Subgroups — #13128561

Order 1664.

1142 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#518	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719510	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88192	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719268	C₂	1	2	yes	maximal, complemented
5	#11719267	C₂	1	2	yes	maximal, complemented
6	#11719266	C₂	1	2	yes	maximal, complemented
7	#11719263	C₂	1	2	yes	maximal, complemented
8	#11719263	C₂	1	2	yes	maximal, complemented
9	#11719262	C₂	1	2	yes	maximal, complemented
10	#11719256	C₂	1	2	yes	maximal, complemented
11	#11719253	C₂	1	2	yes	maximal, complemented
12	#11719229	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719228	C₂	1	1	yes	maximal, characteristic, complemented
14	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719224	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719200	C₂	1	4	yes	maximal, complemented
17	#11719195	C₂	1	4	yes	maximal, complemented
18	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₃	C₂²	1	2	yes	—
20	C₂×#6127	C₂²	1	1	yes	characteristic
21	C₂×#6127	C₂²	1	4	yes	complemented
22	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
23	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
24	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
25	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
26	C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
27	C₁₃×#117	C₂²	1	1	yes	characteristic
28	C₁₃×#117	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₂²⋊C₄	C₂²	1	4	yes	—
30	#88207	C₂²	1	4	yes	—
31	C₂×C₂²⋊Dic₁₃	C₂²	1	2	yes	—
32	#88194	C₂²	1	2	yes	complemented
33	#88192	C₂²	1	2	yes	—
34	#88192	C₂²	1	2	yes	—
35	#88192	C₂²	1	2	yes	—
36	#88192	C₂²	1	2	yes	—
37	#88192	C₂²	1	2	yes	complemented
38	#88192	C₂²	1	2	yes	complemented
39	#88190	C₂²	1	2	yes	complemented
40	#88184	C₂²	1	4	yes	complemented
41	#88183	C₂²	1	4	yes	complemented
42	#88183	C₂²	1	4	yes	complemented
43	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
44	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
45	#88180	C₂²	1	1	yes	characteristic
46	#88180	C₂²	1	4	yes	complemented
47	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
48	#88178	C₂²	1	4	yes	complemented
49	#88151	C₂²	1	1	yes	characteristic, complemented
50	#88151	C₂²	1	1	yes	characteristic, complemented
51	#88149	C₂²	1	1	yes	characteristic, complemented
52	#88149	C₂²	1	1	yes	characteristic, complemented
53	#88146	C₂²	1	1	yes	characteristic, complemented
54	#88146	C₂²	1	1	yes	characteristic, complemented
55	#88146	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
57	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
58	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
59	#88144	C₂²	1	2	yes	complemented
60	#88142	C₂²	1	2	yes	complemented
61	#88140	C₂²	1	2	yes	—
62	#88139	C₂²	1	4	yes	complemented
63	#88139	C₂²	1	4	yes	complemented
64	#88138	C₂²	1	4	yes	complemented
65	#88138	C₂²	1	4	yes	complemented
66	#88137	C₂²	1	4	yes	complemented
67	#88137	C₂²	1	4	yes	complemented
68	#88136	C₂²	1	2	yes	—
69	#88135	C₂²	1	4	yes	—
70	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
71	#88133	C₂²	1	4	yes	complemented
72	#88133	C₂²	1	4	yes	complemented
73	#88132	C₂²	1	4	yes	—
74	#88131	C₂²	1	2	yes	—
75	C₄×D₅₂	C₂²	1	2	yes	complemented
76	C₄×D₅₂	C₂²	1	2	yes	complemented
77	C₄×D₅₂	C₂²	1	2	yes	complemented
78	#88126	C₂²	1	2	yes	complemented
79	C₄²×D₁₃	C₂²	1	2	yes	complemented
80	#88124	C₂²	1	2	yes	complemented
81	#88123	C₂²	1	2	yes	complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂⁴×C₁₃	C₂³	1	2	yes	—
84	C₂³×D₁₃	C₂³	1	1	yes	characteristic
85	C₂×D₄×C₁₃	—	2	4	no	—
86	C₂×D₄×C₁₃	C₂³	1	2	yes	—
87	C₂×D₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
89	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
90	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₃	—	4	4	no	—
92	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
93	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
94	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
95	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
96	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
97	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
98	C₂²×Dic₁₃	C₂³	1	2	yes	—
99	#6127	—	2	4	no	—
100	#6127	—	4	8	no	—
101	C₂×D₅₂	C₂³	1	1	yes	characteristic
102	C₂×D₅₂	C₂³	1	2	yes	—
103	C₂×D₅₂	C₂³	1	2	yes	—
104	C₂×C₄×D₁₃	—	2	4	no	—
105	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂³	1	2	yes	—
110	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂³	1	2	yes	—
112	C₂×C₄×D₁₃	C₂³	1	4	yes	—
113	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
114	C₂×Dic₂₆	C₂³	1	4	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	1	yes	characteristic
118	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
119	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
120	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
122	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
123	C₄²×C₁₃	C₂³	1	2	yes	—
124	C₄²×C₁₃	C₂³	1	2	yes	—
125	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
126	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
127	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
128	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
129	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
130	#6103	C₂³	1	2	yes	—
131	#6103	C₂³	1	2	yes	—
132	#6103	C₂³	1	4	yes	—
133	#6103	C₂³	1	2	yes	—
134	#6103	C₂³	1	2	yes	—
135	#6103	C₂³	1	2	yes	—
136	#6103	C₂³	1	2	yes	—
137	C₄⋊Dic₁₃	C₂³	1	2	yes	—
138	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₃	C₂³	1	2	yes	—
140	C₄⋊Dic₁₃	C₂³	1	4	yes	—
141	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
142	C₄⋊Dic₁₃	C₂³	1	2	yes	—
143	C₄⋊Dic₁₃	C₂³	1	2	yes	—
144	#6101	C₂³	1	4	yes	—
145	#6101	C₂³	1	4	yes	—
146	#6101	C₂³	1	4	yes	—
147	#6101	C₂³	1	2	yes	—
148	#6101	C₂³	1	2	yes	—
149	C₄×Dic₁₃	C₂³	1	4	yes	—
150	C₄×Dic₁₃	C₂³	1	2	yes	—
151	C₄×Dic₁₃	C₂³	1	2	yes	—
152	C₄×Dic₁₃	C₂³	1	2	yes	—
153	#3494	—	13	1	no	maximal, Sylow
154	C₂³×C₁₃	—	2	4	no	—
155	C₂³×C₁₃	—	4	2	no	—
156	C₂³×C₁₃	—	4	2	no	—
157	C₂³×C₁₃	C₂⁴	1	4	yes	—
158	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
159	C₂²×D₁₃	—	2	2	no	—
160	C₂²×D₁₃	—	2	2	no	—
161	C₂²×D₁₃	—	4	1	no	—
162	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
163	C₂²×D₁₃	C₂⁴	1	2	yes	—
164	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
165	D₄×C₁₃	—	2	4	no	—
166	D₄×C₁₃	—	2	4	no	—
167	C₂×C₄×C₁₃	—	4	4	no	—
168	C₂×C₄×C₁₃	—	4	4	no	—
169	C₂×C₄×C₁₃	#41	1	4	yes	complemented
170	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
171	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
172	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
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	4	no	—
177	C₂²⋊D₁₃	—	2	8	no	—
178	C₂²⋊D₁₃	—	4	4	no	—
179	C₂²⋊D₁₃	—	4	4	no	—
180	C₂²⋊D₁₃	—	4	4	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	4	2	no	—
183	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂⁴	1	2	yes	—
185	C₂×Dic₁₃	C₂⁴	1	2	yes	—
186	C₂×Dic₁₃	C₂⁴	1	2	yes	—
187	C₂×Dic₁₃	C₂⁴	1	4	yes	—
188	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
189	D₅₂	—	2	4	no	—
190	D₅₂	—	2	2	no	—
191	D₅₂	—	4	2	no	—
192	C₄×D₁₃	—	2	4	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	2	no	—
197	C₄×D₁₃	—	2	4	no	—
198	C₄×D₁₃	—	4	2	no	—
199	C₄×D₁₃	—	4	4	no	—
200	Dic₂₆	—	2	2	no	—
201	Dic₂₆	—	4	4	no	—
202	#555	—	13	2	no	—
203	#553	—	13	2	no	—
204	#553	—	13	2	no	—
205	#551	—	13	4	no	—
206	#547	—	13	2	no	—
207	#546	—	13	4	no	—
208	#544	—	13	1	no	—
209	#542	—	13	2	no	—
210	#540	—	13	2	no	—
211	#535	—	13	1	no	—
212	#532	—	13	2	no	—
213	#529	—	13	2	no	—
214	#525	—	13	1	no	—
215	C₂×#121	—	13	1	no	—
216	#520	—	13	1	no	—
217	#518	D₁₃	1	1	yes	characteristic, complemented
218	C₂×#117	—	13	1	no	—
219	C₂²×C₁₃	—	2	1	no	—
220	C₂²×C₁₃	—	2	1	no	—
221	C₂²×C₁₃	—	2	4	no	—
222	C₂²×C₁₃	—	2	4	no	—
223	C₂²×C₁₃	—	2	4	no	—
224	C₂²×C₁₃	—	8	4	no	—
225	C₂²×C₁₃	C₂×#41	1	2	yes	—
226	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
227	C₂×D₁₃	—	2	1	no	—
228	C₂×D₁₃	—	2	1	no	—
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	2	no	—
231	C₂×D₁₃	—	2	2	no	—
232	C₂×D₁₃	—	2	1	no	—
233	C₂×D₁₃	—	2	1	no	—
234	C₂×D₁₃	—	2	2	no	—
235	C₂×D₁₃	—	4	4	no	—
236	C₂×D₁₃	H(5,𝔽₂)	1	2	yes	—
237	C₄×C₁₃	—	2	2	no	—
238	C₄×C₁₃	—	2	2	no	—
239	C₄×C₁₃	—	2	2	no	—
240	C₄×C₁₃	—	2	2	no	—
241	C₄×C₁₃	C₂×#41	1	2	yes	—
242	C₄×C₁₃	C₂×#41	1	2	yes	—
243	Dic₁₃	—	2	2	no	—
244	Dic₁₃	—	2	1	no	—
245	Dic₁₃	—	2	1	no	—
246	Dic₁₃	—	2	2	no	—
247	Dic₁₃	—	2	4	no	—
248	Dic₁₃	—	2	2	no	—
249	C₂×#41	—	13	1	no	—
250	C₂×#41	—	13	4	no	—
251	C₂²×D₄	—	13	2	no	—
252	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
253	C₂³×C₄	—	13	1	no	—
254	C₄⋊Q₈	—	13	2	no	—
255	C₄⋊Q₈	—	13	2	no	—
256	#127	—	13	2	no	—
257	#126	—	13	4	no	—
258	#126	—	13	4	no	—
259	#125	—	13	2	no	—
260	#125	—	13	2	no	—
261	#124	—	13	2	no	—
262	#124	—	13	4	no	—
263	#124	—	13	4	no	—
264	#123	—	13	4	no	—
265	#123	—	13	4	no	—
266	#123	—	13	2	no	—
267	#123	—	13	4	no	—
268	#123	—	13	4	no	—
269	C₂²⋊Q₈	—	13	4	no	—
270	C₂²⋊Q₈	—	13	1	no	—
271	C₂²⋊Q₈	—	13	1	no	—
272	C₂²⋊Q₈	—	13	4	no	—
273	#121	—	13	2	no	—
274	#121	—	13	2	no	—
275	#121	—	13	2	no	—
276	#121	—	13	2	no	—
277	#121	—	13	2	no	—
278	#121	—	13	2	no	—
279	#121	—	13	4	no	—
280	#121	—	13	1	no	—
281	#121	—	13	1	no	—
282	#121	—	13	4	no	—
283	#121	—	13	4	no	—
284	#120	—	13	4	no	—
285	#120	—	13	2	no	—
286	C₄×Q₈	—	13	2	no	—
287	C₄×D₄	—	13	4	no	—
288	C₄×D₄	—	13	4	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	C₂×D₁₃	1	2	yes	complemented
294	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
295	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
296	C₄×D₄	C₂×D₁₃	1	2	yes	complemented
297	#117	—	13	1	no	—
298	#117	—	13	4	no	—
299	#117	—	13	1	no	—
300	#117	—	13	1	no	—
301	#117	—	13	2	no	—
302	#117	—	13	2	no	—
303	#117	—	13	2	no	—
304	#117	C₂×D₁₃	1	1	yes	characteristic
305	#117	C₂×D₁₃	1	1	yes	characteristic
306	C₂×C₄⋊C₄	—	13	1	no	—
307	C₂×C₄⋊C₄	—	13	1	no	—
308	C₂×C₄⋊C₄	—	13	1	no	—
309	C₂×C₄⋊C₄	—	13	2	no	—
310	C₂×C₂²⋊C₄	—	13	2	no	—
311	C₂×C₂²⋊C₄	—	13	2	no	—
312	C₂×C₂²⋊C₄	C₂×D₁₃	1	4	yes	—
313	C₂×C₄²	—	13	2	no	—
314	C₂×C₁₃	—	2	2	no	—
315	C₂×C₁₃	—	4	4	no	—
316	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
317	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
318	C₂×C₁₃	#585	1	1	yes	characteristic
319	D₁₃	—	2	2	no	—
320	D₁₃	—	4	2	no	—
321	D₁₃	—	4	1	no	—
322	C₂⁴	—	13	1	no	—
323	C₂⁴	C₂²×D₁₃	1	2	yes	—
324	#41	—	26	4	no	—
325	#41	—	52	8	no	—
326	C₂×Q₈	—	13	1	no	—
327	C₂×Q₈	—	13	4	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	13	2	no	—
330	C₂×D₄	—	13	4	no	—
331	C₂×D₄	—	13	4	no	—
332	C₂×D₄	—	13	4	no	—
333	C₂×D₄	—	13	4	no	—
334	C₂×D₄	—	13	1	no	—
335	C₂×D₄	—	13	2	no	—
336	C₂×D₄	—	13	2	no	—
337	C₂×D₄	—	52	4	no	—
338	C₂×D₄	C₂²×D₁₃	1	2	yes	—
339	C₂×D₄	C₂²×D₁₃	1	2	yes	—
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	1	no	—
345	C₂²×C₄	—	13	2	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	2	no	—
349	C₂²×C₄	—	13	4	no	—
350	C₂²×C₄	—	26	4	no	—
351	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
352	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
353	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
354	C₄⋊C₄	—	13	2	no	—
355	C₄⋊C₄	—	13	1	no	—
356	C₄⋊C₄	—	13	1	no	—
357	C₄⋊C₄	—	13	2	no	—
358	C₄⋊C₄	—	13	2	no	—
359	C₄⋊C₄	—	13	2	no	—
360	C₄⋊C₄	—	13	4	no	—
361	C₄⋊C₄	—	13	2	no	—
362	C₄⋊C₄	—	13	4	no	—
363	C₄⋊C₄	—	13	4	no	—
364	C₄⋊C₄	—	13	4	no	—
365	C₄⋊C₄	—	13	2	no	—
366	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
369	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
370	C₂²⋊C₄	—	13	2	no	—
371	C₂²⋊C₄	—	13	4	no	—
372	C₂²⋊C₄	—	13	4	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	4	no	—
378	C₂²⋊C₄	—	13	2	no	—
379	C₂²⋊C₄	—	13	2	no	—
380	C₂²⋊C₄	—	13	2	no	—
381	C₂²⋊C₄	—	13	2	no	—
382	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
383	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
384	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
385	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
386	C₄²	—	13	2	no	—
387	C₄²	—	13	2	no	—
388	C₄²	—	13	2	no	—
389	C₄²	—	13	4	no	—
390	C₄²	C₂²×D₁₃	1	2	yes	—
391	C₄²	C₂²×D₁₃	1	2	yes	—
392	C₁₃	#3494	1	1	yes	characteristic, complemented, Sylow
393	C₂³	—	2	4	no	—
394	C₂³	—	4	2	no	—
395	C₂³	—	4	2	no	—
396	C₂³	—	13	1	no	—
397	C₂³	—	13	1	no	—
398	C₂³	—	13	2	no	—
399	C₂³	—	26	2	no	—
400	C₂³	—	26	2	no	—
401	C₂³	—	52	1	no	—
402	C₂³	C₂³×D₁₃	1	4	yes	—
403	C₂³	C₂³×D₁₃	1	1	yes	characteristic
404	Q₈	—	26	2	no	—
405	Q₈	—	52	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	2	4	no	—
408	D₄	—	26	4	no	—
409	D₄	—	26	8	no	—
410	D₄	—	26	4	no	—
411	D₄	—	26	2	no	—
412	D₄	—	52	2	no	—
413	D₄	—	52	4	no	—
414	D₄	—	52	4	no	—
415	D₄	—	52	4	no	—
416	C₂×C₄	—	4	4	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	13	1	no	—
419	C₂×C₄	—	13	2	no	—
420	C₂×C₄	—	13	2	no	—
421	C₂×C₄	—	13	2	no	—
422	C₂×C₄	—	13	4	no	—
423	C₂×C₄	—	13	1	no	—
424	C₂×C₄	—	26	4	no	—
425	C₂×C₄	—	26	2	no	—
426	C₂×C₄	—	26	2	no	—
427	C₂×C₄	—	26	2	no	—
428	C₂×C₄	—	26	2	no	—
429	C₂×C₄	—	26	2	no	—
430	C₂×C₄	—	26	4	no	—
431	C₂×C₄	—	52	2	no	—
432	C₂×C₄	—	52	4	no	—
433	C₂×C₄	—	52	2	no	—
434	C₂×C₄	#6127	1	4	yes	complemented
435	C₂×C₄	C₂³×D₁₃	1	2	yes	—
436	C₂×C₄	C₂³×D₁₃	1	2	yes	—
437	C₂×C₄	C₂³×D₁₃	1	2	yes	—
438	C₂×C₄	C₂³×D₁₃	1	2	yes	—
439	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
440	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	8	4	no	—
447	C₂²	—	13	2	no	—
448	C₂²	—	26	1	no	—
449	C₂²	—	26	1	no	—
450	C₂²	—	26	1	no	—
451	C₂²	—	26	2	no	—
452	C₂²	—	26	2	no	—
453	C₂²	—	26	1	no	—
454	C₂²	—	26	2	no	—
455	C₂²	—	26	1	no	—
456	C₂²	—	52	4	no	—
457	C₂²	C₂×#6127	1	2	yes	—
458	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
459	C₄	—	2	2	no	—
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	26	1	no	—
464	C₄	—	26	1	no	—
465	C₄	—	26	2	no	—
466	C₄	—	26	2	no	—
467	C₄	—	26	4	no	—
468	C₄	—	26	2	no	—
469	C₄	C₂×#6127	1	2	yes	—
470	C₄	C₂×#6127	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	4	4	no	—
473	C₂	—	26	2	no	—
474	C₂	—	52	1	no	—
475	C₂	—	52	2	no	—
476	C₂	C₂²×#6127	1	1	yes	characteristic
477	C₂	D₁₃×H(5,𝔽₂)	1	1	yes	characteristic
478	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#518	C₂
hypercenter	#518	D₁₃
hypocenter	C₁₃	#3494
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #518

Complements

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

N	H ≅ G/N	type
1. C₁₃×#518	C₂	semidirect
2. #11719510	C₂	semidirect
3. C₂×#88192	C₂	semidirect
4. #11719268	C₂	semidirect
5. #11719267	C₂	semidirect
6. #11719266	C₂	semidirect
7. #11719263	C₂	semidirect
8. #11719263	C₂	semidirect
9. #11719262	C₂	semidirect
10. #11719256	C₂	semidirect
11. #11719253	C₂	semidirect
12. #11719229	C₂	semidirect
13. #11719228	C₂	semidirect
14. D₁₃×#117	C₂	semidirect
15. #11719224	C₂	semidirect
16. #11719200	C₂	semidirect
17. #11719195	C₂	semidirect
21. C₂×#6127	C₂²	semidirect
23. C₄×D₄×C₁₃	C₂²	semidirect
24. C₄×D₄×C₁₃	C₂²	semidirect
25. C₄×D₄×C₁₃	C₂²	semidirect
26. C₄×D₄×C₁₃	C₂²	semidirect
32. #88194	C₂²	semidirect
37. #88192	C₂²	semidirect
38. #88192	C₂²	semidirect
39. #88190	C₂²	semidirect
40. #88184	C₂²	semidirect
41. #88183	C₂²	semidirect
42. #88183	C₂²	semidirect
43. C₄×C₂²⋊D₁₃	C₂²	semidirect
44. C₄×C₂²⋊D₁₃	C₂²	semidirect
46. #88180	C₂²	semidirect
48. #88178	C₂²	semidirect
49. #88151	C₂²	semidirect
50. #88151	C₂²	semidirect
51. #88149	C₂²	semidirect
52. #88149	C₂²	semidirect
53. #88146	C₂²	semidirect
54. #88146	C₂²	semidirect
55. #88146	C₂²	semidirect
56. C₄⋊C₄×D₁₃	C₂²	semidirect
57. C₄⋊C₄×D₁₃	C₂²	semidirect
58. C₄⋊C₄×D₁₃	C₂²	semidirect
59. #88144	C₂²	semidirect
60. #88142	C₂²	semidirect
62. #88139	C₂²	semidirect
63. #88139	C₂²	semidirect
64. #88138	C₂²	semidirect
65. #88138	C₂²	semidirect
66. #88137	C₂²	semidirect
67. #88137	C₂²	semidirect
71. #88133	C₂²	semidirect
72. #88133	C₂²	semidirect
75. C₄×D₅₂	C₂²	semidirect
76. C₄×D₅₂	C₂²	semidirect
77. C₄×D₅₂	C₂²	semidirect
78. #88126	C₂²	semidirect
79. C₄²×D₁₃	C₂²	semidirect
80. #88124	C₂²	semidirect
81. #88123	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
169. C₂×C₄×C₁₃	#41	semidirect
217. #518	D₁₃	semidirect
293. C₄×D₄	C₂×D₁₃	semidirect
294. C₄×D₄	C₂×D₁₃	semidirect
295. C₄×D₄	C₂×D₁₃	semidirect
296. C₄×D₄	C₂×D₁₃	semidirect
392. C₁₃	#3494	semidirect
434. C₂×C₄	#6127	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#518	2
#11719510	2
C₂×#88192	2
#11719268	2
#11719267	2
#11719266	2
#11719263	2
#11719262	2
#11719256	2
#11719253	2
#11719229	2
#11719228	2
D₁₃×#117	2
#11719224	2
#11719200	2
#11719195	2
#3494	13