Subgroups — #13128715

Order 1664.

992 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
5	D₁₃×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
6	#11719399	C₂	1	2	yes	maximal, complemented
7	#11719390	C₂	1	2	yes	maximal, complemented
8	#11719346	C₂	1	2	yes	maximal, complemented
9	#11719344	C₂	1	2	yes	maximal, complemented
10	#11719333	C₂	1	2	yes	maximal
11	#11719330	C₂	1	2	yes	maximal, complemented
12	#11719288	C₂	1	2	yes	maximal, complemented
13	#11719286	C₂	1	2	yes	maximal, complemented
14	#11719277	C₂	1	2	yes	maximal, complemented
15	#11719274	C₂	1	2	yes	maximal, complemented
16	#11719238	C₂	1	2	yes	maximal, complemented
17	#11719234	C₂	1	2	yes	maximal, complemented
18	C₄×#6127	C₂	1	1	yes	maximal, characteristic
19	#11719175	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×Q₈×D₁₃	C₂²	1	2	yes	—
21	C₂×#6127	C₂²	1	1	yes	characteristic
22	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₁₃×#125	C₂²	1	2	yes	—
25	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
26	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	—
27	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
28	C₄×Q₈×C₁₃	C₂²	1	2	yes	—
29	C₁₃×#117	C₂²	1	2	yes	—
30	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic
31	#88200	C₂²	1	2	yes	—
32	#88200	C₂²	1	2	yes	—
33	#88200	C₂²	1	2	yes	—
34	Q₈×Dic₁₃	C₂²	1	2	yes	—
35	Q₈×Dic₁₃	C₂²	1	2	yes	—
36	Q₈×Dic₁₃	C₂²	1	2	yes	—
37	#88198	C₂²	1	2	yes	—
38	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
42	#88180	C₂²	1	2	yes	—
43	#88180	C₂²	1	1	yes	characteristic
44	#88178	C₂²	1	2	yes	—
45	#88178	C₂²	1	2	yes	—
46	#88152	C₂²	1	4	yes	—
47	#88151	C₂²	1	2	yes	—
48	#88151	C₂²	1	2	yes	—
49	#88151	C₂²	1	2	yes	—
50	#88148	C₂²	1	4	yes	—
51	#88146	C₂²	1	2	yes	—
52	#88146	C₂²	1	2	yes	—
53	#88146	C₂²	1	2	yes	—
54	#88146	C₂²	1	4	yes	—
55	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
56	C₄⋊C₄×D₁₃	C₂²	1	2	yes	—
57	#88144	C₂²	1	2	yes	—
58	#88144	C₂²	1	2	yes	—
59	#88144	C₂²	1	2	yes	—
60	#88144	C₂²	1	4	yes	—
61	#88143	C₂²	1	4	yes	—
62	#88143	C₂²	1	4	yes	—
63	#88142	C₂²	1	2	yes	—
64	#88142	C₂²	1	2	yes	—
65	#88142	C₂²	1	4	yes	—
66	#88141	C₂²	1	2	yes	—
67	#88141	C₂²	1	2	yes	—
68	#88141	C₂²	1	2	yes	—
69	#88141	C₂²	1	4	yes	—
70	#88139	C₂²	1	4	yes	—
71	#88137	C₂²	1	4	yes	—
72	#88133	C₂²	1	4	yes	—
73	#88133	C₂²	1	4	yes	—
74	#88130	C₂²	1	4	yes	—
75	C₄×D₅₂	C₂²	1	1	yes	characteristic
76	C₄×D₅₂	C₂²	1	1	yes	characteristic
77	#88126	C₂²	1	1	yes	characteristic
78	#88126	C₂²	1	1	yes	characteristic
79	#88126	C₂²	1	4	yes	—
80	C₄²×D₁₃	C₂²	1	1	yes	characteristic
81	C₄²×D₁₃	C₂²	1	1	yes	characteristic
82	#88124	C₂²	1	2	yes	—
83	#88124	C₂²	1	4	yes	—
84	#88123	C₂²	1	1	yes	characteristic
85	#88123	C₂²	1	1	yes	characteristic
86	C₄×Dic₂₆	C₂²	1	2	yes	—
87	C₄×Dic₂₆	C₂²	1	2	yes	—
88	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
89	C₄×Dic₂₆	C₂²	1	1	yes	characteristic
90	C₄×Dic₂₆	C₂²	1	4	yes	—
91	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
92	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
93	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
95	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₃	C₂³	1	1	yes	characteristic
98	Q₈×D₁₃	—	2	8	no	—
99	#6127	—	2	4	no	—
100	C₂×D₅₂	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	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂³	1	4	yes	—
107	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
108	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
109	C₂×Dic₂₆	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	4	yes	—
114	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
115	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
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	C₄²×C₁₃	C₂³	1	1	yes	characteristic
120	C₄²×C₁₃	C₂³	1	1	yes	characteristic
121	C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₄²×C₁₃	C₂³	1	4	yes	—
123	C₄²×C₁₃	C₂³	1	1	yes	characteristic
124	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
125	C₂²⋊Dic₁₃	C₂³	1	1	yes	characteristic
126	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
127	#6103	C₂³	1	1	yes	characteristic
128	#6103	C₂³	1	1	yes	characteristic
129	#6103	C₂³	1	1	yes	characteristic
130	#6103	C₂³	1	1	yes	characteristic
131	#6103	C₂³	1	4	yes	—
132	#6103	C₂³	1	4	yes	—
133	#6103	C₂³	1	4	yes	—
134	C₄⋊Dic₁₃	C₂³	1	2	yes	—
135	C₄⋊Dic₁₃	C₂³	1	2	yes	—
136	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
137	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
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	4	yes	—
143	#6101	C₂³	1	1	yes	characteristic
144	#6101	C₂³	1	4	yes	—
145	#6101	C₂³	1	1	yes	characteristic
146	#6101	C₂³	1	4	yes	—
147	#6101	C₂³	1	1	yes	characteristic
148	#6101	C₂³	1	1	yes	characteristic
149	#6101	C₂³	1	4	yes	—
150	#6101	C₂³	1	4	yes	—
151	#6101	C₂³	1	4	yes	—
152	#6101	C₂³	1	4	yes	—
153	#6101	C₂³	1	4	yes	—
154	C₄×Dic₁₃	C₂³	1	4	yes	—
155	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
156	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
157	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
158	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
159	C₄×Dic₁₃	C₂³	1	4	yes	—
160	C₄×Dic₁₃	C₂³	1	4	yes	—
161	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
162	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
163	C₄×Dic₁₃	C₂³	1	4	yes	—
164	#3509	—	13	1	no	maximal, Sylow
165	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
167	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
168	Q₈×C₁₃	—	2	4	no	—
169	Q₈×C₁₃	—	2	4	no	—
170	C₂×C₄×C₁₃	—	2	2	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	2	no	—
173	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
176	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
178	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
179	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
181	C₂²⋊D₁₃	—	2	2	no	—
182	C₂²⋊D₁₃	—	2	2	no	—
183	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
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	1	yes	characteristic
189	C₂×Dic₁₃	C₂⁴	1	4	yes	—
190	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
191	D₅₂	—	2	2	no	—
192	C₄×D₁₃	—	2	8	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	2	no	—
198	C₄×D₁₃	#41	1	4	yes	—
199	Dic₂₆	—	2	4	no	—
200	Dic₂₆	—	2	4	no	—
201	Dic₂₆	—	2	2	no	—
202	Dic₂₆	—	2	8	no	—
203	#557	—	13	2	no	—
204	#557	—	13	2	no	—
205	#556	—	13	2	no	—
206	#556	—	13	2	no	—
207	#552	—	13	2	no	—
208	#552	—	13	2	no	—
209	#552	—	13	2	no	—
210	#552	—	13	2	no	—
211	#541	—	13	2	no	—
212	#541	—	13	2	no	—
213	#536	—	13	2	no	—
214	#533	—	13	1	no	—
215	#533	—	13	1	no	—
216	#533	—	13	1	no	—
217	#533	—	13	1	no	—
218	#533	D₁₃	1	1	yes	characteristic, complemented
219	C₂×C₄⋊Q₈	—	13	1	no	—
220	#519	—	13	2	no	—
221	C₄×#41	—	13	1	no	—
222	C₂²×C₁₃	—	2	1	no	—
223	C₂²×C₁₃	—	2	1	no	—
224	C₂²×C₁₃	—	2	1	no	—
225	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
226	C₂×D₁₃	—	2	1	no	—
227	C₂×D₁₃	—	2	1	no	—
228	C₂×D₁₃	—	2	1	no	—
229	C₂×D₁₃	—	2	1	no	—
230	C₂×D₁₃	—	2	1	no	—
231	C₂×D₁₃	C₂×#41	1	2	yes	—
232	C₄×C₁₃	—	2	4	no	—
233	C₄×C₁₃	—	2	1	no	—
234	C₄×C₁₃	—	2	1	no	—
235	C₄×C₁₃	—	2	1	no	—
236	C₄×C₁₃	—	2	4	no	—
237	C₄×C₁₃	C₂×#41	1	2	yes	—
238	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
239	C₄×C₁₃	2₋¹⁺⁴	1	2	yes	—
240	Dic₁₃	—	2	4	no	—
241	Dic₁₃	—	2	1	no	—
242	Dic₁₃	—	2	4	no	—
243	Dic₁₃	—	2	1	no	—
244	Dic₁₃	—	2	1	no	—
245	Dic₁₃	—	2	1	no	—
246	Dic₁₃	—	2	1	no	—
247	Dic₁₃	C₂×#41	1	2	yes	—
248	C₂×#41	—	13	1	no	—
249	C₂²×Q₈	—	13	2	no	—
250	C₄⋊Q₈	—	13	2	no	—
251	C₄⋊Q₈	—	13	2	no	—
252	C₄⋊Q₈	—	13	2	no	—
253	C₄⋊Q₈	—	13	4	no	—
254	C₄⋊Q₈	—	13	1	no	—
255	C₄⋊Q₈	—	13	1	no	—
256	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
257	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic
258	#126	—	13	4	no	—
259	#126	—	13	4	no	—
260	#126	—	13	4	no	—
261	#126	—	13	4	no	—
262	#125	—	13	2	no	—
263	#125	—	13	2	no	—
264	#125	—	13	2	no	—
265	#125	—	13	4	no	—
266	#125	—	13	4	no	—
267	#125	—	13	4	no	—
268	#125	—	13	2	no	—
269	#125	—	13	4	no	—
270	#125	C₂×D₁₃	1	2	yes	—
271	#124	—	13	4	no	—
272	#123	—	13	4	no	—
273	#123	—	13	4	no	—
274	C₂²⋊Q₈	—	13	2	no	—
275	C₂²⋊Q₈	—	13	2	no	—
276	C₂²⋊Q₈	—	13	2	no	—
277	C₂²⋊Q₈	—	13	2	no	—
278	C₂²⋊Q₈	—	13	2	no	—
279	C₂²⋊Q₈	—	13	2	no	—
280	C₂²⋊Q₈	—	13	2	no	—
281	C₂²⋊Q₈	—	13	2	no	—
282	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
283	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	—
284	C₄×Q₈	—	13	2	no	—
285	C₄×Q₈	—	13	2	no	—
286	C₄×Q₈	—	13	2	no	—
287	C₄×Q₈	—	13	2	no	—
288	C₄×Q₈	—	13	4	no	—
289	C₄×Q₈	—	13	2	no	—
290	C₄×Q₈	—	13	2	no	—
291	C₄×Q₈	—	13	1	no	—
292	C₄×Q₈	—	13	1	no	—
293	C₄×Q₈	—	13	2	no	—
294	C₄×Q₈	—	13	4	no	—
295	C₄×Q₈	—	13	2	no	—
296	C₄×Q₈	C₂×D₁₃	1	2	yes	—
297	C₄×Q₈	C₂×D₁₃	1	2	yes	—
298	C₄×D₄	—	13	1	no	—
299	C₄×D₄	—	13	1	no	—
300	C₄×D₄	—	13	1	no	—
301	C₄×D₄	—	13	1	no	—
302	C₄×D₄	—	13	1	no	—
303	C₄×D₄	—	13	1	no	—
304	#117	—	13	1	no	—
305	#117	—	13	2	no	—
306	#117	—	13	2	no	—
307	#117	—	13	4	no	—
308	#117	—	13	2	no	—
309	#117	—	13	2	no	—
310	#117	—	13	1	no	—
311	#117	—	13	1	no	—
312	#117	—	13	4	no	—
313	#117	C₂×D₁₃	1	2	yes	—
314	C₂×C₄⋊C₄	—	13	2	no	—
315	C₂×C₄⋊C₄	—	13	2	no	—
316	C₂×C₄²	—	13	1	no	—
317	C₂×C₄²	—	13	1	no	—
318	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic
319	C₂×C₁₃	—	4	1	no	—
320	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
321	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
322	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	D₁₃	—	2	2	no	—
324	D₁₃	—	4	1	no	—
325	#41	—	26	4	no	—
326	C₂×Q₈	—	13	2	no	—
327	C₂×Q₈	—	13	2	no	—
328	C₂×Q₈	—	13	4	no	—
329	C₂×Q₈	—	13	1	no	—
330	C₂×Q₈	—	26	8	no	—
331	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
332	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
333	C₂×D₄	—	13	1	no	—
334	C₂×D₄	—	13	1	no	—
335	C₂×D₄	—	13	1	no	—
336	C₂²×C₄	—	13	1	no	—
337	C₂²×C₄	—	13	1	no	—
338	C₂²×C₄	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	4	no	—
343	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
344	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
345	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
346	C₄⋊C₄	—	13	2	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	1	no	—
352	C₄⋊C₄	—	13	1	no	—
353	C₄⋊C₄	—	13	1	no	—
354	C₄⋊C₄	—	13	1	no	—
355	C₄⋊C₄	—	13	1	no	—
356	C₄⋊C₄	—	13	1	no	—
357	C₄⋊C₄	—	13	2	no	—
358	C₄⋊C₄	—	13	4	no	—
359	C₄⋊C₄	—	13	4	no	—
360	C₄⋊C₄	—	13	4	no	—
361	C₄⋊C₄	—	13	4	no	—
362	C₄⋊C₄	—	13	4	no	—
363	C₄⋊C₄	—	13	4	no	—
364	C₄⋊C₄	—	13	4	no	—
365	C₄⋊C₄	—	13	4	no	—
366	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
367	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
368	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
369	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
370	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
371	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
372	C₂²⋊C₄	—	13	1	no	—
373	C₂²⋊C₄	—	13	1	no	—
374	C₂²⋊C₄	—	13	4	no	—
375	C₂²⋊C₄	—	13	1	no	—
376	C₂²⋊C₄	—	13	1	no	—
377	C₂²⋊C₄	—	13	4	no	—
378	C₂²⋊C₄	—	13	1	no	—
379	C₂²⋊C₄	—	13	1	no	—
380	C₂²⋊C₄	—	13	4	no	—
381	C₂²⋊C₄	—	13	4	no	—
382	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
383	C₄²	—	13	1	no	—
384	C₄²	—	13	1	no	—
385	C₄²	—	13	1	no	—
386	C₄²	—	13	1	no	—
387	C₄²	—	13	1	no	—
388	C₄²	—	13	1	no	—
389	C₄²	—	13	4	no	—
390	C₄²	—	13	4	no	—
391	C₄²	—	13	4	no	—
392	C₄²	—	13	4	no	—
393	C₄²	C₂²×D₁₃	1	1	yes	characteristic
394	C₄²	C₂²×D₁₃	1	1	yes	characteristic
395	C₄²	C₂²×D₁₃	1	1	yes	characteristic
396	C₄²	C₂²×D₁₃	1	1	yes	characteristic
397	C₄²	C₂²×D₁₃	1	4	yes	—
398	C₁₃	#3509	1	1	yes	characteristic, complemented, Sylow
399	C₂³	—	13	1	no	—
400	C₂³	—	13	1	no	—
401	C₂³	C₂³×D₁₃	1	1	yes	characteristic
402	Q₈	—	2	4	no	—
403	Q₈	—	2	4	no	—
404	Q₈	—	26	8	no	—
405	Q₈	—	26	2	no	—
406	Q₈	—	26	4	no	—
407	Q₈	—	26	4	no	—
408	D₄	—	26	2	no	—
409	D₄	—	26	2	no	—
410	D₄	—	26	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	13	1	no	—
415	C₂×C₄	—	13	4	no	—
416	C₂×C₄	—	13	1	no	—
417	C₂×C₄	—	13	1	no	—
418	C₂×C₄	—	13	4	no	—
419	C₂×C₄	—	13	1	no	—
420	C₂×C₄	—	13	1	no	—
421	C₂×C₄	—	13	4	no	—
422	C₂×C₄	—	13	1	no	—
423	C₂×C₄	—	26	8	no	—
424	C₂×C₄	—	26	2	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	C₂³×D₁₃	1	1	yes	characteristic
430	C₂×C₄	C₂³×D₁₃	1	4	yes	—
431	C₂×C₄	C₂³×D₁₃	1	4	yes	—
432	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
433	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
434	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
435	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
436	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	13	2	no	—
441	C₂²	—	26	1	no	—
442	C₂²	—	26	1	no	—
443	C₂²	—	26	1	no	—
444	C₂²	—	26	1	no	—
445	C₂²	—	26	1	no	—
446	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
447	C₄	—	2	1	no	—
448	C₄	—	2	1	no	—
449	C₄	—	2	4	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	4	no	—
452	C₄	—	13	2	no	—
453	C₄	—	26	1	no	—
454	C₄	—	26	1	no	—
455	C₄	—	26	4	no	—
456	C₄	—	26	1	no	—
457	C₄	—	26	4	no	—
458	C₄	—	26	1	no	—
459	C₄	—	26	1	no	—
460	C₄	#88254	1	2	yes	—
461	C₄	#41×D₁₃	1	2	yes	—
462	C₄	#88257	1	2	yes	—
463	C₂	—	4	1	no	—
464	C₂	—	26	2	no	—
465	C₂	—	52	1	no	—
466	C₂	C₂×#88254	1	1	yes	characteristic
467	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
468	C₂	C₂×#88257	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#533	C₂
prime radical	C₂×#6127	C₂²
hypercenter	#533	D₁₃
hypocenter	C₁₃	#3509
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #533

Complements

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

N	H ≅ G/N	type
1. C₁₃×#533	C₂	semidirect
2. #11719433	C₂	semidirect
3. #11719433	C₂	semidirect
4. #11719433	C₂	semidirect
5. D₁₃×C₄⋊Q₈	C₂	semidirect
6. #11719399	C₂	semidirect
7. #11719390	C₂	semidirect
8. #11719346	C₂	semidirect
9. #11719344	C₂	semidirect
11. #11719330	C₂	semidirect
12. #11719288	C₂	semidirect
13. #11719286	C₂	semidirect
14. #11719277	C₂	semidirect
15. #11719274	C₂	semidirect
16. #11719238	C₂	semidirect
17. #11719234	C₂	semidirect
19. #11719175	C₂	semidirect
218. #533	D₁₃	semidirect
398. C₁₃	#3509	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#533	2
#11719433	2
D₁₃×C₄⋊Q₈	2
#11719399	2
#11719390	2
#11719346	2
#11719344	2
#11719333	2
#11719330	2
#11719288	2
#11719286	2
#11719277	2
#11719274	2
#11719238	2
#11719234	2
C₄×#6127	2
#11719175	2
#3509	13