Subgroups — #13129131

Order 1664.

1032 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719538	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719522	C₂	1	1	yes	maximal, characteristic, complemented
5	Q₈×C₂²⋊D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719440	C₂	1	2	yes	maximal, complemented
7	#11719435	C₂	1	2	yes	maximal, complemented
8	#11719383	C₂	1	2	yes	maximal, complemented
9	#11719374	C₂	1	2	yes	maximal, complemented
10	#11719372	C₂	1	2	yes	maximal, complemented
11	#11719366	C₂	1	2	yes	maximal, complemented
12	#11719365	C₂	1	2	yes	maximal, complemented
13	#11719362	C₂	1	2	yes	maximal, complemented
14	#11719348	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719347	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719340	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719338	C₂	1	1	yes	maximal, characteristic, complemented
18	#11719336	C₂	1	1	yes	maximal, characteristic, complemented
19	#11719332	C₂	1	1	yes	maximal, characteristic, complemented
20	D₁₃×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
21	#11719330	C₂	1	1	yes	maximal, characteristic, complemented
22	#11719238	C₂	1	1	yes	maximal, characteristic, complemented
23	#11719235	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
25	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂×#6131	C₂²	1	1	yes	characteristic
27	C₂×Q₈×D₁₃	C₂²	1	1	yes	characteristic
28	C₂×#6127	C₂²	1	1	yes	characteristic, complemented
29	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
31	C₁₃×#124	C₂²	1	2	yes	—
32	C₁₃×#123	C₂²	1	2	yes	—
33	C₁₃×#123	C₂²	1	2	yes	complemented
34	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
35	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
36	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
37	C₁₃×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
38	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
39	#88201	C₂²	1	2	yes	—
40	#88201	C₂²	1	1	yes	characteristic, complemented
41	#88200	C₂²	1	1	yes	characteristic
42	#88200	C₂²	1	2	yes	—
43	#88200	C₂²	1	1	yes	characteristic
44	#88200	C₂²	1	1	yes	characteristic
45	#88200	C₂²	1	1	yes	characteristic
46	#88200	C₂²	1	2	yes	complemented
47	#88200	C₂²	1	2	yes	complemented
48	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
49	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
50	#88198	C₂²	1	2	yes	complemented
51	#88198	C₂²	1	1	yes	characteristic, complemented
52	#88193	C₂²	1	2	yes	—
53	#88193	C₂²	1	2	yes	complemented
54	#88192	C₂²	1	1	yes	characteristic
55	#88192	C₂²	1	1	yes	characteristic
56	#88192	C₂²	1	2	yes	—
57	#88191	C₂²	1	1	yes	characteristic
58	#88191	C₂²	1	1	yes	characteristic
59	#88189	C₂²	1	1	yes	characteristic
60	#88189	C₂²	1	1	yes	characteristic
61	#88184	C₂²	1	2	yes	—
62	#88184	C₂²	1	1	yes	characteristic
63	#88184	C₂²	1	1	yes	characteristic, complemented
64	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
65	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
67	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
68	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
69	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
70	#88180	C₂²	1	1	yes	characteristic
71	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
72	#88178	C₂²	1	1	yes	characteristic
73	#88178	C₂²	1	1	yes	characteristic, complemented
74	#88178	C₂²	1	2	yes	complemented
75	#88152	C₂²	1	2	yes	—
76	#88152	C₂²	1	2	yes	complemented
77	#88151	C₂²	1	2	yes	—
78	#88151	C₂²	1	1	yes	characteristic
79	#88151	C₂²	1	2	yes	complemented
80	#88150	C₂²	1	2	yes	—
81	#88150	C₂²	1	2	yes	complemented
82	#88149	C₂²	1	1	yes	characteristic
83	#88148	C₂²	1	2	yes	—
84	#88148	C₂²	1	2	yes	—
85	#88147	C₂²	1	2	yes	—
86	#88147	C₂²	1	2	yes	—
87	#88147	C₂²	1	1	yes	characteristic, complemented
88	#88146	C₂²	1	1	yes	characteristic
89	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
90	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
91	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
92	#88144	C₂²	1	2	yes	complemented
93	#88144	C₂²	1	2	yes	complemented
94	#88144	C₂²	1	1	yes	characteristic, complemented
95	#88143	C₂²	1	2	yes	complemented
96	#88143	C₂²	1	2	yes	complemented
97	#88142	C₂²	1	1	yes	characteristic, complemented
98	#88141	C₂²	1	1	yes	characteristic, complemented
99	#88140	C₂²	1	2	yes	—
100	#88139	C₂²	1	2	yes	—
101	#88139	C₂²	1	2	yes	—
102	#88139	C₂²	1	2	yes	complemented
103	#88138	C₂²	1	2	yes	—
104	#88138	C₂²	1	2	yes	—
105	#88138	C₂²	1	2	yes	—
106	#88137	C₂²	1	2	yes	—
107	#88137	C₂²	1	2	yes	complemented
108	#88137	C₂²	1	2	yes	complemented
109	#88136	C₂²	1	2	yes	—
110	#88135	C₂²	1	2	yes	—
111	#88135	C₂²	1	2	yes	—
112	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
113	#88133	C₂²	1	2	yes	—
114	#88133	C₂²	1	2	yes	—
115	#88133	C₂²	1	2	yes	complemented
116	#88132	C₂²	1	2	yes	—
117	#88132	C₂²	1	2	yes	complemented
118	#88131	C₂²	1	2	yes	complemented
119	#88130	C₂²	1	2	yes	—
120	#88130	C₂²	1	2	yes	complemented
121	C₄×D₅₂	C₂²	1	2	yes	—
122	C₄×Dic₂₆	C₂²	1	2	yes	complemented
123	C₂³×D₁₃	C₂³	1	1	yes	characteristic
124	C₁₃×#41	—	4	2	no	—
125	C₂×Q₈×C₁₃	—	4	2	no	—
126	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
127	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
128	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
129	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
130	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
131	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
132	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
133	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
135	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
136	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
137	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
143	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
144	C₂²×Dic₁₃	C₂³	1	2	yes	—
145	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
146	#6131	—	4	2	no	—
147	Q₈×D₁₃	—	4	2	no	—
148	#6127	—	4	2	no	—
149	C₂×D₅₂	C₂³	1	2	yes	—
150	C₂×D₅₂	C₂³	1	1	yes	characteristic
151	C₂×D₅₂	C₂³	1	2	yes	—
152	C₂×C₄×D₁₃	—	4	2	no	—
153	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
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×C₄×D₁₃	C₂³	1	2	yes	—
159	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₁₃	C₂³	1	2	yes	—
161	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
162	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
163	C₂×Dic₂₆	C₂³	1	2	yes	—
164	C₂×Dic₂₆	C₂³	1	2	yes	—
165	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
166	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
167	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
168	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
169	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
170	C₁₃×C₄⋊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	2	yes	—
175	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
176	C₄²×C₁₃	C₂³	1	2	yes	—
177	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
179	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
180	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
181	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
182	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
183	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
184	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
185	#6103	C₂³	1	1	yes	characteristic
186	#6103	C₂³	1	2	yes	—
187	#6103	C₂³	1	1	yes	characteristic
188	#6103	C₂³	1	2	yes	—
189	#6103	C₂³	1	2	yes	—
190	#6103	C₂³	1	2	yes	—
191	#6103	C₂³	1	2	yes	—
192	#6103	C₂³	1	2	yes	—
193	#6103	C₂³	1	2	yes	—
194	#6103	C₂³	1	2	yes	—
195	#6103	C₂³	1	2	yes	—
196	#6103	C₂³	1	1	yes	characteristic
197	#6103	C₂³	1	2	yes	—
198	#6103	C₂³	1	1	yes	characteristic
199	C₄⋊Dic₁₃	C₂³	1	2	yes	—
200	C₄⋊Dic₁₃	C₂³	1	2	yes	—
201	C₄⋊Dic₁₃	C₂³	1	2	yes	—
202	C₄⋊Dic₁₃	C₂³	1	2	yes	—
203	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
204	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
205	C₄⋊Dic₁₃	C₂³	1	2	yes	—
206	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
208	#6101	C₂³	1	1	yes	characteristic
209	#6101	C₂³	1	2	yes	—
210	#6101	C₂³	1	2	yes	—
211	#6101	C₂³	1	2	yes	—
212	#6101	C₂³	1	1	yes	characteristic
213	#6101	C₂³	1	2	yes	—
214	#6101	C₂³	1	2	yes	—
215	#6101	C₂³	1	2	yes	—
216	#6101	C₂³	1	2	yes	—
217	#6101	C₂³	1	2	yes	—
218	#6101	C₂³	1	2	yes	—
219	#6101	C₂³	1	1	yes	characteristic
220	#6101	C₂³	1	2	yes	—
221	#6101	C₂³	1	1	yes	characteristic
222	C₄×Dic₁₃	C₂³	1	2	yes	—
223	C₄×Dic₁₃	C₂³	1	2	yes	—
224	C₄×Dic₁₃	C₂³	1	2	yes	—
225	C₄×Dic₁₃	C₂³	1	2	yes	—
226	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
227	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
228	#3541	—	13	1	no	maximal, Sylow
229	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
230	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
231	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
232	C₂²×D₁₃	—	2	2	no	—
233	C₂²×D₁₃	—	4	1	no	—
234	C₂²×D₁₃	—	4	1	no	—
235	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
236	C₂²×D₁₃	C₂⁴	1	2	yes	—
237	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
238	Q₈×C₁₃	—	2	2	no	—
239	Q₈×C₁₃	—	2	2	no	—
240	Q₈×C₁₃	—	4	2	no	—
241	Q₈×C₁₃	—	4	1	no	—
242	D₄×C₁₃	—	4	1	no	—
243	D₄×C₁₃	—	4	1	no	—
244	D₄×C₁₃	—	4	1	no	—
245	C₂×C₄×C₁₃	—	2	2	no	—
246	C₂×C₄×C₁₃	—	2	2	no	—
247	C₂×C₄×C₁₃	—	2	2	no	—
248	C₂×C₄×C₁₃	—	4	2	no	—
249	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
250	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
251	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
252	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
254	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
255	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
256	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
257	C₂²⋊D₁₃	—	2	2	no	—
258	C₂²⋊D₁₃	—	2	2	no	—
259	C₂²⋊D₁₃	—	4	2	no	—
260	C₂²⋊D₁₃	—	4	1	no	—
261	C₂²⋊D₁₃	—	4	2	no	—
262	C₂²⋊D₁₃	—	4	1	no	—
263	C₂²⋊D₁₃	—	4	2	no	—
264	C₂×Dic₁₃	—	4	1	no	—
265	C₂×Dic₁₃	—	4	2	no	—
266	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
267	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
268	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₁₃	C₂⁴	1	2	yes	—
271	C₂×Dic₁₃	C₂⁴	1	2	yes	—
272	C₂×Dic₁₃	C₂⁴	1	2	yes	—
273	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
275	D₅₂	—	2	4	no	—
276	D₅₂	—	2	2	no	—
277	D₅₂	—	4	2	no	—
278	C₄×D₁₃	—	2	2	no	—
279	C₄×D₁₃	—	2	2	no	—
280	C₄×D₁₃	—	4	1	no	—
281	C₄×D₁₃	—	4	1	no	—
282	C₄×D₁₃	—	4	2	no	—
283	C₄×D₁₃	—	4	2	no	—
284	C₄×D₁₃	—	4	2	no	—
285	C₄×D₁₃	—	4	2	no	—
286	C₄×D₁₃	—	4	2	no	—
287	Dic₂₆	—	2	2	no	—
288	Dic₂₆	—	4	2	no	—
289	Dic₂₆	—	4	2	no	—
290	#563	—	13	2	no	—
291	#562	—	13	2	no	—
292	#556	—	13	1	no	—
293	#554	—	13	2	no	—
294	#554	—	13	1	no	—
295	#553	—	13	2	no	—
296	#553	—	13	1	no	—
297	#552	—	13	1	no	—
298	D₄×Q₈	—	13	1	no	—
299	#548	—	13	1	no	—
300	#548	—	13	1	no	—
301	#547	—	13	1	no	—
302	#542	—	13	2	no	—
303	#542	—	13	1	no	—
304	#541	—	13	1	no	—
305	#539	—	13	2	no	—
306	#538	—	13	2	no	—
307	#538	—	13	2	no	—
308	#537	—	13	1	no	—
309	#536	D₁₃	1	1	yes	characteristic, complemented
310	#525	—	13	1	no	—
311	#525	—	13	1	no	—
312	C₂×C₂²⋊Q₈	—	13	1	no	—
313	C₂²×C₁₃	—	2	1	no	—
314	C₂²×C₁₃	—	2	1	no	—
315	C₂²×C₁₃	—	2	1	no	—
316	C₂²×C₁₃	—	2	1	no	—
317	C₂²×C₁₃	—	2	1	no	—
318	C₂²×C₁₃	—	2	1	no	—
319	C₂²×C₁₃	—	2	1	no	—
320	C₂²×C₁₃	—	2	1	no	—
321	C₂²×C₁₃	—	2	1	no	—
322	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
323	C₂×D₁₃	—	2	1	no	—
324	C₂×D₁₃	—	2	1	no	—
325	C₂×D₁₃	—	2	1	no	—
326	C₂×D₁₃	—	2	2	no	—
327	C₂×D₁₃	—	2	2	no	—
328	C₂×D₁₃	—	2	1	no	—
329	C₂×D₁₃	—	2	2	no	—
330	C₂×D₁₃	—	2	1	no	—
331	C₂×D₁₃	—	4	4	no	—
332	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
333	C₄×C₁₃	—	2	2	no	—
334	C₄×C₁₃	—	2	1	no	—
335	C₄×C₁₃	—	2	1	no	—
336	C₄×C₁₃	—	2	2	no	—
337	C₄×C₁₃	—	2	1	no	—
338	C₄×C₁₃	—	2	2	no	—
339	C₄×C₁₃	—	2	2	no	—
340	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
341	Dic₁₃	—	2	2	no	—
342	Dic₁₃	—	2	1	no	—
343	Dic₁₃	—	2	1	no	—
344	Dic₁₃	—	2	1	no	—
345	Dic₁₃	—	2	1	no	—
346	Dic₁₃	—	2	1	no	—
347	Dic₁₃	—	2	2	no	—
348	Dic₁₃	—	2	1	no	—
349	Dic₁₃	—	2	2	no	—
350	C₂×#41	—	13	1	no	—
351	C₂×#41	—	13	1	no	—
352	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
353	C₂²×Q₈	—	13	1	no	—
354	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
355	C₂³×C₄	—	13	1	no	—
356	C₄⋊Q₈	—	13	1	no	—
357	C₄⋊Q₈	—	13	2	no	—
358	C₄⋊Q₈	—	13	1	no	—
359	C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
360	#126	—	13	2	no	—
361	#126	—	13	2	no	—
362	#126	—	13	2	no	—
363	#126	—	13	2	no	—
364	#126	—	13	2	no	—
365	#126	—	13	2	no	—
366	#126	—	13	2	no	—
367	#125	—	13	2	no	—
368	#125	—	13	2	no	—
369	#125	—	13	1	no	—
370	#125	—	13	2	no	—
371	#125	—	13	2	no	—
372	#124	—	13	2	no	—
373	#124	—	13	1	no	—
374	#124	—	13	2	no	—
375	#124	—	13	2	no	—
376	#124	—	13	2	no	—
377	#124	C₂×D₁₃	1	2	yes	—
378	#123	—	13	1	no	—
379	#123	—	13	1	no	—
380	#123	—	13	2	no	—
381	#123	—	13	2	no	—
382	#123	—	13	2	no	—
383	#123	—	13	2	no	—
384	#123	—	13	2	no	—
385	#123	—	13	2	no	—
386	#123	C₂×D₁₃	1	2	yes	—
387	#123	C₂×D₁₃	1	2	yes	complemented
388	C₂²⋊Q₈	—	13	1	no	—
389	C₂²⋊Q₈	—	13	1	no	—
390	C₂²⋊Q₈	—	13	1	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	—	13	1	no	—
396	C₂²⋊Q₈	—	13	1	no	—
397	C₂²⋊Q₈	—	13	2	no	—
398	C₂²⋊Q₈	—	13	1	no	—
399	C₂²⋊Q₈	—	13	2	no	—
400	C₂²⋊Q₈	—	13	2	no	—
401	C₂²⋊Q₈	—	13	2	no	—
402	C₂²⋊Q₈	—	13	2	no	—
403	C₂²⋊Q₈	—	13	2	no	—
404	C₂²⋊Q₈	—	13	2	no	—
405	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
406	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
407	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
408	C₂²⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
409	#121	—	13	1	no	—
410	#121	—	13	1	no	—
411	#121	—	13	2	no	—
412	#121	—	13	2	no	—
413	#121	—	13	2	no	—
414	#121	—	13	1	no	—
415	#121	—	13	1	no	—
416	#121	—	13	2	no	—
417	#121	—	13	1	no	—
418	#121	—	13	2	no	—
419	#121	—	13	2	no	—
420	#121	—	13	2	no	—
421	#120	—	13	1	no	—
422	#120	—	13	1	no	—
423	#120	—	13	2	no	—
424	C₄×Q₈	—	13	1	no	—
425	C₄×Q₈	—	13	1	no	—
426	C₄×Q₈	—	13	1	no	—
427	C₄×Q₈	—	13	2	no	—
428	C₄×D₄	—	13	1	no	—
429	C₄×D₄	—	13	1	no	—
430	C₄×D₄	—	13	1	no	—
431	C₄×D₄	—	13	1	no	—
432	C₄×D₄	—	13	2	no	—
433	C₄×D₄	—	13	2	no	—
434	C₄×D₄	—	13	2	no	—
435	C₄×D₄	—	13	2	no	—
436	C₄×D₄	—	13	1	no	—
437	C₄×D₄	—	13	2	no	—
438	C₄×D₄	—	13	2	no	—
439	C₄×D₄	—	13	2	no	—
440	#117	—	13	1	no	—
441	#117	—	13	1	no	—
442	#117	—	13	2	no	—
443	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
444	C₂×C₄⋊C₄	—	13	1	no	—
445	C₂×C₄⋊C₄	—	13	1	no	—
446	C₂×C₄⋊C₄	—	13	2	no	—
447	C₂×C₄⋊C₄	—	13	2	no	—
448	C₂×C₂²⋊C₄	—	13	2	no	—
449	C₂×C₁₃	—	4	1	no	—
450	C₂×C₁₃	—	4	1	no	—
451	C₂×C₁₃	—	4	1	no	—
452	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
453	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
454	C₂×C₁₃	#585	1	1	yes	characteristic
455	D₁₃	—	2	2	no	—
456	D₁₃	—	4	2	no	—
457	D₁₃	—	4	1	no	—
458	C₂⁴	—	13	1	no	—
459	#41	—	4	2	no	—
460	#41	—	52	2	no	—
461	#41	—	52	2	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	13	1	no	—
464	C₂×Q₈	—	13	2	no	—
465	C₂×Q₈	—	13	2	no	—
466	C₂×Q₈	—	52	2	no	—
467	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
468	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
469	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
470	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
471	C₂×D₄	—	13	1	no	—
472	C₂×D₄	—	13	1	no	—
473	C₂×D₄	—	13	1	no	—
474	C₂×D₄	—	13	2	no	—
475	C₂×D₄	—	13	1	no	—
476	C₂×D₄	—	13	2	no	—
477	C₂×D₄	—	13	2	no	—
478	C₂×D₄	—	13	2	no	—
479	C₂×D₄	—	13	1	no	—
480	C₂×D₄	—	13	2	no	—
481	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
482	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
483	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
484	C₂²×C₄	—	13	2	no	—
485	C₂²×C₄	—	13	1	no	—
486	C₂²×C₄	—	13	1	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	2	no	—
492	C₂²×C₄	—	13	2	no	—
493	C₂²×C₄	—	13	2	no	—
494	C₂²×C₄	—	13	1	no	—
495	C₂²×C₄	—	52	2	no	—
496	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
497	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
498	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
499	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
500	C₄⋊C₄	—	13	1	no	—
501	C₄⋊C₄	—	13	1	no	—
502	C₄⋊C₄	—	13	2	no	—
503	C₄⋊C₄	—	13	2	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	2	no	—
509	C₄⋊C₄	—	13	1	no	—
510	C₄⋊C₄	—	13	1	no	—
511	C₄⋊C₄	—	13	2	no	—
512	C₄⋊C₄	—	13	1	no	—
513	C₄⋊C₄	—	13	1	no	—
514	C₄⋊C₄	—	13	2	no	—
515	C₄⋊C₄	—	13	1	no	—
516	C₄⋊C₄	—	13	2	no	—
517	C₄⋊C₄	—	13	2	no	—
518	C₄⋊C₄	—	13	2	no	—
519	C₄⋊C₄	—	13	2	no	—
520	C₄⋊C₄	—	13	2	no	—
521	C₄⋊C₄	—	13	2	no	—
522	C₄⋊C₄	—	13	2	no	—
523	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
524	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
525	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
526	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
527	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
528	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
529	C₂²⋊C₄	—	13	2	no	—
530	C₂²⋊C₄	—	13	1	no	—
531	C₂²⋊C₄	—	13	1	no	—
532	C₂²⋊C₄	—	13	1	no	—
533	C₂²⋊C₄	—	13	1	no	—
534	C₂²⋊C₄	—	13	2	no	—
535	C₂²⋊C₄	—	13	1	no	—
536	C₂²⋊C₄	—	13	1	no	—
537	C₂²⋊C₄	—	13	2	no	—
538	C₂²⋊C₄	—	13	2	no	—
539	C₂²⋊C₄	—	13	2	no	—
540	C₂²⋊C₄	—	13	1	no	—
541	C₂²⋊C₄	—	13	2	no	—
542	C₂²⋊C₄	—	13	1	no	—
543	C₂²⋊C₄	—	13	1	no	—
544	C₂²⋊C₄	—	13	1	no	—
545	C₂²⋊C₄	—	13	2	no	—
546	C₂²⋊C₄	—	13	2	no	—
547	C₂²⋊C₄	—	13	2	no	—
548	C₂²⋊C₄	—	13	2	no	—
549	C₂²⋊C₄	—	13	2	no	—
550	C₂²⋊C₄	—	13	2	no	—
551	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
552	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
553	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
554	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
555	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
556	C₄²	—	13	2	no	—
557	C₄²	—	13	1	no	—
558	C₄²	—	13	1	no	—
559	C₄²	—	13	2	no	—
560	C₄²	—	13	2	no	—
561	C₄²	—	13	2	no	—
562	C₄²	C₂²×D₁₃	1	2	yes	—
563	C₁₃	#3541	1	1	yes	characteristic, complemented, Sylow
564	C₂³	—	13	1	no	—
565	C₂³	—	13	1	no	—
566	C₂³	—	13	2	no	—
567	C₂³	—	26	2	no	—
568	C₂³	—	52	1	no	—
569	C₂³	—	52	1	no	—
570	C₂³	C₂³×D₁₃	1	1	yes	characteristic
571	C₂³	C₂³×D₁₃	1	1	yes	characteristic
572	C₂³	C₂³×D₁₃	1	1	yes	characteristic
573	Q₈	—	2	2	no	—
574	Q₈	—	2	2	no	—
575	Q₈	—	4	2	no	—
576	Q₈	—	4	1	no	—
577	Q₈	—	26	2	no	—
578	Q₈	—	52	2	no	—
579	Q₈	—	52	2	no	—
580	D₄	—	4	1	no	—
581	D₄	—	4	1	no	—
582	D₄	—	4	1	no	—
583	D₄	—	26	4	no	—
584	D₄	—	26	2	no	—
585	D₄	—	26	2	no	—
586	D₄	—	26	2	no	—
587	D₄	—	52	2	no	—
588	D₄	—	52	1	no	—
589	D₄	—	52	2	no	—
590	D₄	—	52	2	no	—
591	D₄	—	52	1	no	—
592	D₄	—	52	2	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	4	2	no	—
597	C₂×C₄	—	13	1	no	—
598	C₂×C₄	—	13	1	no	—
599	C₂×C₄	—	13	1	no	—
600	C₂×C₄	—	13	2	no	—
601	C₂×C₄	—	13	1	no	—
602	C₂×C₄	—	13	1	no	—
603	C₂×C₄	—	13	2	no	—
604	C₂×C₄	—	13	2	no	—
605	C₂×C₄	—	13	1	no	—
606	C₂×C₄	—	26	2	no	—
607	C₂×C₄	—	26	2	no	—
608	C₂×C₄	—	52	2	no	—
609	C₂×C₄	—	52	2	no	—
610	C₂×C₄	—	52	1	no	—
611	C₂×C₄	—	52	1	no	—
612	C₂×C₄	—	52	2	no	—
613	C₂×C₄	—	52	2	no	—
614	C₂×C₄	—	52	2	no	—
615	C₂×C₄	—	52	2	no	—
616	C₂×C₄	—	52	1	no	—
617	C₂×C₄	C₂³×D₁₃	1	2	yes	—
618	C₂×C₄	C₂³×D₁₃	1	2	yes	—
619	C₂×C₄	C₂³×D₁₃	1	2	yes	—
620	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
621	C₂×C₄	C₂³×D₁₃	1	2	yes	—
622	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
623	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
624	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
625	C₂²	—	2	1	no	—
626	C₂²	—	2	1	no	—
627	C₂²	—	2	1	no	—
628	C₂²	—	2	1	no	—
629	C₂²	—	2	1	no	—
630	C₂²	—	2	1	no	—
631	C₂²	—	2	1	no	—
632	C₂²	—	2	1	no	—
633	C₂²	—	2	1	no	—
634	C₂²	—	13	2	no	—
635	C₂²	—	26	1	no	—
636	C₂²	—	26	1	no	—
637	C₂²	—	26	1	no	—
638	C₂²	—	26	2	no	—
639	C₂²	—	26	2	no	—
640	C₂²	—	26	1	no	—
641	C₂²	—	26	2	no	—
642	C₂²	—	26	1	no	—
643	C₂²	—	52	4	no	—
644	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
645	C₄	—	2	1	no	—
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	26	1	no	—
653	C₄	—	26	1	no	—
654	C₄	—	26	2	no	—
655	C₄	—	26	1	no	—
656	C₄	—	26	1	no	—
657	C₄	—	26	1	no	—
658	C₄	—	26	2	no	—
659	C₄	—	26	2	no	—
660	C₄	—	26	1	no	—
661	C₄	#88251	1	2	yes	—
662	C₂	—	4	1	no	—
663	C₂	—	4	1	no	—
664	C₂	—	4	1	no	—
665	C₂	—	26	2	no	—
666	C₂	—	52	1	no	—
667	C₂	—	52	2	no	—
668	C₂	C₂×#88251	1	1	yes	characteristic
669	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic
670	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#536	C₂
hypercenter	#536	D₁₃
hypocenter	C₁₃	#3541
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #536

Complements

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

N	H ≅ G/N	type
1. C₁₃×#536	C₂	semidirect
2. #11719538	C₂	semidirect
3. #11719533	C₂	semidirect
4. #11719522	C₂	semidirect
5. Q₈×C₂²⋊D₁₃	C₂	semidirect
6. #11719440	C₂	semidirect
7. #11719435	C₂	semidirect
8. #11719383	C₂	semidirect
9. #11719374	C₂	semidirect
10. #11719372	C₂	semidirect
11. #11719366	C₂	semidirect
12. #11719365	C₂	semidirect
13. #11719362	C₂	semidirect
14. #11719348	C₂	semidirect
15. #11719347	C₂	semidirect
16. #11719340	C₂	semidirect
17. #11719338	C₂	semidirect
18. #11719336	C₂	semidirect
19. #11719332	C₂	semidirect
20. D₁₃×C₂²⋊Q₈	C₂	semidirect
21. #11719330	C₂	semidirect
22. #11719238	C₂	semidirect
23. #11719235	C₂	semidirect
25. C₂²×Q₈×C₁₃	C₂²	semidirect
28. C₂×#6127	C₂²	semidirect
30. C₁₃×C₄⋊Q₈	C₂²	semidirect
33. C₁₃×#123	C₂²	semidirect
36. C₁₃×C₂²⋊Q₈	C₂²	semidirect
37. C₁₃×C₂²⋊Q₈	C₂²	semidirect
38. C₁₃×#117	C₂²	semidirect
40. #88201	C₂²	semidirect
46. #88200	C₂²	semidirect
47. #88200	C₂²	semidirect
48. Q₈×Dic₁₃	C₂²	semidirect
49. Q₈×Dic₁₃	C₂²	semidirect
50. #88198	C₂²	semidirect
51. #88198	C₂²	semidirect
53. #88193	C₂²	semidirect
63. #88184	C₂²	semidirect
69. C₄×C₂²⋊D₁₃	C₂²	semidirect
71. C₂×C₄⋊Dic₁₃	C₂²	semidirect
73. #88178	C₂²	semidirect
74. #88178	C₂²	semidirect
76. #88152	C₂²	semidirect
79. #88151	C₂²	semidirect
81. #88150	C₂²	semidirect
87. #88147	C₂²	semidirect
91. C₄⋊C₄×D₁₃	C₂²	semidirect
92. #88144	C₂²	semidirect
93. #88144	C₂²	semidirect
94. #88144	C₂²	semidirect
95. #88143	C₂²	semidirect
96. #88143	C₂²	semidirect
97. #88142	C₂²	semidirect
98. #88141	C₂²	semidirect
102. #88139	C₂²	semidirect
107. #88137	C₂²	semidirect
108. #88137	C₂²	semidirect
115. #88133	C₂²	semidirect
117. #88132	C₂²	semidirect
118. #88131	C₂²	semidirect
120. #88130	C₂²	semidirect
122. C₄×Dic₂₆	C₂²	semidirect
309. #536	D₁₃	semidirect
354. C₂²×Q₈	C₂×D₁₃	semidirect
359. C₄⋊Q₈	C₂×D₁₃	semidirect
387. #123	C₂×D₁₃	semidirect
407. C₂²⋊Q₈	C₂×D₁₃	semidirect
408. C₂²⋊Q₈	C₂×D₁₃	semidirect
443. #117	C₂×D₁₃	semidirect
563. C₁₃	#3541	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₃×#536	2
#11719538	2
#11719533	2
#11719522	2
Q₈×C₂²⋊D₁₃	2
#11719440	2
#11719435	2
#11719383	2
#11719374	2
#11719372	2
#11719366	2
#11719365	2
#11719362	2
#11719348	2
#11719347	2
#11719340	2
#11719338	2
#11719336	2
#11719332	2
D₁₃×C₂²⋊Q₈	2
#11719330	2
#11719238	2
#11719235	2
#3541	13