Subgroups — #13128402

Order 1664.

1132 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719439	C₂	1	1	yes	maximal, characteristic, complemented
3	#11719433	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719399	C₂	1	2	yes	maximal, complemented
5	#11719396	C₂	1	2	yes	maximal, complemented
6	#11719347	C₂	1	2	yes	maximal, complemented
7	#11719342	C₂	1	4	yes	maximal, complemented
8	#11719332	C₂	1	2	yes	maximal, complemented
9	#11719329	C₂	1	4	yes	maximal, complemented
10	#11719289	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#6131	C₂	1	1	yes	maximal, characteristic, complemented
12	#11719260	C₂	1	1	yes	maximal, characteristic, complemented
13	#11719259	C₂	1	2	yes	maximal, complemented
14	C₄×D₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#6129	C₂	1	2	yes	maximal, complemented
16	#11719219	C₂	1	2	yes	maximal, complemented
17	C₂×#88146	C₂	1	2	yes	maximal, complemented
18	C₂×#6131	C₂²	1	1	yes	characteristic
19	C₂×#6129	C₂²	1	2	yes	—
20	C₂×D₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₃	C₂²	1	2	yes	—
22	C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
23	C₁₃×#125	C₂²	1	2	yes	complemented
24	C₁₃×C₂²⋊Q₈	C₂²	1	4	yes	complemented
25	C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
26	C₄×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
27	C₄×D₄×C₁₃	C₂²	1	2	yes	—
28	C₄×D₄×C₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	2	yes	complemented
30	#88201	C₂²	1	4	yes	complemented
31	#88200	C₂²	1	2	yes	—
32	#88200	C₂²	1	2	yes	complemented
33	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
34	Q₈×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
35	D₄×Dic₁₃	C₂²	1	1	yes	characteristic
36	#88184	C₂²	1	4	yes	—
37	#88184	C₂²	1	2	yes	complemented
38	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	—
39	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
40	C₂×#6103	C₂²	1	4	yes	—
41	C₂×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
42	C₂×C₄×Dic₁₃	C₂²	1	4	yes	complemented
43	#88152	C₂²	1	4	yes	complemented
44	#88152	C₂²	1	4	yes	complemented
45	#88152	C₂²	1	4	yes	complemented
46	#88151	C₂²	1	2	yes	—
47	#88151	C₂²	1	2	yes	complemented
48	#88149	C₂²	1	2	yes	—
49	#88149	C₂²	1	2	yes	complemented
50	#88148	C₂²	1	4	yes	—
51	#88148	C₂²	1	4	yes	complemented
52	#88147	C₂²	1	1	yes	characteristic
53	#88147	C₂²	1	2	yes	—
54	#88147	C₂²	1	1	yes	characteristic, complemented
55	#88147	C₂²	1	4	yes	complemented
56	#88146	C₂²	1	2	yes	—
57	#88146	C₂²	1	1	yes	characteristic
58	#88146	C₂²	1	4	yes	—
59	#88146	C₂²	1	2	yes	complemented
60	#88146	C₂²	1	2	yes	complemented
61	#88146	C₂²	1	2	yes	complemented
62	#88146	C₂²	1	4	yes	complemented
63	#88146	C₂²	1	2	yes	complemented
64	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
65	#88144	C₂²	1	2	yes	complemented
66	#88144	C₂²	1	4	yes	complemented
67	#88141	C₂²	1	2	yes	complemented
68	#88140	C₂²	1	4	yes	—
69	#88140	C₂²	1	4	yes	complemented
70	#88136	C₂²	1	4	yes	—
71	#88135	C₂²	1	2	yes	—
72	#88135	C₂²	1	4	yes	complemented
73	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
74	#88131	C₂²	1	4	yes	complemented
75	#88129	C₂²	1	2	yes	—
76	C₄×D₅₂	C₂²	1	1	yes	characteristic
77	C₄×D₅₂	C₂²	1	2	yes	—
78	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
79	C₄²×D₁₃	C₂²	1	1	yes	characteristic
80	C₄²×D₁₃	C₂²	1	2	yes	complemented
81	#88123	C₂²	1	1	yes	characteristic, complemented
82	C₄×Dic₂₆	C₂²	1	2	yes	complemented
83	C₂³×D₁₃	C₂³	1	2	yes	—
84	C₂×Q₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂×D₄×C₁₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
89	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
90	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
91	C₂²×Dic₁₃	C₂³	1	4	yes	—
92	C₂²×Dic₁₃	C₂³	1	2	yes	—
93	#6131	—	2	4	no	—
94	#6129	—	2	8	no	—
95	D₄×D₁₃	—	2	4	no	—
96	C₂×D₅₂	C₂³	1	1	yes	characteristic
97	C₂×D₅₂	C₂³	1	2	yes	—
98	C₂×D₅₂	C₂³	1	1	yes	characteristic
99	C₂×D₅₂	C₂³	1	4	yes	—
100	C₂×C₄×D₁₃	—	2	8	no	—
101	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂³	1	2	yes	—
103	C₂×C₄×D₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₃	C₂³	1	2	yes	—
105	C₂×C₄×D₁₃	C₂³	1	2	yes	—
106	C₂×C₄×D₁₃	C₂³	1	2	yes	—
107	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂³	1	2	yes	—
109	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
110	C₂×Dic₂₆	C₂³	1	2	yes	—
111	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
112	C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
113	C₁₃×C₄⋊C₄	C₂³	1	4	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	2	yes	—
120	C₄²×C₁₃	C₂³	1	2	yes	—
121	C₄²×C₁₃	C₂³	1	1	yes	characteristic
122	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
123	#6103	C₂³	1	2	yes	—
124	#6103	C₂³	1	2	yes	—
125	#6103	C₂³	1	2	yes	—
126	#6103	C₂³	1	2	yes	—
127	#6103	C₂³	1	4	yes	—
128	#6103	C₂³	1	4	yes	—
129	#6103	C₂³	1	2	yes	—
130	#6103	C₂³	1	4	yes	—
131	#6103	C₂³	1	4	yes	—
132	#6103	C₂³	1	4	yes	—
133	#6103	C₂³	1	4	yes	—
134	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
135	C₄⋊Dic₁₃	C₂³	1	2	yes	—
136	C₄⋊Dic₁₃	C₂³	1	2	yes	—
137	C₄⋊Dic₁₃	C₂³	1	2	yes	—
138	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
139	C₄⋊Dic₁₃	C₂³	1	4	yes	—
140	C₄⋊Dic₁₃	C₂³	1	4	yes	—
141	#6101	C₂³	1	4	yes	—
142	#6101	C₂³	1	4	yes	—
143	#6101	C₂³	1	2	yes	—
144	C₄×Dic₁₃	C₂³	1	4	yes	—
145	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
146	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
147	C₄×Dic₁₃	C₂³	1	1	yes	characteristic
148	C₄×Dic₁₃	C₂³	1	2	yes	—
149	C₄×Dic₁₃	C₂³	1	2	yes	—
150	C₄×Dic₁₃	C₂³	1	4	yes	—
151	C₄×Dic₁₃	C₂³	1	4	yes	—
152	#3475	—	13	1	no	maximal, Sylow
153	C₂³×C₁₃	C₂⁴	1	2	yes	—
154	C₂²×D₁₃	—	2	4	no	—
155	C₂²×D₁₃	—	2	4	no	—
156	C₂²×D₁₃	—	4	2	no	—
157	C₂²×D₁₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₃	C₂⁴	1	2	yes	—
159	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
160	Q₈×C₁₃	—	2	2	no	—
161	Q₈×C₁₃	—	4	2	no	—
162	D₄×C₁₃	#41	1	4	yes	complemented
163	C₂×C₄×C₁₃	—	2	4	no	—
164	C₂×C₄×C₁₃	—	4	4	no	—
165	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
166	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
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	—	2	8	no	—
174	C₂×Dic₁₃	—	2	8	no	—
175	C₂×Dic₁₃	—	2	4	no	—
176	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₃	C₂⁴	1	2	yes	—
178	C₂×Dic₁₃	C₂⁴	1	2	yes	—
179	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂⁴	1	4	yes	—
181	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
182	D₅₂	—	2	4	no	—
183	D₅₂	—	2	2	no	—
184	D₅₂	—	2	2	no	—
185	D₅₂	—	4	4	no	—
186	C₄×D₁₃	—	2	4	no	—
187	C₄×D₁₃	—	2	4	no	—
188	C₄×D₁₃	—	2	2	no	—
189	C₄×D₁₃	—	2	4	no	—
190	C₄×D₁₃	—	2	4	no	—
191	C₄×D₁₃	—	2	4	no	—
192	C₄×D₁₃	—	4	2	no	—
193	C₄×D₁₃	—	4	1	no	—
194	C₄×D₁₃	#41	1	4	yes	complemented
195	Dic₂₆	—	2	4	no	—
196	#556	—	13	1	no	—
197	#555	—	13	1	no	—
198	#554	D₁₃	1	1	yes	characteristic, complemented
199	#553	—	13	2	no	—
200	#552	—	13	2	no	—
201	#552	—	13	2	no	—
202	#551	—	13	4	no	—
203	#547	—	13	1	no	—
204	#546	—	13	2	no	—
205	#533	—	13	1	no	—
206	#529	—	13	2	no	—
207	#529	—	13	4	no	—
208	#525	—	13	2	no	—
209	C₄×#41	—	13	1	no	—
210	C₄×#41	—	13	2	no	—
211	C₂×C₄×D₄	—	13	1	no	—
212	C₂×#117	—	13	2	no	—
213	C₂²×C₁₃	—	2	2	no	—
214	C₂²×C₁₃	—	2	2	no	—
215	C₂²×C₁₃	C₂×#41	1	4	yes	—
216	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
217	C₂×D₁₃	—	2	1	no	—
218	C₂×D₁₃	—	2	1	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	—	2	2	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	2	yes	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	—	2	2	no	—
229	C₄×C₁₃	—	2	2	no	—
230	C₄×C₁₃	—	2	1	no	—
231	C₄×C₁₃	—	2	4	no	—
232	C₄×C₁₃	C₂×#41	1	2	yes	—
233	C₄×C₁₃	C₂×#41	1	2	yes	—
234	Dic₁₃	—	2	4	no	—
235	Dic₁₃	—	2	2	no	—
236	Dic₁₃	—	2	2	no	—
237	Dic₁₃	—	2	1	no	—
238	Dic₁₃	—	2	1	no	—
239	Dic₁₃	C₂×#41	1	2	yes	—
240	C₂×#41	—	13	1	no	—
241	C₂×#41	—	13	2	no	—
242	C₂²×D₄	—	13	1	no	—
243	C₂³×C₄	—	13	2	no	—
244	C₄⋊Q₈	—	13	1	no	—
245	C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
246	#126	—	13	4	no	—
247	#126	—	13	4	no	—
248	#126	—	13	4	no	—
249	#125	—	13	4	no	—
250	#125	—	13	2	no	—
251	#125	C₂×D₁₃	1	2	yes	complemented
252	#124	—	13	4	no	—
253	#124	—	13	2	no	—
254	#123	—	13	4	no	—
255	#123	—	13	4	no	—
256	#123	—	13	4	no	—
257	#123	—	13	4	no	—
258	C₂²⋊Q₈	—	13	2	no	—
259	C₂²⋊Q₈	—	13	2	no	—
260	C₂²⋊Q₈	—	13	2	no	—
261	C₂²⋊Q₈	—	13	2	no	—
262	C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
263	C₂²⋊Q₈	C₂×D₁₃	1	4	yes	complemented
264	#121	—	13	2	no	—
265	#121	—	13	4	no	—
266	#121	—	13	2	no	—
267	#121	—	13	2	no	—
268	#120	—	13	4	no	—
269	C₄×Q₈	—	13	1	no	—
270	C₄×Q₈	—	13	2	no	—
271	C₄×Q₈	—	13	2	no	—
272	C₄×Q₈	—	13	2	no	—
273	C₄×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
274	C₄×D₄	—	13	1	no	—
275	C₄×D₄	—	13	2	no	—
276	C₄×D₄	—	13	4	no	—
277	C₄×D₄	—	13	1	no	—
278	C₄×D₄	—	13	2	no	—
279	C₄×D₄	—	13	1	no	—
280	C₄×D₄	—	13	4	no	—
281	C₄×D₄	—	13	2	no	—
282	C₄×D₄	—	13	4	no	—
283	C₄×D₄	—	13	1	no	—
284	C₄×D₄	—	13	2	no	—
285	C₄×D₄	—	13	1	no	—
286	C₄×D₄	C₂×D₁₃	1	1	yes	characteristic
287	C₄×D₄	C₂×D₁₃	1	2	yes	—
288	#117	—	13	1	no	—
289	#117	—	13	2	no	—
290	#117	—	13	4	no	—
291	#117	—	13	4	no	—
292	#117	—	13	2	no	—
293	#117	—	13	2	no	—
294	#117	—	13	2	no	—
295	#117	—	13	2	no	—
296	#117	—	13	4	no	—
297	C₂×C₄⋊C₄	—	13	2	no	—
298	C₂×C₄⋊C₄	—	13	1	no	—
299	C₂×C₄⋊C₄	C₂×D₁₃	1	2	yes	complemented
300	C₂×C₂²⋊C₄	—	13	4	no	—
301	C₂×C₂²⋊C₄	—	13	2	no	—
302	C₂×C₄²	—	13	4	no	—
303	C₂×C₄²	—	13	1	no	—
304	C₂×C₄²	—	13	2	no	—
305	C₂×C₁₃	—	2	4	no	—
306	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
307	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
308	C₂×C₁₃	#585	1	1	yes	characteristic
309	D₁₃	—	2	2	no	—
310	D₁₃	—	4	2	no	—
311	D₁₃	—	4	2	no	—
312	C₂⁴	—	13	2	no	—
313	#41	—	26	4	no	—
314	#41	—	26	8	no	—
315	C₂×Q₈	—	13	2	no	—
316	C₂×Q₈	C₂²×D₁₃	1	1	yes	characteristic
317	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
318	C₂×D₄	—	13	4	no	—
319	C₂×D₄	—	13	2	no	—
320	C₂×D₄	—	13	2	no	—
321	C₂×D₄	—	13	1	no	—
322	C₂×D₄	—	13	1	no	—
323	C₂×D₄	—	13	4	no	—
324	C₂×D₄	—	26	4	no	—
325	C₂×D₄	C₂²×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	2	no	—
328	C₂²×C₄	—	13	4	no	—
329	C₂²×C₄	—	13	1	no	—
330	C₂²×C₄	—	13	2	no	—
331	C₂²×C₄	—	13	2	no	—
332	C₂²×C₄	—	13	2	no	—
333	C₂²×C₄	—	13	2	no	—
334	C₂²×C₄	—	13	2	no	—
335	C₂²×C₄	—	13	1	no	—
336	C₂²×C₄	—	13	2	no	—
337	C₂²×C₄	—	26	8	no	—
338	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
339	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
340	C₄⋊C₄	—	13	1	no	—
341	C₄⋊C₄	—	13	1	no	—
342	C₄⋊C₄	—	13	2	no	—
343	C₄⋊C₄	—	13	4	no	—
344	C₄⋊C₄	—	13	2	no	—
345	C₄⋊C₄	—	13	4	no	—
346	C₄⋊C₄	—	13	4	no	—
347	C₄⋊C₄	—	13	2	no	—
348	C₄⋊C₄	—	13	4	no	—
349	C₄⋊C₄	—	13	2	no	—
350	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
353	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
354	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
355	C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
356	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
357	C₂²⋊C₄	—	13	2	no	—
358	C₂²⋊C₄	—	13	2	no	—
359	C₂²⋊C₄	—	13	4	no	—
360	C₂²⋊C₄	—	13	4	no	—
361	C₂²⋊C₄	—	13	4	no	—
362	C₂²⋊C₄	—	13	2	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	4	no	—
369	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
370	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
371	C₄²	—	13	2	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	4	no	—
374	C₄²	—	13	4	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	13	2	no	—
377	C₄²	—	13	4	no	—
378	C₄²	—	13	1	no	—
379	C₄²	C₂²×D₁₃	1	1	yes	characteristic
380	C₄²	C₂²×D₁₃	1	2	yes	—
381	C₁₃	#3475	1	1	yes	characteristic, complemented, Sylow
382	C₂³	—	13	1	no	—
383	C₂³	—	13	2	no	—
384	C₂³	—	13	2	no	—
385	C₂³	—	26	4	no	—
386	C₂³	—	26	4	no	—
387	C₂³	—	52	2	no	—
388	C₂³	C₂³×D₁₃	1	2	yes	—
389	Q₈	—	2	2	no	—
390	Q₈	—	4	2	no	—
391	Q₈	—	26	4	no	—
392	D₄	—	26	4	no	—
393	D₄	—	26	4	no	—
394	D₄	—	26	8	no	—
395	D₄	—	26	2	no	—
396	D₄	—	26	2	no	—
397	D₄	—	52	4	no	—
398	D₄	#6131	1	4	yes	complemented
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	4	4	no	—
401	C₂×C₄	—	13	1	no	—
402	C₂×C₄	—	13	4	no	—
403	C₂×C₄	—	13	2	no	—
404	C₂×C₄	—	13	2	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	4	no	—
407	C₂×C₄	—	13	1	no	—
408	C₂×C₄	—	26	4	no	—
409	C₂×C₄	—	26	4	no	—
410	C₂×C₄	—	26	4	no	—
411	C₂×C₄	—	26	4	no	—
412	C₂×C₄	—	26	8	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	4	no	—
415	C₂×C₄	—	26	4	no	—
416	C₂×C₄	—	52	2	no	—
417	C₂×C₄	—	52	1	no	—
418	C₂×C₄	C₂³×D₁₃	1	2	yes	—
419	C₂×C₄	C₂³×D₁₃	1	4	yes	—
420	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
421	C₂×C₄	C₂³×D₁₃	1	2	yes	—
422	C₂×C₄	C₂³×D₁₃	1	2	yes	—
423	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
424	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	13	2	no	—
428	C₂²	—	26	1	no	—
429	C₂²	—	26	1	no	—
430	C₂²	—	26	2	no	—
431	C₂²	—	26	2	no	—
432	C₂²	—	26	2	no	—
433	C₂²	—	26	2	no	—
434	C₂²	—	26	2	no	—
435	C₂²	—	26	2	no	—
436	C₂²	—	52	8	no	—
437	C₂²	C₂×#6131	1	4	yes	—
438	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	4	no	—
443	C₄	—	2	1	no	—
444	C₄	—	13	2	no	—
445	C₄	—	26	2	no	—
446	C₄	—	26	1	no	—
447	C₄	—	26	4	no	—
448	C₄	—	26	2	no	—
449	C₄	—	26	1	no	—
450	C₄	C₂×#6131	1	2	yes	—
451	C₄	#41×D₁₃	1	2	yes	—
452	C₂	—	2	4	no	—
453	C₂	—	26	2	no	—
454	C₂	—	52	2	no	—
455	C₂	—	52	2	no	—
456	C₂	C₂²×#6131	1	1	yes	characteristic
457	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
458	C₂	#11719650	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#554	C₂
hypercenter	#554	D₁₃
hypocenter	C₁₃	#3475
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. C₁₃×#554	C₂	semidirect
2. #11719439	C₂	semidirect
3. #11719433	C₂	semidirect
4. #11719399	C₂	semidirect
5. #11719396	C₂	semidirect
6. #11719347	C₂	semidirect
7. #11719342	C₂	semidirect
8. #11719332	C₂	semidirect
9. #11719329	C₂	semidirect
10. #11719289	C₂	semidirect
11. C₄×#6131	C₂	semidirect
12. #11719260	C₂	semidirect
13. #11719259	C₂	semidirect
14. C₄×D₄×D₁₃	C₂	semidirect
15. C₄×#6129	C₂	semidirect
16. #11719219	C₂	semidirect
17. C₂×#88146	C₂	semidirect
22. C₁₃×C₄⋊Q₈	C₂²	semidirect
23. C₁₃×#125	C₂²	semidirect
24. C₁₃×C₂²⋊Q₈	C₂²	semidirect
25. C₁₃×C₂²⋊Q₈	C₂²	semidirect
26. C₄×Q₈×C₁₃	C₂²	semidirect
29. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
30. #88201	C₂²	semidirect
32. #88200	C₂²	semidirect
33. Q₈×Dic₁₃	C₂²	semidirect
34. Q₈×Dic₁₃	C₂²	semidirect
37. #88184	C₂²	semidirect
39. C₄×C₂²⋊D₁₃	C₂²	semidirect
41. C₂×C₄⋊Dic₁₃	C₂²	semidirect
42. C₂×C₄×Dic₁₃	C₂²	semidirect
43. #88152	C₂²	semidirect
44. #88152	C₂²	semidirect
45. #88152	C₂²	semidirect
47. #88151	C₂²	semidirect
49. #88149	C₂²	semidirect
51. #88148	C₂²	semidirect
54. #88147	C₂²	semidirect
55. #88147	C₂²	semidirect
59. #88146	C₂²	semidirect
60. #88146	C₂²	semidirect
61. #88146	C₂²	semidirect
62. #88146	C₂²	semidirect
63. #88146	C₂²	semidirect
65. #88144	C₂²	semidirect
66. #88144	C₂²	semidirect
67. #88141	C₂²	semidirect
69. #88140	C₂²	semidirect
72. #88135	C₂²	semidirect
74. #88131	C₂²	semidirect
78. C₄×D₅₂	C₂²	semidirect
80. C₄²×D₁₃	C₂²	semidirect
81. #88123	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
162. D₄×C₁₃	#41	semidirect
194. C₄×D₁₃	#41	semidirect
198. #554	D₁₃	semidirect
245. C₄⋊Q₈	C₂×D₁₃	semidirect
251. #125	C₂×D₁₃	semidirect
262. C₂²⋊Q₈	C₂×D₁₃	semidirect
263. C₂²⋊Q₈	C₂×D₁₃	semidirect
273. C₄×Q₈	C₂×D₁₃	semidirect
299. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
381. C₁₃	#3475	semidirect
398. D₄	#6131	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#554	2
#11719439	2
#11719433	2
#11719399	2
#11719396	2
#11719347	2
#11719342	2
#11719332	2
#11719329	2
#11719289	2
C₄×#6131	2
#11719260	2
#11719259	2
C₄×D₄×D₁₃	2
C₄×#6129	2
#11719219	2
C₂×#88146	2
#3475	13