Subgroups — C₂×#13130638 #16797166

Order 3328.

1102 conjugacy classes of subgroups.

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

	subgroup	G/H
center	C₂×C₈	C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	#41
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1772
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #13130638	C₂	direct (N × H)
12. D₁₃⋊#108	C₄	semidirect
14. C₂×#88104	C₄	semidirect
15. C₂×#88103	C₄	semidirect
16. #11719092	C₄	semidirect
18. C₂×#88102	C₄	semidirect
19. C₂×#88101	C₄	semidirect
24. C₂×C₄×C₈×C₁₃	C₄	semidirect
25. C₂×C₈×Dic₁₃	C₄	semidirect
26. C₂×C₈×Dic₁₃	C₄	semidirect
27. C₂×C₄×#1055	C₄	semidirect
28. C₄×C₈×D₁₃	C₄	semidirect
74. #88104	C₂×C₄	semidirect
75. #88103	C₂×C₄	semidirect
76. #88102	C₂×C₄	semidirect
77. #88101	C₂×C₄	semidirect
80. C₄×C₈×C₁₃	C₂×C₄	semidirect
81. C₈×Dic₁₃	C₂×C₄	semidirect
82. C₈×Dic₁₃	C₂×C₄	semidirect
83. C₄×#1055	C₂×C₄	semidirect
238. C₂×C₄×C₈	#261	semidirect
317. C₄×C₈	C₂×#261	semidirect
320. C₂×C₁₃	#1772	semidirect
324. D₁₃	#1772	semidirect
398. C₁₃	C₂×#1772	semidirect
483. C₂	#13130638	direct (N × H)

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
C₂×#11719089	2
#13130638	2
C₂×#11718234	2
C₂×C₄×C₈×D₁₃	2
C₂×#1772	13

Subgroups — C2×#13130638 #16797166

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13130638 #16797166