Subgroups — #16797182

Order 3328.

1010 conjugacy classes of subgroups.

The subgroup lattice has 526 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×#11719092	C₂	1	1	yes	maximal, characteristic
3	#13131399	C₂	1	2	yes	maximal
4	#13130642	C₂	1	4	yes	maximal, complemented
5	#13130638	C₂	1	4	yes	maximal, complemented
6	#13130517	C₂	1	2	yes	maximal
7	D₁₃×#405	C₂	1	1	yes	maximal, characteristic
8	C₂×#88237	C₂²	1	2	yes	—
9	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂×M₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
12	D₁₃×#117	C₂²	1	1	yes	characteristic
13	#11719099	—	2	4	no	—
14	M₁₆×#261	—	2	4	no	—
15	D₁₃⋊#108	C₄	1	2	yes	complemented
16	D₁₃⋊#108	C₄	1	2	yes	complemented
17	D₁₃⋊#108	C₂²	1	2	yes	—
18	D₁₃⋊#108	C₂²	1	2	yes	—
19	C₂×#88104	C₄	1	2	yes	complemented
20	C₂×#88103	C₄	1	2	yes	complemented
21	#11719092	C₄	1	2	yes	complemented
22	#11719092	C₄	1	2	yes	complemented
23	#11719092	C₂²	1	2	yes	—
24	#11719092	C₂²	1	2	yes	—
25	C₂×#88102	C₄	1	2	yes	complemented
26	C₂×#88101	C₄	1	2	yes	complemented
27	#11719089	C₂²	1	8	yes	—
28	C₁₃×#405	C₄	1	1	yes	characteristic, complemented
29	#11718783	C₄	1	1	yes	characteristic, complemented
30	#11718762	C₄	1	1	yes	characteristic, complemented
31	#11718658	C₄	1	1	yes	characteristic, complemented
32	#11718369	C₄	1	2	yes	complemented
33	D₁₃×#97	C₂²	1	2	yes	—
34	#11718350	C₄	1	2	yes	complemented
35	C₄×C₈×D₁₃	C₂²	1	2	yes	—
36	#11718234	C₂²	1	8	yes	—
37	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊#261	—	2	2	no	—
39	C₂×#6122	—	2	2	no	—
40	#88237	—	2	2	no	—
41	#88237	—	2	2	no	—
42	#88237	C₂×C₄	1	4	yes	—
43	#88237	C₂³	1	4	yes	—
44	C₂×C₄⋊#261	C₂×C₄	1	4	yes	—
45	C₂×C₄×#261	—	2	2	no	—
46	D₁₃⋊M₁₆	—	2	2	no	—
47	D₁₃⋊M₁₆	—	2	2	no	—
48	D₁₃⋊M₁₆	C₂×C₄	1	4	yes	—
49	D₁₃⋊M₁₆	C₂³	1	4	yes	—
50	C₂×#6118	C₂×C₄	1	4	yes	—
51	C₂×D₁₃⋊C₈	—	2	2	no	—
52	C₂×C₁₃×M₁₆	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
54	C₁₃×#117	C₂×C₄	1	1	yes	characteristic
55	#88180	C₂×C₄	1	1	yes	characteristic
56	C₂×#6099	C₂×C₄	1	1	yes	characteristic
57	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
58	M₁₆×D₁₃	D₄	1	2	yes	—
59	M₁₆×D₁₃	D₄	1	2	yes	—
60	M₁₆×D₁₃	Q₈	1	2	yes	—
61	M₁₆×D₁₃	Q₈	1	2	yes	—
62	C₂×#6094	C₂×C₄	1	2	yes	—
63	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
64	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
67	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
68	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
69	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
70	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
74	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
75	C₂×C₈×D₁₃	C₂³	1	2	yes	—
76	#88146	—	2	1	no	—
77	C₄⋊C₄×D₁₃	—	2	1	no	—
78	C₂²⋊C₄×D₁₃	—	2	1	no	—
79	#88131	—	2	1	no	—
80	#88126	C₂×C₄	1	2	yes	—
81	C₄²×D₁₃	C₂³	1	2	yes	—
82	#88104	C₂×C₄	1	4	yes	complemented
83	#88104	C₂×C₄	1	4	yes	complemented
84	#88103	C₂×C₄	1	4	yes	complemented
85	#88103	C₂×C₄	1	4	yes	complemented
86	#88102	C₂×C₄	1	4	yes	—
87	#88102	C₂×C₄	1	4	yes	—
88	#88101	C₂×C₄	1	4	yes	—
89	#88101	C₂×C₄	1	4	yes	—
90	#88100	—	2	8	no	—
91	C₈×#261	—	2	8	no	—
92	C₁₃×#97	C₂×C₄	1	2	yes	complemented
93	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	complemented
94	#88055	C₂×C₄	1	2	yes	complemented
95	#88055	C₂×C₄	1	2	yes	complemented
96	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
97	C₈×Dic₁₃	C₂×C₄	1	2	yes	complemented
98	#88043	C₂×C₄	1	2	yes	complemented
99	C₄×#1055	C₂×C₄	1	2	yes	complemented
100	#20446	—	13	1	no	maximal, Sylow
101	C₂³×D₁₃	#41	1	1	yes	characteristic
102	C₂²×#261	—	2	4	no	—
103	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₁₃	#41	1	1	yes	characteristic
105	C₂×C₄×D₁₃	—	2	2	no	—
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
114	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
115	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
116	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
117	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
118	C₂²⋊#261	—	2	4	no	—
119	C₂²⋊#261	—	2	4	no	—
120	#6122	—	2	4	no	—
121	#6122	—	2	4	no	—
122	C₂×#1057	—	2	4	no	—
123	C₄⋊#261	—	2	4	no	—
124	C₄⋊#261	C₂²×C₄	1	8	yes	—
125	C₄×#261	—	2	4	no	—
126	C₄×#261	—	2	4	no	—
127	#6118	—	2	4	no	—
128	#6118	C₂²×C₄	1	8	yes	—
129	D₁₃⋊C₈	—	2	4	no	—
130	D₁₃⋊C₈	—	2	4	no	—
131	C₁₃×M₁₆	C₄⋊C₄	1	2	yes	—
132	C₁₃×M₁₆	C₄⋊C₄	1	2	yes	—
133	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
134	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
135	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
136	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
140	C₁₃×C₄⋊C₄	—	2	1	no	—
141	C₁₃×C₂²⋊C₄	—	2	1	no	—
142	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
143	C₂²⋊Dic₁₃	—	2	1	no	—
144	#6103	—	2	2	no	—
145	C₄⋊Dic₁₃	—	2	1	no	—
146	#6101	—	2	2	no	—
147	C₄×Dic₁₃	—	2	2	no	—
148	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
149	#6099	C₄⋊C₄	1	2	yes	—
150	#6099	C₄⋊C₄	1	2	yes	—
151	C₂×#1055	C₄²	1	1	yes	characteristic
152	C₂×#1055	C₄²	1	1	yes	characteristic
153	C₂×#1055	C₄²	1	1	yes	characteristic
154	C₂×#1055	C₄²	1	1	yes	characteristic
155	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
156	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
157	C₂×#1055	C₂²×C₄	1	2	yes	—
158	#6094	C₄⋊C₄	1	4	yes	—
159	#6094	C₄⋊C₄	1	4	yes	—
160	C₈×D₁₃	C₄²	1	1	yes	characteristic
161	C₈×D₁₃	C₄²	1	1	yes	characteristic
162	C₈×D₁₃	C₄²	1	1	yes	characteristic
163	C₈×D₁₃	C₄²	1	1	yes	characteristic
164	C₈×D₁₃	C₄²	1	1	yes	characteristic
165	C₈×D₁₃	C₄²	1	1	yes	characteristic
166	C₈×D₁₃	C₄²	1	1	yes	characteristic
167	C₈×D₁₃	C₄²	1	1	yes	characteristic
168	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
169	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
171	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
172	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
173	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
174	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
175	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
176	C₈×D₁₃	C₂×D₄	1	4	yes	—
177	C₈×D₁₃	C₂×Q₈	1	4	yes	—
178	C₂²×#108	—	13	1	no	—
179	C₂×#427	—	13	1	no	—
180	#2873	—	13	2	no	—
181	C₂×#405	—	13	1	no	—
182	#1773	—	13	4	no	—
183	#1772	—	13	4	no	—
184	#1733	—	13	2	no	—
185	C₂³×C₁₃	#117	1	1	yes	characteristic
186	C₂²×D₁₃	—	4	2	no	—
187	C₂²×D₁₃	#117	1	1	yes	characteristic
188	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
189	C₂²×D₁₃	C₄×D₄	1	1	yes	characteristic
190	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
191	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
192	C₂²×D₁₃	C₂×#41	1	1	yes	characteristic
193	C₂×#261	—	2	8	no	—
194	C₂×#261	—	8	4	no	—
195	C₂×C₄×C₁₃	—	2	2	no	—
196	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
197	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
198	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₄×C₁₃	#117	1	1	yes	characteristic
201	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
202	C₂×Dic₁₃	—	2	2	no	—
203	C₂×Dic₁₃	#117	1	1	yes	characteristic
204	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
205	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
206	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
207	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
208	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
209	C₄×D₁₃	—	4	4	no	—
210	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
211	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
212	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
213	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
214	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
215	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
216	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
217	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
218	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
219	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
220	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
221	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
222	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
223	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
224	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
225	C₄×D₁₃	C₂²×Q₈	1	1	yes	characteristic
226	#1057	—	2	8	no	—
227	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
228	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
229	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
230	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
231	C₈×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
232	#1055	C₂×C₄²	1	1	yes	characteristic
233	#1055	C₂×C₄²	1	1	yes	characteristic
234	#1055	C₂×C₄²	1	1	yes	characteristic
235	#1055	C₂×C₄²	1	1	yes	characteristic
236	#1055	C₂×C₄⋊C₄	1	4	yes	—
237	C₂²×M₁₆	—	13	1	no	—
238	C₂²×M₁₆	—	13	2	no	—
239	C₂³×C₈	—	13	1	no	—
240	C₂×#117	—	13	1	no	—
241	C₂×#117	—	13	2	no	—
242	C₂×#108	—	13	2	no	—
243	C₂×#108	—	13	2	no	—
244	C₂×#108	—	13	2	no	—
245	C₂×#108	—	13	2	no	—
246	C₂×#108	—	13	2	no	—
247	C₂×#108	—	13	2	no	—
248	#427	—	13	2	no	—
249	#427	—	13	2	no	—
250	#427	—	13	2	no	—
251	#427	—	13	2	no	—
252	C₂×#107	—	13	2	no	—
253	C₂×#106	—	13	2	no	—
254	#405	—	13	1	no	—
255	#405	—	13	1	no	—
256	#405	—	13	1	no	—
257	#405	—	13	2	no	—
258	#405	—	13	2	no	—
259	#405	—	13	8	no	—
260	#405	—	26	4	no	—
261	#405	#261	1	1	yes	characteristic, complemented
262	C₄×M₁₆	—	26	4	no	—
263	C₂×#97	—	13	2	no	—
264	C₂×C₄×C₈	—	13	2	no	—
265	#339	—	13	8	no	—
266	C₂²×C₁₃	—	4	1	no	—
267	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
268	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
269	C₂²×C₁₃	C₂×#117	1	1	yes	characteristic
270	C₂×D₁₃	—	2	2	no	—
271	C₂×D₁₃	—	2	2	no	—
272	C₂×D₁₃	—	2	2	no	—
273	C₂×D₁₃	—	4	1	no	—
274	C₂×D₁₃	—	4	1	no	—
275	C₂×D₁₃	—	4	1	no	—
276	C₂×D₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
277	C₂×D₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
278	C₂×D₁₃	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
280	#261	—	4	8	no	—
281	C₄×C₁₃	—	4	2	no	—
282	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
283	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
284	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
285	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
286	Dic₁₃	—	4	2	no	—
287	Dic₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
288	Dic₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
289	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
290	Dic₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
291	C₂³×C₄	—	13	1	no	—
292	C₂×M₁₆	—	13	1	no	—
293	C₂×M₁₆	—	13	2	no	—
294	C₂×M₁₆	—	13	2	no	—
295	C₂×M₁₆	—	13	2	no	—
296	C₂×M₁₆	—	13	2	no	—
297	C₂×M₁₆	—	13	2	no	—
298	C₂×M₁₆	—	13	4	no	—
299	C₂×M₁₆	—	13	4	no	—
300	C₂×M₁₆	—	13	4	no	—
301	C₂×M₁₆	—	26	2	no	—
302	C₂×M₁₆	—	26	2	no	—
303	C₂×M₁₆	—	26	2	no	—
304	C₂×M₁₆	C₂×#261	1	1	yes	characteristic
305	C₂²×C₈	—	13	1	no	—
306	C₂²×C₈	—	13	1	no	—
307	C₂²×C₈	—	13	1	no	—
308	C₂²×C₈	—	13	1	no	—
309	C₂²×C₈	—	13	1	no	—
310	C₂²×C₈	—	13	1	no	—
311	C₂²×C₈	—	13	1	no	—
312	C₂²×C₈	—	13	1	no	—
313	C₂²×C₈	—	13	1	no	—
314	C₂²×C₈	—	13	1	no	—
315	C₂²×C₈	—	13	1	no	—
316	C₂²×C₈	—	13	1	no	—
317	C₂²×C₈	—	13	1	no	—
318	C₂²×C₈	—	13	2	no	—
319	C₂²×C₈	—	26	2	no	—
320	C₂²×C₈	C₂×#261	1	1	yes	characteristic
321	#117	—	13	1	no	—
322	#117	—	13	2	no	—
323	#117	—	13	4	no	—
324	#117	—	13	4	no	—
325	#117	—	26	1	no	—
326	#117	—	26	1	no	—
327	#117	—	26	2	no	—
328	#117	—	26	2	no	—
329	#117	C₂×#261	1	1	yes	characteristic
330	C₂×C₄⋊C₄	—	13	4	no	—
331	C₂×C₄⋊C₄	—	26	1	no	—
332	C₂×C₂²⋊C₄	—	26	1	no	—
333	C₂×C₂²⋊C₄	—	26	2	no	—
334	C₂×C₄²	—	13	2	no	—
335	C₂×C₄²	—	26	2	no	—
336	#108	—	13	4	no	—
337	#108	—	13	4	no	—
338	#108	—	13	4	no	—
339	#108	—	13	4	no	—
340	#107	—	13	4	no	—
341	#107	—	13	4	no	—
342	#106	—	13	4	no	—
343	#106	—	13	4	no	—
344	#97	—	13	2	no	—
345	#97	—	13	2	no	—
346	#97	—	13	2	no	—
347	#97	—	26	8	no	—
348	#97	C₂×#261	1	2	yes	complemented
349	C₄×C₈	—	13	2	no	—
350	C₄×C₈	—	13	2	no	—
351	C₄×C₈	—	13	2	no	—
352	C₄×C₈	—	26	8	no	—
353	C₄×C₈	C₂×#261	1	2	yes	complemented
354	C₂×C₁₃	—	2	1	no	—
355	C₂×C₁₃	—	2	1	no	—
356	C₂×C₁₃	—	2	1	no	—
357	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
358	D₁₃	—	2	1	no	—
359	D₁₃	—	2	1	no	—
360	D₁₃	—	2	1	no	—
361	D₁₃	#2957	1	2	yes	—
362	C₂⁴	—	13	1	no	—
363	C₂²×C₄	—	13	1	no	—
364	C₂²×C₄	—	13	1	no	—
365	C₂²×C₄	—	13	1	no	—
366	C₂²×C₄	—	13	1	no	—
367	C₂²×C₄	—	13	1	no	—
368	C₂²×C₄	—	13	1	no	—
369	C₂²×C₄	—	13	1	no	—
370	C₂²×C₄	—	13	1	no	—
371	C₂²×C₄	—	13	1	no	—
372	C₂²×C₄	—	13	1	no	—
373	C₂²×C₄	—	13	1	no	—
374	C₂²×C₄	—	13	1	no	—
375	C₂²×C₄	—	13	1	no	—
376	C₂²×C₄	—	26	2	no	—
377	C₂²×C₄	—	26	4	no	—
378	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
379	M₁₆	—	13	2	no	—
380	M₁₆	—	13	2	no	—
381	M₁₆	—	13	4	no	—
382	M₁₆	—	13	4	no	—
383	M₁₆	—	13	8	no	—
384	M₁₆	—	26	4	no	—
385	M₁₆	—	26	4	no	—
386	M₁₆	—	26	4	no	—
387	M₁₆	C₄⋊#261	1	2	yes	—
388	M₁₆	C₄⋊#261	1	2	yes	—
389	C₂×C₈	—	13	1	no	—
390	C₂×C₈	—	13	1	no	—
391	C₂×C₈	—	13	1	no	—
392	C₂×C₈	—	13	1	no	—
393	C₂×C₈	—	13	1	no	—
394	C₂×C₈	—	13	2	no	—
395	C₂×C₈	—	13	1	no	—
396	C₂×C₈	—	13	1	no	—
397	C₂×C₈	—	13	1	no	—
398	C₂×C₈	—	13	1	no	—
399	C₂×C₈	—	13	1	no	—
400	C₂×C₈	—	13	1	no	—
401	C₂×C₈	—	13	1	no	—
402	C₂×C₈	—	13	1	no	—
403	C₂×C₈	—	13	1	no	—
404	C₂×C₈	—	13	1	no	—
405	C₂×C₈	—	13	1	no	—
406	C₂×C₈	—	13	1	no	—
407	C₂×C₈	—	13	1	no	—
408	C₂×C₈	—	13	1	no	—
409	C₂×C₈	—	13	1	no	—
410	C₂×C₈	—	13	1	no	—
411	C₂×C₈	—	13	1	no	—
412	C₂×C₈	—	13	4	no	—
413	C₂×C₈	—	13	4	no	—
414	C₂×C₈	—	26	4	no	—
415	C₂×C₈	—	26	4	no	—
416	C₂×C₈	—	26	4	no	—
417	C₂×C₈	C₄×#261	1	1	yes	characteristic
418	C₂×C₈	C₄×#261	1	1	yes	characteristic
419	C₂×C₈	C₄×#261	1	1	yes	characteristic
420	C₂×C₈	C₄×#261	1	1	yes	characteristic
421	C₂×C₈	C₂²×#261	1	1	yes	characteristic
422	C₂×C₈	C₂²×#261	1	1	yes	characteristic
423	C₂×C₈	C₂²×#261	1	2	yes	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	13	8	no	—
426	C₄⋊C₄	—	26	2	no	—
427	C₄⋊C₄	—	26	4	no	—
428	C₄⋊C₄	—	26	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₂²⋊C₄	—	26	2	no	—
431	C₂²⋊C₄	—	26	4	no	—
432	C₂²⋊C₄	—	26	4	no	—
433	C₂²⋊C₄	—	26	1	no	—
434	C₄²	—	13	2	no	—
435	C₄²	—	26	2	no	—
436	C₄²	—	26	4	no	—
437	C₄²	—	26	4	no	—
438	C₄²	C₂²×#261	1	2	yes	—
439	C₁₃	#20446	1	1	yes	characteristic, complemented, Sylow
440	C₂³	—	13	1	no	—
441	C₂³	—	13	1	no	—
442	C₂³	—	13	1	no	—
443	C₂³	—	13	1	no	—
444	C₂³	—	13	1	no	—
445	C₂³	—	13	1	no	—
446	C₂³	—	52	2	no	—
447	C₂³	#88237	1	1	yes	characteristic
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	13	1	no	—
450	C₂×C₄	—	13	1	no	—
451	C₂×C₄	—	13	1	no	—
452	C₂×C₄	—	13	1	no	—
453	C₂×C₄	—	13	1	no	—
454	C₂×C₄	—	13	1	no	—
455	C₂×C₄	—	13	1	no	—
456	C₂×C₄	—	13	1	no	—
457	C₂×C₄	—	13	1	no	—
458	C₂×C₄	—	13	1	no	—
459	C₂×C₄	—	13	1	no	—
460	C₂×C₄	—	13	1	no	—
461	C₂×C₄	—	13	1	no	—
462	C₂×C₄	—	13	1	no	—
463	C₂×C₄	—	13	1	no	—
464	C₂×C₄	—	13	1	no	—
465	C₂×C₄	—	13	1	no	—
466	C₂×C₄	—	13	1	no	—
467	C₂×C₄	—	13	1	no	—
468	C₂×C₄	—	13	1	no	—
469	C₂×C₄	—	13	1	no	—
470	C₂×C₄	—	13	1	no	—
471	C₂×C₄	—	26	8	no	—
472	C₂×C₄	—	26	2	no	—
473	C₂×C₄	—	52	4	no	—
474	C₂×C₄	—	104	4	no	—
475	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
476	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
477	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
478	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
479	C₂×C₄	#88237	1	1	yes	characteristic
480	C₂×C₄	C₂³×#261	1	1	yes	characteristic
481	C₈	—	13	1	no	—
482	C₈	—	13	1	no	—
483	C₈	—	13	1	no	—
484	C₈	—	13	1	no	—
485	C₈	—	13	4	no	—
486	C₈	—	26	8	no	—
487	C₈	C₂×C₄×#261	1	1	yes	characteristic
488	C₈	C₂×C₄×#261	1	1	yes	characteristic
489	C₈	C₂×C₄×#261	1	1	yes	characteristic
490	C₈	C₂×C₄×#261	1	1	yes	characteristic
491	C₈	C₂×C₄⋊#261	1	4	yes	—
492	C₂²	—	4	1	no	—
493	C₂²	—	13	1	no	—
494	C₂²	—	13	1	no	—
495	C₂²	—	13	1	no	—
496	C₂²	—	13	1	no	—
497	C₂²	—	26	2	no	—
498	C₂²	—	26	2	no	—
499	C₂²	—	26	2	no	—
500	C₂²	—	52	1	no	—
501	C₂²	—	52	1	no	—
502	C₂²	—	52	1	no	—
503	C₂²	C₄×C₄⋊#261	1	1	yes	characteristic
504	C₂²	C₄×C₄⋊#261	1	1	yes	characteristic
505	C₂²	C₂×#88237	1	1	yes	characteristic
506	C₄	—	4	2	no	—
507	C₄	—	13	1	no	—
508	C₄	—	13	1	no	—
509	C₄	—	13	1	no	—
510	C₄	—	13	1	no	—
511	C₄	—	52	2	no	—
512	C₄	—	52	8	no	—
513	C₄	C₄×C₄⋊#261	1	1	yes	characteristic
514	C₄	C₄×C₄⋊#261	1	1	yes	characteristic
515	C₄	C₂²×C₄×#261	1	1	yes	characteristic
516	C₄	C₂²×C₄⋊#261	1	1	yes	characteristic
517	C₂	—	2	1	no	—
518	C₂	—	2	1	no	—
519	C₂	—	2	1	no	—
520	C₂	—	13	2	no	—
521	C₂	—	26	1	no	—
522	C₂	—	26	1	no	—
523	C₂	—	26	1	no	—
524	C₂	C₂×C₄×C₄⋊#261	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₁₃×#405	C₄
socle	C₂×C₁₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	#405	#261
hypocenter	C₁₃	#20446
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #405

Complements

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

N	H ≅ G/N	type
4. #13130642	C₂	semidirect
5. #13130638	C₂	semidirect
15. D₁₃⋊#108	C₄	semidirect
16. D₁₃⋊#108	C₄	semidirect
19. C₂×#88104	C₄	semidirect
20. C₂×#88103	C₄	semidirect
21. #11719092	C₄	semidirect
22. #11719092	C₄	semidirect
25. C₂×#88102	C₄	semidirect
26. C₂×#88101	C₄	semidirect
28. C₁₃×#405	C₄	semidirect
29. #11718783	C₄	semidirect
30. #11718762	C₄	semidirect
31. #11718658	C₄	semidirect
32. #11718369	C₄	semidirect
34. #11718350	C₄	semidirect
82. #88104	C₂×C₄	semidirect
83. #88104	C₂×C₄	semidirect
84. #88103	C₂×C₄	semidirect
85. #88103	C₂×C₄	semidirect
92. C₁₃×#97	C₂×C₄	semidirect
93. C₄×C₈×C₁₃	C₂×C₄	semidirect
94. #88055	C₂×C₄	semidirect
95. #88055	C₂×C₄	semidirect
96. C₈×Dic₁₃	C₂×C₄	semidirect
97. C₈×Dic₁₃	C₂×C₄	semidirect
98. #88043	C₂×C₄	semidirect
99. C₄×#1055	C₂×C₄	semidirect
261. #405	#261	semidirect
348. #97	C₂×#261	semidirect
353. C₄×C₈	C₂×#261	semidirect
439. C₁₃	#20446	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×#11719092	2
#13131399	2
#13130642	2
#13130638	2
#13130517	2
D₁₃×#405	2
#20446	13