Subgroups — #13128578

Order 1664.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃×#519	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719521	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#88200	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719289	C₂	1	2	yes	maximal, complemented
5	#11719288	C₂	1	2	yes	maximal, complemented
6	#11719287	C₂	1	2	yes	maximal, complemented
7	#11719286	C₂	1	2	yes	maximal, complemented
8	#11719286	C₂	1	2	yes	maximal, complemented
9	#11719285	C₂	1	2	yes	maximal, complemented
10	#11719284	C₂	1	2	yes	maximal, complemented
11	#11719283	C₂	1	2	yes	maximal, complemented
12	#11719236	C₂	1	4	yes	maximal, complemented
13	#11719232	C₂	1	4	yes	maximal, complemented
14	#11719229	C₂	1	1	yes	maximal, characteristic
15	#11719228	C₂	1	1	yes	maximal, characteristic, complemented
16	D₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
17	#11719224	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic
19	C₂×#6127	C₂²	1	1	yes	characteristic
20	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
21	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
22	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
23	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
24	C₄×Q₈×C₁₃	C₂²	1	2	yes	complemented
25	C₁₃×#117	C₂²	1	1	yes	characteristic
26	C₁₃×#117	C₂²	1	1	yes	characteristic
27	C₁₃×#117	C₂²	1	4	yes	—
28	#88201	C₂²	1	2	yes	complemented
29	#88200	C₂²	1	2	yes	—
30	#88200	C₂²	1	2	yes	—
31	#88200	C₂²	1	2	yes	—
32	#88200	C₂²	1	2	yes	—
33	#88200	C₂²	1	2	yes	complemented
34	#88200	C₂²	1	2	yes	complemented
35	#88198	C₂²	1	2	yes	complemented
36	#88183	C₂²	1	4	yes	—
37	C₂×#6103	C₂²	1	2	yes	—
38	#88180	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
40	C₂×#6101	C₂²	1	2	yes	—
41	#88152	C₂²	1	4	yes	—
42	#88152	C₂²	1	4	yes	complemented
43	#88151	C₂²	1	1	yes	characteristic
44	#88151	C₂²	1	1	yes	characteristic
45	#88150	C₂²	1	4	yes	—
46	#88150	C₂²	1	4	yes	complemented
47	#88149	C₂²	1	1	yes	characteristic
48	#88149	C₂²	1	1	yes	characteristic
49	#88148	C₂²	1	4	yes	—
50	#88148	C₂²	1	4	yes	—
51	#88146	C₂²	1	1	yes	characteristic
52	#88146	C₂²	1	1	yes	characteristic
53	#88146	C₂²	1	2	yes	complemented
54	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
55	C₄⋊C₄×D₁₃	C₂²	1	1	yes	characteristic
56	C₄⋊C₄×D₁₃	C₂²	1	2	yes	complemented
57	#88144	C₂²	1	2	yes	complemented
58	#88143	C₂²	1	4	yes	complemented
59	#88143	C₂²	1	4	yes	complemented
60	#88142	C₂²	1	2	yes	complemented
61	#88140	C₂²	1	2	yes	—
62	#88136	C₂²	1	2	yes	—
63	#88135	C₂²	1	4	yes	—
64	C₂²⋊C₄×D₁₃	C₂²	1	2	yes	—
65	#88132	C₂²	1	4	yes	—
66	#88131	C₂²	1	2	yes	—
67	#88130	C₂²	1	4	yes	—
68	#88130	C₂²	1	4	yes	complemented
69	#88129	C₂²	1	4	yes	—
70	C₄×D₅₂	C₂²	1	2	yes	—
71	C₄×D₅₂	C₂²	1	2	yes	—
72	C₄×D₅₂	C₂²	1	4	yes	—
73	C₄×D₅₂	C₂²	1	2	yes	complemented
74	#88126	C₂²	1	2	yes	—
75	#88126	C₂²	1	4	yes	—
76	#88126	C₂²	1	4	yes	complemented
77	C₄²×D₁₃	C₂²	1	2	yes	—
78	#88124	C₂²	1	2	yes	complemented
79	#88124	C₂²	1	4	yes	complemented
80	#88123	C₂²	1	2	yes	complemented
81	C₄×Dic₂₆	C₂²	1	2	yes	complemented
82	C₄×Dic₂₆	C₂²	1	4	yes	complemented
83	C₂³×D₁₃	C₂³	1	1	yes	characteristic
84	C₂×Q₈×C₁₃	—	2	4	no	—
85	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
86	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
87	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
88	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
89	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
90	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₂³	1	2	yes	—
92	#6127	—	2	4	no	—
93	C₂×D₅₂	C₂³	1	2	yes	—
94	C₂×D₅₂	C₂³	1	1	yes	characteristic
95	C₂×D₅₂	C₂³	1	2	yes	—
96	C₂×C₄×D₁₃	—	2	4	no	—
97	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂³	1	2	yes	—
99	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂³	1	2	yes	—
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×Dic₂₆	C₂³	1	1	yes	characteristic
106	C₂×Dic₂₆	C₂³	1	4	yes	—
107	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
108	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
109	C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
110	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
111	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
112	C₁₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
113	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
114	C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
115	C₄²×C₁₃	C₂³	1	2	yes	—
116	C₄²×C₁₃	C₂³	1	4	yes	—
117	C₄²×C₁₃	C₂³	1	2	yes	—
118	C₄²×C₁₃	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
120	#6103	C₂³	1	2	yes	—
121	#6103	C₂³	1	4	yes	—
122	#6103	C₂³	1	2	yes	—
123	#6103	C₂³	1	2	yes	—
124	#6103	C₂³	1	2	yes	—
125	#6103	C₂³	1	4	yes	—
126	#6103	C₂³	1	4	yes	—
127	#6103	C₂³	1	2	yes	—
128	#6103	C₂³	1	2	yes	—
129	#6103	C₂³	1	4	yes	—
130	#6103	C₂³	1	4	yes	—
131	C₄⋊Dic₁₃	C₂³	1	2	yes	—
132	C₄⋊Dic₁₃	C₂³	1	2	yes	—
133	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
134	C₄⋊Dic₁₃	C₂³	1	4	yes	—
135	C₄⋊Dic₁₃	C₂³	1	2	yes	—
136	C₄⋊Dic₁₃	C₂³	1	2	yes	—
137	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
138	#6101	C₂³	1	4	yes	—
139	#6101	C₂³	1	4	yes	—
140	#6101	C₂³	1	4	yes	—
141	#6101	C₂³	1	2	yes	—
142	#6101	C₂³	1	4	yes	—
143	#6101	C₂³	1	4	yes	—
144	#6101	C₂³	1	4	yes	—
145	#6101	C₂³	1	4	yes	—
146	#6101	C₂³	1	2	yes	—
147	C₄×Dic₁₃	C₂³	1	2	yes	—
148	C₄×Dic₁₃	C₂³	1	4	yes	—
149	C₄×Dic₁₃	C₂³	1	2	yes	—
150	C₄×Dic₁₃	C₂³	1	2	yes	—
151	#3495	—	13	1	no	maximal, Sylow
152	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
153	C₂²×D₁₃	—	2	2	no	—
154	C₂²×D₁₃	—	2	2	no	—
155	C₂²×D₁₃	—	4	1	no	—
156	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₁₃	C₂⁴	1	2	yes	—
158	C₂²×D₁₃	C₂⁴	1	1	yes	characteristic
159	Q₈×C₁₃	—	2	4	no	—
160	Q₈×C₁₃	—	2	4	no	—
161	C₂×C₄×C₁₃	—	2	4	no	—
162	C₂×C₄×C₁₃	#41	1	4	yes	—
163	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
165	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
166	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
168	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
169	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂²⋊D₁₃	—	2	4	no	—
171	C₂×Dic₁₃	—	2	2	no	—
172	C₂×Dic₁₃	—	4	2	no	—
173	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₃	C₂⁴	1	2	yes	—
176	C₂×Dic₁₃	C₂⁴	1	2	yes	—
177	C₂×Dic₁₃	C₂⁴	1	4	yes	—
178	C₂×Dic₁₃	C₂⁴	1	1	yes	characteristic
179	D₅₂	—	2	4	no	—
180	D₅₂	—	2	2	no	—
181	D₅₂	—	4	2	no	—
182	C₄×D₁₃	—	2	4	no	—
183	C₄×D₁₃	—	2	2	no	—
184	C₄×D₁₃	—	2	2	no	—
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	4	no	—
188	C₄×D₁₃	—	4	2	no	—
189	C₄×D₁₃	—	4	4	no	—
190	Dic₂₆	—	2	2	no	—
191	Dic₂₆	—	4	4	no	—
192	#556	—	13	2	no	—
193	#554	—	13	2	no	—
194	#552	—	13	2	no	—
195	#552	—	13	2	no	—
196	#552	—	13	4	no	—
197	#551	—	13	4	no	—
198	#544	—	13	1	no	—
199	#542	—	13	2	no	—
200	#541	—	13	2	no	—
201	#536	—	13	1	no	—
202	#533	—	13	2	no	—
203	#529	—	13	2	no	—
204	#525	—	13	1	no	—
205	C₂×C₂²⋊Q₈	—	13	1	no	—
206	#520	—	13	1	no	—
207	#519	D₁₃	1	1	yes	characteristic, complemented
208	C₂×#117	—	13	1	no	—
209	C₂²×C₁₃	—	2	1	no	—
210	C₂²×C₁₃	—	2	1	no	—
211	C₂²×C₁₃	C₂×#41	1	2	yes	—
212	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
213	C₂×D₁₃	—	2	1	no	—
214	C₂×D₁₃	—	2	1	no	—
215	C₂×D₁₃	—	2	1	no	—
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	2	2	no	—
218	C₂×D₁₃	—	2	1	no	—
219	C₂×D₁₃	—	2	2	no	—
220	C₂×D₁₃	—	2	1	no	—
221	C₂×D₁₃	—	4	4	no	—
222	C₂×D₁₃	2₋¹⁺⁴	1	2	yes	—
223	C₄×C₁₃	—	2	4	no	—
224	C₄×C₁₃	—	2	2	no	—
225	C₄×C₁₃	—	2	2	no	—
226	C₄×C₁₃	—	2	2	no	—
227	C₄×C₁₃	—	2	2	no	—
228	C₄×C₁₃	C₂×#41	1	2	yes	—
229	C₄×C₁₃	C₂×#41	1	2	yes	—
230	Dic₁₃	—	2	2	no	—
231	Dic₁₃	—	2	1	no	—
232	Dic₁₃	—	2	1	no	—
233	Dic₁₃	—	2	2	no	—
234	Dic₁₃	—	2	2	no	—
235	Dic₁₃	—	2	4	no	—
236	C₂×#41	—	13	1	no	—
237	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic
238	C₂³×C₄	—	13	1	no	—
239	C₄⋊Q₈	—	13	2	no	—
240	C₄⋊Q₈	—	13	2	no	—
241	C₄⋊Q₈	—	13	2	no	—
242	#126	—	13	4	no	—
243	#126	—	13	4	no	—
244	#126	—	13	4	no	—
245	#126	—	13	4	no	—
246	#125	—	13	2	no	—
247	#125	—	13	4	no	—
248	#125	—	13	4	no	—
249	#125	—	13	4	no	—
250	#125	—	13	2	no	—
251	#124	—	13	2	no	—
252	#124	—	13	4	no	—
253	#123	—	13	4	no	—
254	#123	—	13	4	no	—
255	#123	—	13	4	no	—
256	#123	—	13	2	no	—
257	C₂²⋊Q₈	—	13	2	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	—	13	2	no	—
263	C₂²⋊Q₈	—	13	1	no	—
264	C₂²⋊Q₈	—	13	1	no	—
265	C₂²⋊Q₈	—	13	4	no	—
266	C₂²⋊Q₈	—	13	4	no	—
267	C₂²⋊Q₈	—	13	4	no	—
268	#121	—	13	1	no	—
269	#121	—	13	1	no	—
270	#120	—	13	2	no	—
271	C₄×Q₈	—	13	2	no	—
272	C₄×Q₈	—	13	4	no	—
273	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
274	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
275	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
276	C₄×Q₈	C₂×D₁₃	1	2	yes	complemented
277	C₄×D₄	—	13	4	no	—
278	C₄×D₄	—	13	2	no	—
279	C₄×D₄	—	13	2	no	—
280	C₄×D₄	—	13	2	no	—
281	C₄×D₄	—	13	4	no	—
282	#117	—	13	1	no	—
283	#117	—	13	1	no	—
284	#117	—	13	1	no	—
285	#117	—	13	2	no	—
286	#117	—	13	2	no	—
287	#117	—	13	2	no	—
288	#117	—	13	4	no	—
289	#117	—	13	4	no	—
290	#117	C₂×D₁₃	1	1	yes	characteristic
291	#117	C₂×D₁₃	1	1	yes	characteristic
292	#117	C₂×D₁₃	1	4	yes	—
293	C₂×C₄⋊C₄	—	13	1	no	—
294	C₂×C₄⋊C₄	—	13	2	no	—
295	C₂×C₄⋊C₄	—	13	1	no	—
296	C₂×C₄⋊C₄	—	13	1	no	—
297	C₂×C₄⋊C₄	—	13	2	no	—
298	C₂×C₂²⋊C₄	—	13	2	no	—
299	C₂×C₂²⋊C₄	—	13	2	no	—
300	C₂×C₄²	—	13	2	no	—
301	C₂×C₁₃	—	2	2	no	—
302	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
303	C₂×C₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
304	C₂×C₁₃	#585	1	1	yes	characteristic
305	D₁₃	—	2	2	no	—
306	D₁₃	—	4	2	no	—
307	D₁₃	—	4	1	no	—
308	C₂⁴	—	13	1	no	—
309	#41	—	26	4	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	13	1	no	—
312	C₂×Q₈	—	13	4	no	—
313	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
314	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
315	C₂×D₄	—	13	2	no	—
316	C₂×D₄	—	13	2	no	—
317	C₂×D₄	—	13	1	no	—
318	C₂×D₄	—	13	2	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	2	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	2	no	—
323	C₂²×C₄	—	13	1	no	—
324	C₂²×C₄	—	13	2	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	2	no	—
328	C₂²×C₄	—	13	4	no	—
329	C₂²×C₄	—	26	4	no	—
330	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
331	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
332	C₄⋊C₄	—	13	2	no	—
333	C₄⋊C₄	—	13	2	no	—
334	C₄⋊C₄	—	13	1	no	—
335	C₄⋊C₄	—	13	1	no	—
336	C₄⋊C₄	—	13	2	no	—
337	C₄⋊C₄	—	13	4	no	—
338	C₄⋊C₄	—	13	2	no	—
339	C₄⋊C₄	—	13	4	no	—
340	C₄⋊C₄	—	13	4	no	—
341	C₄⋊C₄	—	13	4	no	—
342	C₄⋊C₄	—	13	4	no	—
343	C₄⋊C₄	—	13	4	no	—
344	C₄⋊C₄	—	13	2	no	—
345	C₄⋊C₄	—	13	2	no	—
346	C₄⋊C₄	—	13	4	no	—
347	C₄⋊C₄	—	13	4	no	—
348	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
350	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
351	C₄⋊C₄	C₂²×D₁₃	1	1	yes	characteristic
352	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
353	C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
354	C₂²⋊C₄	—	13	2	no	—
355	C₂²⋊C₄	—	13	2	no	—
356	C₂²⋊C₄	—	13	2	no	—
357	C₂²⋊C₄	—	13	4	no	—
358	C₂²⋊C₄	—	13	4	no	—
359	C₂²⋊C₄	—	13	2	no	—
360	C₂²⋊C₄	—	13	2	no	—
361	C₂²⋊C₄	—	13	4	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	C₂²×D₁₃	1	2	yes	—
367	C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
368	C₄²	—	13	2	no	—
369	C₄²	—	13	2	no	—
370	C₄²	—	13	2	no	—
371	C₄²	—	13	4	no	—
372	C₄²	C₂²×D₁₃	1	2	yes	—
373	C₄²	C₂²×D₁₃	1	4	yes	—
374	C₄²	C₂²×D₁₃	1	4	yes	—
375	C₄²	C₂²×D₁₃	1	2	yes	—
376	C₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
377	C₂³	—	13	1	no	—
378	C₂³	—	13	1	no	—
379	C₂³	—	13	2	no	—
380	C₂³	—	26	2	no	—
381	C₂³	—	26	2	no	—
382	C₂³	—	52	1	no	—
383	C₂³	C₂³×D₁₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	26	2	no	—
387	Q₈	—	52	4	no	—
388	D₄	—	26	4	no	—
389	D₄	—	26	4	no	—
390	D₄	—	26	2	no	—
391	D₄	—	52	2	no	—
392	C₂×C₄	—	2	4	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	2	no	—
395	C₂×C₄	—	13	2	no	—
396	C₂×C₄	—	13	2	no	—
397	C₂×C₄	—	13	4	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	26	4	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	4	no	—
406	C₂×C₄	—	52	4	no	—
407	C₂×C₄	—	52	2	no	—
408	C₂×C₄	—	52	2	no	—
409	C₂×C₄	#6127	1	4	yes	—
410	C₂×C₄	C₂³×D₁₃	1	2	yes	—
411	C₂×C₄	C₂³×D₁₃	1	2	yes	—
412	C₂×C₄	C₂³×D₁₃	1	2	yes	—
413	C₂×C₄	C₂³×D₁₃	1	2	yes	—
414	C₂×C₄	C₂³×D₁₃	1	4	yes	—
415	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	13	2	no	—
420	C₂²	—	26	1	no	—
421	C₂²	—	26	1	no	—
422	C₂²	—	26	1	no	—
423	C₂²	—	26	2	no	—
424	C₂²	—	26	2	no	—
425	C₂²	—	26	1	no	—
426	C₂²	—	26	2	no	—
427	C₂²	—	26	1	no	—
428	C₂²	—	52	4	no	—
429	C₂²	C₂×#6127	1	2	yes	—
430	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
431	C₄	—	2	4	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	2	no	—
436	C₄	—	26	1	no	—
437	C₄	—	26	1	no	—
438	C₄	—	26	2	no	—
439	C₄	—	26	2	no	—
440	C₄	—	26	4	no	—
441	C₄	—	26	2	no	—
442	C₄	C₂×#6127	1	2	yes	—
443	C₄	C₂×#6127	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	26	2	no	—
446	C₂	—	52	1	no	—
447	C₂	—	52	2	no	—
448	C₂	C₂²×#6127	1	1	yes	characteristic
449	C₂	D₁₃×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂	#11719652	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₁₃×#519	C₂
prime radical	#11719229	C₂
hypercenter	#519	D₁₃
hypocenter	C₁₃	#3495
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ #519

Complements

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

N	H ≅ G/N	type
1. C₁₃×#519	C₂	semidirect
2. #11719521	C₂	semidirect
3. C₂×#88200	C₂	semidirect
4. #11719289	C₂	semidirect
5. #11719288	C₂	semidirect
6. #11719287	C₂	semidirect
7. #11719286	C₂	semidirect
8. #11719286	C₂	semidirect
9. #11719285	C₂	semidirect
10. #11719284	C₂	semidirect
11. #11719283	C₂	semidirect
12. #11719236	C₂	semidirect
13. #11719232	C₂	semidirect
15. #11719228	C₂	semidirect
16. D₁₃×#117	C₂	semidirect
17. #11719224	C₂	semidirect
21. C₄×Q₈×C₁₃	C₂²	semidirect
22. C₄×Q₈×C₁₃	C₂²	semidirect
23. C₄×Q₈×C₁₃	C₂²	semidirect
24. C₄×Q₈×C₁₃	C₂²	semidirect
28. #88201	C₂²	semidirect
33. #88200	C₂²	semidirect
34. #88200	C₂²	semidirect
35. #88198	C₂²	semidirect
42. #88152	C₂²	semidirect
46. #88150	C₂²	semidirect
53. #88146	C₂²	semidirect
56. C₄⋊C₄×D₁₃	C₂²	semidirect
57. #88144	C₂²	semidirect
58. #88143	C₂²	semidirect
59. #88143	C₂²	semidirect
60. #88142	C₂²	semidirect
68. #88130	C₂²	semidirect
73. C₄×D₅₂	C₂²	semidirect
76. #88126	C₂²	semidirect
78. #88124	C₂²	semidirect
79. #88124	C₂²	semidirect
80. #88123	C₂²	semidirect
81. C₄×Dic₂₆	C₂²	semidirect
82. C₄×Dic₂₆	C₂²	semidirect
207. #519	D₁₃	semidirect
273. C₄×Q₈	C₂×D₁₃	semidirect
274. C₄×Q₈	C₂×D₁₃	semidirect
275. C₄×Q₈	C₂×D₁₃	semidirect
276. C₄×Q₈	C₂×D₁₃	semidirect
376. C₁₃	#3495	semidirect

Maximal subgroups

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

subgroup	index
C₁₃×#519	2
#11719521	2
C₂×#88200	2
#11719289	2
#11719288	2
#11719287	2
#11719286	2
#11719285	2
#11719284	2
#11719283	2
#11719236	2
#11719232	2
#11719229	2
#11719228	2
D₁₃×#117	2
#11719224	2
#3495	13