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
200	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
203	C₄⋊Dic₁₃	C₂³	1	2	yes	—
204	C₄⋊Dic₁₃	C₂³	1	2	yes	—
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	#6101	C₂³	1	1	yes	characteristic
207	#6101	C₂³	1	2	yes	—
208	#6101	C₂³	1	2	yes	—
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	1	yes	characteristic
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	2	yes	—
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	1	yes	characteristic
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	1	yes	characteristic
217	#6101	C₂³	1	1	yes	characteristic
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	2	yes	—
220	#6101	C₂³	1	1	yes	characteristic
221	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
224	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	2	yes	—
228	#3520	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	2	yes	—
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂²×D₁₃	—	2	4	no	—
232	C₂²×D₁₃	—	2	4	no	—
233	C₂²×D₁₃	—	4	2	no	—
234	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
235	C₂²×D₁₃	C₂⁴	1	2	yes	—
236	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
237	Q₈×C₁₃	—	2	2	no	—
238	Q₈×C₁₃	—	4	2	no	—
239	D₄×C₁₃	—	2	2	no	—
240	D₄×C₁₃	—	4	2	no	—
241	C₂×C₄×C₁₃	—	2	2	no	—
242	C₂×C₄×C₁₃	—	4	2	no	—
243	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
244	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
252	C₂²⋊D₁₃	—	2	4	no	—
253	C₂²⋊D₁₃	—	2	4	no	—
254	C₂²⋊D₁₃	—	2	2	no	—
255	C₂²⋊D₁₃	—	2	2	no	—
256	C₂²⋊D₁₃	—	4	2	no	—
257	C₂×Dic₁₃	—	2	4	no	—
258	C₂×Dic₁₃	—	4	2	no	—
259	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
260	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
261	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₁₃	C₂⁴	1	2	yes	—
263	C₂×Dic₁₃	C₂⁴	1	2	yes	—
264	C₂×Dic₁₃	C₂⁴	1	2	yes	—
265	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	D₅₂	—	2	4	no	—
269	D₅₂	—	2	2	no	—
270	D₅₂	#41	1	4	yes	complemented
271	C₄×D₁₃	—	2	4	no	—
272	C₄×D₁₃	—	2	4	no	—
273	C₄×D₁₃	—	2	2	no	—
274	C₄×D₁₃	—	2	2	no	—
275	C₄×D₁₃	—	2	2	no	—
276	C₄×D₁₃	—	2	2	no	—
277	C₄×D₁₃	—	2	4	no	—
278	C₄×D₁₃	—	4	2	no	—
279	C₄×D₁₃	—	4	2	no	—
280	C₄×D₁₃	—	4	2	no	—
281	C₄×D₁₃	—	4	2	no	—
282	C₄×D₁₃	—	4	2	no	—
283	Dic₂₆	—	2	2	no	—
284	Dic₂₆	—	2	4	no	—
285	Dic₂₆	—	2	2	no	—
286	Dic₂₆	—	4	2	no	—
287	#556	—	13	1	no	—
288	#554	—	13	1	no	—
289	#554	—	13	1	no	—
290	#552	—	13	2	no	—
291	#551	—	13	2	no	—
292	#551	—	13	2	no	—
293	D₄×Q₈	—	13	1	no	—
294	#548	—	13	2	no	—
295	#547	—	13	1	no	—
296	#547	—	13	1	no	—
297	#546	—	13	1	no	—
298	#546	—	13	1	no	—
299	#542	—	13	1	no	—
300	#542	D₁₃	1	1	yes	characteristic, complemented
301	#539	—	13	2	no	—
302	#539	—	13	2	no	—
303	#533	—	13	1	no	—
304	#529	—	13	1	no	—
305	#525	—	13	2	no	—
306	C₂×C₂²⋊Q₈	—	13	2	no	—
307	#520	—	13	1	no	—
308	#520	—	13	1	no	—
309	C₂×C₄×D₄	—	13	1	no	—
310	C₂²×C₁₃	—	2	1	no	—
311	C₂²×C₁₃	—	2	2	no	—
312	C₂²×C₁₃	—	2	2	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	2	no	—
316	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
317	C₂×D₁₃	—	2	1	no	—
318	C₂×D₁₃	—	2	2	no	—
319	C₂×D₁₃	—	2	1	no	—
320	C₂×D₁₃	—	2	2	no	—
321	C₂×D₁₃	—	2	1	no	—
322	C₂×D₁₃	—	2	1	no	—
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	4	8	no	—
325	C₂×D₁₃	C₂×#41	1	4	yes	—
326	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
327	C₄×C₁₃	—	2	1	no	—
328	C₄×C₁₃	—	2	2	no	—
329	C₄×C₁₃	—	2	2	no	—
330	C₄×C₁₃	—	2	1	no	—
331	C₄×C₁₃	—	2	2	no	—
332	C₄×C₁₃	—	2	1	no	—
333	C₄×C₁₃	—	2	1	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	C₂×#41	1	2	yes	—
336	Dic₁₃	—	2	2	no	—
337	Dic₁₃	—	2	1	no	—
338	Dic₁₃	—	2	1	no	—
339	Dic₁₃	—	2	1	no	—
340	Dic₁₃	—	2	2	no	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
345	C₂×#41	—	13	1	no	—
346	C₂×#41	—	13	2	no	—
347	C₂×#41	—	13	1	no	—
348	C₂²×Q₈	—	13	2	no	—
349	C₂²×D₄	—	13	1	no	—
350	C₂³×C₄	—	13	2	no	—
351	C₄⋊Q₈	—	13	1	no	—
352	C₄⋊Q₈	—	13	1	no	—
353	C₄⋊Q₈	—	13	1	no	—
354	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
355	#126	—	13	1	no	—
356	#126	—	13	1	no	—
357	#126	—	13	2	no	—
358	#126	—	13	2	no	—
359	#126	—	13	2	no	—
360	#126	C₂×D₁₃	1	2	yes	complemented
361	#125	—	13	1	no	—
362	#125	—	13	2	no	—
363	#125	—	13	2	no	—
364	#125	—	13	2	no	—
365	#124	—	13	1	no	—
366	#124	—	13	1	no	—
367	#124	—	13	2	no	—
368	#124	C₂×D₁₃	1	1	yes	characteristic
369	#124	C₂×D₁₃	1	2	yes	complemented
370	#123	—	13	2	no	—
371	#123	—	13	2	no	—
372	#123	—	13	1	no	—
373	#123	—	13	2	no	—
374	#123	—	13	1	no	—
375	#123	—	13	2	no	—
376	#123	—	13	2	no	—
377	#123	—	13	2	no	—
378	#123	—	13	2	no	—
379	#123	C₂×D₁₃	1	2	yes	complemented
380	C₂²⋊Q₈	—	13	2	no	—
381	C₂²⋊Q₈	—	13	1	no	—
382	C₂²⋊Q₈	—	13	2	no	—
383	C₂²⋊Q₈	—	13	2	no	—
384	C₂²⋊Q₈	—	13	2	no	—
385	C₂²⋊Q₈	—	13	1	no	—
386	C₂²⋊Q₈	—	13	2	no	—
387	C₂²⋊Q₈	—	13	2	no	—
388	C₂²⋊Q₈	—	13	2	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	2	no	—
391	C₂²⋊Q₈	—	13	1	no	—
392	C₂²⋊Q₈	—	13	2	no	—
393	C₂²⋊Q₈	—	13	2	no	—
394	C₂²⋊Q₈	—	13	2	no	—
395	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
396	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
397	#121	—	13	2	no	—
398	#121	—	13	1	no	—
399	#121	—	13	1	no	—
400	#121	—	13	2	no	—
401	#121	—	13	2	no	—
402	#121	C₂×D₁₃	1	1	yes	characteristic
403	#120	—	13	2	no	—
404	#120	—	13	2	no	—
405	C₄×Q₈	—	13	1	no	—
406	C₄×Q₈	—	13	1	no	—
407	C₄×Q₈	—	13	1	no	—
408	C₄×Q₈	—	13	1	no	—
409	C₄×Q₈	—	13	2	no	—
410	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
411	C₄×D₄	—	13	1	no	—
412	C₄×D₄	—	13	2	no	—
413	C₄×D₄	—	13	1	no	—
414	C₄×D₄	—	13	1	no	—
415	C₄×D₄	—	13	1	no	—
416	C₄×D₄	—	13	2	no	—
417	C₄×D₄	—	13	1	no	—
418	C₄×D₄	—	13	2	no	—
419	C₄×D₄	—	13	2	no	—
420	C₄×D₄	—	13	2	no	—
421	C₄×D₄	—	13	2	no	—
422	C₄×D₄	—	13	2	no	—
423	C₄×D₄	—	13	1	no	—
424	C₄×D₄	—	13	1	no	—
425	C₄×D₄	—	13	2	no	—
426	C₄×D₄	—	13	1	no	—
427	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
428	#117	—	13	2	no	—
429	#117	—	13	2	no	—
430	#117	—	13	1	no	—
431	#117	—	13	2	no	—
432	#117	—	13	2	no	—
433	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
434	C₂×C₄⋊C₄	—	13	1	no	—
435	C₂×C₄⋊C₄	—	13	1	no	—
436	C₂×C₄⋊C₄	—	13	2	no	—
437	C₂×C₄⋊C₄	—	13	2	no	—
438	C₂×C₄⋊C₄	—	13	1	no	—
439	C₂×C₄⋊C₄	—	13	2	no	—
440	C₂×C₂²⋊C₄	—	13	2	no	—
441	C₂×C₂²⋊C₄	—	13	2	no	—
442	C₂×C₂²⋊C₄	—	13	2	no	—
443	C₂×C₄²	—	13	1	no	—
444	C₂×C₁₃	—	4	2	no	—
445	C₂×C₁₃	—	4	1	no	—
446	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
447	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
449	D₁₃	—	2	2	no	—
450	D₁₃	—	2	4	no	—
451	D₁₃	—	4	1	no	—
452	C₂⁴	—	13	2	no	—
453	#41	—	26	4	no	—
454	#41	—	26	4	no	—
455	#41	—	52	4	no	—
456	C₂×Q₈	—	13	1	no	—
457	C₂×Q₈	—	13	1	no	—
458	C₂×Q₈	—	13	2	no	—
459	C₂×Q₈	—	13	2	no	—
460	C₂×Q₈	—	52	4	no	—
461	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
462	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
463	C₂×D₄	—	13	1	no	—
464	C₂×D₄	—	13	2	no	—
465	C₂×D₄	—	13	2	no	—
466	C₂×D₄	—	13	1	no	—
467	C₂×D₄	—	13	2	no	—
468	C₂×D₄	—	13	1	no	—
469	C₂×D₄	—	13	1	no	—
470	C₂×D₄	—	13	2	no	—
471	C₂×D₄	—	26	4	no	—
472	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
473	C₂×D₄	C₂²×D₁₃	1	2	yes	—
474	C₂²×C₄	—	13	2	no	—
475	C₂²×C₄	—	13	2	no	—
476	C₂²×C₄	—	13	1	no	—
477	C₂²×C₄	—	13	1	no	—
478	C₂²×C₄	—	13	1	no	—
479	C₂²×C₄	—	13	2	no	—
480	C₂²×C₄	—	13	2	no	—
481	C₂²×C₄	—	13	1	no	—
482	C₂²×C₄	—	13	2	no	—
483	C₂²×C₄	—	13	2	no	—
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	13	2	no	—
486	C₂²×C₄	—	13	2	no	—
487	C₂²×C₄	—	13	2	no	—
488	C₂²×C₄	—	52	4	no	—
489	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
490	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
491	C₄⋊C₄	—	13	1	no	—
492	C₄⋊C₄	—	13	1	no	—
493	C₄⋊C₄	—	13	2	no	—
494	C₄⋊C₄	—	13	2	no	—
495	C₄⋊C₄	—	13	1	no	—
496	C₄⋊C₄	—	13	2	no	—
497	C₄⋊C₄	—	13	2	no	—
498	C₄⋊C₄	—	13	1	no	—
499	C₄⋊C₄	—	13	2	no	—
500	C₄⋊C₄	—	13	2	no	—
501	C₄⋊C₄	—	13	2	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	1	no	—
504	C₄⋊C₄	—	13	1	no	—
505	C₄⋊C₄	—	13	2	no	—
506	C₄⋊C₄	—	13	2	no	—
507	C₄⋊C₄	—	13	2	no	—
508	C₄⋊C₄	—	13	1	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	2	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
515	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
516	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
517	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
518	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
519	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
520	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
521	C₂²⋊C₄	—	13	2	no	—
522	C₂²⋊C₄	—	13	2	no	—
523	C₂²⋊C₄	—	13	2	no	—
524	C₂²⋊C₄	—	13	2	no	—
525	C₂²⋊C₄	—	13	1	no	—
526	C₂²⋊C₄	—	13	1	no	—
527	C₂²⋊C₄	—	13	1	no	—
528	C₂²⋊C₄	—	13	1	no	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	2	no	—
531	C₂²⋊C₄	—	13	2	no	—
532	C₂²⋊C₄	—	13	2	no	—
533	C₂²⋊C₄	—	13	2	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	—	13	1	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	1	no	—
540	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
541	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
542	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
543	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
544	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
545	C₂²⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
546	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
547	C₄²	—	13	1	no	—
548	C₄²	—	13	1	no	—
549	C₄²	—	13	1	no	—
550	C₄²	—	13	2	no	—
551	C₄²	—	13	2	no	—
552	C₄²	—	13	2	no	—
553	C₄²	—	13	1	no	—
554	C₄²	C₂²×D₁₃	1	1	yes	characteristic
555	C₄²	C₂²×D₁₃	1	2	yes	—
556	C₄²	C₂²×D₁₃	1	1	yes	characteristic
557	C₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
558	C₂³	—	13	1	no	—
559	C₂³	—	13	2	no	—
560	C₂³	—	13	1	no	—
561	C₂³	—	26	4	no	—
562	C₂³	—	26	4	no	—
563	C₂³	—	52	2	no	—
564	C₂³	C₂³×D₁₃	1	2	yes	—
565	C₂³	C₂³×D₁₃	1	1	yes	characteristic
566	Q₈	—	2	2	no	—
567	Q₈	—	4	2	no	—
568	Q₈	—	26	2	no	—
569	Q₈	—	26	4	no	—
570	Q₈	—	26	2	no	—
571	Q₈	—	52	2	no	—
572	D₄	—	2	2	no	—
573	D₄	—	4	2	no	—
574	D₄	—	13	4	no	—
575	D₄	—	26	2	no	—
576	D₄	—	26	4	no	—
577	D₄	—	26	2	no	—
578	D₄	—	26	2	no	—
579	D₄	—	26	4	no	—
580	D₄	—	26	4	no	—
581	D₄	—	52	2	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	2	no	—
584	C₂×C₄	—	13	1	no	—
585	C₂×C₄	—	13	1	no	—
586	C₂×C₄	—	13	1	no	—
587	C₂×C₄	—	13	2	no	—
588	C₂×C₄	—	13	1	no	—
589	C₂×C₄	—	13	2	no	—
590	C₂×C₄	—	13	1	no	—
591	C₂×C₄	—	13	2	no	—
592	C₂×C₄	—	13	1	no	—
593	C₂×C₄	—	26	2	no	—
594	C₂×C₄	—	26	4	no	—
595	C₂×C₄	—	26	2	no	—
596	C₂×C₄	—	26	4	no	—
597	C₂×C₄	—	26	4	no	—
598	C₂×C₄	—	26	4	no	—
599	C₂×C₄	—	26	2	no	—
600	C₂×C₄	—	26	2	no	—
601	C₂×C₄	—	52	2	no	—
602	C₂×C₄	—	52	2	no	—
603	C₂×C₄	—	52	2	no	—
604	C₂×C₄	—	52	2	no	—
605	C₂×C₄	—	52	2	no	—
606	C₂×C₄	—	52	2	no	—
607	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
608	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
609	C₂×C₄	C₂³×D₁₃	1	2	yes	—
610	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
611	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
612	C₂×C₄	C₂³×D₁₃	1	2	yes	—
613	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
614	C₂×C₄	C₂³×D₁₃	1	2	yes	—
615	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
616	C₂²	—	2	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	1	no	—
620	C₂²	—	2	1	no	—
621	C₂²	—	2	2	no	—
622	C₂²	—	13	4	no	—
623	C₂²	—	13	2	no	—
624	C₂²	—	26	1	no	—
625	C₂²	—	26	2	no	—
626	C₂²	—	26	1	no	—
627	C₂²	—	26	2	no	—
628	C₂²	—	26	1	no	—
629	C₂²	—	26	1	no	—
630	C₂²	—	26	1	no	—
631	C₂²	—	52	8	no	—
632	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
633	C₄	—	2	1	no	—
634	C₄	—	2	2	no	—
635	C₄	—	2	1	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	1	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	1	no	—
641	C₄	—	13	2	no	—
642	C₄	—	26	1	no	—
643	C₄	—	26	1	no	—
644	C₄	—	26	2	no	—
645	C₄	—	26	2	no	—
646	C₄	—	26	2	no	—
647	C₄	—	26	1	no	—
648	C₄	—	26	1	no	—
649	C₄	—	26	1	no	—
650	C₄	#41×D₁₃	1	2	yes	—
651	C₂	—	4	2	no	—
652	C₂	—	4	1	no	—
653	C₂	—	26	2	no	—
654	C₂	—	26	4	no	—
655	C₂	—	52	1	no	—
656	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
657	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
658	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
hypercenter	#542	D₁₃
hypocenter	C₁₃	#3520
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. #11719435	C₂	semidirect
3. #11719432	C₂	semidirect
4. #11719413	C₂	semidirect
5. #11719410	C₂	semidirect
6. #11719384	C₂	semidirect
7. #11719382	C₂	semidirect
8. #11719381	C₂	semidirect
9. #11719376	C₂	semidirect
10. #11719365	C₂	semidirect
11. #11719361	C₂	semidirect
12. #11719343	C₂	semidirect
13. #11719340	C₂	semidirect
14. #11719336	C₂	semidirect
15. D₁₃×C₂²⋊Q₈	C₂	semidirect
16. #11719317	C₂	semidirect
17. #11719316	C₂	semidirect
18. #11719283	C₂	semidirect
19. #11719279	C₂	semidirect
20. #11719266	C₂	semidirect
21. C₄×D₄×D₁₃	C₂	semidirect
22. #11719233	C₂	semidirect
23. #11719228	C₂	semidirect
25. C₂×Q₈×D₁₃	C₂²	semidirect
26. C₂×#6129	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
31. C₁₃×#126	C₂²	semidirect
33. C₁₃×#124	C₂²	semidirect
34. C₁₃×#123	C₂²	semidirect
35. C₁₃×C₂²⋊Q₈	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₄×Q₈×C₁₃	C₂²	semidirect
40. C₁₃×#117	C₂²	semidirect
43. #88200	C₂²	semidirect
44. #88200	C₂²	semidirect
45. Q₈×Dic₁₃	C₂²	semidirect
46. #88198	C₂²	semidirect
51. #88189	C₂²	semidirect
53. #88183	C₂²	semidirect
56. C₄×C₂²⋊D₁₃	C₂²	semidirect
57. C₂×C₄⋊Dic₁₃	C₂²	semidirect
58. #88178	C₂²	semidirect
59. #88152	C₂²	semidirect
62. #88151	C₂²	semidirect
65. #88150	C₂²	semidirect
66. #88150	C₂²	semidirect
68. #88148	C₂²	semidirect
72. #88147	C₂²	semidirect
73. #88146	C₂²	semidirect
75. C₄⋊C₄×D₁₃	C₂²	semidirect
76. C₄⋊C₄×D₁₃	C₂²	semidirect
77. C₄⋊C₄×D₁₃	C₂²	semidirect
78. C₄⋊C₄×D₁₃	C₂²	semidirect
79. #88144	C₂²	semidirect
80. #88143	C₂²	semidirect
81. #88143	C₂²	semidirect
82. #88143	C₂²	semidirect
83. #88142	C₂²	semidirect
84. #88142	C₂²	semidirect
85. #88139	C₂²	semidirect
86. #88139	C₂²	semidirect
89. #88138	C₂²	semidirect
93. #88137	C₂²	semidirect
94. #88137	C₂²	semidirect
98. #88135	C₂²	semidirect
99. #88135	C₂²	semidirect
103. #88133	C₂²	semidirect
104. #88133	C₂²	semidirect
105. #88133	C₂²	semidirect
106. #88133	C₂²	semidirect
107. #88132	C₂²	semidirect
108. #88132	C₂²	semidirect
109. #88132	C₂²	semidirect
110. #88131	C₂²	semidirect
114. C₄×D₅₂	C₂²	semidirect
116. #88126	C₂²	semidirect
117. #88126	C₂²	semidirect
119. C₄×Dic₂₆	C₂²	semidirect
120. C₄×Dic₂₆	C₂²	semidirect
121. C₄×Dic₂₆	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
270. D₅₂	#41	semidirect
300. #542	D₁₃	semidirect
354. C₄⋊Q₈	C₂×D₁₃	semidirect
360. #126	C₂×D₁₃	semidirect
369. #124	C₂×D₁₃	semidirect
379. #123	C₂×D₁₃	semidirect
395. C₂²⋊Q₈	C₂×D₁₃	semidirect
396. C₂²⋊Q₈	C₂×D₁₃	semidirect
410. C₄×Q₈	C₂×D₁₃	semidirect
433. #117	C₂×D₁₃	semidirect
557. C₁₃	#3520	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
#11719435	2
#11719432	2
#11719413	2
#11719410	2
#11719384	2
#11719382	2
#11719381	2
#11719376	2
#11719365	2
#11719361	2
#11719343	2
#11719340	2
#11719336	2
D₁₃×C₂²⋊Q₈	2
#11719317	2
#11719316	2
#11719283	2
#11719279	2
#11719266	2
C₄×D₄×D₁₃	2
#11719233	2
#11719228	2
#3520	13