Subgroups — #16785747

Order 3328.

730 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃⋊#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
3	#13130544	C₂	1	2	yes	maximal
4	#13130517	C₂	1	2	yes	maximal
5	D₁₃×#427	C₂	1	1	yes	maximal, characteristic
6	C₂×#88237	C₂²	1	1	yes	characteristic
7	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
8	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	D₁₃×#117	C₂²	1	2	yes	—
11	D₁₃⋊#108	—	2	1	no	—
12	D₁₃⋊#108	—	2	1	no	—
13	D₁₃⋊#108	—	2	1	no	—
14	D₁₃⋊#108	—	2	1	no	—
15	C₂×#88104	C₄	1	2	yes	complemented
16	C₂×#88103	C₄	1	2	yes	complemented
17	#11719089	—	2	1	no	—
18	#11719089	—	2	1	no	—
19	#11719089	C₄	1	2	yes	complemented
20	#11719089	C₄	1	2	yes	complemented
21	C₂×#88100	—	2	1	no	—
22	C₂×C₈×#261	—	2	1	no	—
23	C₁₃×#427	C₄	1	1	yes	characteristic, complemented
24	#11718767	C₄	1	1	yes	characteristic, complemented
25	#11718659	C₄	1	2	yes	complemented
26	#11718541	—	2	1	no	—
27	D₁₃×#107	—	2	1	no	—
28	#11718521	—	2	1	no	—
29	D₁₃×#106	—	2	1	no	—
30	#11718239	—	2	4	no	—
31	#11718234	—	2	4	no	—
32	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
33	C₂×C₂²⋊#261	—	2	1	no	—
34	C₂×#6122	—	2	2	no	—
35	C₂×#6122	D₄	1	2	yes	—
36	#88237	—	2	1	no	—
37	#88237	—	2	1	no	—
38	#88237	C₂×C₄	1	2	yes	—
39	#88237	D₄	1	2	yes	—
40	C₂×C₄⋊#261	Q₈	1	2	yes	—
41	C₂×C₄×#261	—	2	1	no	—
42	D₁₃⋊M₁₆	—	2	1	no	—
43	D₁₃⋊M₁₆	—	2	1	no	—
44	D₁₃⋊M₁₆	—	2	2	no	—
45	D₁₃⋊M₁₆	—	2	2	no	—
46	D₁₃⋊M₁₆	—	2	2	no	—
47	D₁₃⋊M₁₆	—	2	2	no	—
48	D₁₃⋊M₁₆	C₂×C₄	1	2	yes	—
49	D₁₃⋊M₁₆	Q₈	1	2	yes	—
50	C₂×#6118	—	2	1	no	—
51	C₂×#6118	C₂×C₄	1	4	yes	—
52	C₂×D₁₃⋊C₈	—	2	1	no	—
53	C₂×D₁₃⋊C₈	—	2	2	no	—
54	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
55	C₁₃×#117	C₂×C₄	1	2	yes	—
56	#88180	C₂×C₄	1	2	yes	—
57	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
63	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
68	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
69	C₂×C₈×D₁₃	Q₈	1	1	yes	characteristic
70	#88146	—	2	2	no	—
71	C₄⋊C₄×D₁₃	—	2	2	no	—
72	C₂²⋊C₄×D₁₃	—	2	2	no	—
73	#88131	—	2	2	no	—
74	#88126	—	2	2	no	—
75	C₄²×D₁₃	—	2	2	no	—
76	#88104	—	2	2	no	—
77	#88104	—	2	2	no	—
78	#88103	—	2	2	no	—
79	#88103	—	2	2	no	—
80	#88100	—	2	2	no	—
81	#88100	—	2	2	no	—
82	C₈×#261	—	2	2	no	—
83	C₈×#261	—	2	2	no	—
84	C₁₃×#107	—	2	1	no	—
85	C₁₃×#106	—	2	1	no	—
86	#88058	—	2	1	no	—
87	#88057	—	2	1	no	—
88	#88048	—	2	2	no	—
89	#88047	—	2	2	no	—
90	#10872	—	13	1	no	maximal, Sylow
91	C₂³×D₁₃	#41	1	1	yes	characteristic
92	C₂²×#261	—	2	2	no	—
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	—	4	2	no	—
96	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
98	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
99	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
105	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
106	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
107	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
108	C₂²⋊#261	—	2	2	no	—
109	C₂²⋊#261	—	2	2	no	—
110	#6122	—	2	2	no	—
111	#6122	—	4	2	no	—
112	#6122	—	4	2	no	—
113	#6122	C₄⋊C₄	1	4	yes	—
114	C₂×#1057	—	2	2	no	—
115	C₂×#1057	—	2	4	no	—
116	C₄⋊#261	—	2	2	no	—
117	C₄⋊#261	C₄⋊C₄	1	4	yes	—
118	C₄×#261	—	2	2	no	—
119	C₄×#261	—	2	2	no	—
120	#6118	—	2	2	no	—
121	#6118	—	2	2	no	—
122	#6118	—	2	4	no	—
123	#6118	—	2	4	no	—
124	D₁₃⋊C₈	—	2	2	no	—
125	D₁₃⋊C₈	—	2	2	no	—
126	D₁₃⋊C₈	—	4	2	no	—
127	D₁₃⋊C₈	—	4	2	no	—
128	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
129	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
130	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₈×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₈×C₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₁₃×C₄⋊C₄	—	2	2	no	—
135	C₁₃×C₂²⋊C₄	—	2	2	no	—
136	C₄²×C₁₃	—	2	2	no	—
137	C₂²⋊Dic₁₃	—	2	2	no	—
138	#6103	—	4	2	no	—
139	C₄⋊Dic₁₃	—	2	2	no	—
140	#6101	—	4	2	no	—
141	C₄×Dic₁₃	—	2	2	no	—
142	C₄×Dic₁₃	—	4	2	no	—
143	C₂×#1055	C₄²	1	1	yes	characteristic
144	C₂×#1055	C₄²	1	1	yes	characteristic
145	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²⋊C₄	1	1	yes	characteristic
147	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
148	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
149	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
150	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
151	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
152	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
153	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
154	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
155	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
156	C₈×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
157	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
158	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
159	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
160	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
161	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
162	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
163	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
164	C₈×D₁₃	C₄⋊C₄	1	1	yes	characteristic
165	C₂²×#108	—	13	1	no	—
166	C₂×#427	—	13	1	no	—
167	C₂×#405	—	13	1	no	—
168	C₂×#344	—	13	2	no	—
169	#1733	—	13	2	no	—
170	C₂³×C₁₃	C₄×D₄	1	1	yes	characteristic
171	C₂²×D₁₃	—	4	2	no	—
172	C₂²×D₁₃	#117	1	1	yes	characteristic
173	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
174	C₂²×D₁₃	#121	1	1	yes	characteristic
175	C₂²×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
176	C₂²×D₁₃	#124	1	1	yes	characteristic
177	C₂²×D₁₃	#125	1	1	yes	characteristic
178	C₂×#261	—	2	4	no	—
179	C₂×#261	—	4	4	no	—
180	C₂×C₄×C₁₃	—	4	2	no	—
181	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
187	C₂×Dic₁₃	—	4	2	no	—
188	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂×Dic₁₃	#121	1	1	yes	characteristic
191	C₂×Dic₁₃	#121	1	1	yes	characteristic
192	C₂×Dic₁₃	#127	1	1	yes	characteristic
193	C₂×Dic₁₃	C₄⋊Q₈	1	1	yes	characteristic
194	C₄×D₁₃	—	8	4	no	—
195	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	C₄×D₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
198	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₄×D₁₃	#117	1	1	yes	characteristic
201	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
202	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
203	C₄×D₁₃	#121	1	1	yes	characteristic
204	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
205	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
206	C₄×D₁₃	C₂²⋊Q₈	1	1	yes	characteristic
207	C₄×D₁₃	#124	1	1	yes	characteristic
208	C₄×D₁₃	#125	1	1	yes	characteristic
209	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
210	C₄×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
211	#1057	—	2	4	no	—
212	#1057	—	4	4	no	—
213	C₈×C₁₃	#95	1	1	yes	characteristic
214	C₈×C₁₃	#95	1	1	yes	characteristic
215	C₈×C₁₃	#95	1	1	yes	characteristic
216	C₈×C₁₃	#95	1	1	yes	characteristic
217	#1055	#95	1	1	yes	characteristic
218	#1055	#95	1	1	yes	characteristic
219	#1055	#95	1	1	yes	characteristic
220	#1055	#95	1	1	yes	characteristic
221	C₂²×M₁₆	—	13	1	no	—
222	C₂²×M₁₆	—	13	2	no	—
223	C₂³×C₈	—	13	1	no	—
224	C₂×#117	—	13	1	no	—
225	C₂×#117	—	13	2	no	—
226	C₂×#108	—	13	2	no	—
227	C₂×#108	—	13	2	no	—
228	C₂×#108	—	26	1	no	—
229	C₂×#108	—	26	1	no	—
230	C₂×#108	—	26	1	no	—
231	C₂×#108	—	26	1	no	—
232	#427	—	13	1	no	—
233	#427	—	13	2	no	—
234	#427	—	26	1	no	—
235	#427	—	26	1	no	—
236	#427	#261	1	1	yes	characteristic, complemented
237	C₂×#107	—	26	1	no	—
238	C₂×#106	—	26	1	no	—
239	#405	—	13	2	no	—
240	#405	—	13	2	no	—
241	#405	—	26	1	no	—
242	#405	—	26	1	no	—
243	C₂×#97	—	26	1	no	—
244	C₂×C₄×C₈	—	26	1	no	—
245	#344	—	26	4	no	—
246	#339	—	26	4	no	—
247	C₂²×C₁₃	—	4	1	no	—
248	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
249	C₂²×C₁₃	#389	1	1	yes	characteristic
250	C₂²×C₁₃	#390	1	1	yes	characteristic
251	C₂×D₁₃	—	2	2	no	—
252	C₂×D₁₃	—	2	2	no	—
253	C₂×D₁₃	—	2	2	no	—
254	C₂×D₁₃	—	4	1	no	—
255	C₂×D₁₃	—	4	1	no	—
256	C₂×D₁₃	—	4	1	no	—
257	C₂×D₁₃	#380	1	1	yes	characteristic
258	C₂×D₁₃	#382	1	1	yes	characteristic
259	C₂×D₁₃	#389	1	1	yes	characteristic
260	C₂×D₁₃	#391	1	1	yes	characteristic
261	#261	—	4	4	no	—
262	C₄×C₁₃	—	8	2	no	—
263	C₄×C₁₃	C₂×#95	1	1	yes	characteristic
264	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
265	C₄×C₁₃	#389	1	1	yes	characteristic
266	C₄×C₁₃	#391	1	1	yes	characteristic
267	Dic₁₃	—	8	2	no	—
268	Dic₁₃	#380	1	1	yes	characteristic
269	Dic₁₃	#384	1	1	yes	characteristic
270	Dic₁₃	#389	1	1	yes	characteristic
271	Dic₁₃	#390	1	1	yes	characteristic
272	C₂³×C₄	—	13	1	no	—
273	C₂×M₁₆	—	13	2	no	—
274	C₂×M₁₆	—	13	2	no	—
275	C₂×M₁₆	—	13	2	no	—
276	C₂×M₁₆	—	13	4	no	—
277	C₂×M₁₆	—	26	1	no	—
278	C₂×M₁₆	—	26	1	no	—
279	C₂×M₁₆	—	26	1	no	—
280	C₂×M₁₆	—	26	2	no	—
281	C₂×M₁₆	—	26	2	no	—
282	C₂×M₁₆	—	26	2	no	—
283	C₂×M₁₆	—	26	2	no	—
284	C₂×M₁₆	—	26	2	no	—
285	C₂²×C₈	—	13	1	no	—
286	C₂²×C₈	—	13	1	no	—
287	C₂²×C₈	—	13	1	no	—
288	C₂²×C₈	—	13	1	no	—
289	C₂²×C₈	—	13	1	no	—
290	C₂²×C₈	—	13	1	no	—
291	C₂²×C₈	—	13	1	no	—
292	C₂²×C₈	—	13	1	no	—
293	C₂²×C₈	—	13	1	no	—
294	C₂²×C₈	—	13	1	no	—
295	C₂²×C₈	—	13	1	no	—
296	C₂²×C₈	—	13	1	no	—
297	C₂²×C₈	—	13	1	no	—
298	C₂²×C₈	—	26	1	no	—
299	C₂²×C₈	—	26	2	no	—
300	C₂²×C₈	C₂×#261	1	1	yes	characteristic
301	#117	—	13	2	no	—
302	#117	—	13	2	no	—
303	#117	—	13	2	no	—
304	#117	—	26	2	no	—
305	#117	—	26	1	no	—
306	#117	—	26	1	no	—
307	#117	—	26	2	no	—
308	#117	—	26	2	no	—
309	#117	C₂×#261	1	2	yes	—
310	C₂×C₄⋊C₄	—	13	2	no	—
311	C₂×C₄⋊C₄	—	26	2	no	—
312	C₂×C₂²⋊C₄	—	26	2	no	—
313	C₂×C₂²⋊C₄	—	26	1	no	—
314	C₂×C₄²	—	26	2	no	—
315	C₂×C₄²	—	26	1	no	—
316	#108	—	26	2	no	—
317	#108	—	26	2	no	—
318	#108	—	26	2	no	—
319	#108	—	26	2	no	—
320	#107	—	2	1	no	—
321	#107	—	26	2	no	—
322	#107	—	26	1	no	—
323	#106	—	2	1	no	—
324	#106	—	26	2	no	—
325	#106	—	26	1	no	—
326	#97	—	26	2	no	—
327	#97	—	26	2	no	—
328	C₄×C₈	—	26	2	no	—
329	C₄×C₈	—	26	2	no	—
330	C₂×C₁₃	—	2	1	no	—
331	C₂×C₁₃	—	2	1	no	—
332	C₂×C₁₃	—	2	1	no	—
333	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
334	D₁₃	—	2	1	no	—
335	D₁₃	—	2	1	no	—
336	D₁₃	—	2	1	no	—
337	D₁₃	#1814	1	2	yes	—
338	C₂⁴	—	13	1	no	—
339	C₂²×C₄	—	13	1	no	—
340	C₂²×C₄	—	13	1	no	—
341	C₂²×C₄	—	13	1	no	—
342	C₂²×C₄	—	13	1	no	—
343	C₂²×C₄	—	13	1	no	—
344	C₂²×C₄	—	13	1	no	—
345	C₂²×C₄	—	13	1	no	—
346	C₂²×C₄	—	13	1	no	—
347	C₂²×C₄	—	13	1	no	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	26	2	no	—
353	C₂²×C₄	—	52	2	no	—
354	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
355	M₁₆	—	13	4	no	—
356	M₁₆	—	26	2	no	—
357	M₁₆	—	26	2	no	—
358	M₁₆	—	26	2	no	—
359	M₁₆	—	26	4	no	—
360	M₁₆	—	26	4	no	—
361	M₁₆	—	52	2	no	—
362	M₁₆	—	52	2	no	—
363	C₂×C₈	—	13	1	no	—
364	C₂×C₈	—	13	1	no	—
365	C₂×C₈	—	13	1	no	—
366	C₂×C₈	—	13	1	no	—
367	C₂×C₈	—	13	1	no	—
368	C₂×C₈	—	13	1	no	—
369	C₂×C₈	—	13	1	no	—
370	C₂×C₈	—	13	1	no	—
371	C₂×C₈	—	13	1	no	—
372	C₂×C₈	—	13	1	no	—
373	C₂×C₈	—	13	1	no	—
374	C₂×C₈	—	13	1	no	—
375	C₂×C₈	—	13	1	no	—
376	C₂×C₈	—	13	1	no	—
377	C₂×C₈	—	13	1	no	—
378	C₂×C₈	—	13	1	no	—
379	C₂×C₈	—	13	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	1	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	13	1	no	—
385	C₂×C₈	—	26	2	no	—
386	C₂×C₈	—	26	2	no	—
387	C₂×C₈	—	26	2	no	—
388	C₂×C₈	—	26	4	no	—
389	C₂×C₈	—	52	2	no	—
390	C₂×C₈	—	52	2	no	—
391	C₂×C₈	C₄×#261	1	1	yes	characteristic
392	C₂×C₈	C₄×#261	1	1	yes	characteristic
393	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
394	C₂×C₈	C₄⋊#261	1	1	yes	characteristic
395	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
396	C₂×C₈	C₂²⋊#261	1	1	yes	characteristic
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	13	4	no	—
399	C₄⋊C₄	—	26	2	no	—
400	C₄⋊C₄	—	26	2	no	—
401	C₄⋊C₄	—	52	2	no	—
402	C₂²⋊C₄	—	2	2	no	—
403	C₂²⋊C₄	—	26	2	no	—
404	C₂²⋊C₄	—	26	2	no	—
405	C₂²⋊C₄	—	26	2	no	—
406	C₂²⋊C₄	—	52	2	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	26	2	no	—
409	C₄²	—	26	2	no	—
410	C₄²	—	26	2	no	—
411	C₄²	—	52	2	no	—
412	C₁₃	#10872	1	1	yes	characteristic, complemented, Sylow
413	C₂³	—	13	1	no	—
414	C₂³	—	13	1	no	—
415	C₂³	—	13	1	no	—
416	C₂³	—	13	1	no	—
417	C₂³	—	13	1	no	—
418	C₂³	—	13	1	no	—
419	C₂³	—	52	2	no	—
420	C₂³	D₄×#261	1	1	yes	characteristic
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	13	1	no	—
423	C₂×C₄	—	13	1	no	—
424	C₂×C₄	—	13	1	no	—
425	C₂×C₄	—	13	1	no	—
426	C₂×C₄	—	13	1	no	—
427	C₂×C₄	—	13	1	no	—
428	C₂×C₄	—	13	1	no	—
429	C₂×C₄	—	13	1	no	—
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	13	1	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	1	no	—
439	C₂×C₄	—	13	1	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	1	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	26	4	no	—
445	C₂×C₄	—	52	4	no	—
446	C₂×C₄	—	52	2	no	—
447	C₂×C₄	—	104	4	no	—
448	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
449	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
450	C₂×C₄	D₄×#261	1	1	yes	characteristic
451	C₂×C₄	Q₈×#261	1	1	yes	characteristic
452	C₂×C₄	Q₈×#261	1	1	yes	characteristic
453	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
454	C₈	—	13	1	no	—
455	C₈	—	13	1	no	—
456	C₈	—	13	1	no	—
457	C₈	—	13	1	no	—
458	C₈	—	26	4	no	—
459	C₈	—	52	4	no	—
460	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
461	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
462	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
463	C₈	(C₂×#261)⋊C₄	1	1	yes	characteristic
464	C₂²	—	4	1	no	—
465	C₂²	—	13	1	no	—
466	C₂²	—	13	1	no	—
467	C₂²	—	13	1	no	—
468	C₂²	—	13	1	no	—
469	C₂²	—	26	2	no	—
470	C₂²	—	26	2	no	—
471	C₂²	—	26	2	no	—
472	C₂²	—	52	1	no	—
473	C₂²	—	52	1	no	—
474	C₂²	—	52	1	no	—
475	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
476	C₂²	#11719083	1	1	yes	characteristic
477	C₂²	#11719151	1	1	yes	characteristic
478	C₄	—	8	2	no	—
479	C₄	—	13	1	no	—
480	C₄	—	13	1	no	—
481	C₄	—	13	1	no	—
482	C₄	—	13	1	no	—
483	C₄	—	52	4	no	—
484	C₄	—	104	2	no	—
485	C₄	C₄⋊C₄×#261	1	1	yes	characteristic
486	C₄	#11719083	1	1	yes	characteristic
487	C₄	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
488	C₄	(C₂×#261)⋊Q₈	1	1	yes	characteristic
489	C₂	—	2	1	no	—
490	C₂	—	2	1	no	—
491	C₂	—	2	1	no	—
492	C₂	—	13	2	no	—
493	C₂	—	26	1	no	—
494	C₂	—	26	1	no	—
495	C₂	—	26	1	no	—
496	C₂	#13130013	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#11719083
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂²×C₄	C₂²×#261
Fitting	C₁₃×#427	C₄
socle	C₂×C₁₃	C₄⋊#95
prime radical	C₂³×D₁₃	#41
cosocle	C₂²×C₄×D₁₃	C₂³
hypercenter	#427	#261
hypocenter	C₁₃	#10872
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #427

Complements

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

N	H ≅ G/N	type
15. C₂×#88104	C₄	semidirect
16. C₂×#88103	C₄	semidirect
19. #11719089	C₄	semidirect
20. #11719089	C₄	semidirect
23. C₁₃×#427	C₄	semidirect
24. #11718767	C₄	semidirect
25. #11718659	C₄	semidirect
236. #427	#261	semidirect
412. C₁₃	#10872	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃⋊#108	2
C₂×#11719089	2
#13130544	2
#13130517	2
D₁₃×#427	2
#10872	13