Subgroups — #15833514

Order 3328.

594 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13125436	C₂	1	1	yes	maximal, characteristic
2	#13123811	C₂	1	1	yes	maximal, characteristic
3	#13113743	C₂	1	2	yes	maximal, complemented
4	#13113736	C₂	1	2	yes	maximal, complemented
5	C₈×#6107	C₂	1	2	yes	maximal, complemented
6	C₈×#6106	C₂	1	2	yes	maximal, complemented
7	#13113601	C₂	1	1	yes	maximal, characteristic, complemented
8	#13113309	C₂	1	1	yes	maximal, characteristic, complemented
9	#13113299	C₂	1	1	yes	maximal, characteristic
10	C₈×#6099	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₃×#533	C₂²	1	1	yes	characteristic
13	#11719184	C₂²	1	1	yes	characteristic
14	C₁₃×#446	—	2	1	no	—
15	C₁₃×#446	C₂²	1	2	yes	—
16	C₈×Q₈×C₁₃	—	2	1	no	—
17	C₈×Q₈×C₁₃	C₂²	1	2	yes	—
18	C₁₃×#424	—	2	1	no	—
19	C₁₃×#423	C₂²	1	1	yes	characteristic
20	C₁₃×#405	—	2	1	no	—
21	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
22	#11718772	—	2	1	no	—
23	C₈×C₂²⋊D₁₃	—	2	1	no	—
24	#11718750	C₄	1	1	yes	characteristic
25	#11718747	C₄	1	1	yes	characteristic
26	#11718743	C₄	1	1	yes	characteristic
27	#11718741	C₄	1	1	yes	characteristic
28	#11718713	C₄	1	2	yes	—
29	#11718710	C₄	1	2	yes	—
30	C₄×#6107	C₂²	1	2	yes	—
31	C₄×#6106	C₂²	1	2	yes	—
32	#11718587	C₂²	1	1	yes	characteristic
33	#11718586	C₂²	1	1	yes	characteristic
34	C₄×#6099	C₂²	1	1	yes	characteristic
35	#11718351	—	2	1	no	—
36	#11718350	—	2	1	no	—
37	#11718349	C₂²	1	1	yes	characteristic
38	C₈×D₅₂	C₂²	1	1	yes	characteristic
39	#11718340	C₂²	1	1	yes	characteristic
40	C₈×Dic₂₆	C₂²	1	1	yes	characteristic
41	Q₈⋊#1055	C₂²	1	2	yes	—
42	Q₈⋊#1055	C₂²	1	2	yes	—
43	#11718076	C₂²	1	2	yes	—
44	#11718075	C₂²	1	2	yes	—
45	#11718072	C₂²	1	2	yes	—
46	#11718071	C₂²	1	2	yes	—
47	#11718046	C₂²	1	2	yes	—
48	C₈×#1055	C₂²	1	2	yes	—
49	C₂×C₁₃×M₁₆	—	2	1	no	—
50	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
51	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
52	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
53	C₁₃×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#125	—	2	1	no	—
55	C₁₃×C₂²⋊Q₈	—	2	1	no	—
56	C₁₃×C₂²⋊Q₈	C₂×C₄	1	2	yes	—
57	C₄×Q₈×C₁₃	—	2	1	no	—
58	C₄×Q₈×C₁₃	C₂³	1	2	yes	—
59	C₁₃×#117	—	2	1	no	—
60	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
61	C₂×#6107	C₂×C₄	1	2	yes	—
62	C₂×#6106	C₂×C₄	1	2	yes	—
63	#88184	C₂×C₄	1	1	yes	characteristic
64	#88183	—	2	1	no	—
65	C₄×C₂²⋊D₁₃	—	2	1	no	—
66	#88178	C₂×C₄	1	1	yes	characteristic
67	C₂×#6099	C₂×C₄	1	2	yes	—
68	C₂×#6094	—	2	1	no	—
69	C₂×C₈×D₁₃	—	2	1	no	—
70	#88130	—	2	1	no	—
71	#88129	C₂×C₄	1	1	yes	characteristic
72	C₄×D₅₂	C₂³	1	1	yes	characteristic
73	#88126	—	2	1	no	—
74	#88124	C₂×C₄	1	1	yes	characteristic
75	C₄×Dic₂₆	C₂³	1	1	yes	characteristic
76	C₁₃×C₄⋊C₈	—	2	2	no	—
77	C₁₃×C₄⋊C₈	—	2	2	no	—
78	C₁₃×C₄⋊C₈	—	2	1	no	—
79	C₁₃×C₄⋊C₈	C₂³	1	2	yes	—
80	C₁₃×#97	—	2	2	no	—
81	C₄×C₈×C₁₃	—	2	2	no	—
82	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
83	C₄×C₈×C₁₃	D₄	1	1	yes	characteristic
84	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
85	C₄×C₈×C₁₃	C₂³	1	1	yes	characteristic
86	#88075	C₂×C₄	1	2	yes	—
87	#88075	C₂×C₄	1	2	yes	—
88	C₂²⋊#1055	—	2	1	no	—
89	C₂²⋊#1055	—	2	1	no	—
90	#88060	—	2	1	no	—
91	#88060	—	2	1	no	—
92	#88055	—	2	1	no	—
93	#88054	—	2	1	no	—
94	#88054	—	2	1	no	—
95	C₈×Dic₁₃	—	2	1	no	—
96	#88050	C₂×C₄	1	2	yes	—
97	#88049	C₂×C₄	1	2	yes	—
98	#88048	C₂×C₄	1	2	yes	—
99	#88047	C₂×C₄	1	2	yes	—
100	C₄⋊#1055	—	2	1	no	—
101	C₄⋊#1055	C₂³	1	1	yes	characteristic
102	C₄⋊#1055	C₂³	1	1	yes	characteristic
103	#88043	—	2	1	no	—
104	#88043	C₂×C₄	1	1	yes	characteristic
105	#88043	C₂×C₄	1	1	yes	characteristic
106	C₄×#1055	C₂³	1	2	yes	—
107	C₄×#1055	C₂³	1	2	yes	—
108	#17965	—	13	1	no	maximal, Sylow
109	C₂×Q₈×C₁₃	—	2	1	no	—
110	C₂×Q₈×C₁₃	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₁₃	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₁₃	—	2	1	no	—
115	C₂×D₅₂	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₁₃	—	2	1	no	—
117	C₂×Dic₂₆	C₂²×C₄	1	1	yes	characteristic
118	C₁₃×M₁₆	—	4	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	—	2	2	no	—
121	C₂×C₈×C₁₃	—	4	1	no	—
122	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
125	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
126	C₁₃×C₄⋊C₄	—	2	1	no	—
127	C₁₃×C₄⋊C₄	—	2	1	no	—
128	C₁₃×C₄⋊C₄	—	2	1	no	—
129	C₁₃×C₄⋊C₄	—	2	2	no	—
130	C₁₃×C₄⋊C₄	—	2	2	no	—
131	C₁₃×C₄⋊C₄	C₂²×C₄	1	2	yes	—
132	C₁₃×C₂²⋊C₄	—	2	2	no	—
133	C₄²×C₁₃	—	2	2	no	—
134	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₁₃	#41	1	1	yes	characteristic
137	C₄²×C₁₃	C₂⁴	1	1	yes	characteristic
138	C₂²⋊Dic₁₃	—	2	1	no	—
139	#6107	—	2	4	no	—
140	#6106	—	2	4	no	—
141	#6103	—	2	1	no	—
142	#6103	—	2	1	no	—
143	#6103	—	2	1	no	—
144	#6103	—	2	1	no	—
145	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
146	C₄⋊Dic₁₃	C₂²×C₄	1	1	yes	characteristic
147	#6101	—	2	1	no	—
148	#6101	—	2	1	no	—
149	#6101	—	2	1	no	—
150	#6101	—	2	1	no	—
151	C₄×Dic₁₃	—	2	1	no	—
152	#6099	—	2	4	no	—
153	C₂×#1055	—	2	1	no	—
154	C₂×#1055	—	2	1	no	—
155	C₂×#1055	—	2	2	no	—
156	C₂×#1055	C₂²×C₄	1	2	yes	—
157	C₂×#1055	C₂²×C₄	1	2	yes	—
158	#6094	—	4	2	no	—
159	C₈×D₁₃	—	4	2	no	—
160	#3172	—	13	1	no	—
161	#2966	—	13	1	no	—
162	#2960	D₁₃	1	1	yes	characteristic, complemented
163	#1593	—	13	2	no	—
164	#1592	—	13	2	no	—
165	C₈×Q₁₆	—	13	2	no	—
166	C₈×SD₁₆	—	13	2	no	—
167	#1569	—	13	1	no	—
168	#1497	—	13	1	no	—
169	#1495	—	13	1	no	—
170	C₈×M₁₆	—	13	1	no	—
171	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
172	C₂²×D₁₃	—	2	1	no	—
173	Q₈×C₁₃	—	2	2	no	—
174	Q₈×C₁₃	—	2	2	no	—
175	Q₈×C₁₃	—	4	2	no	—
176	C₂×C₄×C₁₃	—	2	2	no	—
177	C₂×C₄×C₁₃	—	2	1	no	—
178	C₂×C₄×C₁₃	—	2	1	no	—
179	C₂×C₄×C₁₃	—	2	2	no	—
180	C₂×C₄×C₁₃	—	2	2	no	—
181	C₂×C₄×C₁₃	—	4	1	no	—
182	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
188	C₂²⋊D₁₃	—	4	2	no	—
189	C₂×Dic₁₃	—	2	1	no	—
190	C₂×Dic₁₃	—	2	1	no	—
191	C₂×Dic₁₃	—	2	1	no	—
192	D₅₂	—	2	2	no	—
193	C₄×D₁₃	—	4	1	no	—
194	C₄×D₁₃	—	4	1	no	—
195	Dic₂₆	—	2	2	no	—
196	C₈×C₁₃	—	2	1	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	—	4	2	no	—
200	C₈×C₁₃	#137	1	2	yes	—
201	#1055	—	2	2	no	—
202	#1055	—	4	2	no	—
203	#1055	—	4	1	no	—
204	#1055	—	4	1	no	—
205	#1055	#131	1	4	yes	—
206	#533	C₂×D₁₃	1	1	yes	characteristic
207	#529	—	13	1	no	—
208	#501	—	13	1	no	—
209	#497	—	13	1	no	—
210	#491	—	13	1	no	—
211	#489	—	13	1	no	—
212	#470	—	13	2	no	—
213	#468	—	13	2	no	—
214	#446	—	2	1	no	—
215	#446	—	13	1	no	—
216	#446	C₂×D₁₃	1	2	yes	—
217	C₈×Q₈	—	2	1	no	—
218	C₈×Q₈	—	13	1	no	—
219	C₈×Q₈	C₂×D₁₃	1	2	yes	—
220	C₄×Q₁₆	—	13	2	no	—
221	C₄×SD₁₆	—	13	2	no	—
222	#436	—	13	1	no	—
223	#435	—	26	1	no	—
224	C₈×D₄	—	13	1	no	—
225	C₈×D₄	—	26	1	no	—
226	#433	—	26	1	no	—
227	#432	—	13	1	no	—
228	#431	—	13	1	no	—
229	#424	—	2	1	no	—
230	#423	C₂×D₁₃	1	1	yes	characteristic
231	#405	—	2	1	no	—
232	#405	—	26	1	no	—
233	C₄×M₁₆	—	13	1	no	—
234	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
235	#335	—	13	2	no	—
236	#334	—	13	2	no	—
237	Q₈⋊C₈	—	13	2	no	—
238	Q₈⋊C₈	—	13	2	no	—
239	Q₈⋊C₈	—	13	2	no	—
240	D₄⋊C₈	—	13	2	no	—
241	#322	—	13	2	no	—
242	C₈²	—	13	2	no	—
243	C₂²×C₁₃	—	2	1	no	—
244	C₂²×C₁₃	—	2	1	no	—
245	C₂²×C₁₃	—	2	1	no	—
246	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
247	C₂×D₁₃	—	4	1	no	—
248	C₂×D₁₃	—	4	1	no	—
249	C₂×D₁₃	—	4	1	no	—
250	C₄×C₁₃	—	2	1	no	—
251	C₄×C₁₃	—	2	1	no	—
252	C₄×C₁₃	—	2	1	no	—
253	C₄×C₁₃	—	2	1	no	—
254	C₄×C₁₃	—	4	2	no	—
255	C₄×C₁₃	—	4	2	no	—
256	C₄×C₁₃	C₂×#131	1	2	yes	—
257	C₄×C₁₃	C₂×#137	1	1	yes	characteristic
258	C₄×C₁₃	#575	1	1	yes	characteristic
259	Dic₁₃	—	4	1	no	—
260	Dic₁₃	—	4	1	no	—
261	Dic₁₃	—	4	1	no	—
262	C₂×Q₁₆	—	13	2	no	—
263	C₂×SD₁₆	—	13	2	no	—
264	C₂×M₁₆	—	2	1	no	—
265	C₂×M₁₆	—	13	2	no	—
266	C₂×M₁₆	—	26	1	no	—
267	C₂²×C₈	—	26	1	no	—
268	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
269	C₂²×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
270	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
271	C₄⋊Q₈	C₄×D₁₃	1	1	yes	characteristic
272	#126	—	26	1	no	—
273	#125	—	2	1	no	—
274	#125	—	13	1	no	—
275	#124	—	13	1	no	—
276	#123	—	26	1	no	—
277	C₂²⋊Q₈	—	2	1	no	—
278	C₂²⋊Q₈	—	13	1	no	—
279	C₂²⋊Q₈	C₄×D₁₃	1	2	yes	—
280	#121	—	13	1	no	—
281	C₄×Q₈	—	2	1	no	—
282	C₄×Q₈	—	13	1	no	—
283	C₄×Q₈	C₂²×D₁₃	1	2	yes	—
284	C₄×D₄	—	13	1	no	—
285	C₄×D₄	—	26	1	no	—
286	#117	—	2	1	no	—
287	#117	—	26	1	no	—
288	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
289	#107	—	13	2	no	—
290	#106	—	13	2	no	—
291	C₄⋊C₈	—	2	2	no	—
292	C₄⋊C₈	—	2	2	no	—
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	13	1	no	—
295	C₄⋊C₈	—	13	1	no	—
296	C₄⋊C₈	—	26	1	no	—
297	C₄⋊C₈	—	26	1	no	—
298	C₄⋊C₈	—	26	1	no	—
299	C₄⋊C₈	C₂²×D₁₃	1	2	yes	—
300	#103	—	13	2	no	—
301	#103	—	13	2	no	—
302	#103	—	13	2	no	—
303	#102	—	13	2	no	—
304	C₂²⋊C₈	—	26	1	no	—
305	C₂²⋊C₈	—	26	1	no	—
306	C₂²⋊C₈	—	26	1	no	—
307	C₂²⋊C₈	—	26	1	no	—
308	#97	—	2	2	no	—
309	#97	—	13	1	no	—
310	#97	—	13	1	no	—
311	#97	—	26	1	no	—
312	#97	—	26	1	no	—
313	C₄×C₈	—	2	2	no	—
314	C₄×C₈	—	13	2	no	—
315	C₄×C₈	—	13	2	no	—
316	C₄×C₈	—	26	1	no	—
317	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
318	C₄×C₈	C₂²⋊D₁₃	1	1	yes	characteristic
319	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
320	C₄×C₈	C₂²×D₁₃	1	1	yes	characteristic
321	C₂×C₁₃	—	4	1	no	—
322	C₂×C₁₃	#2931	1	1	yes	characteristic
323	C₂×C₁₃	C₄×#137	1	1	yes	characteristic
324	C₂×C₁₃	#2955	1	1	yes	characteristic
325	D₁₃	—	8	1	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	13	1	no	—
328	C₂×Q₈	C₂×C₄×D₁₃	1	2	yes	—
329	C₂×D₄	—	13	1	no	—
330	C₂×D₄	—	26	1	no	—
331	C₂²×C₄	—	26	1	no	—
332	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
333	C₂²×C₄	#6127	1	1	yes	characteristic
334	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
335	Q₁₆	—	26	4	no	—
336	SD₁₆	—	26	4	no	—
337	M₁₆	—	4	2	no	—
338	M₁₆	—	26	4	no	—
339	M₁₆	—	52	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	13	2	no	—
344	C₂×C₈	—	13	2	no	—
345	C₂×C₈	—	26	2	no	—
346	C₂×C₈	—	26	1	no	—
347	C₂×C₈	—	26	1	no	—
348	C₂×C₈	—	52	2	no	—
349	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
350	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
351	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
352	C₂×C₈	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	2	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	13	1	no	—
359	C₄⋊C₄	—	13	1	no	—
360	C₄⋊C₄	—	26	1	no	—
361	C₄⋊C₄	—	26	1	no	—
362	C₄⋊C₄	—	26	1	no	—
363	C₄⋊C₄	—	26	1	no	—
364	C₄⋊C₄	C₂×C₄×D₁₃	1	2	yes	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₂²⋊C₄	—	26	1	no	—
367	C₂²⋊C₄	—	26	1	no	—
368	C₂²⋊C₄	—	26	1	no	—
369	C₂²⋊C₄	—	26	1	no	—
370	C₂²⋊C₄	—	26	1	no	—
371	C₄²	—	2	2	no	—
372	C₄²	—	26	1	no	—
373	C₄²	C₂×C₄×D₁₃	1	1	yes	characteristic
374	C₄²	#6127	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
376	C₄²	C₂³×D₁₃	1	1	yes	characteristic
377	C₁₃	#17965	1	1	yes	characteristic, complemented, Sylow
378	C₂³	—	26	1	no	—
379	C₂³	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
380	Q₈	—	2	2	no	—
381	Q₈	—	2	2	no	—
382	Q₈	—	4	2	no	—
383	Q₈	—	26	2	no	—
384	D₄	—	26	2	no	—
385	D₄	—	52	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	26	1	no	—
393	C₂×C₄	—	26	1	no	—
394	C₂×C₄	—	26	1	no	—
395	C₂×C₄	—	52	1	no	—
396	C₂×C₄	—	52	1	no	—
397	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
398	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
399	C₂×C₄	C₄×C₂²⋊D₁₃	1	1	yes	characteristic
400	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
401	C₂×C₄	C₂×#6127	1	1	yes	characteristic
402	C₂×C₄	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	2	1	no	—
406	C₈	—	4	2	no	—
407	C₈	—	13	4	no	—
408	C₈	—	26	2	no	—
409	C₈	—	52	2	no	—
410	C₈	—	52	1	no	—
411	C₈	—	52	1	no	—
412	C₈	#88196	1	2	yes	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	52	1	no	—
417	C₂²	—	52	1	no	—
418	C₂²	—	52	1	no	—
419	C₂²	C₂×C₄×C₂²⋊D₁₃	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	4	2	no	—
425	C₄	—	4	2	no	—
426	C₄	—	52	1	no	—
427	C₄	—	52	1	no	—
428	C₄	—	52	1	no	—
429	C₄	D₁₃×#131	1	2	yes	—
430	C₄	C₂×#88196	1	1	yes	characteristic
431	C₄	#11719527	1	1	yes	characteristic
432	C₂	—	4	1	no	—
433	C₂	—	104	1	no	—
434	C₂	#13123546	1	1	yes	characteristic
435	C₂	C₄×#88196	1	1	yes	characteristic
436	C₂	#13123737	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₁₃
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₄²	C₂³×D₁₃
Fitting	C₁₃×#2960	C₂
socle	C₂²×C₁₃	C₂×C₄×D₄
prime radical	#88184	C₂×C₄
cosocle	C₄²×C₁₃	C₂⁴
hypercenter	#2960	D₁₃
hypocenter	C₁₃	#17965
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2960

Complements

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

N	H ≅ G/N	type
3. #13113743	C₂	semidirect
4. #13113736	C₂	semidirect
5. C₈×#6107	C₂	semidirect
6. C₈×#6106	C₂	semidirect
7. #13113601	C₂	semidirect
8. #13113309	C₂	semidirect
10. C₈×#6099	C₂	semidirect
11. C₁₃×#2960	C₂	semidirect
162. #2960	D₁₃	semidirect
377. C₁₃	#17965	semidirect

Maximal subgroups

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

subgroup	index
#13125436	2
#13123811	2
#13113743	2
#13113736	2
C₈×#6107	2
C₈×#6106	2
#13113601	2
#13113309	2
#13113299	2
C₈×#6099	2
C₁₃×#2960	2
#17965	13