Subgroups — #13129355

Order 1664.

1160 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	#11719522	C₂	1	2	yes	maximal, complemented
3	D₄×C₂²⋊D₁₃	C₂	1	2	yes	maximal, complemented
4	#11719389	C₂	1	2	yes	maximal, complemented
5	#11719388	C₂	1	2	yes	maximal, complemented
6	#11719387	C₂	1	2	yes	maximal, complemented
7	#11719386	C₂	1	2	yes	maximal, complemented
8	#11719383	C₂	1	4	yes	maximal, complemented
9	#11719381	C₂	1	2	yes	maximal, complemented
10	#11719379	C₂	1	2	yes	maximal, complemented
11	#11719199	C₂	1	2	yes	maximal, complemented
12	#11719198	C₂	1	2	yes	maximal, complemented
13	#11719195	C₂	1	4	yes	maximal, complemented
14	#11719184	C₂	1	1	yes	maximal, characteristic, complemented
15	#11719182	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×Q₈×C₁₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×D₄×C₁₃	C₂²	1	1	yes	characteristic
18	C₂²×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
19	C₂×#6131	C₂²	1	2	yes	complemented
20	C₂×D₄×D₁₃	C₂²	1	2	yes	complemented
21	C₂×#6127	C₂²	1	2	yes	complemented
22	C₁₃×#124	C₂²	1	2	yes	complemented
23	C₁₃×#124	C₂²	1	2	yes	complemented
24	C₁₃×#124	C₂²	1	2	yes	complemented
25	C₁₃×#124	C₂²	1	2	yes	complemented
26	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
27	C₂×C₁₃×C₂²⋊C₄	C₂²	1	2	yes	complemented
28	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
29	#88207	C₂²	1	4	yes	complemented
30	#88201	C₂²	1	2	yes	complemented
31	#88201	C₂²	1	4	yes	complemented
32	#88200	C₂²	1	2	yes	complemented
33	#88200	C₂²	1	4	yes	complemented
34	Q₈×Dic₁₃	C₂²	1	2	yes	complemented
35	#88194	C₂²	1	2	yes	—
36	#88193	C₂²	1	4	yes	complemented
37	#88192	C₂²	1	2	yes	—
38	#88191	C₂²	1	4	yes	complemented
39	D₄×Dic₁₃	C₂²	1	2	yes	complemented
40	#88184	C₂²	1	1	yes	characteristic
41	#88184	C₂²	1	2	yes	complemented
42	#88184	C₂²	1	2	yes	complemented
43	#88184	C₂²	1	4	yes	complemented
44	#88183	C₂²	1	2	yes	complemented
45	C₄×C₂²⋊D₁₃	C₂²	1	2	yes	complemented
46	C₄×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
47	#88178	C₂²	1	1	yes	characteristic, complemented
48	#88140	C₂²	1	4	yes	complemented
49	#88140	C₂²	1	4	yes	complemented
50	#88139	C₂²	1	4	yes	complemented
51	#88139	C₂²	1	4	yes	complemented
52	#88138	C₂²	1	4	yes	complemented
53	#88138	C₂²	1	4	yes	complemented
54	#88138	C₂²	1	4	yes	complemented
55	#88137	C₂²	1	4	yes	complemented
56	#88137	C₂²	1	4	yes	complemented
57	#88136	C₂²	1	4	yes	complemented
58	#88136	C₂²	1	4	yes	complemented
59	#88136	C₂²	1	4	yes	complemented
60	#88135	C₂²	1	4	yes	complemented
61	C₂²⋊C₄×D₁₃	C₂²	1	4	yes	complemented
62	#88133	C₂²	1	4	yes	complemented
63	#88132	C₂²	1	4	yes	complemented
64	#88130	C₂²	1	2	yes	complemented
65	#88129	C₂²	1	2	yes	complemented
66	#88129	C₂²	1	1	yes	characteristic, complemented
67	#88128	C₂²	1	1	yes	characteristic, complemented
68	C₄×D₅₂	C₂²	1	2	yes	complemented
69	C₄×D₅₂	C₂²	1	2	yes	complemented
70	C₄×D₅₂	C₂²	1	1	yes	characteristic, complemented
71	#88126	C₂²	1	2	yes	complemented
72	#88124	C₂²	1	1	yes	characteristic, complemented
73	#88123	C₂²	1	1	yes	characteristic, complemented
74	C₄×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
75	C₂⁴×C₁₃	C₂³	1	2	yes	—
76	C₂³×D₁₃	C₂³	1	4	yes	—
77	C₂×Q₈×C₁₃	—	4	2	no	—
78	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
79	C₂×Q₈×C₁₃	C₂³	1	2	yes	—
80	C₂×D₄×C₁₃	—	4	2	no	—
81	C₂×D₄×C₁₃	C₂³	1	2	yes	—
82	C₂×D₄×C₁₃	C₂³	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂³	1	2	yes	—
87	C₂×C₂²⋊D₁₃	—	4	8	no	—
88	C₂×C₂²⋊D₁₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
90	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
91	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
92	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
93	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
94	C₂²×Dic₁₃	C₂³	1	4	yes	—
95	#6131	—	4	4	no	—
96	D₄×D₁₃	—	4	4	no	—
97	#6127	—	4	4	no	—
98	C₂×D₅₂	C₂³	1	2	yes	—
99	C₂×D₅₂	C₂³	1	2	yes	—
100	C₂×D₅₂	C₂³	1	1	yes	characteristic
101	C₂×D₅₂	C₂³	1	2	yes	—
102	C₂×D₅₂	C₂³	1	4	yes	—
103	C₂×C₄×D₁₃	C₂³	1	2	yes	—
104	C₂×C₄×D₁₃	C₂³	1	4	yes	—
105	C₂×C₄×D₁₃	C₂³	1	4	yes	—
106	C₂×Dic₂₆	C₂³	1	1	yes	characteristic
107	C₂×Dic₂₆	C₂³	1	2	yes	—
108	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
109	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
110	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
117	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₃	C₂³	1	2	yes	—
119	#6103	C₂³	1	2	yes	—
120	#6103	C₂³	1	2	yes	—
121	#6103	C₂³	1	4	yes	—
122	#6103	C₂³	1	4	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	4	yes	—
128	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
129	C₄⋊Dic₁₃	C₂³	1	2	yes	—
130	C₄⋊Dic₁₃	C₂³	1	2	yes	—
131	C₄⋊Dic₁₃	C₂³	1	1	yes	characteristic
132	C₄⋊Dic₁₃	C₂³	1	4	yes	—
133	#6101	C₂³	1	2	yes	—
134	#6101	C₂³	1	2	yes	—
135	#6101	C₂³	1	2	yes	—
136	#6101	C₂³	1	2	yes	—
137	#6101	C₂³	1	4	yes	—
138	C₄×Dic₁₃	C₂³	1	2	yes	—
139	C₄×Dic₁₃	C₂³	1	4	yes	—
140	#3558	—	13	1	no	maximal, Sylow
141	C₂³×C₁₃	—	2	4	no	—
142	C₂³×C₁₃	—	4	2	no	—
143	C₂³×C₁₃	—	4	2	no	—
144	C₂³×C₁₃	C₂⁴	1	4	yes	—
145	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
146	C₂²×D₁₃	—	4	4	no	—
147	C₂²×D₁₃	—	4	4	no	—
148	C₂²×D₁₃	—	4	4	no	—
149	C₂²×D₁₃	C₂⁴	1	2	yes	—
150	C₂²×D₁₃	C₂⁴	1	4	yes	—
151	Q₈×C₁₃	—	2	4	no	—
152	Q₈×C₁₃	—	4	2	no	—
153	D₄×C₁₃	—	2	4	no	—
154	D₄×C₁₃	—	4	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	4	1	no	—
158	C₂×C₄×C₁₃	—	4	2	no	—
159	C₂×C₄×C₁₃	C₂⁴	1	4	yes	—
160	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
166	C₂²⋊D₁₃	—	2	8	no	—
167	C₂²⋊D₁₃	—	2	4	no	—
168	C₂²⋊D₁₃	—	4	4	no	—
169	C₂²⋊D₁₃	—	4	4	no	—
170	C₂²⋊D₁₃	—	4	4	no	—
171	C₂²⋊D₁₃	—	4	4	no	—
172	C₂×Dic₁₃	—	4	4	no	—
173	C₂×Dic₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₃	C₂⁴	1	4	yes	—
176	C₂×Dic₁₃	C₂⁴	1	2	yes	—
177	D₅₂	—	2	4	no	—
178	D₅₂	—	4	1	no	—
179	D₅₂	—	4	2	no	—
180	D₅₂	—	4	2	no	—
181	D₅₂	—	4	4	no	—
182	C₄×D₁₃	—	2	4	no	—
183	C₄×D₁₃	—	4	4	no	—
184	C₄×D₁₃	—	4	4	no	—
185	Dic₂₆	—	4	1	no	—
186	Dic₂₆	—	4	2	no	—
187	#562	—	13	2	no	—
188	H(3,𝔽₄)	—	13	2	no	—
189	#559	—	13	2	no	—
190	#548	—	13	2	no	—
191	#546	—	13	2	no	—
192	#546	—	13	4	no	—
193	D₄²	—	13	2	no	—
194	#542	—	13	2	no	—
195	#538	—	13	4	no	—
196	#538	—	13	2	no	—
197	#535	—	13	2	no	—
198	#534	—	13	2	no	—
199	#532	—	13	1	no	—
200	#529	—	13	1	no	—
201	C₂×#124	D₁₃	1	1	yes	characteristic, complemented
202	C₂²×C₁₃	—	2	1	no	—
203	C₂²×C₁₃	—	2	1	no	—
204	C₂²×C₁₃	—	2	4	no	—
205	C₂²×C₁₃	—	2	4	no	—
206	C₂²×C₁₃	—	2	4	no	—
207	C₂²×C₁₃	—	8	4	no	—
208	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
209	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
210	C₂×D₁₃	—	2	2	no	—
211	C₂×D₁₃	—	2	4	no	—
212	C₂×D₁₃	—	2	4	no	—
213	C₂×D₁₃	—	2	2	no	—
214	C₂×D₁₃	—	2	4	no	—
215	C₂×D₁₃	—	2	2	no	—
216	C₂×D₁₃	—	8	8	no	—
217	C₄×C₁₃	—	2	1	no	—
218	C₄×C₁₃	—	2	1	no	—
219	C₄×C₁₃	—	2	4	no	—
220	C₄×C₁₃	—	2	1	no	—
221	C₄×C₁₃	—	2	1	no	—
222	C₄×C₁₃	—	2	1	no	—
223	C₄×C₁₃	H(5,𝔽₂)	1	2	yes	—
224	Dic₁₃	—	2	4	no	—
225	Dic₁₃	—	2	2	no	—
226	Dic₁₃	—	2	2	no	—
227	Dic₁₃	—	2	2	no	—
228	C₂×#41	—	13	2	no	—
229	C₂×#41	—	13	2	no	—
230	C₂²×Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
231	C₂²×D₄	—	13	4	no	—
232	C₂²×D₄	—	13	2	no	—
233	C₂²×D₄	C₂×D₁₃	1	1	yes	characteristic
234	C₄⋊Q₈	—	13	1	no	—
235	#127	—	13	2	no	—
236	#127	—	13	1	no	—
237	#126	—	13	4	no	—
238	#126	—	13	2	no	—
239	#125	—	13	1	no	—
240	#124	—	13	2	no	—
241	#124	—	13	4	no	—
242	#124	—	13	4	no	—
243	#124	—	13	4	no	—
244	#124	—	13	1	no	—
245	#124	—	13	2	no	—
246	#124	C₂×D₁₃	1	2	yes	complemented
247	#124	C₂×D₁₃	1	2	yes	complemented
248	#124	C₂×D₁₃	1	2	yes	complemented
249	#124	C₂×D₁₃	1	2	yes	complemented
250	#123	—	13	2	no	—
251	#123	—	13	4	no	—
252	#123	—	13	4	no	—
253	#123	—	13	4	no	—
254	#123	—	13	4	no	—
255	C₂²⋊Q₈	—	13	4	no	—
256	C₂²⋊Q₈	—	13	2	no	—
257	C₂²⋊Q₈	—	13	1	no	—
258	C₂²⋊Q₈	—	13	4	no	—
259	#121	—	13	4	no	—
260	#121	—	13	2	no	—
261	#121	—	13	1	no	—
262	#121	—	13	2	no	—
263	#121	—	13	2	no	—
264	#121	—	13	4	no	—
265	#121	—	13	4	no	—
266	#121	—	13	4	no	—
267	#121	—	13	4	no	—
268	#120	—	13	4	no	—
269	#120	—	13	4	no	—
270	#120	—	13	4	no	—
271	#120	—	13	4	no	—
272	#120	—	13	4	no	—
273	C₄×Q₈	—	13	2	no	—
274	C₄×Q₈	—	13	1	no	—
275	C₄×D₄	—	13	2	no	—
276	C₄×D₄	—	13	2	no	—
277	C₄×D₄	—	13	4	no	—
278	C₄×D₄	—	13	4	no	—
279	C₄×D₄	—	13	1	no	—
280	C₄×D₄	—	13	2	no	—
281	C₄×D₄	—	13	2	no	—
282	#117	—	13	2	no	—
283	C₂×C₂²⋊C₄	—	13	4	no	—
284	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
285	C₂×C₂²⋊C₄	C₂×D₁₃	1	2	yes	complemented
286	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
287	C₂×C₁₃	—	2	2	no	—
288	C₂×C₁₃	—	4	4	no	—
289	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
290	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₁₃	#585	1	1	yes	characteristic
292	D₁₃	—	4	4	no	—
293	D₁₃	—	4	2	no	—
294	C₂⁴	—	13	4	no	—
295	C₂⁴	C₂²×D₁₃	1	2	yes	—
296	#41	—	52	4	no	—
297	#41	—	52	4	no	—
298	C₂×Q₈	—	4	2	no	—
299	C₂×Q₈	—	13	1	no	—
300	C₂×Q₈	—	13	2	no	—
301	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
302	C₂×Q₈	C₂²×D₁₃	1	2	yes	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	13	4	no	—
305	C₂×D₄	—	13	2	no	—
306	C₂×D₄	—	13	4	no	—
307	C₂×D₄	—	13	4	no	—
308	C₂×D₄	—	13	4	no	—
309	C₂×D₄	—	13	4	no	—
310	C₂×D₄	—	13	2	no	—
311	C₂×D₄	—	13	1	no	—
312	C₂×D₄	—	13	2	no	—
313	C₂×D₄	—	13	4	no	—
314	C₂×D₄	—	13	2	no	—
315	C₂×D₄	—	52	4	no	—
316	C₂×D₄	—	52	8	no	—
317	C₂×D₄	C₂²×D₁₃	1	2	yes	—
318	C₂×D₄	C₂²×D₁₃	1	2	yes	—
319	C₂²×C₄	—	13	4	no	—
320	C₂²×C₄	—	13	2	no	—
321	C₂²×C₄	—	13	4	no	—
322	C₂²×C₄	—	13	4	no	—
323	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
325	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₃	1	2	yes	—
327	C₄⋊C₄	—	13	2	no	—
328	C₄⋊C₄	—	13	2	no	—
329	C₄⋊C₄	—	13	2	no	—
330	C₄⋊C₄	—	13	2	no	—
331	C₄⋊C₄	—	13	2	no	—
332	C₄⋊C₄	—	13	4	no	—
333	C₄⋊C₄	—	13	2	no	—
334	C₄⋊C₄	—	13	1	no	—
335	C₄⋊C₄	—	13	4	no	—
336	C₄⋊C₄	—	13	1	no	—
337	C₂²⋊C₄	—	13	4	no	—
338	C₂²⋊C₄	—	13	2	no	—
339	C₂²⋊C₄	—	13	4	no	—
340	C₂²⋊C₄	—	13	2	no	—
341	C₂²⋊C₄	—	13	4	no	—
342	C₂²⋊C₄	—	13	2	no	—
343	C₂²⋊C₄	—	13	2	no	—
344	C₂²⋊C₄	—	13	2	no	—
345	C₂²⋊C₄	—	13	4	no	—
346	C₂²⋊C₄	—	13	4	no	—
347	C₂²⋊C₄	—	13	4	no	—
348	C₂²⋊C₄	—	13	4	no	—
349	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
350	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
351	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
352	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
353	C₄²	—	13	2	no	—
354	C₄²	—	13	4	no	—
355	C₄²	C₂²×D₁₃	1	1	yes	characteristic
356	C₄²	C₂²×D₁₃	1	1	yes	characteristic
357	C₄²	C₂²×D₁₃	1	1	yes	characteristic
358	C₄²	C₂²×D₁₃	1	1	yes	characteristic
359	C₁₃	#3558	1	1	yes	characteristic, complemented, Sylow
360	C₂³	—	2	4	no	—
361	C₂³	—	4	2	no	—
362	C₂³	—	4	2	no	—
363	C₂³	—	13	2	no	—
364	C₂³	—	13	4	no	—
365	C₂³	—	52	4	no	—
366	C₂³	—	52	4	no	—
367	C₂³	—	52	4	no	—
368	C₂³	C₂³×D₁₃	1	4	yes	—
369	C₂³	C₂³×D₁₃	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	52	1	no	—
373	Q₈	—	52	2	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	2	no	—
376	D₄	—	26	4	no	—
377	D₄	—	26	8	no	—
378	D₄	—	26	4	no	—
379	D₄	—	52	2	no	—
380	D₄	—	52	1	no	—
381	D₄	—	52	4	no	—
382	D₄	—	52	2	no	—
383	D₄	—	52	4	no	—
384	D₄	—	52	4	no	—
385	D₄	—	52	4	no	—
386	D₄	—	52	4	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	2	no	—
391	C₂×C₄	—	13	2	no	—
392	C₂×C₄	—	13	4	no	—
393	C₂×C₄	—	13	2	no	—
394	C₂×C₄	—	13	2	no	—
395	C₂×C₄	—	26	4	no	—
396	C₂×C₄	—	52	4	no	—
397	C₂×C₄	—	52	4	no	—
398	C₂×C₄	—	52	4	no	—
399	C₂×C₄	C₂³×D₁₃	1	4	yes	—
400	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
402	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
403	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
404	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
405	C₂×C₄	C₂³×D₁₃	1	1	yes	characteristic
406	C₂²	—	2	1	no	—
407	C₂²	—	2	1	no	—
408	C₂²	—	2	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	8	4	no	—
412	C₂²	—	26	2	no	—
413	C₂²	—	26	4	no	—
414	C₂²	—	26	4	no	—
415	C₂²	—	26	2	no	—
416	C₂²	—	26	4	no	—
417	C₂²	—	26	2	no	—
418	C₂²	—	104	8	no	—
419	C₂²	#88256	1	2	yes	—
420	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
421	C₄	—	2	1	no	—
422	C₄	—	2	4	no	—
423	C₄	—	2	1	no	—
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	26	2	no	—
428	C₄	—	26	2	no	—
429	C₄	—	26	4	no	—
430	C₄	—	26	2	no	—
431	C₄	#88251	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	4	4	no	—
434	C₂	—	52	2	no	—
435	C₂	—	52	4	no	—
436	C₂	C₂×#88251	1	1	yes	characteristic
437	C₂	C₂×#88256	1	1	yes	characteristic
438	C₂	#11719648	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₃
commutator, socle, cosocle	C₂²×C₁₃	C₂⁵
Fitting	C₂×C₁₃×#124	C₂
hypercenter	C₂×#124	D₁₃
hypocenter	C₁₃	#3558
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#124	C₂	semidirect
2. #11719522	C₂	semidirect
3. D₄×C₂²⋊D₁₃	C₂	semidirect
4. #11719389	C₂	semidirect
5. #11719388	C₂	semidirect
6. #11719387	C₂	semidirect
7. #11719386	C₂	semidirect
8. #11719383	C₂	semidirect
9. #11719381	C₂	semidirect
10. #11719379	C₂	semidirect
11. #11719199	C₂	semidirect
12. #11719198	C₂	semidirect
13. #11719195	C₂	semidirect
14. #11719184	C₂	semidirect
15. #11719182	C₂	semidirect
16. C₂²×Q₈×C₁₃	C₂²	semidirect
18. C₂²×C₂²⋊D₁₃	C₂²	semidirect
19. C₂×#6131	C₂²	semidirect
20. C₂×D₄×D₁₃	C₂²	semidirect
21. C₂×#6127	C₂²	semidirect
22. C₁₃×#124	C₂²	semidirect
23. C₁₃×#124	C₂²	semidirect
24. C₁₃×#124	C₂²	semidirect
25. C₁₃×#124	C₂²	semidirect
26. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
27. C₂×C₁₃×C₂²⋊C₄	C₂²	semidirect
28. C₂×C₄²×C₁₃	C₂²	semidirect
29. #88207	C₂²	semidirect
30. #88201	C₂²	semidirect
31. #88201	C₂²	semidirect
32. #88200	C₂²	semidirect
33. #88200	C₂²	semidirect
34. Q₈×Dic₁₃	C₂²	semidirect
36. #88193	C₂²	semidirect
38. #88191	C₂²	semidirect
39. D₄×Dic₁₃	C₂²	semidirect
41. #88184	C₂²	semidirect
42. #88184	C₂²	semidirect
43. #88184	C₂²	semidirect
44. #88183	C₂²	semidirect
45. C₄×C₂²⋊D₁₃	C₂²	semidirect
46. C₄×C₂²⋊D₁₃	C₂²	semidirect
47. #88178	C₂²	semidirect
48. #88140	C₂²	semidirect
49. #88140	C₂²	semidirect
50. #88139	C₂²	semidirect
51. #88139	C₂²	semidirect
52. #88138	C₂²	semidirect
53. #88138	C₂²	semidirect
54. #88138	C₂²	semidirect
55. #88137	C₂²	semidirect
56. #88137	C₂²	semidirect
57. #88136	C₂²	semidirect
58. #88136	C₂²	semidirect
59. #88136	C₂²	semidirect
60. #88135	C₂²	semidirect
61. C₂²⋊C₄×D₁₃	C₂²	semidirect
62. #88133	C₂²	semidirect
63. #88132	C₂²	semidirect
64. #88130	C₂²	semidirect
65. #88129	C₂²	semidirect
66. #88129	C₂²	semidirect
67. #88128	C₂²	semidirect
68. C₄×D₅₂	C₂²	semidirect
69. C₄×D₅₂	C₂²	semidirect
70. C₄×D₅₂	C₂²	semidirect
71. #88126	C₂²	semidirect
72. #88124	C₂²	semidirect
73. #88123	C₂²	semidirect
74. C₄×Dic₂₆	C₂²	semidirect
201. C₂×#124	D₁₃	semidirect
230. C₂²×Q₈	C₂×D₁₃	semidirect
246. #124	C₂×D₁₃	semidirect
247. #124	C₂×D₁₃	semidirect
248. #124	C₂×D₁₃	semidirect
249. #124	C₂×D₁₃	semidirect
284. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
285. C₂×C₂²⋊C₄	C₂×D₁₃	semidirect
286. C₂×C₄²	C₂×D₁₃	semidirect
359. C₁₃	#3558	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₁₃×#124	2
#11719522	2
D₄×C₂²⋊D₁₃	2
#11719389	2
#11719388	2
#11719387	2
#11719386	2
#11719383	2
#11719381	2
#11719379	2
#11719199	2
#11719198	2
#11719195	2
#11719184	2
#11719182	2
#3558	13