Subgroups — #16798321

Order 3328.

894 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131283	C₂	1	2	yes	maximal
2	#13130773	C₂	1	2	yes	maximal, complemented
3	#13130758	C₂	1	2	yes	maximal, complemented
4	#13130713	C₂	1	2	yes	maximal
5	#13130712	C₂	1	2	yes	maximal
6	C₄×#88102	C₂	1	2	yes	maximal, complemented
7	C₄×#88101	C₂	1	2	yes	maximal, complemented
8	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
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	#11719136	C₂²	1	4	yes	—
13	#11719135	—	2	2	no	—
14	C₄×C₂²⋊#261	—	2	2	no	—
15	C₂×#88102	C₂²	1	4	yes	—
16	C₂×#88101	C₂²	1	4	yes	—
17	#11719061	—	2	2	no	—
18	#11719060	C₂²	1	4	yes	—
19	C₄×C₄⋊#261	C₂²	1	4	yes	—
20	#11719057	—	2	2	no	—
21	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
22	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
23	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
24	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
25	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
26	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
27	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
28	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic, complemented
29	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₁₃	C₂²	1	1	yes	characteristic
33	#11718265	C₂²	1	4	yes	—
34	#11718265	C₂²	1	4	yes	—
35	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
37	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×C₂²⋊#261	—	2	4	no	—
39	C₂×C₄⋊#261	C₂³	1	8	yes	—
40	C₂×C₄×#261	—	2	4	no	—
41	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
47	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
48	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₁₃	—	2	4	no	—
50	C₂×C₈×D₁₃	—	2	4	no	—
51	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
59	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
60	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₃	D₄	1	1	yes	characteristic
62	C₄²×D₁₃	D₄	1	1	yes	characteristic
63	C₄²×D₁₃	Q₈	1	1	yes	characteristic
64	C₄²×D₁₃	Q₈	1	1	yes	characteristic
65	C₄²×D₁₃	C₂³	1	1	yes	characteristic
66	C₄²×D₁₃	C₂³	1	1	yes	characteristic
67	(C₂×#261)⋊C₄	—	2	4	no	—
68	(C₂×#261)⋊C₄	—	2	4	no	—
69	(C₂×#261)⋊C₄	—	2	4	no	—
70	(C₂×#261)⋊C₄	—	2	4	no	—
71	#88102	—	2	8	no	—
72	#88101	—	2	8	no	—
73	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
74	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
77	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
78	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
79	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
80	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
85	C₄×#1055	C₂×C₄	1	1	yes	characteristic
86	C₄×#1055	C₂×C₄	1	1	yes	characteristic
87	C₄×#1055	C₂×C₄	1	1	yes	characteristic
88	C₄×#1055	C₂×C₄	1	1	yes	characteristic
89	#20818	—	13	1	no	maximal, Sylow
90	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×#261	—	2	8	no	—
92	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₄×D₁₃	—	2	4	no	—
99	C₂×C₄×D₁₃	—	2	4	no	—
100	C₂×C₄×D₁₃	—	2	2	no	—
101	C₂×C₄×D₁₃	—	2	2	no	—
102	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
113	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
114	C₂²⋊#261	—	4	8	no	—
115	C₄⋊#261	—	2	8	no	—
116	C₄⋊#261	—	2	8	no	—
117	C₄×#261	—	4	8	no	—
118	C₂×C₈×C₁₃	—	2	2	no	—
119	C₂×C₈×C₁₃	—	2	2	no	—
120	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
138	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
139	C₄×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	C₈×D₁₃	—	2	2	no	—
147	C₈×D₁₃	—	2	2	no	—
148	C₈×D₁₃	—	2	2	no	—
149	C₈×D₁₃	—	2	2	no	—
150	C₈×D₁₃	—	2	2	no	—
151	C₈×D₁₃	—	2	2	no	—
152	C₈×D₁₃	#41	1	4	yes	—
153	C₈×D₁₃	#41	1	4	yes	—
154	C₂²×C₄×C₈	—	13	1	no	—
155	#2283	—	13	2	no	—
156	#1846	—	13	2	no	—
157	#1835	—	13	2	no	—
158	#1808	—	13	2	no	—
159	#1807	—	13	2	no	—
160	C₄×#107	—	13	2	no	—
161	C₄×#106	—	13	2	no	—
162	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂²×D₁₃	—	2	2	no	—
164	C₂²×D₁₃	—	2	2	no	—
165	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×D₁₃	#135	1	4	yes	—
167	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
168	C₂×#261	—	4	8	no	—
169	C₂×#261	—	4	8	no	—
170	C₂×#261	—	4	8	no	—
171	C₂×C₄×C₁₃	—	2	2	no	—
172	C₂×C₄×C₁₃	—	2	1	no	—
173	C₂×C₄×C₁₃	—	2	1	no	—
174	C₂×C₄×C₁₃	—	2	2	no	—
175	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₁₃	C₂×C₄⋊C₄	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	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
185	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
190	C₄×D₁₃	—	2	2	no	—
191	C₄×D₁₃	—	2	2	no	—
192	C₄×D₁₃	—	2	2	no	—
193	C₄×D₁₃	—	2	2	no	—
194	C₄×D₁₃	—	2	2	no	—
195	C₄×D₁₃	—	2	2	no	—
196	C₄×D₁₃	—	2	1	no	—
197	C₄×D₁₃	—	2	1	no	—
198	C₄×D₁₃	—	2	2	no	—
199	C₄×D₁₃	—	2	2	no	—
200	C₄×D₁₃	—	2	2	no	—
201	C₄×D₁₃	#135	1	4	yes	—
202	C₄×D₁₃	C₂×#41	1	2	yes	—
203	C₄×D₁₃	C₂×#41	1	2	yes	—
204	C₈×C₁₃	—	2	1	no	—
205	C₈×C₁₃	—	2	1	no	—
206	C₈×C₁₃	#117	1	2	yes	—
207	C₈×C₁₃	#117	1	2	yes	—
208	#1055	—	2	1	no	—
209	#1055	—	2	1	no	—
210	#1055	#117	1	2	yes	—
211	#1055	#117	1	2	yes	—
212	C₂³×C₈	—	13	1	no	—
213	C₂³×C₈	—	13	1	no	—
214	C₂²×C₄²	—	13	1	no	—
215	C₂×#107	—	13	4	no	—
216	C₂×#106	—	13	4	no	—
217	C₂×C₄×C₈	—	13	1	no	—
218	C₂×C₄×C₈	—	13	1	no	—
219	C₂×C₄×C₈	—	13	1	no	—
220	C₂×C₄×C₈	—	13	1	no	—
221	C₂×C₄×C₈	—	13	1	no	—
222	C₂×C₄×C₈	—	13	1	no	—
223	C₂×C₄×C₈	—	13	1	no	—
224	C₂×C₄×C₈	—	13	1	no	—
225	C₂×C₄×C₈	—	13	1	no	—
226	C₂×C₄×C₈	—	13	1	no	—
227	C₂×C₄×C₈	—	13	1	no	—
228	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
229	#383	—	26	2	no	—
230	#382	—	13	4	no	—
231	#381	—	26	2	no	—
232	#380	—	13	4	no	—
233	C₄×C₄⋊C₄	—	13	4	no	—
234	C₄×C₂²⋊C₄	—	26	2	no	—
235	#376	—	26	2	no	—
236	#340	—	13	4	no	—
237	#340	—	13	4	no	—
238	C₂²×C₁₃	—	2	1	no	—
239	C₂²×C₁₃	—	2	1	no	—
240	C₂²×C₁₃	#427	1	2	yes	—
241	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
242	C₂×D₁₃	—	2	1	no	—
243	C₂×D₁₃	—	2	1	no	—
244	C₂×D₁₃	—	2	8	no	—
245	C₂×D₁₃	#427	1	2	yes	—
246	C₂×D₁₃	#532	1	2	yes	—
247	C₂×D₁₃	C₂×#135	1	2	yes	—
248	C₂×D₁₃	C₂×#135	1	2	yes	—
249	#261	—	8	8	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	#427	1	2	yes	—
255	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
256	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
257	Dic₁₃	—	2	1	no	—
258	Dic₁₃	—	2	1	no	—
259	Dic₁₃	—	2	1	no	—
260	Dic₁₃	—	2	1	no	—
261	Dic₁₃	#427	1	2	yes	—
262	Dic₁₃	#533	1	2	yes	—
263	C₂³×C₄	—	13	1	no	—
264	C₂³×C₄	—	13	1	no	—
265	C₂³×C₄	—	13	1	no	—
266	C₂²×C₈	—	13	1	no	—
267	C₂²×C₈	—	13	1	no	—
268	C₂²×C₈	—	13	1	no	—
269	C₂²×C₈	—	13	1	no	—
270	C₂²×C₈	—	13	1	no	—
271	C₂²×C₈	—	13	1	no	—
272	C₂²×C₈	—	13	1	no	—
273	C₂²×C₈	—	13	1	no	—
274	C₂²×C₈	—	13	1	no	—
275	C₂²×C₈	—	13	1	no	—
276	C₂²×C₈	—	26	4	no	—
277	C₂²×C₈	—	26	4	no	—
278	C₂²×C₈	C₂×#261	1	1	yes	characteristic
279	C₂²×C₈	C₂×#261	1	1	yes	characteristic
280	C₂×C₄⋊C₄	—	13	8	no	—
281	C₂×C₂²⋊C₄	—	26	4	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	—	13	1	no	—
288	C₂×C₄²	—	13	1	no	—
289	C₂×C₄²	—	13	1	no	—
290	C₂×C₄²	—	13	1	no	—
291	C₂×C₄²	—	13	1	no	—
292	C₂×C₄²	—	13	1	no	—
293	C₂×C₄²	—	26	4	no	—
294	C₂×C₄²	C₂×#261	1	1	yes	characteristic
295	#107	—	26	8	no	—
296	#106	—	26	8	no	—
297	C₄×C₈	—	13	1	no	—
298	C₄×C₈	—	13	1	no	—
299	C₄×C₈	—	13	1	no	—
300	C₄×C₈	—	13	1	no	—
301	C₄×C₈	—	13	1	no	—
302	C₄×C₈	—	13	1	no	—
303	C₄×C₈	—	13	1	no	—
304	C₄×C₈	—	13	1	no	—
305	C₄×C₈	—	13	1	no	—
306	C₄×C₈	—	13	1	no	—
307	C₄×C₈	—	13	1	no	—
308	C₄×C₈	—	13	1	no	—
309	C₄×C₈	C₂×#261	1	1	yes	characteristic
310	C₄×C₈	C₂×#261	1	1	yes	characteristic
311	C₄×C₈	C₂×#261	1	1	yes	characteristic
312	C₄×C₈	C₂×#261	1	1	yes	characteristic
313	#95	—	26	4	no	—
314	#95	—	26	4	no	—
315	#95	—	26	4	no	—
316	#95	—	26	4	no	—
317	C₂×C₁₃	—	2	2	no	—
318	C₂×C₁₃	#2285	1	1	yes	characteristic
319	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
320	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
321	D₁₃	—	2	2	no	—
322	D₁₃	#3168	1	4	yes	—
323	C₂⁴	—	13	1	no	—
324	C₂²×C₄	—	13	1	no	—
325	C₂²×C₄	—	13	1	no	—
326	C₂²×C₄	—	13	1	no	—
327	C₂²×C₄	—	13	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	—	26	2	no	—
340	C₂²×C₄	—	26	2	no	—
341	C₂²×C₄	—	26	4	no	—
342	C₂²×C₄	—	26	4	no	—
343	C₂²×C₄	—	26	8	no	—
344	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
345	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
346	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	13	1	no	—
351	C₂×C₈	—	13	4	no	—
352	C₂×C₈	—	13	4	no	—
353	C₂×C₈	—	13	1	no	—
354	C₂×C₈	—	13	1	no	—
355	C₂×C₈	—	26	2	no	—
356	C₂×C₈	—	26	2	no	—
357	C₂×C₈	—	26	2	no	—
358	C₂×C₈	—	26	2	no	—
359	C₂×C₈	—	26	2	no	—
360	C₂×C₈	—	26	2	no	—
361	C₂×C₈	—	26	2	no	—
362	C₂×C₈	—	26	2	no	—
363	C₂×C₈	C₂²×#261	1	1	yes	characteristic
364	C₂×C₈	C₂²×#261	1	1	yes	characteristic
365	C₂×C₈	C₂²×#261	1	1	yes	characteristic
366	C₂×C₈	C₂²×#261	1	1	yes	characteristic
367	C₄⋊C₄	—	26	8	no	—
368	C₄⋊C₄	—	26	8	no	—
369	C₂²⋊C₄	—	52	8	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₄²	—	13	1	no	—
375	C₄²	—	13	1	no	—
376	C₄²	—	13	1	no	—
377	C₄²	—	13	1	no	—
378	C₄²	—	13	1	no	—
379	C₄²	—	13	1	no	—
380	C₄²	—	13	1	no	—
381	C₄²	—	13	1	no	—
382	C₄²	—	52	8	no	—
383	C₄²	C₄⋊#261	1	1	yes	characteristic
384	C₄²	C₄⋊#261	1	1	yes	characteristic
385	C₄²	C₂²×#261	1	1	yes	characteristic
386	C₄²	C₂²×#261	1	1	yes	characteristic
387	C₁₃	#20818	1	1	yes	characteristic, complemented, Sylow
388	C₂³	—	13	1	no	—
389	C₂³	—	13	4	no	—
390	C₂³	—	13	1	no	—
391	C₂³	—	26	2	no	—
392	C₂³	—	26	2	no	—
393	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	13	1	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	4	no	—
401	C₂×C₄	—	13	2	no	—
402	C₂×C₄	—	13	2	no	—
403	C₂×C₄	—	13	1	no	—
404	C₂×C₄	—	13	1	no	—
405	C₂×C₄	—	13	1	no	—
406	C₂×C₄	—	13	1	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	—	26	2	no	—
409	C₂×C₄	—	26	2	no	—
410	C₂×C₄	—	26	2	no	—
411	C₂×C₄	—	26	2	no	—
412	C₂×C₄	—	26	2	no	—
413	C₂×C₄	—	26	2	no	—
414	C₂×C₄	—	26	2	no	—
415	C₂×C₄	—	26	2	no	—
416	C₂×C₄	—	26	2	no	—
417	C₂×C₄	—	26	2	no	—
418	C₂×C₄	—	26	2	no	—
419	C₂×C₄	—	26	1	no	—
420	C₂×C₄	—	26	1	no	—
421	C₂×C₄	—	52	8	no	—
422	C₂×C₄	—	52	8	no	—
423	C₂×C₄	—	52	8	no	—
424	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
426	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
427	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
428	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
429	C₂×C₄	C₂³×#261	1	1	yes	characteristic
430	C₈	—	2	1	no	—
431	C₈	—	2	1	no	—
432	C₈	—	13	2	no	—
433	C₈	—	13	2	no	—
434	C₈	—	26	1	no	—
435	C₈	—	26	1	no	—
436	C₈	#88237	1	2	yes	—
437	C₈	#88237	1	2	yes	—
438	C₂²	—	2	1	no	—
439	C₂²	—	2	1	no	—
440	C₂²	—	13	2	no	—
441	C₂²	—	13	2	no	—
442	C₂²	—	13	2	no	—
443	C₂²	—	13	2	no	—
444	C₂²	—	26	8	no	—
445	C₂²	—	26	1	no	—
446	C₂²	—	26	1	no	—
447	C₂²	#11719092	1	2	yes	—
448	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
449	C₄	—	2	1	no	—
450	C₄	—	2	1	no	—
451	C₄	—	2	1	no	—
452	C₄	—	2	1	no	—
453	C₄	—	13	2	no	—
454	C₄	—	13	2	no	—
455	C₄	—	26	1	no	—
456	C₄	—	26	1	no	—
457	C₄	—	26	1	no	—
458	C₄	—	26	1	no	—
459	C₄	—	104	8	no	—
460	C₄	#11719092	1	2	yes	—
461	C₄	C₂×#88237	1	1	yes	characteristic
462	C₄	C₂×#88237	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	13	4	no	—
465	C₂	—	26	2	no	—
466	C₂	#13131285	1	1	yes	characteristic
467	C₂	C₂×#11719092	1	1	yes	characteristic
468	C₂	C₂×#11719092	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#20818
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13130773	C₂	semidirect
3. #13130758	C₂	semidirect
6. C₄×#88102	C₂	semidirect
7. C₄×#88101	C₂	semidirect
21. C₂×C₄×C₈×C₁₃	C₄	semidirect
22. C₂×C₈×Dic₁₃	C₄	semidirect
23. C₂×C₈×Dic₁₃	C₄	semidirect
24. C₂×C₄×#1055	C₄	semidirect
25. C₄×C₈×D₁₃	C₄	semidirect
26. C₄×C₈×D₁₃	C₄	semidirect
27. C₄×C₈×D₁₃	C₄	semidirect
28. C₄×C₈×D₁₃	C₄	semidirect
228. C₂×C₄×C₈	#261	semidirect
387. C₁₃	#20818	semidirect

Maximal subgroups

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

subgroup	index
#13131283	2
#13130773	2
#13130758	2
#13130713	2
#13130712	2
C₄×#88102	2
C₄×#88101	2
C₂×C₄×C₈×D₁₃	2
#20818	13