Subgroups — #16794939

Order 3328.

762 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131512	C₂	1	2	yes	maximal
2	#13130398	C₂	1	2	yes	maximal, complemented
3	#13130396	C₂	1	2	yes	maximal, complemented
4	#13130393	C₂	1	2	yes	maximal, complemented
5	#13130390	C₂	1	2	yes	maximal, complemented
6	#13130385	C₂	1	2	yes	maximal, complemented
7	#13130383	C₂	1	2	yes	maximal, complemented
8	C₂²×C₈×Dic₁₃	C₂	1	1	yes	maximal, characteristic
9	C₂³×C₈×C₁₃	C₄	1	1	yes	characteristic
10	C₂²×C₄×Dic₁₃	C₂²	1	1	yes	characteristic
11	C₂³×#1055	C₄	1	1	yes	characteristic
12	#11719169	—	2	2	no	—
13	#11719130	C₂²	1	4	yes	—
14	#11719129	C₂²	1	4	yes	—
15	#11719128	—	2	2	no	—
16	#11719125	—	2	2	no	—
17	C₄×#6122	—	2	2	no	—
18	#11719119	C₂²	1	4	yes	—
19	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
20	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
21	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
22	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
23	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
24	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic
25	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₁₃	C₂²	1	1	yes	characteristic
31	#11718256	C₂²	1	4	yes	complemented
32	#11718255	C₂²	1	4	yes	complemented
33	#11718254	C₂²	1	4	yes	complemented
34	#11718253	C₂²	1	4	yes	complemented
35	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂³×Dic₁₃	D₄	1	1	yes	characteristic
37	C₂³×Dic₁₃	Q₈	1	1	yes	characteristic
38	C₂×#6122	—	2	4	no	—
39	C₂²×C₈×C₁₃	—	2	4	no	—
40	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
50	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
51	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
53	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
54	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
55	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₁₃	C₂³	1	1	yes	characteristic
58	C₂²×#1055	—	2	4	no	—
59	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
60	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
63	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
64	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
65	C₂²⋊#1057	—	2	4	no	—
66	C₂²⋊#1057	—	2	4	no	—
67	#88112	—	2	4	no	—
68	#88110	—	2	4	no	—
69	C₄⋊#1057	C₂³	1	8	yes	—
70	C₄×#1057	—	2	4	no	—
71	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₁₃	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	C₂³	1	1	yes	characteristic
84	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
85	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
86	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
87	#17793	—	13	1	no	maximal, Sylow
88	C₂⁴×C₁₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	—	2	2	no	—
90	C₂²×C₄×C₁₃	—	2	2	no	—
91	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
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×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
97	C₂²×Dic₁₃	—	2	4	no	—
98	C₂²×Dic₁₃	—	2	4	no	—
99	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
101	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
102	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
103	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
104	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
105	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
106	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
111	#6122	—	4	8	no	—
112	C₂×#1057	—	2	8	no	—
113	C₂×C₈×C₁₃	—	2	2	no	—
114	C₂×C₈×C₁₃	—	2	2	no	—
115	C₂×C₈×C₁₃	—	2	2	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	M₁₆	1	4	yes	complemented
119	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
126	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
127	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
128	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
130	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
131	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×Q₈	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	C₂⁴	1	1	yes	characteristic
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	—	2	2	no	—
141	C₂×#1055	—	2	2	no	—
142	C₂×#1055	—	2	2	no	—
143	C₂×#1055	—	2	2	no	—
144	C₂×#1055	M₁₆	1	4	yes	complemented
145	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
146	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
147	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
148	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
149	#2920	—	13	2	no	—
150	C₂²×C₄×C₈	—	13	1	no	—
151	#1568	—	13	2	no	—
152	#1568	—	13	2	no	—
153	#1567	—	13	2	no	—
154	#1566	—	13	2	no	—
155	#1564	—	13	2	no	—
156	#1564	—	13	2	no	—
157	C₂³×C₁₃	—	2	2	no	—
158	C₂³×C₁₃	—	2	2	no	—
159	C₂³×C₁₃	—	2	2	no	—
160	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₁₃	—	2	2	no	—
164	C₂×C₄×C₁₃	—	2	1	no	—
165	C₂×C₄×C₁₃	—	2	1	no	—
166	C₂×C₄×C₁₃	—	2	1	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	2	no	—
169	C₂×C₄×C₁₃	—	2	2	no	—
170	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
174	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
175	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
176	C₂×Dic₁₃	—	2	2	no	—
177	C₂×Dic₁₃	—	2	2	no	—
178	C₂×Dic₁₃	—	2	2	no	—
179	C₂×Dic₁₃	—	2	2	no	—
180	C₂×Dic₁₃	—	2	2	no	—
181	C₂×Dic₁₃	—	2	2	no	—
182	C₂×Dic₁₃	—	2	2	no	—
183	C₂×Dic₁₃	—	2	2	no	—
184	C₂×Dic₁₃	—	2	2	no	—
185	C₂×Dic₁₃	—	2	2	no	—
186	C₂×Dic₁₃	#108	1	4	yes	—
187	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
188	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
190	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
191	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
192	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
193	C₂×Dic₁₃	#135	1	4	yes	—
194	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
195	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
196	#1057	—	4	8	no	—
197	C₈×C₁₃	—	2	1	no	—
198	C₈×C₁₃	—	2	1	no	—
199	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
200	C₈×C₁₃	C₂×M₁₆	1	2	yes	—
201	#1055	—	2	1	no	—
202	#1055	—	2	1	no	—
203	#1055	C₂×M₁₆	1	2	yes	—
204	#1055	C₂×M₁₆	1	2	yes	—
205	C₂³×C₈	—	13	1	no	—
206	C₂³×C₈	#261	1	1	yes	characteristic
207	C₂²×C₄²	—	13	1	no	—
208	#432	—	13	4	no	—
209	#432	—	26	2	no	—
210	#431	—	13	4	no	—
211	#431	—	26	2	no	—
212	#423	—	13	4	no	—
213	#407	—	26	2	no	—
214	C₄×M₁₆	—	26	2	no	—
215	C₂×C₄×C₈	—	13	1	no	—
216	C₂×C₄×C₈	—	13	1	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	#335	—	13	4	no	—
228	#335	—	13	4	no	—
229	#334	—	13	4	no	—
230	#334	—	13	4	no	—
231	C₂²×C₁₃	—	2	8	no	—
232	C₂²×C₁₃	—	2	1	no	—
233	C₂²×C₁₃	—	2	1	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	—	2	1	no	—
237	C₂²×C₁₃	—	2	1	no	—
238	C₂²×C₁₃	#423	1	2	yes	—
239	C₂²×C₁₃	#427	1	2	yes	—
240	C₂²×C₁₃	C₂×#108	1	2	yes	—
241	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
242	C₄×C₁₃	—	2	1	no	—
243	C₄×C₁₃	—	2	1	no	—
244	C₄×C₁₃	#423	1	2	yes	—
245	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
246	C₄×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
247	Dic₁₃	—	2	1	no	—
248	Dic₁₃	—	2	1	no	—
249	Dic₁₃	—	2	1	no	—
250	Dic₁₃	—	2	1	no	—
251	Dic₁₃	#427	1	2	yes	—
252	Dic₁₃	C₂×#108	1	2	yes	—
253	Dic₁₃	C₂×#108	1	2	yes	—
254	Dic₁₃	C₂×#135	1	2	yes	—
255	C₂³×C₄	—	13	1	no	—
256	C₂³×C₄	—	13	1	no	—
257	C₂³×C₄	C₂×#261	1	1	yes	characteristic
258	C₂×M₁₆	—	26	4	no	—
259	C₂²×C₈	—	2	4	no	—
260	C₂²×C₈	—	13	1	no	—
261	C₂²×C₈	—	13	1	no	—
262	C₂²×C₈	—	13	1	no	—
263	C₂²×C₈	—	13	1	no	—
264	C₂²×C₈	—	13	1	no	—
265	C₂²×C₈	—	13	1	no	—
266	C₂²×C₈	—	26	4	no	—
267	C₂²×C₈	C₂×#261	1	1	yes	characteristic
268	C₂²×C₈	C₂×#261	1	1	yes	characteristic
269	C₂²×C₈	C₂×#261	1	1	yes	characteristic
270	C₂²×C₈	C₂×#261	1	1	yes	characteristic
271	C₂²×C₈	C₂×#261	1	1	yes	characteristic
272	C₂²×C₈	C₂×#261	1	1	yes	characteristic
273	C₂×C₄²	—	13	1	no	—
274	C₂×C₄²	—	13	1	no	—
275	C₂×C₄²	—	13	1	no	—
276	C₂×C₄²	—	13	1	no	—
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	—	13	1	no	—
279	C₂×C₄²	—	13	1	no	—
280	C₂×C₄²	—	13	1	no	—
281	C₂×C₄²	—	13	1	no	—
282	C₂×C₄²	—	13	1	no	—
283	C₂×C₄²	—	13	1	no	—
284	C₂×C₄²	—	13	1	no	—
285	C₄⋊C₈	—	13	8	no	—
286	C₄⋊C₈	—	26	4	no	—
287	C₂²⋊C₈	—	26	4	no	—
288	C₂²⋊C₈	—	26	4	no	—
289	#97	—	26	4	no	—
290	C₄×C₈	—	13	1	no	—
291	C₄×C₈	—	13	1	no	—
292	C₄×C₈	—	13	1	no	—
293	C₄×C₈	—	13	1	no	—
294	C₄×C₈	—	13	1	no	—
295	C₄×C₈	—	13	1	no	—
296	C₄×C₈	—	13	1	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	—	26	4	no	—
307	C₂×C₁₃	—	2	2	no	—
308	C₂×C₁₃	—	2	2	no	—
309	C₂×C₁₃	—	2	2	no	—
310	C₂×C₁₃	C₂×#423	1	1	yes	characteristic
311	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
312	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
313	C₂⁴	C₄⋊#261	1	1	yes	characteristic
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	13	1	no	—
317	C₂²×C₄	—	13	1	no	—
318	C₂²×C₄	—	13	1	no	—
319	C₂²×C₄	—	13	1	no	—
320	C₂²×C₄	—	13	1	no	—
321	C₂²×C₄	—	13	1	no	—
322	C₂²×C₄	—	13	1	no	—
323	C₂²×C₄	—	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	—	26	4	no	—
329	C₂²×C₄	—	26	4	no	—
330	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
331	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
332	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
333	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
334	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
335	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
336	M₁₆	—	52	8	no	—
337	C₂×C₈	—	2	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	13	4	no	—
343	C₂×C₈	—	13	1	no	—
344	C₂×C₈	—	13	1	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	1	no	—
347	C₂×C₈	—	26	2	no	—
348	C₂×C₈	—	26	2	no	—
349	C₂×C₈	—	26	2	no	—
350	C₂×C₈	—	26	2	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	26	8	no	—
353	C₂×C₈	#6122	1	4	yes	complemented
354	C₂×C₈	C₂²×#261	1	1	yes	characteristic
355	C₂×C₈	C₂²×#261	1	1	yes	characteristic
356	C₂×C₈	C₂²×#261	1	1	yes	characteristic
357	C₂×C₈	C₂²×#261	1	1	yes	characteristic
358	C₄²	—	13	1	no	—
359	C₄²	—	13	1	no	—
360	C₄²	—	13	1	no	—
361	C₄²	—	13	1	no	—
362	C₄²	—	13	1	no	—
363	C₄²	—	13	1	no	—
364	C₄²	—	13	1	no	—
365	C₄²	—	13	1	no	—
366	C₄²	—	13	1	no	—
367	C₄²	—	13	1	no	—
368	C₄²	—	13	1	no	—
369	C₄²	—	13	1	no	—
370	C₄²	—	13	1	no	—
371	C₄²	—	13	1	no	—
372	C₄²	—	13	1	no	—
373	C₄²	—	13	1	no	—
374	C₁₃	#17793	1	1	yes	characteristic, complemented, Sylow
375	C₂³	—	2	2	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
379	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
380	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	13	4	no	—
389	C₂×C₄	—	13	4	no	—
390	C₂×C₄	—	13	1	no	—
391	C₂×C₄	—	13	1	no	—
392	C₂×C₄	—	13	1	no	—
393	C₂×C₄	—	13	1	no	—
394	C₂×C₄	—	13	1	no	—
395	C₂×C₄	—	13	1	no	—
396	C₂×C₄	—	13	1	no	—
397	C₂×C₄	—	13	1	no	—
398	C₂×C₄	—	26	2	no	—
399	C₂×C₄	—	26	2	no	—
400	C₂×C₄	—	26	2	no	—
401	C₂×C₄	—	26	2	no	—
402	C₂×C₄	—	26	2	no	—
403	C₂×C₄	—	26	2	no	—
404	C₂×C₄	—	26	2	no	—
405	C₂×C₄	—	26	2	no	—
406	C₂×C₄	—	26	2	no	—
407	C₂×C₄	—	26	2	no	—
408	C₂×C₄	D₁₃⋊M₁₆	1	2	yes	—
409	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
410	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
411	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
412	C₂×C₄	C₂×#6122	1	2	yes	—
413	C₂×C₄	C₂³×#261	1	1	yes	characteristic
414	C₈	—	2	1	no	—
415	C₈	—	2	1	no	—
416	C₈	—	13	2	no	—
417	C₈	—	13	2	no	—
418	C₈	—	26	1	no	—
419	C₈	—	26	1	no	—
420	C₈	—	52	8	no	—
421	C₈	C₂×#6122	1	2	yes	—
422	C₈	C₂×#6122	1	2	yes	—
423	C₂²	—	2	8	no	—
424	C₂²	—	2	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	#11719092	1	2	yes	—
431	C₂²	D₁₃⋊#108	1	2	yes	—
432	C₂²	#11719129	1	2	yes	—
433	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
434	C₄	—	2	1	no	—
435	C₄	—	2	1	no	—
436	C₄	—	13	2	no	—
437	C₄	—	13	2	no	—
438	C₄	—	13	2	no	—
439	C₄	—	13	2	no	—
440	C₄	—	26	1	no	—
441	C₄	—	26	1	no	—
442	C₄	—	26	1	no	—
443	C₄	—	26	1	no	—
444	C₄	#11719129	1	2	yes	—
445	C₄	C₂×D₁₃⋊M₁₆	1	1	yes	characteristic
446	C₄	C₂²×#6122	1	1	yes	characteristic
447	C₂	—	2	2	no	—
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	C₂×#11719129	1	1	yes	characteristic
451	C₂	C₂×#11719092	1	1	yes	characteristic
452	C₂	C₂×D₁₃⋊#108	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	C₂³×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂⁴×C₁₃	C₄⋊C₄
cosocle	C₄×Dic₁₃	C₂⁴
hypercenter	C₂³×C₈	#261
hypocenter	C₁₃	#17793
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
2. #13130398	C₂	semidirect
3. #13130396	C₂	semidirect
4. #13130393	C₂	semidirect
5. #13130390	C₂	semidirect
6. #13130385	C₂	semidirect
7. #13130383	C₂	semidirect
31. #11718256	C₂²	semidirect
32. #11718255	C₂²	semidirect
33. #11718254	C₂²	semidirect
34. #11718253	C₂²	semidirect
118. C₂×C₈×C₁₃	M₁₆	semidirect
144. C₂×#1055	M₁₆	semidirect
353. C₂×C₈	#6122	semidirect
374. C₁₃	#17793	semidirect

Maximal subgroups

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

subgroup	index
#13131512	2
#13130398	2
#13130396	2
#13130393	2
#13130390	2
#13130385	2
#13130383	2
C₂²×C₈×Dic₁₃	2
#17793	13