Subgroups — #13128884

Order 1664.

1124 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719431	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719412	C₂	1	4	yes	maximal, complemented
5	#11719410	C₂	1	4	yes	maximal, complemented
6	#11719387	C₂	1	2	yes	maximal, complemented
7	#11719381	C₂	1	2	yes	maximal, complemented
8	#11719338	C₂	1	2	yes	maximal, complemented
9	D₁₃×C₂²⋊Q₈	C₂	1	2	yes	maximal, complemented
10	#11719285	C₂	1	1	yes	maximal, characteristic, complemented
11	#11719284	C₂	1	2	yes	maximal, complemented
12	Q₈×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719279	C₂	1	2	yes	maximal, complemented
14	#11719256	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#11719234	C₂	1	2	yes	maximal, complemented
17	#11719229	C₂	1	2	yes	maximal, complemented
18	C₂×#6131	C₂²	1	2	yes	—
19	C₂×Q₈×D₁₃	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂×#6127	C₂²	1	2	yes	complemented
22	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
24	C₁₃×#126	C₂²	1	4	yes	complemented
25	C₁₃×#124	C₂²	1	2	yes	—
26	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
27	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
28	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
30	C₁₃×#117	C₂²	1	2	yes	complemented
31	#88201	C₂²	1	1	yes	characteristic, complemented
32	#88200	C₂²	1	2	yes	—
33	#88200	C₂²	1	1	yes	characteristic
34	#88200	C₂²	1	2	yes	complemented
35	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
36	#88192	C₂²	1	2	yes	—
37	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
38	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
39	#88178	C₂²	1	2	yes	complemented
40	#88152	C₂²	1	2	yes	complemented
41	#88151	C₂²	1	2	yes	—
42	#88151	C₂²	1	2	yes	complemented
43	#88151	C₂²	1	4	yes	complemented
44	#88150	C₂²	1	4	yes	—
45	#88150	C₂²	1	4	yes	complemented
46	#88149	C₂²	1	1	yes	characteristic
47	#88149	C₂²	1	2	yes	complemented
48	#88148	C₂²	1	2	yes	—
49	#88148	C₂²	1	4	yes	complemented
50	#88147	C₂²	1	1	yes	characteristic
51	#88147	C₂²	1	4	yes	complemented
52	#88146	C₂²	1	2	yes	—
53	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
54	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
55	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
56	C₄⋊C₄×D₁₃	C₂²	1	4	yes	complemented
57	#88144	C₂²	1	2	yes	complemented
58	#88144	C₂²	1	1	yes	characteristic, complemented
59	#88141	C₂²	1	2	yes	complemented
60	#88140	C₂²	1	4	yes	complemented
61	#88139	C₂²	1	4	yes	complemented
62	#88138	C₂²	1	4	yes	—
63	#88137	C₂²	1	4	yes	—
64	#88137	C₂²	1	4	yes	complemented
65	#88136	C₂²	1	4	yes	—
66	#88135	C₂²	1	2	yes	—
67	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
68	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	—
69	#88133	C₂²	1	4	yes	complemented
70	#88132	C₂²	1	4	yes	complemented
71	C₄×D₅₂	C₂²	1	1	yes	characteristic
72	C₄×D₅₂	C₂²	1	4	yes	—
73	C₄×D₅₂	C₂²	1	2	yes	—
74	C₄×D₅₂	C₂²	1	2	yes	—
75	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
76	C₄×D₅₂	C₂²	1	4	yes	complemented
77	#88126	C₂²	1	4	yes	complemented
78	#88126	C₂²	1	2	yes	complemented
79	C₄²×D₁₃	C₂²	1	1	yes	characteristic
80	#88124	C₂²	1	4	yes	complemented
81	#88123	C₂²	1	1	yes	characteristic, complemented
82	#88123	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
85	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
90	C₂²×Dic₁₃	C₂³	1	2	yes	—
91	#6131	—	2	8	no	—
92	Q₈×D₁₃	—	4	4	no	—
93	D₄×D₁₃	—	2	4	no	—
94	#6127	—	4	4	no	—
95	C₂×D₅₂	C₂³	1	2	yes	—
96	C₂×D₅₂	C₂³	1	4	yes	—
97	C₂×D₅₂	C₂³	1	1	yes	characteristic
98	C₂×D₅₂	C₂³	1	1	yes	characteristic
99	C₂×C₄×D₁₃	—	4	4	no	—
100	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₃	C₂³	1	4	yes	—
105	C₂×C₄×D₁₃	C₂³	1	2	yes	—
106	C₂×C₄×D₁₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₃	C₂³	1	4	yes	—
108	C₂×C₄×D₁₃	C₂³	1	4	yes	—
109	C₂×C₄×D₁₃	C₂³	1	2	yes	—
110	C₂×Dic₂₆	C₂³	1	2	yes	—
111	C₂×Dic₂₆	C₂³	1	4	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
115	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
116	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
117	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
118	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
119	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
120	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
121	C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₄²×C₁₃	C₂³	1	2	yes	—
123	C₄²×C₁₃	C₂³	1	4	yes	—
124	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
125	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
126	#6103	C₂³	1	2	yes	—
127	#6103	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	2	yes	—
132	#6103	C₂³	1	4	yes	—
133	#6103	C₂³	1	2	yes	—
134	#6103	C₂³	1	4	yes	—
135	#6103	C₂³	1	2	yes	—
136	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₁₃	C₂³	1	2	yes	—
138	C₄⋊Dic₁₃	C₂³	1	4	yes	—
139	C₄⋊Dic₁₃	C₂³	1	2	yes	—
140	C₄⋊Dic₁₃	C₂³	1	2	yes	—
141	C₄⋊Dic₁₃	C₂³	1	4	yes	—
142	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
143	#6101	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	1	yes	characteristic
150	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
151	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
152	C₄×Dic₁₃	C₂³	1	4	yes	—
153	#3520	—	13	1	no	maximal, Sylow
154	C₂³×C₁₃	C₂⁴	1	2	yes	—
155	C₂²×D₁₃	—	2	4	no	—
156	C₂²×D₁₃	—	2	4	no	—
157	C₂²×D₁₃	—	4	2	no	—
158	C₂²×D₁₃	C₂⁴	1	2	yes	—
159	C₂²×D₁₃	C₂⁴	1	2	yes	—
160	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
161	Q₈×C₁₃	—	2	4	no	—
162	Q₈×C₁₃	—	2	2	no	—
163	D₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	4	no	—
165	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
170	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²⋊D₁₃	—	2	4	no	—
173	C₂²⋊D₁₃	—	4	4	no	—
174	C₂×Dic₁₃	—	4	2	no	—
175	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×Dic₁₃	C₂⁴	1	4	yes	—
179	C₂×Dic₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₃	C₂⁴	1	2	yes	—
181	D₅₂	—	2	8	no	—
182	D₅₂	—	2	4	no	—
183	D₅₂	—	2	2	no	—
184	D₅₂	#41	1	4	yes	complemented
185	C₄×D₁₃	—	2	8	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	2	no	—
188	C₄×D₁₃	—	2	4	no	—
189	C₄×D₁₃	—	2	2	no	—
190	C₄×D₁₃	—	2	4	no	—
191	C₄×D₁₃	—	4	2	no	—
192	C₄×D₁₃	—	4	2	no	—
193	C₄×D₁₃	—	4	4	no	—
194	C₄×D₁₃	—	4	4	no	—
195	Dic₂₆	—	2	4	no	—
196	Dic₂₆	—	4	4	no	—
197	#556	D₁₃	1	1	yes	characteristic, complemented
198	#554	—	13	2	no	—
199	#552	—	13	2	no	—
200	#551	—	13	4	no	—
201	D₄×Q₈	—	13	1	no	—
202	#548	—	13	2	no	—
203	#547	—	13	1	no	—
204	#547	—	13	1	no	—
205	#546	—	13	2	no	—
206	#542	—	13	2	no	—
207	#539	—	13	4	no	—
208	#533	—	13	1	no	—
209	#529	—	13	1	no	—
210	#525	—	13	2	no	—
211	C₂×C₂²⋊Q₈	—	13	2	no	—
212	#520	—	13	2	no	—
213	C₂×C₄×D₄	—	13	1	no	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	—	2	2	no	—
216	C₂²×C₁₃	—	2	2	no	—
217	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
218	C₂×D₁₃	—	2	1	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	—	2	1	no	—
221	C₂×D₁₃	—	2	2	no	—
222	C₂×D₁₃	—	2	2	no	—
223	C₂×D₁₃	—	2	2	no	—
224	C₂×D₁₃	—	2	2	no	—
225	C₂×D₁₃	—	4	8	no	—
226	C₂×D₁₃	C₂×#41	1	4	yes	—
227	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
228	C₄×C₁₃	—	2	4	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	2	no	—
231	C₄×C₁₃	—	2	1	no	—
232	C₄×C₁₃	—	2	2	no	—
233	C₄×C₁₃	C₂×#41	1	2	yes	—
234	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
235	Dic₁₃	—	2	2	no	—
236	Dic₁₃	—	2	1	no	—
237	Dic₁₃	—	2	4	no	—
238	Dic₁₃	—	2	2	no	—
239	Dic₁₃	—	2	1	no	—
240	Dic₁₃	—	2	1	no	—
241	C₂×#41	—	13	2	no	—
242	C₂×#41	—	13	2	no	—
243	C₂²×Q₈	—	13	2	no	—
244	C₂²×D₄	—	13	1	no	—
245	C₂³×C₄	—	13	2	no	—
246	C₄⋊Q₈	—	13	1	no	—
247	C₄⋊Q₈	—	13	2	no	—
248	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
249	#126	—	13	2	no	—
250	#126	—	13	4	no	—
251	#126	C₂×D₁₃	1	4	yes	complemented
252	#125	—	13	1	no	—
253	#125	—	13	2	no	—
254	#125	—	13	4	no	—
255	#124	—	13	1	no	—
256	#124	—	13	4	no	—
257	#124	C₂×D₁₃	1	2	yes	—
258	#123	—	13	2	no	—
259	#123	—	13	4	no	—
260	#123	—	13	4	no	—
261	#123	—	13	4	no	—
262	#123	—	13	4	no	—
263	C₂²⋊Q₈	—	13	1	no	—
264	C₂²⋊Q₈	—	13	2	no	—
265	C₂²⋊Q₈	—	13	2	no	—
266	C₂²⋊Q₈	—	13	2	no	—
267	C₂²⋊Q₈	—	13	2	no	—
268	C₂²⋊Q₈	—	13	4	no	—
269	C₂²⋊Q₈	—	13	2	no	—
270	C₂²⋊Q₈	—	13	4	no	—
271	C₂²⋊Q₈	—	13	4	no	—
272	C₂²⋊Q₈	—	13	4	no	—
273	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
274	#121	—	13	2	no	—
275	#121	—	13	1	no	—
276	#121	—	13	2	no	—
277	#121	—	13	4	no	—
278	#120	—	13	4	no	—
279	C₄×Q₈	—	13	2	no	—
280	C₄×Q₈	—	13	2	no	—
281	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
282	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
283	C₄×D₄	—	13	1	no	—
284	C₄×D₄	—	13	2	no	—
285	C₄×D₄	—	13	1	no	—
286	C₄×D₄	—	13	4	no	—
287	C₄×D₄	—	13	2	no	—
288	C₄×D₄	—	13	1	no	—
289	C₄×D₄	—	13	4	no	—
290	C₄×D₄	—	13	2	no	—
291	C₄×D₄	—	13	4	no	—
292	C₄×D₄	—	13	2	no	—
293	C₄×D₄	—	13	1	no	—
294	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
295	#117	—	13	2	no	—
296	#117	—	13	2	no	—
297	#117	—	13	4	no	—
298	#117	C₂×D₁₃	1	2	yes	complemented
299	C₂×C₄⋊C₄	—	13	1	no	—
300	C₂×C₄⋊C₄	—	13	4	no	—
301	C₂×C₄⋊C₄	—	13	2	no	—
302	C₂×C₄⋊C₄	—	13	2	no	—
303	C₂×C₂²⋊C₄	—	13	2	no	—
304	C₂×C₂²⋊C₄	—	13	4	no	—
305	C₂×C₄²	—	13	1	no	—
306	C₂×C₁₃	—	4	2	no	—
307	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
308	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
309	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	D₁₃	—	2	2	no	—
311	D₁₃	—	2	4	no	—
312	D₁₃	—	4	2	no	—
313	C₂⁴	—	13	2	no	—
314	#41	—	26	8	no	—
315	#41	—	52	4	no	—
316	C₂×Q₈	—	13	2	no	—
317	C₂×Q₈	—	13	4	no	—
318	C₂×Q₈	—	52	4	no	—
319	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
320	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₂×D₄	—	13	2	no	—
322	C₂×D₄	—	13	4	no	—
323	C₂×D₄	—	13	1	no	—
324	C₂×D₄	—	13	2	no	—
325	C₂×D₄	—	13	4	no	—
326	C₂×D₄	—	13	1	no	—
327	C₂×D₄	—	26	4	no	—
328	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
329	C₂²×C₄	—	13	2	no	—
330	C₂²×C₄	—	13	1	no	—
331	C₂²×C₄	—	13	1	no	—
332	C₂²×C₄	—	13	1	no	—
333	C₂²×C₄	—	13	4	no	—
334	C₂²×C₄	—	13	2	no	—
335	C₂²×C₄	—	13	2	no	—
336	C₂²×C₄	—	13	4	no	—
337	C₂²×C₄	—	13	2	no	—
338	C₂²×C₄	—	13	2	no	—
339	C₂²×C₄	—	13	4	no	—
340	C₂²×C₄	—	52	4	no	—
341	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
342	C₄⋊C₄	—	13	2	no	—
343	C₄⋊C₄	—	13	4	no	—
344	C₄⋊C₄	—	13	1	no	—
345	C₄⋊C₄	—	13	2	no	—
346	C₄⋊C₄	—	13	1	no	—
347	C₄⋊C₄	—	13	2	no	—
348	C₄⋊C₄	—	13	4	no	—
349	C₄⋊C₄	—	13	4	no	—
350	C₄⋊C₄	—	13	2	no	—
351	C₄⋊C₄	—	13	2	no	—
352	C₄⋊C₄	—	13	4	no	—
353	C₄⋊C₄	—	13	2	no	—
354	C₄⋊C₄	—	13	4	no	—
355	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
356	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
357	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
358	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
359	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
360	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
361	C₂²⋊C₄	—	13	2	no	—
362	C₂²⋊C₄	—	13	4	no	—
363	C₂²⋊C₄	—	13	2	no	—
364	C₂²⋊C₄	—	13	2	no	—
365	C₂²⋊C₄	—	13	4	no	—
366	C₂²⋊C₄	—	13	2	no	—
367	C₂²⋊C₄	—	13	4	no	—
368	C₂²⋊C₄	—	13	2	no	—
369	C₂²⋊C₄	—	13	2	no	—
370	C₂²⋊C₄	—	13	2	no	—
371	C₂²⋊C₄	—	13	4	no	—
372	C₂²⋊C₄	—	13	2	no	—
373	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
374	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
375	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
376	C₄²	—	13	1	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	4	no	—
380	C₄²	C₂²×D₁₃	1	1	yes	characteristic
381	C₄²	C₂²×D₁₃	1	4	yes	—
382	C₄²	C₂²×D₁₃	1	2	yes	—
383	C₁₃	#3520	1	1	yes	characteristic, complemented, Sylow
384	C₂³	—	13	1	no	—
385	C₂³	—	13	2	no	—
386	C₂³	—	13	2	no	—
387	C₂³	—	26	4	no	—
388	C₂³	—	26	4	no	—
389	C₂³	—	52	2	no	—
390	C₂³	C₂³×D₁₃	1	2	yes	—
391	Q₈	—	2	4	no	—
392	Q₈	—	2	2	no	—
393	Q₈	—	26	4	no	—
394	Q₈	—	52	4	no	—
395	D₄	—	2	2	no	—
396	D₄	—	13	4	no	—
397	D₄	—	26	4	no	—
398	D₄	—	26	8	no	—
399	D₄	—	26	4	no	—
400	D₄	—	26	2	no	—
401	D₄	—	52	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	4	no	—
407	C₂×C₄	—	13	2	no	—
408	C₂×C₄	—	13	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	8	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	4	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	4	no	—
415	C₂×C₄	—	52	2	no	—
416	C₂×C₄	—	52	2	no	—
417	C₂×C₄	—	52	4	no	—
418	C₂×C₄	—	52	4	no	—
419	C₂×C₄	—	52	2	no	—
420	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₃	1	4	yes	—
422	C₂×C₄	C₂³×D₁₃	1	2	yes	—
423	C₂×C₄	C₂³×D₁₃	1	2	yes	—
424	C₂×C₄	C₂³×D₁₃	1	2	yes	—
425	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
426	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	13	4	no	—
431	C₂²	—	13	2	no	—
432	C₂²	—	26	1	no	—
433	C₂²	—	26	2	no	—
434	C₂²	—	26	1	no	—
435	C₂²	—	26	2	no	—
436	C₂²	—	26	2	no	—
437	C₂²	—	26	2	no	—
438	C₂²	—	26	2	no	—
439	C₂²	—	52	8	no	—
440	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
441	C₄	—	2	4	no	—
442	C₄	—	2	2	no	—
443	C₄	—	2	2	no	—
444	C₄	—	2	1	no	—
445	C₄	—	2	2	no	—
446	C₄	—	26	2	no	—
447	C₄	—	26	1	no	—
448	C₄	—	26	1	no	—
449	C₄	—	26	2	no	—
450	C₄	—	26	4	no	—
451	C₄	—	26	1	no	—
452	C₄	#41×D₁₃	1	2	yes	—
453	C₄	#88256	1	2	yes	—
454	C₂	—	4	2	no	—
455	C₂	—	26	2	no	—
456	C₂	—	26	4	no	—
457	C₂	—	52	2	no	—
458	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
459	C₂	C₂×#88256	1	1	yes	characteristic
460	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#556	C₂
hypercenter	#556	D₁₃
hypocenter	C₁₃	#3520
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. C₁₃×#556	C₂	semidirect
2. #11719433	C₂	semidirect
3. #11719431	C₂	semidirect
4. #11719412	C₂	semidirect
5. #11719410	C₂	semidirect
6. #11719387	C₂	semidirect
7. #11719381	C₂	semidirect
8. #11719338	C₂	semidirect
9. D₁₃×C₂²⋊Q₈	C₂	semidirect
10. #11719285	C₂	semidirect
11. #11719284	C₂	semidirect
12. Q₈×D₅₂	C₂	semidirect
13. #11719279	C₂	semidirect
14. #11719256	C₂	semidirect
15. C₄×D₄×D₁₃	C₂	semidirect
16. #11719234	C₂	semidirect
17. #11719229	C₂	semidirect
19. C₂×Q₈×D₁₃	C₂²	semidirect
21. C₂×#6127	C₂²	semidirect
23. C₁₃×C₄⋊Q₈	C₂²	semidirect
24. C₁₃×#126	C₂²	semidirect
26. C₁₃×C₂²⋊Q₈	C₂²	semidirect
27. C₄×Q₈×C₁₃	C₂²	semidirect
28. C₄×Q₈×C₁₃	C₂²	semidirect
30. C₁₃×#117	C₂²	semidirect
31. #88201	C₂²	semidirect
34. #88200	C₂²	semidirect
35. Q₈×Dic₁₃	C₂²	semidirect
39. #88178	C₂²	semidirect
40. #88152	C₂²	semidirect
42. #88151	C₂²	semidirect
43. #88151	C₂²	semidirect
45. #88150	C₂²	semidirect
47. #88149	C₂²	semidirect
49. #88148	C₂²	semidirect
51. #88147	C₂²	semidirect
54. C₄⋊C₄×D₁₃	C₂²	semidirect
55. C₄⋊C₄×D₁₃	C₂²	semidirect
56. C₄⋊C₄×D₁₃	C₂²	semidirect
57. #88144	C₂²	semidirect
58. #88144	C₂²	semidirect
59. #88141	C₂²	semidirect
60. #88140	C₂²	semidirect
61. #88139	C₂²	semidirect
64. #88137	C₂²	semidirect
69. #88133	C₂²	semidirect
70. #88132	C₂²	semidirect
75. C₄×D₅₂	C₂²	semidirect
76. C₄×D₅₂	C₂²	semidirect
77. #88126	C₂²	semidirect
78. #88126	C₂²	semidirect
80. #88124	C₂²	semidirect
81. #88123	C₂²	semidirect
82. #88123	C₂²	semidirect
184. D₅₂	#41	semidirect
197. #556	D₁₃	semidirect
248. C₄⋊Q₈	C₂×D₁₃	semidirect
251. #126	C₂×D₁₃	semidirect
273. C₂²⋊Q₈	C₂×D₁₃	semidirect
281. C₄×Q₈	C₂×D₁₃	semidirect
282. C₄×Q₈	C₂×D₁₃	semidirect
298. #117	C₂×D₁₃	semidirect
383. C₁₃	#3520	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#556	2
#11719433	2
#11719431	2
#11719412	2
#11719410	2
#11719387	2
#11719381	2
#11719338	2
D₁₃×C₂²⋊Q₈	2
#11719285	2
#11719284	2
Q₈×D₅₂	2
#11719279	2
#11719256	2
C₄×D₄×D₁₃	2
#11719234	2
#11719229	2
#3520	13