Subgroups — #13129113

Order 1664.

1058 conjugacy classes of subgroups.

The subgroup lattice has 430 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	#11719535	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719533	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719522	C₂	1	2	yes	maximal, complemented
5	#11719438	C₂	1	4	yes	maximal, complemented
6	#11719388	C₂	1	2	yes	maximal, complemented
7	#11719384	C₂	1	2	yes	maximal, complemented
8	#11719371	C₂	1	2	yes	maximal, complemented
9	#11719369	C₂	1	2	yes	maximal, complemented
10	#11719362	C₂	1	4	yes	maximal, complemented
11	#11719348	C₂	1	2	yes	maximal, complemented
12	#11719346	C₂	1	2	yes	maximal, complemented
13	#11719335	C₂	1	2	yes	maximal, complemented
14	#11719332	C₂	1	2	yes	maximal, complemented
15	#11719237	C₂	1	2	yes	maximal, complemented
16	C₂×C₁₃×#41	C₂²	1	1	yes	characteristic
17	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
18	C₂×#6131	C₂²	1	2	yes	—
19	C₂²×D₅₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
21	C₁₃×C₄⋊Q₈	C₂²	1	2	yes	complemented
22	C₁₃×#124	C₂²	1	2	yes	—
23	C₁₃×#123	C₂²	1	2	yes	complemented
24	C₁₃×#123	C₂²	1	2	yes	complemented
25	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
28	#88201	C₂²	1	2	yes	complemented
29	#88201	C₂²	1	4	yes	complemented
30	#88201	C₂²	1	2	yes	complemented
31	#88200	C₂²	1	2	yes	complemented
32	#88200	C₂²	1	4	yes	complemented
33	#88200	C₂²	1	2	yes	complemented
34	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
35	#88194	C₂²	1	2	yes	—
36	#88192	C₂²	1	2	yes	—
37	#88191	C₂²	1	1	yes	characteristic
38	#88191	C₂²	1	2	yes	—
39	#88191	C₂²	1	1	yes	characteristic, complemented
40	#88191	C₂²	1	2	yes	complemented
41	#88189	C₂²	1	1	yes	characteristic
42	#88189	C₂²	1	1	yes	characteristic, complemented
43	#88184	C₂²	1	2	yes	—
44	#88184	C₂²	1	2	yes	complemented
45	#88184	C₂²	1	4	yes	complemented
46	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
47	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
48	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
49	#88180	C₂²	1	1	yes	characteristic, complemented
50	#88180	C₂²	1	1	yes	characteristic, complemented
51	#88152	C₂²	1	4	yes	complemented
52	#88152	C₂²	1	4	yes	complemented
53	#88151	C₂²	1	4	yes	complemented
54	#88149	C₂²	1	4	yes	—
55	#88149	C₂²	1	2	yes	—
56	#88148	C₂²	1	4	yes	complemented
57	#88148	C₂²	1	4	yes	complemented
58	#88147	C₂²	1	4	yes	complemented
59	#88147	C₂²	1	2	yes	complemented
60	#88146	C₂²	1	2	yes	complemented
61	#88142	C₂²	1	2	yes	complemented
62	#88141	C₂²	1	4	yes	complemented
63	#88139	C₂²	1	4	yes	—
64	#88139	C₂²	1	4	yes	complemented
65	#88139	C₂²	1	4	yes	complemented
66	#88138	C₂²	1	4	yes	complemented
67	#88137	C₂²	1	4	yes	complemented
68	#88136	C₂²	1	4	yes	—
69	#88136	C₂²	1	4	yes	complemented
70	#88135	C₂²	1	4	yes	complemented
71	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
72	#88133	C₂²	1	4	yes	complemented
73	#88129	C₂²	1	4	yes	complemented
74	#88126	C₂²	1	4	yes	complemented
75	C₂³×D₁₃	C₂³	1	2	yes	—
76	C₂³×D₁₃	C₂³	1	1	yes	characteristic
77	C₁₃×#41	—	4	2	no	—
78	C₂×Q₈×C₁₃	—	4	2	no	—
79	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
80	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
81	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
83	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
88	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
91	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
92	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
93	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
94	#6131	—	4	4	no	—
95	C₂×D₅₂	—	4	2	no	—
96	C₂×D₅₂	C₂³	1	2	yes	—
97	C₂×D₅₂	C₂³	1	4	yes	—
98	C₂×D₅₂	C₂³	1	4	yes	—
99	C₂×D₅₂	C₂³	1	2	yes	—
100	C₂×C₄×D₁₃	—	4	2	no	—
101	C₂×C₄×D₁₃	C₂³	1	2	yes	—
102	C₂×C₄×D₁₃	C₂³	1	4	yes	—
103	C₂×C₄×D₁₃	C₂³	1	4	yes	—
104	C₂×C₄×D₁₃	C₂³	1	2	yes	—
105	C₂×Dic₂₆	C₂³	1	4	yes	—
106	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
108	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
112	C₄²×C₁₃	C₂³	1	2	yes	—
113	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
117	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
118	#6103	C₂³	1	4	yes	—
119	#6103	C₂³	1	4	yes	—
120	#6103	C₂³	1	2	yes	—
121	#6103	C₂³	1	4	yes	—
122	#6103	C₂³	1	4	yes	—
123	#6103	C₂³	1	4	yes	—
124	#6103	C₂³	1	4	yes	—
125	#6103	C₂³	1	4	yes	—
126	#6103	C₂³	1	4	yes	—
127	#6103	C₂³	1	2	yes	—
128	C₄⋊Dic₁₃	C₂³	1	4	yes	—
129	C₄⋊Dic₁₃	C₂³	1	2	yes	—
130	C₄⋊Dic₁₃	C₂³	1	2	yes	—
131	#6101	C₂³	1	2	yes	—
132	#6101	C₂³	1	4	yes	—
133	#6101	C₂³	1	4	yes	—
134	#6101	C₂³	1	2	yes	—
135	C₄×Dic₁₃	C₂³	1	4	yes	—
136	C₄×Dic₁₃	C₂³	1	4	yes	—
137	C₄×Dic₁₃	C₂³	1	2	yes	—
138	C₄×Dic₁₃	C₂³	1	2	yes	—
139	#3540	—	13	1	no	maximal, Sylow
140	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
142	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
143	C₂²×D₁₃	—	4	1	no	—
144	C₂²×D₁₃	—	4	2	no	—
145	C₂²×D₁₃	—	4	2	no	—
146	C₂²×D₁₃	—	4	4	no	—
147	C₂²×D₁₃	C₂⁴	1	2	yes	—
148	C₂²×D₁₃	C₂⁴	1	4	yes	—
149	Q₈×C₁₃	—	2	4	no	—
150	Q₈×C₁₃	—	4	2	no	—
151	Q₈×C₁₃	—	4	1	no	—
152	D₄×C₁₃	—	4	1	no	—
153	D₄×C₁₃	—	4	1	no	—
154	D₄×C₁₃	—	4	1	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
161	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
162	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂²⋊D₁₃	—	4	2	no	—
166	C₂²⋊D₁₃	—	4	4	no	—
167	C₂²⋊D₁₃	—	4	4	no	—
168	C₂²⋊D₁₃	—	4	2	no	—
169	C₂×Dic₁₃	—	4	1	no	—
170	C₂×Dic₁₃	C₂⁴	1	4	yes	—
171	C₂×Dic₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₃	C₂⁴	1	2	yes	—
174	D₅₂	—	2	4	no	—
175	D₅₂	—	4	2	no	—
176	D₅₂	—	4	4	no	—
177	D₅₂	—	4	4	no	—
178	C₄×D₁₃	—	2	4	no	—
179	C₄×D₁₃	—	4	2	no	—
180	C₄×D₁₃	—	4	4	no	—
181	C₄×D₁₃	—	4	4	no	—
182	Dic₂₆	—	4	4	no	—
183	H(3,𝔽₄)	—	13	2	no	—
184	#560	—	13	2	no	—
185	#559	—	13	2	no	—
186	#556	—	13	2	no	—
187	#555	—	13	2	no	—
188	#551	—	13	2	no	—
189	#548	—	13	2	no	—
190	#546	—	13	2	no	—
191	#542	—	13	4	no	—
192	#542	—	13	2	no	—
193	#538	—	13	4	no	—
194	#536	D₁₃	1	1	yes	characteristic, complemented
195	#535	—	13	1	no	—
196	#525	—	13	1	no	—
197	#525	—	13	2	no	—
198	C₂²×C₁₃	—	2	1	no	—
199	C₂²×C₁₃	—	2	1	no	—
200	C₂²×C₁₃	—	2	1	no	—
201	C₂²×C₁₃	—	2	2	no	—
202	C₂²×C₁₃	—	2	2	no	—
203	C₂²×C₁₃	—	2	2	no	—
204	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
205	C₂×D₁₃	—	2	2	no	—
206	C₂×D₁₃	—	2	4	no	—
207	C₂×D₁₃	—	2	4	no	—
208	C₂×D₁₃	—	2	2	no	—
209	C₂×D₁₃	—	2	4	no	—
210	C₂×D₁₃	—	2	2	no	—
211	C₂×D₁₃	—	4	4	no	—
212	C₂×D₁₃	—	8	4	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	—	2	4	no	—
215	C₄×C₁₃	—	2	1	no	—
216	C₄×C₁₃	—	2	1	no	—
217	C₄×C₁₃	—	2	4	no	—
218	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
219	Dic₁₃	—	2	2	no	—
220	Dic₁₃	—	2	2	no	—
221	Dic₁₃	—	2	4	no	—
222	Dic₁₃	—	2	2	no	—
223	C₂×#41	—	13	2	no	—
224	C₂×#41	C₂×D₁₃	1	1	yes	characteristic
225	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
226	C₂²×D₄	—	13	1	no	—
227	C₂³×C₄	—	13	1	no	—
228	C₄⋊Q₈	—	13	2	no	—
229	C₄⋊Q₈	C₂×D₁₃	1	2	yes	complemented
230	#127	—	13	2	no	—
231	#126	—	13	4	no	—
232	#126	—	13	4	no	—
233	#126	—	13	4	no	—
234	#124	—	13	2	no	—
235	#124	—	13	2	no	—
236	#124	—	13	4	no	—
237	#124	—	13	4	no	—
238	#124	—	13	4	no	—
239	#124	—	13	4	no	—
240	#124	—	13	4	no	—
241	#124	C₂×D₁₃	1	2	yes	—
242	#123	—	13	1	no	—
243	#123	—	13	1	no	—
244	#123	—	13	4	no	—
245	#123	—	13	4	no	—
246	#123	—	13	4	no	—
247	#123	C₂×D₁₃	1	2	yes	complemented
248	#123	C₂×D₁₃	1	2	yes	complemented
249	C₂²⋊Q₈	—	13	2	no	—
250	C₂²⋊Q₈	—	13	2	no	—
251	C₂²⋊Q₈	—	13	4	no	—
252	C₂²⋊Q₈	—	13	4	no	—
253	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
254	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
255	#121	—	13	2	no	—
256	#121	—	13	2	no	—
257	#121	—	13	2	no	—
258	#121	—	13	4	no	—
259	#121	—	13	2	no	—
260	#121	—	13	4	no	—
261	#121	—	13	4	no	—
262	#120	—	13	1	no	—
263	#120	—	13	1	no	—
264	#120	—	13	2	no	—
265	#120	—	13	2	no	—
266	#120	—	13	4	no	—
267	#120	—	13	4	no	—
268	C₄×Q₈	—	13	2	no	—
269	C₄×Q₈	—	13	4	no	—
270	C₄×D₄	—	13	2	no	—
271	C₄×D₄	—	13	2	no	—
272	C₄×D₄	—	13	4	no	—
273	C₄×D₄	—	13	4	no	—
274	C₄×D₄	—	13	2	no	—
275	C₄×D₄	—	13	4	no	—
276	#117	—	13	1	no	—
277	#117	—	13	1	no	—
278	#117	—	13	2	no	—
279	#117	—	13	4	no	—
280	#117	C₂×D₁₃	1	1	yes	characteristic, complemented
281	C₂×C₂²⋊C₄	—	13	4	no	—
282	C₂×C₁₃	—	4	1	no	—
283	C₂×C₁₃	—	4	1	no	—
284	C₂×C₁₃	—	4	1	no	—
285	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
286	C₂×C₁₃	#585	1	2	yes	—
287	D₁₃	—	4	2	no	—
288	D₁₃	—	4	4	no	—
289	C₂⁴	—	13	2	no	—
290	C₂⁴	—	13	1	no	—
291	#41	—	4	2	no	—
292	#41	—	52	4	no	—
293	C₂×Q₈	—	4	2	no	—
294	C₂×Q₈	—	13	4	no	—
295	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
296	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
297	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
298	C₂×D₄	—	13	2	no	—
299	C₂×D₄	—	13	4	no	—
300	C₂×D₄	—	13	2	no	—
301	C₂×D₄	—	13	4	no	—
302	C₂×D₄	—	13	2	no	—
303	C₂×D₄	—	13	4	no	—
304	C₂×D₄	—	13	4	no	—
305	C₂×D₄	—	13	2	no	—
306	C₂×D₄	—	52	2	no	—
307	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
308	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
309	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
310	C₂²×C₄	—	13	1	no	—
311	C₂²×C₄	—	13	2	no	—
312	C₂²×C₄	—	13	4	no	—
313	C₂²×C₄	—	13	4	no	—
314	C₂²×C₄	—	13	2	no	—
315	C₂²×C₄	—	52	2	no	—
316	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
317	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
318	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
319	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
320	C₄⋊C₄	—	13	2	no	—
321	C₄⋊C₄	—	13	2	no	—
322	C₄⋊C₄	—	13	2	no	—
323	C₄⋊C₄	—	13	4	no	—
324	C₄⋊C₄	—	13	4	no	—
325	C₄⋊C₄	—	13	2	no	—
326	C₄⋊C₄	—	13	4	no	—
327	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
328	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
329	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
330	C₂²⋊C₄	—	13	2	no	—
331	C₂²⋊C₄	—	13	2	no	—
332	C₂²⋊C₄	—	13	1	no	—
333	C₂²⋊C₄	—	13	1	no	—
334	C₂²⋊C₄	—	13	2	no	—
335	C₂²⋊C₄	—	13	4	no	—
336	C₂²⋊C₄	—	13	4	no	—
337	C₂²⋊C₄	—	13	4	no	—
338	C₂²⋊C₄	—	13	4	no	—
339	C₂²⋊C₄	—	13	2	no	—
340	C₂²⋊C₄	—	13	4	no	—
341	C₂²⋊C₄	—	13	4	no	—
342	C₂²⋊C₄	—	13	4	no	—
343	C₂²⋊C₄	—	13	2	no	—
344	C₂²⋊C₄	—	13	4	no	—
345	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
346	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
347	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
348	C₄²	—	13	4	no	—
349	C₄²	—	13	2	no	—
350	C₄²	—	13	2	no	—
351	C₄²	—	13	4	no	—
352	C₄²	C₂²×D₁₃	1	2	yes	—
353	C₁₃	#3540	1	1	yes	characteristic, complemented, Sylow
354	C₂³	—	13	2	no	—
355	C₂³	—	13	4	no	—
356	C₂³	—	52	1	no	—
357	C₂³	—	52	2	no	—
358	C₂³	—	52	2	no	—
359	C₂³	—	52	4	no	—
360	C₂³	C₂³×D₁₃	1	1	yes	characteristic
361	C₂³	C₂³×D₁₃	1	1	yes	characteristic
362	C₂³	C₂³×D₁₃	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	4	2	no	—
365	Q₈	—	4	1	no	—
366	Q₈	—	52	4	no	—
367	D₄	—	4	1	no	—
368	D₄	—	4	1	no	—
369	D₄	—	4	1	no	—
370	D₄	—	26	4	no	—
371	D₄	—	52	4	no	—
372	D₄	—	52	2	no	—
373	D₄	—	52	4	no	—
374	D₄	—	52	2	no	—
375	D₄	—	52	4	no	—
376	D₄	—	52	4	no	—
377	D₄	—	52	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	13	2	no	—
383	C₂×C₄	—	13	4	no	—
384	C₂×C₄	—	13	2	no	—
385	C₂×C₄	—	13	2	no	—
386	C₂×C₄	—	26	4	no	—
387	C₂×C₄	—	52	4	no	—
388	C₂×C₄	—	52	2	no	—
389	C₂×C₄	—	52	4	no	—
390	C₂×C₄	—	52	1	no	—
391	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₃	1	4	yes	—
393	C₂×C₄	C₂³×D₁₃	1	4	yes	—
394	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
395	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
396	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	2	no	—
401	C₂²	—	2	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	26	2	no	—
404	C₂²	—	26	4	no	—
405	C₂²	—	26	4	no	—
406	C₂²	—	26	2	no	—
407	C₂²	—	26	2	no	—
408	C₂²	—	26	4	no	—
409	C₂²	—	52	4	no	—
410	C₂²	—	104	4	no	—
411	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	2	4	no	—
416	C₄	—	2	4	no	—
417	C₄	—	26	2	no	—
418	C₄	—	26	2	no	—
419	C₄	—	26	4	no	—
420	C₄	—	26	2	no	—
421	C₄	#88251	1	2	yes	—
422	C₂	—	4	1	no	—
423	C₂	—	4	1	no	—
424	C₂	—	4	1	no	—
425	C₂	—	52	2	no	—
426	C₂	—	52	4	no	—
427	C₂	C₂×#88251	1	1	yes	characteristic
428	C₂	#11719652	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#536	C₂
hypercenter	#536	D₁₃
hypocenter	C₁₃	#3540
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. #11719535	C₂	semidirect
3. #11719533	C₂	semidirect
4. #11719522	C₂	semidirect
5. #11719438	C₂	semidirect
6. #11719388	C₂	semidirect
7. #11719384	C₂	semidirect
8. #11719371	C₂	semidirect
9. #11719369	C₂	semidirect
10. #11719362	C₂	semidirect
11. #11719348	C₂	semidirect
12. #11719346	C₂	semidirect
13. #11719335	C₂	semidirect
14. #11719332	C₂	semidirect
15. #11719237	C₂	semidirect
17. C₂²×Q₈×C₁₃	C₂²	semidirect
19. C₂²×D₅₂	C₂²	semidirect
20. C₂²×C₄×D₁₃	C₂²	semidirect
21. C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×#123	C₂²	semidirect
24. C₁₃×#123	C₂²	semidirect
25. C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₁₃×#117	C₂²	semidirect
28. #88201	C₂²	semidirect
29. #88201	C₂²	semidirect
30. #88201	C₂²	semidirect
31. #88200	C₂²	semidirect
32. #88200	C₂²	semidirect
33. #88200	C₂²	semidirect
34. Q₈×Dic₁₃	C₂²	semidirect
39. #88191	C₂²	semidirect
40. #88191	C₂²	semidirect
42. #88189	C₂²	semidirect
44. #88184	C₂²	semidirect
45. #88184	C₂²	semidirect
47. C₄×C₂²⋊D₁₃	C₂²	semidirect
48. C₄×C₂²⋊D₁₃	C₂²	semidirect
49. #88180	C₂²	semidirect
50. #88180	C₂²	semidirect
51. #88152	C₂²	semidirect
52. #88152	C₂²	semidirect
53. #88151	C₂²	semidirect
56. #88148	C₂²	semidirect
57. #88148	C₂²	semidirect
58. #88147	C₂²	semidirect
59. #88147	C₂²	semidirect
60. #88146	C₂²	semidirect
61. #88142	C₂²	semidirect
62. #88141	C₂²	semidirect
64. #88139	C₂²	semidirect
65. #88139	C₂²	semidirect
66. #88138	C₂²	semidirect
67. #88137	C₂²	semidirect
69. #88136	C₂²	semidirect
70. #88135	C₂²	semidirect
71. C₂²⋊C₄×D₁₃	C₂²	semidirect
72. #88133	C₂²	semidirect
73. #88129	C₂²	semidirect
74. #88126	C₂²	semidirect
194. #536	D₁₃	semidirect
225. C₂²×Q₈	C₂×D₁₃	semidirect
229. C₄⋊Q₈	C₂×D₁₃	semidirect
247. #123	C₂×D₁₃	semidirect
248. #123	C₂×D₁₃	semidirect
253. C₂²⋊Q₈	C₂×D₁₃	semidirect
254. C₂²⋊Q₈	C₂×D₁₃	semidirect
280. #117	C₂×D₁₃	semidirect
353. C₁₃	#3540	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
#11719535	2
#11719533	2
#11719522	2
#11719438	2
#11719388	2
#11719384	2
#11719371	2
#11719369	2
#11719362	2
#11719348	2
#11719346	2
#11719335	2
#11719332	2
#11719237	2
#3540	13