Subgroups — #13128706

Order 1664.

1232 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#550	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719537	C₂	1	2	yes	maximal, complemented
3	#11719534	C₂	1	2	yes	maximal, complemented
4	#11719423	C₂	1	2	yes	maximal, complemented
5	#11719420	C₂	1	2	yes	maximal, complemented
6	D₁₃×#127	C₂	1	1	yes	maximal, characteristic, complemented
7	#11719418	C₂	1	1	yes	maximal, characteristic, complemented
8	#11719320	C₂	1	4	yes	maximal, complemented
9	#11719317	C₂	1	2	yes	maximal, complemented
10	#11719315	C₂	1	4	yes	maximal, complemented
11	#11719301	C₂	1	2	yes	maximal, complemented
12	#11719290	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719283	C₂	1	1	yes	maximal, characteristic, complemented
14	#11719264	C₂	1	2	yes	maximal, complemented
15	#11719258	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719250	C₂	1	2	yes	maximal, complemented
17	C₄×#6129	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂×#6129	C₂²	1	1	yes	characteristic
20	C₂×#6129	C₂²	1	4	yes	complemented
21	C₂×D₄×D₁₃	C₂²	1	2	yes	—
22	C₂×D₄×D₁₃	C₂²	1	2	yes	—
23	C₂×D₄×D₁₃	C₂²	1	2	yes	—
24	C₂×#6127	C₂²	1	2	yes	complemented
25	C₁₃×#127	C₂²	1	1	yes	characteristic
26	C₁₃×#127	C₂²	1	2	yes	complemented
27	C₁₃×#121	C₂²	1	2	yes	complemented
28	C₁₃×#121	C₂²	1	4	yes	complemented
29	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
30	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
31	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
32	#88201	C₂²	1	2	yes	complemented
33	#88200	C₂²	1	1	yes	characteristic
34	#88198	C₂²	1	1	yes	characteristic, complemented
35	#88194	C₂²	1	2	yes	—
36	#88194	C₂²	1	2	yes	—
37	#88194	C₂²	1	2	yes	—
38	#88194	C₂²	1	2	yes	complemented
39	#88193	C₂²	1	4	yes	complemented
40	#88193	C₂²	1	4	yes	complemented
41	#88193	C₂²	1	4	yes	complemented
42	#88193	C₂²	1	4	yes	complemented
43	#88192	C₂²	1	4	yes	complemented
44	#88191	C₂²	1	4	yes	—
45	#88191	C₂²	1	4	yes	—
46	#88190	C₂²	1	2	yes	complemented
47	#88190	C₂²	1	2	yes	complemented
48	#88189	C₂²	1	4	yes	complemented
49	D₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
50	D₄×Dic₁₃	C₂²	1	2	yes	complemented
51	D₄×Dic₁₃	C₂²	1	2	yes	complemented
52	#88184	C₂²	1	2	yes	complemented
53	#88183	C₂²	1	4	yes	complemented
54	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
55	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
56	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
57	C₂×#6103	C₂²	1	4	yes	—
58	C₂×C₄×Dic₁₃	C₂²	1	2	yes	complemented
59	#88151	C₂²	1	1	yes	characteristic
60	#88150	C₂²	1	2	yes	—
61	#88148	C₂²	1	4	yes	complemented
62	#88147	C₂²	1	2	yes	complemented
63	#88147	C₂²	1	2	yes	complemented
64	#88146	C₂²	1	1	yes	characteristic
65	#88143	C₂²	1	2	yes	complemented
66	#88142	C₂²	1	1	yes	characteristic, complemented
67	#88141	C₂²	1	1	yes	characteristic, complemented
68	#88139	C₂²	1	4	yes	complemented
69	#88138	C₂²	1	4	yes	complemented
70	#88137	C₂²	1	4	yes	complemented
71	#88135	C₂²	1	2	yes	—
72	#88135	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
74	#88131	C₂²	1	2	yes	complemented
75	#88129	C₂²	1	2	yes	complemented
76	#88128	C₂²	1	1	yes	characteristic
77	C₄×D₅₂	C₂²	1	2	yes	complemented
78	#88126	C₂²	1	2	yes	—
79	C₄²×D₁₃	C₂²	1	1	yes	characteristic
80	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	4	yes	—
84	C₁₃×#41	—	4	4	no	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×D₄×C₁₃	C₂³	1	2	yes	—
90	C₂×D₄×C₁₃	C₂³	1	4	yes	—
91	C₂×D₄×C₁₃	C₂³	1	4	yes	—
92	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
98	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
99	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
100	C₂²×Dic₁₃	C₂³	1	2	yes	—
101	C₂²×Dic₁₃	C₂³	1	2	yes	—
102	C₂²×Dic₁₃	C₂³	1	4	yes	—
103	#6129	—	2	4	no	—
104	#6129	—	4	8	no	—
105	D₄×D₁₃	—	2	8	no	—
106	D₄×D₁₃	—	4	4	no	—
107	D₄×D₁₃	—	4	4	no	—
108	#6127	—	4	4	no	—
109	C₂×D₅₂	C₂³	1	2	yes	—
110	C₂×D₅₂	C₂³	1	2	yes	—
111	C₂×D₅₂	C₂³	1	2	yes	—
112	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂³	1	4	yes	—
115	C₂×C₄×D₁₃	C₂³	1	4	yes	—
116	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
117	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
118	C₂×Dic₂₆	C₂³	1	2	yes	—
119	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
120	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
121	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
122	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
123	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
124	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
125	C₄²×C₁₃	C₂³	1	1	yes	characteristic
126	C₄²×C₁₃	C₂³	1	2	yes	—
127	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
128	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
129	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
130	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
131	#6103	C₂³	1	2	yes	—
132	#6103	C₂³	1	2	yes	—
133	#6103	C₂³	1	4	yes	—
134	#6103	C₂³	1	4	yes	—
135	#6103	C₂³	1	4	yes	—
136	#6103	C₂³	1	2	yes	—
137	#6103	C₂³	1	4	yes	—
138	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₃	C₂³	1	2	yes	—
140	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
141	#6101	C₂³	1	2	yes	—
142	#6101	C₂³	1	2	yes	—
143	#6101	C₂³	1	2	yes	—
144	#6101	C₂³	1	2	yes	—
145	#6101	C₂³	1	2	yes	—
146	#6101	C₂³	1	2	yes	—
147	#6101	C₂³	1	2	yes	—
148	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
149	C₄×Dic₁₃	C₂³	1	2	yes	—
150	C₄×Dic₁₃	C₂³	1	2	yes	—
151	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
153	C₄×Dic₁₃	C₂³	1	2	yes	—
154	C₄×Dic₁₃	C₂³	1	2	yes	—
155	#3508	—	13	1	no	maximal, Sylow
156	C₂³×C₁₃	C₂⁴	1	4	yes	—
157	C₂³×C₁₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₃	—	2	8	no	—
159	C₂²×D₁₃	—	4	4	no	—
160	C₂²×D₁₃	—	4	4	no	—
161	C₂²×D₁₃	C₂⁴	1	4	yes	—
162	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
163	Q₈×C₁₃	—	2	2	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	2	2	no	—
166	D₄×C₁₃	—	2	4	no	—
167	D₄×C₁₃	—	4	2	no	—
168	D₄×C₁₃	—	4	4	no	—
169	D₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	—	2	4	no	—
171	C₂×C₄×C₁₃	—	4	4	no	—
172	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
173	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
175	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
176	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂²⋊D₁₃	—	2	4	no	—
179	C₂²⋊D₁₃	—	2	8	no	—
180	C₂²⋊D₁₃	—	2	8	no	—
181	C₂²⋊D₁₃	—	4	4	no	—
182	C₂²⋊D₁₃	—	4	4	no	—
183	C₂²⋊D₁₃	—	4	4	no	—
184	C₂×Dic₁₃	—	2	4	no	—
185	C₂×Dic₁₃	—	2	4	no	—
186	C₂×Dic₁₃	—	4	4	no	—
187	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂⁴	1	2	yes	—
189	C₂×Dic₁₃	C₂⁴	1	2	yes	—
190	C₂×Dic₁₃	C₂⁴	1	2	yes	—
191	C₂×Dic₁₃	C₂⁴	1	2	yes	—
192	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
193	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
194	D₅₂	—	2	4	no	—
195	D₅₂	—	2	4	no	—
196	D₅₂	—	4	2	no	—
197	C₄×D₁₃	—	2	2	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	4	4	no	—
200	C₄×D₁₃	—	4	4	no	—
201	C₄×D₁₃	#41	1	4	yes	complemented
202	Dic₂₆	—	2	2	no	—
203	Dic₂₆	—	2	2	no	—
204	Dic₂₆	—	2	4	no	—
205	#559	—	13	1	no	—
206	#559	—	13	1	no	—
207	#559	—	13	2	no	—
208	#550	—	13	2	no	—
209	#550	—	13	1	no	—
210	#550	D₁₃	1	1	yes	characteristic, complemented
211	#546	—	13	2	no	—
212	#546	—	13	4	no	—
213	#546	—	13	2	no	—
214	#540	—	13	4	no	—
215	#535	—	13	2	no	—
216	#533	—	13	1	no	—
217	#532	—	13	2	no	—
218	#532	—	13	2	no	—
219	C₂×#127	—	13	1	no	—
220	#518	—	13	2	no	—
221	C₄×#41	—	13	1	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	2	2	no	—
225	C₂²×C₁₃	—	2	4	no	—
226	C₂²×C₁₃	—	2	2	no	—
227	C₂²×C₁₃	—	2	4	no	—
228	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	—	2	4	no	—
232	C₂×D₁₃	—	2	4	no	—
233	C₂×D₁₃	—	2	4	no	—
234	C₂×D₁₃	—	8	8	no	—
235	C₂×D₁₃	C₂×#41	1	2	yes	—
236	C₄×C₁₃	—	2	2	no	—
237	C₄×C₁₃	—	2	1	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	C₂×#41	1	2	yes	—
241	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	—	2	2	no	—
244	Dic₁₃	—	2	2	no	—
245	Dic₁₃	—	2	1	no	—
246	Dic₁₃	—	2	2	no	—
247	Dic₁₃	C₂×#41	1	2	yes	—
248	Dic₁₃	H(5,𝔽₂)	1	2	yes	—
249	C₂×#41	—	13	1	no	—
250	C₂×#41	—	13	4	no	—
251	C₂×#41	—	13	2	no	—
252	C₂×#41	C₂×D₁₃	1	2	yes	complemented
253	C₂²×D₄	—	13	2	no	—
254	C₂²×D₄	—	13	2	no	—
255	C₂²×D₄	—	13	2	no	—
256	C₄⋊Q₈	—	13	1	no	—
257	C₄⋊Q₈	—	13	1	no	—
258	#127	—	13	2	no	—
259	#127	—	13	2	no	—
260	#127	—	13	2	no	—
261	#127	—	13	2	no	—
262	#127	—	13	1	no	—
263	#127	C₂×D₁₃	1	1	yes	characteristic
264	#127	C₂×D₁₃	1	2	yes	complemented
265	#125	—	13	2	no	—
266	#124	—	13	2	no	—
267	#124	—	13	2	no	—
268	#124	—	13	2	no	—
269	#124	—	13	4	no	—
270	#124	—	13	2	no	—
271	#123	—	13	4	no	—
272	#123	—	13	4	no	—
273	#123	—	13	4	no	—
274	#123	—	13	4	no	—
275	C₂²⋊Q₈	—	13	1	no	—
276	C₂²⋊Q₈	—	13	2	no	—
277	C₂²⋊Q₈	—	13	1	no	—
278	#121	—	13	4	no	—
279	#121	—	13	4	no	—
280	#121	—	13	4	no	—
281	#121	—	13	4	no	—
282	#121	—	13	4	no	—
283	#121	—	13	2	no	—
284	#121	—	13	4	no	—
285	#121	C₂×D₁₃	1	2	yes	complemented
286	#121	C₂×D₁₃	1	4	yes	complemented
287	#120	—	13	4	no	—
288	#120	—	13	4	no	—
289	C₄×Q₈	—	13	1	no	—
290	C₄×Q₈	—	13	1	no	—
291	C₄×Q₈	—	13	2	no	—
292	C₄×Q₈	—	13	1	no	—
293	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
294	C₄×D₄	—	13	1	no	—
295	C₄×D₄	—	13	2	no	—
296	C₄×D₄	—	13	2	no	—
297	C₄×D₄	—	13	2	no	—
298	C₄×D₄	—	13	4	no	—
299	C₄×D₄	—	13	4	no	—
300	C₄×D₄	—	13	2	no	—
301	C₄×D₄	—	13	2	no	—
302	C₄×D₄	—	13	2	no	—
303	C₄×D₄	—	13	4	no	—
304	C₄×D₄	—	13	2	no	—
305	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic, complemented
306	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
307	#117	—	13	1	no	—
308	#117	—	13	2	no	—
309	#117	—	13	2	no	—
310	C₂×C₂²⋊C₄	—	13	4	no	—
311	C₂×C₂²⋊C₄	—	13	4	no	—
312	C₂×C₄²	—	13	2	no	—
313	C₂×C₄²	—	13	1	no	—
314	C₂×C₁₃	—	4	4	no	—
315	C₂×C₁₃	—	4	2	no	—
316	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
319	D₁₃	—	2	2	no	—
320	D₁₃	—	4	4	no	—
321	C₂⁴	—	13	4	no	—
322	#41	—	4	4	no	—
323	#41	—	26	4	no	—
324	#41	—	52	4	no	—
325	#41	—	52	8	no	—
326	C₂×Q₈	—	13	1	no	—
327	C₂×Q₈	—	13	2	no	—
328	C₂×Q₈	—	13	1	no	—
329	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
330	C₂×D₄	—	13	2	no	—
331	C₂×D₄	—	13	4	no	—
332	C₂×D₄	—	13	4	no	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	13	4	no	—
335	C₂×D₄	—	13	4	no	—
336	C₂×D₄	—	13	2	no	—
337	C₂×D₄	—	13	2	no	—
338	C₂×D₄	—	13	2	no	—
339	C₂×D₄	—	26	8	no	—
340	C₂×D₄	—	52	4	no	—
341	C₂×D₄	—	52	4	no	—
342	C₂×D₄	C₂²×D₁₃	1	2	yes	—
343	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
344	C₂×D₄	C₂²×D₁₃	1	2	yes	—
345	C₂×D₄	C₂²×D₁₃	1	4	yes	—
346	C₂×D₄	C₂²×D₁₃	1	4	yes	—
347	C₂×D₄	C₂²×D₁₃	1	2	yes	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	2	no	—
350	C₂²×C₄	—	13	2	no	—
351	C₂²×C₄	—	13	4	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	4	no	—
355	C₂²×C₄	—	13	4	no	—
356	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
357	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
358	C₄⋊C₄	—	13	1	no	—
359	C₄⋊C₄	—	13	2	no	—
360	C₄⋊C₄	—	13	2	no	—
361	C₄⋊C₄	—	13	2	no	—
362	C₄⋊C₄	—	13	2	no	—
363	C₄⋊C₄	—	13	2	no	—
364	C₄⋊C₄	—	13	1	no	—
365	C₄⋊C₄	—	13	2	no	—
366	C₄⋊C₄	—	13	2	no	—
367	C₄⋊C₄	—	13	2	no	—
368	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
370	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
371	C₂²⋊C₄	—	13	4	no	—
372	C₂²⋊C₄	—	13	2	no	—
373	C₂²⋊C₄	—	13	4	no	—
374	C₂²⋊C₄	—	13	4	no	—
375	C₂²⋊C₄	—	13	2	no	—
376	C₂²⋊C₄	—	13	2	no	—
377	C₂²⋊C₄	—	13	2	no	—
378	C₂²⋊C₄	—	13	4	no	—
379	C₂²⋊C₄	—	13	4	no	—
380	C₂²⋊C₄	—	13	4	no	—
381	C₂²⋊C₄	—	13	4	no	—
382	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
383	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
384	C₄²	—	13	1	no	—
385	C₄²	—	13	2	no	—
386	C₄²	—	13	1	no	—
387	C₄²	—	13	2	no	—
388	C₄²	—	13	2	no	—
389	C₄²	—	13	1	no	—
390	C₄²	—	13	2	no	—
391	C₄²	C₂²×D₁₃	1	1	yes	characteristic
392	C₄²	C₂²×D₁₃	1	2	yes	—
393	C₁₃	#3508	1	1	yes	characteristic, complemented, Sylow
394	C₂³	—	13	1	no	—
395	C₂³	—	13	4	no	—
396	C₂³	—	26	8	no	—
397	C₂³	—	52	4	no	—
398	C₂³	—	52	4	no	—
399	C₂³	C₂³×D₁₃	1	4	yes	—
400	C₂³	C₂³×D₁₃	1	2	yes	—
401	Q₈	—	2	2	no	—
402	Q₈	—	26	4	no	—
403	Q₈	—	26	2	no	—
404	Q₈	—	26	2	no	—
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	4	4	no	—
410	D₄	—	4	4	no	—
411	D₄	—	26	8	no	—
412	D₄	—	26	8	no	—
413	D₄	—	26	4	no	—
414	D₄	—	26	4	no	—
415	D₄	—	26	4	no	—
416	D₄	—	52	2	no	—
417	D₄	—	52	4	no	—
418	D₄	—	52	4	no	—
419	D₄	—	52	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	13	1	no	—
423	C₂×C₄	—	13	1	no	—
424	C₂×C₄	—	13	4	no	—
425	C₂×C₄	—	13	2	no	—
426	C₂×C₄	—	13	2	no	—
427	C₂×C₄	—	13	1	no	—
428	C₂×C₄	—	13	2	no	—
429	C₂×C₄	—	13	2	no	—
430	C₂×C₄	—	26	2	no	—
431	C₂×C₄	—	26	4	no	—
432	C₂×C₄	—	26	4	no	—
433	C₂×C₄	—	26	2	no	—
434	C₂×C₄	—	52	4	no	—
435	C₂×C₄	—	52	4	no	—
436	C₂×C₄	—	52	4	no	—
437	C₂×C₄	C₂³×D₁₃	1	2	yes	—
438	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
439	C₂×C₄	C₂³×D₁₃	1	2	yes	—
440	C₂×C₄	C₂³×D₁₃	1	2	yes	—
441	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
442	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	2	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	4	no	—
449	C₂²	—	13	2	no	—
450	C₂²	—	26	1	no	—
451	C₂²	—	26	1	no	—
452	C₂²	—	26	4	no	—
453	C₂²	—	26	4	no	—
454	C₂²	—	26	4	no	—
455	C₂²	—	104	8	no	—
456	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
457	C₄	—	2	2	no	—
458	C₄	—	2	2	no	—
459	C₄	—	2	1	no	—
460	C₄	—	2	2	no	—
461	C₄	—	13	2	no	—
462	C₄	—	13	2	no	—
463	C₄	—	26	1	no	—
464	C₄	—	26	2	no	—
465	C₄	—	26	2	no	—
466	C₄	—	26	2	no	—
467	C₄	—	26	2	no	—
468	C₄	#88251	1	2	yes	—
469	C₄	#41×D₁₃	1	2	yes	—
470	C₂	—	4	4	no	—
471	C₂	—	4	2	no	—
472	C₂	—	26	2	no	—
473	C₂	—	52	4	no	—
474	C₂	C₂×#88251	1	1	yes	characteristic
475	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
476	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#550	C₂
hypercenter	#550	D₁₃
hypocenter	C₁₃	#3508
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #550

Complements

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

N	H ≅ G/N	type
1. C₁₃×#550	C₂	semidirect
2. #11719537	C₂	semidirect
3. #11719534	C₂	semidirect
4. #11719423	C₂	semidirect
5. #11719420	C₂	semidirect
6. D₁₃×#127	C₂	semidirect
7. #11719418	C₂	semidirect
8. #11719320	C₂	semidirect
9. #11719317	C₂	semidirect
10. #11719315	C₂	semidirect
11. #11719301	C₂	semidirect
12. #11719290	C₂	semidirect
13. #11719283	C₂	semidirect
14. #11719264	C₂	semidirect
15. #11719258	C₂	semidirect
16. #11719250	C₂	semidirect
17. C₄×#6129	C₂	semidirect
18. C₂×C₁₃×#41	C₂²	semidirect
20. C₂×#6129	C₂²	semidirect
24. C₂×#6127	C₂²	semidirect
26. C₁₃×#127	C₂²	semidirect
27. C₁₃×#121	C₂²	semidirect
28. C₁₃×#121	C₂²	semidirect
29. C₄×Q₈×C₁₃	C₂²	semidirect
30. C₄×D₄×C₁₃	C₂²	semidirect
31. C₄×D₄×C₁₃	C₂²	semidirect
32. #88201	C₂²	semidirect
34. #88198	C₂²	semidirect
38. #88194	C₂²	semidirect
39. #88193	C₂²	semidirect
40. #88193	C₂²	semidirect
41. #88193	C₂²	semidirect
42. #88193	C₂²	semidirect
43. #88192	C₂²	semidirect
46. #88190	C₂²	semidirect
47. #88190	C₂²	semidirect
48. #88189	C₂²	semidirect
49. D₄×Dic₁₃	C₂²	semidirect
50. D₄×Dic₁₃	C₂²	semidirect
51. D₄×Dic₁₃	C₂²	semidirect
52. #88184	C₂²	semidirect
53. #88183	C₂²	semidirect
55. C₄×C₂²⋊D₁₃	C₂²	semidirect
56. C₄×C₂²⋊D₁₃	C₂²	semidirect
58. C₂×C₄×Dic₁₃	C₂²	semidirect
61. #88148	C₂²	semidirect
62. #88147	C₂²	semidirect
63. #88147	C₂²	semidirect
65. #88143	C₂²	semidirect
66. #88142	C₂²	semidirect
67. #88141	C₂²	semidirect
68. #88139	C₂²	semidirect
69. #88138	C₂²	semidirect
70. #88137	C₂²	semidirect
72. #88135	C₂²	semidirect
74. #88131	C₂²	semidirect
75. #88129	C₂²	semidirect
77. C₄×D₅₂	C₂²	semidirect
80. C₄×Dic₂₆	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
201. C₄×D₁₃	#41	semidirect
210. #550	D₁₃	semidirect
252. C₂×#41	C₂×D₁₃	semidirect
264. #127	C₂×D₁₃	semidirect
285. #121	C₂×D₁₃	semidirect
286. #121	C₂×D₁₃	semidirect
293. C₄×Q₈	C₂×D₁₃	semidirect
305. C₄×D₄	C₂×D₁₃	semidirect
306. C₄×D₄	C₂×D₁₃	semidirect
393. C₁₃	#3508	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#550	2
#11719537	2
#11719534	2
#11719423	2
#11719420	2
D₁₃×#127	2
#11719418	2
#11719320	2
#11719317	2
#11719315	2
#11719301	2
#11719290	2
#11719283	2
#11719264	2
#11719258	2
#11719250	2
C₄×#6129	2
#3508	13