Subgroups — #13128680

Order 1664.

1140 conjugacy classes of subgroups.

The subgroup lattice has 468 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	#11719533	C₂	1	2	yes	maximal, complemented
3	#11719529	C₂	1	2	yes	maximal, complemented
4	#11719423	C₂	1	1	yes	maximal, characteristic, complemented
5	#11719421	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719420	C₂	1	2	yes	maximal, complemented
7	#11719418	C₂	1	2	yes	maximal, complemented
8	#11719321	C₂	1	2	yes	maximal, complemented
9	#11719318	C₂	1	4	yes	maximal, complemented
10	#11719311	C₂	1	2	yes	maximal, complemented
11	#11719306	C₂	1	4	yes	maximal, complemented
12	#11719289	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	#11719251	C₂	1	2	yes	maximal, complemented
16	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719247	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₁₃×#41	C₂²	1	2	yes	complemented
19	C₂×#6129	C₂²	1	2	yes	—
20	C₂×#6129	C₂²	1	2	yes	complemented
21	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
22	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
23	C₁₃×#127	C₂²	1	2	yes	—
24	C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
25	C₁₃×#121	C₂²	1	4	yes	complemented
26	C₁₃×#121	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
28	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
30	#88200	C₂²	1	1	yes	characteristic
31	#88200	C₂²	1	2	yes	complemented
32	#88198	C₂²	1	1	yes	characteristic, complemented
33	#88194	C₂²	1	2	yes	—
34	#88193	C₂²	1	4	yes	—
35	#88193	C₂²	1	4	yes	—
36	#88193	C₂²	1	4	yes	complemented
37	#88192	C₂²	1	2	yes	—
38	#88192	C₂²	1	2	yes	—
39	#88192	C₂²	1	2	yes	complemented
40	#88191	C₂²	1	4	yes	—
41	#88191	C₂²	1	4	yes	—
42	#88190	C₂²	1	2	yes	—
43	#88190	C₂²	1	2	yes	complemented
44	#88190	C₂²	1	4	yes	complemented
45	#88189	C₂²	1	4	yes	complemented
46	#88189	C₂²	1	4	yes	complemented
47	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
48	D₄×Dic₁₃	C₂²	1	2	yes	complemented
49	D₄×Dic₁₃	C₂²	1	2	yes	complemented
50	D₄×Dic₁₃	C₂²	1	2	yes	complemented
51	D₄×Dic₁₃	C₂²	1	4	yes	complemented
52	#88183	C₂²	1	4	yes	complemented
53	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
54	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	—
55	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
56	#88180	C₂²	1	2	yes	complemented
57	#88178	C₂²	1	2	yes	complemented
58	C₂×#6101	C₂²	1	4	yes	complemented
59	#88152	C₂²	1	4	yes	complemented
60	#88151	C₂²	1	1	yes	characteristic
61	#88150	C₂²	1	2	yes	—
62	#88147	C₂²	1	1	yes	characteristic
63	#88146	C₂²	1	2	yes	complemented
64	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
65	#88143	C₂²	1	2	yes	complemented
66	#88142	C₂²	1	1	yes	characteristic, complemented
67	#88141	C₂²	1	2	yes	complemented
68	#88139	C₂²	1	4	yes	complemented
69	#88137	C₂²	1	4	yes	complemented
70	#88135	C₂²	1	2	yes	—
71	#88135	C₂²	1	4	yes	—
72	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
73	#88133	C₂²	1	4	yes	complemented
74	#88131	C₂²	1	4	yes	complemented
75	#88129	C₂²	1	2	yes	—
76	C₄×D₅₂	C₂²	1	1	yes	characteristic
77	#88126	C₂²	1	2	yes	—
78	C₄²×D₁₃	C₂²	1	1	yes	characteristic
79	#88123	C₂²	1	1	yes	characteristic, complemented
80	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
81	C₄×Dic₂₆	C₂²	1	2	yes	complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₁₃×#41	—	4	4	no	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂×D₄×C₁₃	C₂³	1	2	yes	—
89	C₂×D₄×C₁₃	C₂³	1	4	yes	—
90	C₂×D₄×C₁₃	C₂³	1	2	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	4	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
96	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
97	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
98	C₂²×Dic₁₃	C₂³	1	4	yes	—
99	C₂²×Dic₁₃	C₂³	1	4	yes	—
100	C₂²×Dic₁₃	C₂³	1	2	yes	—
101	#6129	—	2	8	no	—
102	#6129	—	4	4	no	—
103	D₄×D₁₃	—	2	4	no	—
104	C₂×D₅₂	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₃	—	4	4	no	—
106	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂³	1	2	yes	—
108	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂³	1	2	yes	—
110	C₂×C₄×D₁₃	C₂³	1	2	yes	—
111	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
112	C₂×Dic₂₆	C₂³	1	2	yes	—
113	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
114	C₂×Dic₂₆	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
117	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₄²×C₁₃	C₂³	1	2	yes	—
121	C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
123	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
127	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
128	#6103	C₂³	1	2	yes	—
129	#6103	C₂³	1	2	yes	—
130	#6103	C₂³	1	2	yes	—
131	#6103	C₂³	1	4	yes	—
132	#6103	C₂³	1	4	yes	—
133	#6103	C₂³	1	2	yes	—
134	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₁₃	C₂³	1	2	yes	—
136	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₁₃	C₂³	1	2	yes	—
138	C₄⋊Dic₁₃	C₂³	1	2	yes	—
139	#6101	C₂³	1	2	yes	—
140	#6101	C₂³	1	2	yes	—
141	#6101	C₂³	1	2	yes	—
142	#6101	C₂³	1	4	yes	—
143	#6101	C₂³	1	2	yes	—
144	#6101	C₂³	1	2	yes	—
145	#6101	C₂³	1	2	yes	—
146	#6101	C₂³	1	4	yes	—
147	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂³	1	2	yes	—
149	C₄×Dic₁₃	C₂³	1	4	yes	—
150	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂³	1	4	yes	—
153	#3506	—	13	1	no	maximal, Sylow
154	C₂³×C₁₃	C₂⁴	1	2	yes	—
155	C₂³×C₁₃	C₂⁴	1	4	yes	—
156	C₂²×D₁₃	—	2	4	no	—
157	C₂²×D₁₃	—	4	2	no	—
158	C₂²×D₁₃	—	4	2	no	—
159	C₂²×D₁₃	C₂⁴	1	2	yes	—
160	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₁₃	—	2	2	no	—
162	D₄×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	4	no	—
164	D₄×C₁₃	—	2	4	no	—
165	D₄×C₁₃	—	4	4	no	—
166	D₄×C₁₃	—	4	2	no	—
167	D₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	2	4	no	—
169	C₂×C₄×C₁₃	—	4	4	no	—
170	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
174	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
175	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂²⋊D₁₃	—	2	8	no	—
177	C₂²⋊D₁₃	—	2	4	no	—
178	C₂²⋊D₁₃	—	4	4	no	—
179	C₂²⋊D₁₃	—	4	4	no	—
180	C₂×Dic₁₃	—	2	8	no	—
181	C₂×Dic₁₃	—	4	2	no	—
182	C₂×Dic₁₃	—	4	4	no	—
183	C₂×Dic₁₃	C₂⁴	1	2	yes	—
184	C₂×Dic₁₃	C₂⁴	1	2	yes	—
185	C₂×Dic₁₃	C₂⁴	1	4	yes	—
186	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂⁴	1	2	yes	—
189	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
190	D₅₂	—	2	2	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	4	no	—
193	C₄×D₁₃	—	4	2	no	—
194	C₄×D₁₃	—	4	2	no	—
195	C₄×D₁₃	—	4	1	no	—
196	C₄×D₁₃	#41	1	4	yes	complemented
197	Dic₂₆	—	2	4	no	—
198	Dic₂₆	—	2	2	no	—
199	Dic₂₆	—	4	2	no	—
200	#559	—	13	2	no	—
201	#559	—	13	2	no	—
202	#556	—	13	1	no	—
203	#556	—	13	1	no	—
204	#555	—	13	2	no	—
205	#553	—	13	4	no	—
206	#550	—	13	1	no	—
207	#550	D₁₃	1	1	yes	characteristic, complemented
208	#547	—	13	2	no	—
209	#538	—	13	4	no	—
210	#535	—	13	2	no	—
211	#533	—	13	1	no	—
212	#532	—	13	1	no	—
213	#525	—	13	2	no	—
214	#525	—	13	2	no	—
215	#520	—	13	2	no	—
216	C₂×C₄×D₄	—	13	1	no	—
217	C₂²×C₁₃	—	2	4	no	—
218	C₂²×C₁₃	—	2	2	no	—
219	C₂²×C₁₃	—	2	4	no	—
220	C₂²×C₁₃	—	2	2	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	2	2	no	—
223	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
224	C₂×D₁₃	—	2	1	no	—
225	C₂×D₁₃	—	2	1	no	—
226	C₂×D₁₃	—	2	2	no	—
227	C₂×D₁₃	—	2	2	no	—
228	C₂×D₁₃	—	2	2	no	—
229	C₂×D₁₃	—	4	8	no	—
230	C₂×D₁₃	C₂×#41	1	2	yes	—
231	C₄×C₁₃	—	2	2	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	—	2	2	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	C₂×#41	1	2	yes	—
236	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
237	Dic₁₃	—	2	4	no	—
238	Dic₁₃	—	2	2	no	—
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	—	2	2	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	2	2	no	—
243	Dic₁₃	C₂×#41	1	2	yes	—
244	C₂×#41	—	13	2	no	—
245	C₂×#41	—	13	2	no	—
246	C₂×#41	C₂×D₁₃	1	2	yes	complemented
247	C₂²×D₄	—	13	1	no	—
248	C₂³×C₄	—	13	2	no	—
249	C₄⋊Q₈	—	13	1	no	—
250	C₄⋊Q₈	—	13	1	no	—
251	C₄⋊Q₈	—	13	1	no	—
252	#127	—	13	2	no	—
253	#127	C₂×D₁₃	1	2	yes	—
254	#127	C₂×D₁₃	1	1	yes	characteristic, complemented
255	#126	—	13	4	no	—
256	#126	—	13	4	no	—
257	#125	—	13	2	no	—
258	#124	—	13	2	no	—
259	#124	—	13	2	no	—
260	#124	—	13	4	no	—
261	#124	—	13	4	no	—
262	#124	—	13	2	no	—
263	#123	—	13	4	no	—
264	#123	—	13	4	no	—
265	#123	—	13	4	no	—
266	#123	—	13	4	no	—
267	C₂²⋊Q₈	—	13	1	no	—
268	C₂²⋊Q₈	—	13	2	no	—
269	C₂²⋊Q₈	—	13	2	no	—
270	C₂²⋊Q₈	—	13	1	no	—
271	C₂²⋊Q₈	—	13	2	no	—
272	#121	—	13	2	no	—
273	#121	—	13	2	no	—
274	#121	—	13	2	no	—
275	#121	—	13	4	no	—
276	#121	—	13	4	no	—
277	#121	—	13	4	no	—
278	#121	C₂×D₁₃	1	2	yes	complemented
279	#121	C₂×D₁₃	1	4	yes	complemented
280	#120	—	13	4	no	—
281	#120	—	13	4	no	—
282	C₄×Q₈	—	13	2	no	—
283	C₄×Q₈	—	13	2	no	—
284	C₄×Q₈	—	13	1	no	—
285	C₄×Q₈	—	13	2	no	—
286	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
287	C₄×D₄	—	13	1	no	—
288	C₄×D₄	—	13	2	no	—
289	C₄×D₄	—	13	4	no	—
290	C₄×D₄	—	13	2	no	—
291	C₄×D₄	—	13	2	no	—
292	C₄×D₄	—	13	2	no	—
293	C₄×D₄	—	13	4	no	—
294	C₄×D₄	—	13	4	no	—
295	C₄×D₄	—	13	1	no	—
296	C₄×D₄	—	13	2	no	—
297	C₄×D₄	—	13	4	no	—
298	C₄×D₄	—	13	1	no	—
299	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
300	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
301	#117	—	13	2	no	—
302	#117	—	13	2	no	—
303	#117	—	13	4	no	—
304	#117	—	13	2	no	—
305	C₂×C₄⋊C₄	—	13	4	no	—
306	C₂×C₄⋊C₄	—	13	1	no	—
307	C₂×C₂²⋊C₄	—	13	2	no	—
308	C₂×C₄²	—	13	1	no	—
309	C₂×C₁₃	—	4	2	no	—
310	C₂×C₁₃	—	4	4	no	—
311	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
312	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₁₃	#585	1	1	yes	characteristic
314	D₁₃	—	2	2	no	—
315	D₁₃	—	4	2	no	—
316	C₂⁴	—	13	2	no	—
317	#41	—	4	4	no	—
318	#41	—	26	8	no	—
319	#41	—	52	4	no	—
320	C₂×Q₈	—	13	2	no	—
321	C₂×Q₈	—	13	1	no	—
322	C₂×Q₈	—	13	2	no	—
323	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
324	C₂×D₄	—	13	4	no	—
325	C₂×D₄	—	13	2	no	—
326	C₂×D₄	—	13	4	no	—
327	C₂×D₄	—	13	4	no	—
328	C₂×D₄	—	13	1	no	—
329	C₂×D₄	—	26	4	no	—
330	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
331	C₂×D₄	C₂²×D₁₃	1	2	yes	—
332	C₂×D₄	C₂²×D₁₃	1	2	yes	—
333	C₂×D₄	C₂²×D₁₃	1	4	yes	—
334	C₂×D₄	C₂²×D₁₃	1	2	yes	—
335	C₂×D₄	C₂²×D₁₃	1	4	yes	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	4	no	—
338	C₂²×C₄	—	13	4	no	—
339	C₂²×C₄	—	13	2	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	2	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	2	no	—
344	C₂²×C₄	—	13	2	no	—
345	C₂²×C₄	—	52	4	no	—
346	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
347	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
348	C₄⋊C₄	—	13	2	no	—
349	C₄⋊C₄	—	13	2	no	—
350	C₄⋊C₄	—	13	1	no	—
351	C₄⋊C₄	—	13	4	no	—
352	C₄⋊C₄	—	13	4	no	—
353	C₄⋊C₄	—	13	2	no	—
354	C₄⋊C₄	—	13	2	no	—
355	C₄⋊C₄	—	13	1	no	—
356	C₄⋊C₄	—	13	2	no	—
357	C₄⋊C₄	—	13	2	no	—
358	C₄⋊C₄	—	13	2	no	—
359	C₄⋊C₄	—	13	2	no	—
360	C₄⋊C₄	—	13	2	no	—
361	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
362	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
363	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
364	C₂²⋊C₄	—	13	2	no	—
365	C₂²⋊C₄	—	13	4	no	—
366	C₂²⋊C₄	—	13	4	no	—
367	C₂²⋊C₄	—	13	4	no	—
368	C₂²⋊C₄	—	13	4	no	—
369	C₂²⋊C₄	—	13	4	no	—
370	C₂²⋊C₄	—	13	2	no	—
371	C₂²⋊C₄	—	13	2	no	—
372	C₂²⋊C₄	—	13	2	no	—
373	C₂²⋊C₄	—	13	2	no	—
374	C₂²⋊C₄	—	13	4	no	—
375	C₂²⋊C₄	—	13	4	no	—
376	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
377	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	4	no	—
382	C₄²	—	13	4	no	—
383	C₄²	—	13	2	no	—
384	C₄²	C₂²×D₁₃	1	1	yes	characteristic
385	C₄²	C₂²×D₁₃	1	2	yes	—
386	C₁₃	#3506	1	1	yes	characteristic, complemented, Sylow
387	C₂³	—	13	1	no	—
388	C₂³	—	13	2	no	—
389	C₂³	—	26	4	no	—
390	C₂³	—	52	2	no	—
391	C₂³	—	52	2	no	—
392	C₂³	C₂³×D₁₃	1	2	yes	—
393	C₂³	C₂³×D₁₃	1	4	yes	—
394	Q₈	—	2	2	no	—
395	Q₈	—	26	2	no	—
396	Q₈	—	26	4	no	—
397	Q₈	—	52	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	2	2	no	—
400	D₄	—	2	4	no	—
401	D₄	—	4	2	no	—
402	D₄	—	4	4	no	—
403	D₄	—	4	4	no	—
404	D₄	—	26	4	no	—
405	D₄	—	26	8	no	—
406	D₄	—	26	2	no	—
407	D₄	—	52	4	no	—
408	D₄	—	52	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	13	1	no	—
412	C₂×C₄	—	13	4	no	—
413	C₂×C₄	—	13	2	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	4	no	—
416	C₂×C₄	—	13	1	no	—
417	C₂×C₄	—	13	2	no	—
418	C₂×C₄	—	13	2	no	—
419	C₂×C₄	—	26	8	no	—
420	C₂×C₄	—	26	2	no	—
421	C₂×C₄	—	26	4	no	—
422	C₂×C₄	—	52	1	no	—
423	C₂×C₄	—	52	2	no	—
424	C₂×C₄	—	52	2	no	—
425	C₂×C₄	—	52	2	no	—
426	C₂×C₄	—	52	4	no	—
427	C₂×C₄	C₂³×D₁₃	1	2	yes	—
428	C₂×C₄	C₂³×D₁₃	1	2	yes	—
429	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₁₃	1	2	yes	—
431	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
432	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
433	C₂²	—	2	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	2	4	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	2	4	no	—
438	C₂²	—	2	2	no	—
439	C₂²	—	13	2	no	—
440	C₂²	—	26	1	no	—
441	C₂²	—	26	1	no	—
442	C₂²	—	26	2	no	—
443	C₂²	—	26	2	no	—
444	C₂²	—	26	2	no	—
445	C₂²	—	52	8	no	—
446	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
447	C₄	—	2	2	no	—
448	C₄	—	2	2	no	—
449	C₄	—	2	1	no	—
450	C₄	—	2	2	no	—
451	C₄	—	13	2	no	—
452	C₄	—	26	1	no	—
453	C₄	—	26	2	no	—
454	C₄	—	26	2	no	—
455	C₄	—	26	4	no	—
456	C₄	—	26	1	no	—
457	C₄	—	26	2	no	—
458	C₄	#88251	1	2	yes	—
459	C₄	#41×D₁₃	1	2	yes	—
460	C₂	—	4	2	no	—
461	C₂	—	4	4	no	—
462	C₂	—	26	2	no	—
463	C₂	—	52	2	no	—
464	C₂	C₂×#88251	1	1	yes	characteristic
465	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
466	C₂	#11719650	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	#3506
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. #11719533	C₂	semidirect
3. #11719529	C₂	semidirect
4. #11719423	C₂	semidirect
5. #11719421	C₂	semidirect
6. #11719420	C₂	semidirect
7. #11719418	C₂	semidirect
8. #11719321	C₂	semidirect
9. #11719318	C₂	semidirect
10. #11719311	C₂	semidirect
11. #11719306	C₂	semidirect
12. #11719289	C₂	semidirect
13. #11719283	C₂	semidirect
14. #11719264	C₂	semidirect
15. #11719251	C₂	semidirect
16. C₄×D₄×D₁₃	C₂	semidirect
17. #11719247	C₂	semidirect
18. C₂×C₁₃×#41	C₂²	semidirect
20. C₂×#6129	C₂²	semidirect
24. C₁₃×#127	C₂²	semidirect
25. C₁₃×#121	C₂²	semidirect
26. C₁₃×#121	C₂²	semidirect
27. C₄×Q₈×C₁₃	C₂²	semidirect
29. C₄×D₄×C₁₃	C₂²	semidirect
31. #88200	C₂²	semidirect
32. #88198	C₂²	semidirect
36. #88193	C₂²	semidirect
39. #88192	C₂²	semidirect
43. #88190	C₂²	semidirect
44. #88190	C₂²	semidirect
45. #88189	C₂²	semidirect
46. #88189	C₂²	semidirect
48. D₄×Dic₁₃	C₂²	semidirect
49. D₄×Dic₁₃	C₂²	semidirect
50. D₄×Dic₁₃	C₂²	semidirect
51. D₄×Dic₁₃	C₂²	semidirect
52. #88183	C₂²	semidirect
55. C₄×C₂²⋊D₁₃	C₂²	semidirect
56. #88180	C₂²	semidirect
57. #88178	C₂²	semidirect
58. C₂×#6101	C₂²	semidirect
59. #88152	C₂²	semidirect
63. #88146	C₂²	semidirect
65. #88143	C₂²	semidirect
66. #88142	C₂²	semidirect
67. #88141	C₂²	semidirect
68. #88139	C₂²	semidirect
69. #88137	C₂²	semidirect
73. #88133	C₂²	semidirect
74. #88131	C₂²	semidirect
79. #88123	C₂²	semidirect
80. C₄×Dic₂₆	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
196. C₄×D₁₃	#41	semidirect
207. #550	D₁₃	semidirect
246. C₂×#41	C₂×D₁₃	semidirect
254. #127	C₂×D₁₃	semidirect
278. #121	C₂×D₁₃	semidirect
279. #121	C₂×D₁₃	semidirect
286. C₄×Q₈	C₂×D₁₃	semidirect
300. C₄×D₄	C₂×D₁₃	semidirect
386. C₁₃	#3506	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
#11719533	2
#11719529	2
#11719423	2
#11719421	2
#11719420	2
#11719418	2
#11719321	2
#11719318	2
#11719311	2
#11719306	2
#11719289	2
#11719283	2
#11719264	2
#11719251	2
C₄×D₄×D₁₃	2
#11719247	2
#3506	13