Subgroups — #16789119

Order 3328.

570 conjugacy classes of subgroups.

The subgroup lattice has 434 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊M₃₂	C₂	1	1	yes	maximal, characteristic
2	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
3	#13129900	C₂	1	4	yes	maximal, complemented
4	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
5	C₂×D₁₃⋊M₁₆	—	2	1	no	—
6	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
7	D₁₃×#117	—	2	1	no	—
8	C₂×#88106	—	2	1	no	—
9	D₁₃⋊#108	—	2	1	no	—
10	D₁₃⋊#108	—	2	1	no	—
11	D₁₃⋊#108	C₄	1	2	yes	complemented
12	D₁₃⋊#108	C₂²	1	2	yes	—
13	C₂×#88104	—	2	1	no	—
14	C₂×#88103	C₄	1	2	yes	complemented
15	D₁₃⋊M₃₂	—	2	1	no	—
16	D₁₃⋊M₃₂	—	2	1	no	—
17	D₁₃⋊M₃₂	C₄	1	2	yes	complemented
18	D₁₃⋊M₃₂	C₂²	1	2	yes	—
19	C₂×#88098	—	2	1	no	—
20	C₂×D₁₃⋊C₁₆	C₄	1	2	yes	complemented
21	C₁₃×#427	C₄	1	1	yes	characteristic
22	#11718767	C₄	1	1	yes	characteristic
23	#11718659	—	2	1	no	—
24	#11718541	—	2	1	no	—
25	D₁₃×#107	—	2	1	no	—
26	#11718521	C₄	1	2	yes	—
27	D₁₃×#106	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
29	C₂×#6122	—	4	1	no	—
30	D₁₃⋊M₁₆	—	2	2	no	—
31	D₁₃⋊M₁₆	—	2	2	no	—
32	D₁₃⋊M₁₆	—	4	1	no	—
33	D₁₃⋊M₁₆	—	4	1	no	—
34	C₂×#6118	—	2	2	no	—
35	C₂×D₁₃⋊C₈	—	4	1	no	—
36	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
37	C₁₃×#117	—	2	1	no	—
38	#88180	—	2	1	no	—
39	C₂²×#1055	D₄	1	1	yes	characteristic
40	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
46	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
48	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
50	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
52	#88146	—	2	2	no	—
53	C₄⋊C₄×D₁₃	—	2	2	no	—
54	C₂²⋊C₄×D₁₃	—	4	1	no	—
55	#88131	—	4	1	no	—
56	#88126	—	4	1	no	—
57	C₄²×D₁₃	—	4	1	no	—
58	#88106	—	2	2	no	—
59	#88106	—	2	2	no	—
60	C₂×#6092	—	2	2	no	—
61	#88104	—	2	2	no	—
62	#88104	—	2	2	no	—
63	#88103	—	2	2	no	—
64	#88103	C₂×C₄	1	4	yes	—
65	#88098	—	2	2	no	—
66	#88098	—	2	2	no	—
67	D₁₃⋊C₁₆	—	2	2	no	—
68	D₁₃⋊C₁₆	C₂×C₄	1	4	yes	—
69	C₁₃×#107	—	2	1	no	—
70	C₁₃×#106	C₂×C₄	1	2	yes	—
71	#88058	—	2	1	no	—
72	#88057	C₂×C₄	1	2	yes	—
73	#88048	—	2	2	no	—
74	#88047	—	2	2	no	—
75	#12563	—	13	1	no	maximal, Sylow
76	C₂³×D₁₃	SD₁₆	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₁₃	D₈	1	1	yes	characteristic
79	C₂×C₄×D₁₃	—	4	2	no	—
80	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
82	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
84	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
85	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
86	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
87	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
88	C₂×C₄×D₁₃	SD₁₆	1	1	yes	characteristic
89	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
90	C₂×C₄×D₁₃	Q₁₆	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
92	#6122	—	4	2	no	—
93	#6122	—	4	2	no	—
94	C₂×#1057	—	4	2	no	—
95	#6118	—	2	4	no	—
96	#6118	—	4	2	no	—
97	D₁₃⋊C₈	—	4	2	no	—
98	D₁₃⋊C₈	—	4	2	no	—
99	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
100	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
101	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
105	C₁₃×C₄⋊C₄	—	2	2	no	—
106	C₁₃×C₂²⋊C₄	—	4	1	no	—
107	C₄²×C₁₃	—	4	1	no	—
108	C₂²⋊Dic₁₃	—	4	1	no	—
109	#6103	—	4	2	no	—
110	C₄⋊Dic₁₃	—	2	2	no	—
111	#6101	—	4	2	no	—
112	C₄×Dic₁₃	—	4	1	no	—
113	C₄×Dic₁₃	—	4	2	no	—
114	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
115	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
116	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
118	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
119	C₂×#1055	C₂×D₄	1	1	yes	characteristic
120	C₈×D₁₃	C₄²	1	1	yes	characteristic
121	C₈×D₁₃	C₄²	1	1	yes	characteristic
122	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
123	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
124	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
125	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
126	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₈×D₁₃	C₂×D₄	1	1	yes	characteristic
135	C₈×D₁₃	C₂×Q₈	1	1	yes	characteristic
136	#6092	—	2	4	no	—
137	C₂²×M₃₂	—	13	1	no	—
138	C₂²×#108	—	13	1	no	—
139	C₂×#427	—	13	1	no	—
140	#1383	—	13	4	no	—
141	C₂³×C₁₃	#102	1	1	yes	characteristic
142	C₂²×D₁₃	—	4	2	no	—
143	C₂²×D₁₃	#102	1	1	yes	characteristic
144	C₂²×D₁₃	#103	1	1	yes	characteristic
145	C₂²×D₁₃	#103	1	1	yes	characteristic
146	C₂²×D₁₃	#106	1	1	yes	characteristic
147	C₂²×D₁₃	#106	1	1	yes	characteristic
148	C₂²×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
149	C₂×C₄×C₁₃	—	4	2	no	—
150	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
151	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
152	C₂×C₄×C₁₃	#102	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#103	1	1	yes	characteristic
155	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×Dic₁₃	—	4	2	no	—
157	C₂×Dic₁₃	#102	1	1	yes	characteristic
158	C₂×Dic₁₃	#102	1	1	yes	characteristic
159	C₂×Dic₁₃	#102	1	1	yes	characteristic
160	C₂×Dic₁₃	#107	1	1	yes	characteristic
161	C₂×Dic₁₃	#107	1	1	yes	characteristic
162	C₂×Dic₁₃	C₂×D₈	1	1	yes	characteristic
163	C₄×D₁₃	—	8	4	no	—
164	C₄×D₁₃	#95	1	1	yes	characteristic
165	C₄×D₁₃	#95	1	1	yes	characteristic
166	C₄×D₁₃	#102	1	1	yes	characteristic
167	C₄×D₁₃	#102	1	1	yes	characteristic
168	C₄×D₁₃	#103	1	1	yes	characteristic
169	C₄×D₁₃	#103	1	1	yes	characteristic
170	C₄×D₁₃	#103	1	1	yes	characteristic
171	C₄×D₁₃	#103	1	1	yes	characteristic
172	C₄×D₁₃	#106	1	1	yes	characteristic
173	C₄×D₁₃	#106	1	1	yes	characteristic
174	C₄×D₁₃	#107	1	1	yes	characteristic
175	C₄×D₁₃	#107	1	1	yes	characteristic
176	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
178	C₄×D₁₃	C₂×SD₁₆	1	1	yes	characteristic
179	C₄×D₁₃	C₂×Q₁₆	1	1	yes	characteristic
180	#1057	—	4	4	no	—
181	C₈×C₁₃	#95	1	1	yes	characteristic
182	C₈×C₁₃	#95	1	1	yes	characteristic
183	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
184	C₈×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	#1055	#95	1	1	yes	characteristic
186	#1055	#95	1	1	yes	characteristic
187	#1055	C₂×C₂²⋊C₄	1	1	yes	characteristic
188	#1055	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂²×M₁₆	—	26	1	no	—
190	C₂³×C₈	—	13	1	no	—
191	C₂×#117	—	26	1	no	—
192	C₂×M₃₂	—	13	2	no	—
193	C₂×M₃₂	—	13	2	no	—
194	C₂×M₃₂	—	26	1	no	—
195	C₂×M₃₂	—	26	1	no	—
196	C₂×M₃₂	—	26	1	no	—
197	C₂×M₃₂	—	26	1	no	—
198	C₂²×C₁₆	—	13	2	no	—
199	C₂×#108	—	13	2	no	—
200	C₂×#108	—	13	2	no	—
201	C₂×#108	—	13	2	no	—
202	C₂×#108	—	26	1	no	—
203	C₂×#108	—	26	1	no	—
204	C₂×#108	—	26	1	no	—
205	#427	—	13	1	no	—
206	#427	—	13	2	no	—
207	#427	—	26	1	no	—
208	#427	—	26	1	no	—
209	#427	#261	1	1	yes	characteristic
210	C₂×#107	—	26	1	no	—
211	C₂×#106	—	13	2	no	—
212	C₂²×C₁₃	—	4	1	no	—
213	C₂²×C₁₃	#340	1	1	yes	characteristic
214	C₂²×C₁₃	#340	1	1	yes	characteristic
215	C₂²×C₁₃	C₂×#102	1	1	yes	characteristic
216	C₂×D₁₃	—	2	2	no	—
217	C₂×D₁₃	—	2	2	no	—
218	C₂×D₁₃	—	2	2	no	—
219	C₂×D₁₃	—	4	1	no	—
220	C₂×D₁₃	—	4	1	no	—
221	C₂×D₁₃	—	4	1	no	—
222	C₂×D₁₃	#340	1	1	yes	characteristic
223	C₂×D₁₃	#340	1	1	yes	characteristic
224	C₂×D₁₃	C₂×#103	1	1	yes	characteristic
225	C₂×D₁₃	C₂×#106	1	1	yes	characteristic
226	C₄×C₁₃	—	8	2	no	—
227	C₄×C₁₃	#340	1	1	yes	characteristic
228	C₄×C₁₃	#340	1	1	yes	characteristic
229	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
230	C₄×C₁₃	C₂×#103	1	1	yes	characteristic
231	Dic₁₃	—	8	2	no	—
232	Dic₁₃	#340	1	1	yes	characteristic
233	Dic₁₃	#340	1	1	yes	characteristic
234	Dic₁₃	C₂×#102	1	1	yes	characteristic
235	Dic₁₃	C₂×#107	1	1	yes	characteristic
236	C₂³×C₄	—	13	1	no	—
237	C₂×M₁₆	—	26	2	no	—
238	C₂×M₁₆	—	26	2	no	—
239	C₂×M₁₆	—	26	2	no	—
240	C₂×M₁₆	—	52	1	no	—
241	C₂×M₁₆	—	52	1	no	—
242	C₂×M₁₆	—	52	1	no	—
243	C₂²×C₈	—	13	1	no	—
244	C₂²×C₈	—	13	1	no	—
245	C₂²×C₈	—	13	1	no	—
246	C₂²×C₈	—	13	1	no	—
247	C₂²×C₈	—	13	1	no	—
248	C₂²×C₈	—	13	1	no	—
249	C₂²×C₈	—	13	1	no	—
250	C₂²×C₈	—	13	1	no	—
251	C₂²×C₈	—	13	1	no	—
252	C₂²×C₈	—	13	1	no	—
253	C₂²×C₈	—	13	1	no	—
254	C₂²×C₈	—	13	1	no	—
255	C₂²×C₈	—	13	1	no	—
256	C₂²×C₈	—	52	1	no	—
257	C₂²×C₈	C₂×#261	1	1	yes	characteristic
258	#117	—	2	1	no	—
259	#117	—	26	2	no	—
260	#117	—	26	1	no	—
261	#117	—	52	1	no	—
262	#117	—	52	1	no	—
263	C₂×C₄⋊C₄	—	26	2	no	—
264	C₂×C₂²⋊C₄	—	52	1	no	—
265	C₂×C₄²	—	52	1	no	—
266	M₃₂	—	26	2	no	—
267	M₃₂	—	26	2	no	—
268	M₃₂	—	26	2	no	—
269	M₃₂	—	26	2	no	—
270	C₂×C₁₆	—	13	4	no	—
271	C₂×C₁₆	—	26	2	no	—
272	C₂×C₁₆	—	26	2	no	—
273	#108	—	13	4	no	—
274	#108	—	26	2	no	—
275	#108	—	26	2	no	—
276	#108	—	26	2	no	—
277	#107	—	2	1	no	—
278	#107	—	26	2	no	—
279	#107	—	26	1	no	—
280	#106	—	13	2	no	—
281	#106	—	26	2	no	—
282	#106	C₂×#261	1	2	yes	—
283	C₂×C₁₃	—	2	1	no	—
284	C₂×C₁₃	—	2	1	no	—
285	C₂×C₁₃	—	2	1	no	—
286	C₂×C₁₃	C₂×#340	1	1	yes	characteristic
287	D₁₃	—	2	1	no	—
288	D₁₃	—	2	1	no	—
289	D₁₃	—	2	1	no	—
290	D₁₃	#2155	1	2	yes	—
291	C₂⁴	—	13	1	no	—
292	C₂²×C₄	—	13	1	no	—
293	C₂²×C₄	—	13	1	no	—
294	C₂²×C₄	—	13	1	no	—
295	C₂²×C₄	—	13	1	no	—
296	C₂²×C₄	—	13	1	no	—
297	C₂²×C₄	—	13	1	no	—
298	C₂²×C₄	—	13	1	no	—
299	C₂²×C₄	—	13	1	no	—
300	C₂²×C₄	—	13	1	no	—
301	C₂²×C₄	—	13	1	no	—
302	C₂²×C₄	—	13	1	no	—
303	C₂²×C₄	—	13	1	no	—
304	C₂²×C₄	—	13	1	no	—
305	C₂²×C₄	—	52	2	no	—
306	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
307	M₁₆	—	26	4	no	—
308	M₁₆	—	52	2	no	—
309	M₁₆	—	52	2	no	—
310	M₁₆	—	52	2	no	—
311	C₂×C₈	—	13	1	no	—
312	C₂×C₈	—	13	1	no	—
313	C₂×C₈	—	13	1	no	—
314	C₂×C₈	—	13	1	no	—
315	C₂×C₈	—	13	1	no	—
316	C₂×C₈	—	13	1	no	—
317	C₂×C₈	—	13	1	no	—
318	C₂×C₈	—	13	1	no	—
319	C₂×C₈	—	13	1	no	—
320	C₂×C₈	—	13	1	no	—
321	C₂×C₈	—	13	1	no	—
322	C₂×C₈	—	13	1	no	—
323	C₂×C₈	—	13	1	no	—
324	C₂×C₈	—	13	1	no	—
325	C₂×C₈	—	13	1	no	—
326	C₂×C₈	—	13	1	no	—
327	C₂×C₈	—	13	1	no	—
328	C₂×C₈	—	13	1	no	—
329	C₂×C₈	—	13	1	no	—
330	C₂×C₈	—	13	1	no	—
331	C₂×C₈	—	13	1	no	—
332	C₂×C₈	—	13	1	no	—
333	C₂×C₈	—	52	2	no	—
334	C₂×C₈	—	52	2	no	—
335	C₂×C₈	—	52	2	no	—
336	C₂×C₈	C₄×#261	1	1	yes	characteristic
337	C₂×C₈	C₄×#261	1	1	yes	characteristic
338	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
339	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
340	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
341	C₂×C₈	C₂²×#261	1	1	yes	characteristic
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	26	2	no	—
344	C₄⋊C₄	—	52	2	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	52	2	no	—
347	C₂²⋊C₄	—	52	1	no	—
348	C₄²	—	4	1	no	—
349	C₄²	—	52	2	no	—
350	C₄²	—	52	1	no	—
351	C₁₆	—	26	4	no	—
352	C₁₃	#12563	1	1	yes	characteristic, complemented, Sylow
353	C₂³	—	13	1	no	—
354	C₂³	—	13	1	no	—
355	C₂³	—	13	1	no	—
356	C₂³	—	13	1	no	—
357	C₂³	—	13	1	no	—
358	C₂³	—	13	1	no	—
359	C₂³	—	52	2	no	—
360	C₂³	#88115	1	1	yes	characteristic
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	13	1	no	—
363	C₂×C₄	—	13	1	no	—
364	C₂×C₄	—	13	1	no	—
365	C₂×C₄	—	13	1	no	—
366	C₂×C₄	—	13	1	no	—
367	C₂×C₄	—	13	1	no	—
368	C₂×C₄	—	13	1	no	—
369	C₂×C₄	—	13	1	no	—
370	C₂×C₄	—	13	1	no	—
371	C₂×C₄	—	13	1	no	—
372	C₂×C₄	—	13	1	no	—
373	C₂×C₄	—	13	1	no	—
374	C₂×C₄	—	13	1	no	—
375	C₂×C₄	—	13	1	no	—
376	C₂×C₄	—	13	1	no	—
377	C₂×C₄	—	13	1	no	—
378	C₂×C₄	—	13	1	no	—
379	C₂×C₄	—	13	1	no	—
380	C₂×C₄	—	13	1	no	—
381	C₂×C₄	—	13	1	no	—
382	C₂×C₄	—	13	1	no	—
383	C₂×C₄	—	13	1	no	—
384	C₂×C₄	—	52	2	no	—
385	C₂×C₄	—	104	4	no	—
386	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
387	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
388	C₂×C₄	#88115	1	1	yes	characteristic
389	C₂×C₄	#88117	1	1	yes	characteristic
390	C₂×C₄	#88117	1	1	yes	characteristic
391	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
392	C₈	—	13	1	no	—
393	C₈	—	13	1	no	—
394	C₈	—	13	1	no	—
395	C₈	—	13	1	no	—
396	C₈	—	52	4	no	—
397	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
398	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
399	C₈	C₂×C₄×#261	1	1	yes	characteristic
400	C₈	C₂×C₄⋊#261	1	1	yes	characteristic
401	C₂²	—	4	1	no	—
402	C₂²	—	13	1	no	—
403	C₂²	—	13	1	no	—
404	C₂²	—	13	1	no	—
405	C₂²	—	13	1	no	—
406	C₂²	—	26	2	no	—
407	C₂²	—	26	2	no	—
408	C₂²	—	26	2	no	—
409	C₂²	—	52	1	no	—
410	C₂²	—	52	1	no	—
411	C₂²	—	52	1	no	—
412	C₂²	#11718246	1	1	yes	characteristic
413	C₂²	#11718246	1	1	yes	characteristic
414	C₂²	C₂×#88115	1	1	yes	characteristic
415	C₄	—	8	2	no	—
416	C₄	—	13	1	no	—
417	C₄	—	13	1	no	—
418	C₄	—	13	1	no	—
419	C₄	—	13	1	no	—
420	C₄	—	104	2	no	—
421	C₄	#11718246	1	1	yes	characteristic
422	C₄	#11718246	1	1	yes	characteristic
423	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
424	C₄	C₂×#88117	1	1	yes	characteristic
425	C₂	—	2	1	no	—
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	13	2	no	—
429	C₂	—	26	1	no	—
430	C₂	—	26	1	no	—
431	C₂	—	26	1	no	—
432	C₂	C₂×#11718246	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11718246
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂×C₈	C₂²×#261
Fitting	C₁₃×#427	C₄
socle	C₂×C₁₃	C₂×#340
prime radical	C₂³×D₁₃	SD₁₆
cosocle	C₂×C₈×D₁₃	C₂³
hypercenter	#427	#261
hypocenter	C₁₃	#12563
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #427

Complements

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

N	H ≅ G/N	type
3. #13129900	C₂	semidirect
11. D₁₃⋊#108	C₄	semidirect
14. C₂×#88103	C₄	semidirect
17. D₁₃⋊M₃₂	C₄	semidirect
20. C₂×D₁₃⋊C₁₆	C₄	semidirect
352. C₁₃	#12563	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊M₃₂	2
C₂×D₁₃⋊#108	2
#13129900	2
D₁₃×#427	2
#12563	13