Subgroups — #16798331

Order 3328.

810 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13131515	C₂	1	2	yes	maximal
2	#13130776	C₂	1	2	yes	maximal, complemented
3	#13130761	C₂	1	2	yes	maximal, complemented
4	#13130716	C₂	1	2	yes	maximal
5	#13130715	C₂	1	2	yes	maximal
6	C₄×#88104	C₂	1	2	yes	maximal, complemented
7	C₄×#88103	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	#11719128	—	2	2	no	—
13	#11719127	C₂²	1	4	yes	—
14	#11719125	—	2	2	no	—
15	C₂×#88104	C₂²	1	4	yes	—
16	C₂×#88103	C₂²	1	4	yes	—
17	#11719055	—	2	2	no	—
18	#11719053	C₂²	1	4	yes	—
19	#11719049	—	2	2	no	—
20	C₄×#6118	C₂²	1	4	yes	—
21	C₂×C₄×C₈×C₁₃	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×C₄×#1055	C₄	1	1	yes	characteristic
25	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
26	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
27	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
28	C₄×C₈×D₁₃	C₄	1	1	yes	characteristic
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	#11718268	C₂²	1	4	yes	—
34	#11718268	C₂²	1	4	yes	—
35	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
36	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
37	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
38	C₂×#6118	C₂³	1	8	yes	—
39	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
45	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
46	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₃	—	2	4	no	—
48	C₂×C₈×D₁₃	—	2	4	no	—
49	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
56	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
57	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
58	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
59	C₄²×D₁₃	D₄	1	1	yes	characteristic
60	C₄²×D₁₃	D₄	1	1	yes	characteristic
61	C₄²×D₁₃	Q₈	1	1	yes	characteristic
62	C₄²×D₁₃	Q₈	1	1	yes	characteristic
63	C₄²×D₁₃	C₂³	1	1	yes	characteristic
64	C₄²×D₁₃	C₂³	1	1	yes	characteristic
65	C₂²⋊#1057	—	2	4	no	—
66	#88112	—	2	4	no	—
67	#88112	—	2	4	no	—
68	#88111	—	2	4	no	—
69	#88110	—	2	4	no	—
70	C₄×#1057	—	2	4	no	—
71	#88104	—	2	8	no	—
72	#88103	—	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	#20826	—	13	1	no	maximal, Sylow
90	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
91	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
95	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
96	C₂²×Dic₁₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₁₃	—	2	4	no	—
98	C₂×C₄×D₁₃	—	2	4	no	—
99	C₂×C₄×D₁₃	—	2	2	no	—
100	C₂×C₄×D₁₃	—	2	2	no	—
101	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
110	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
111	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
113	C₂×#1057	—	2	8	no	—
114	#6118	—	2	8	no	—
115	#6118	—	2	8	no	—
116	C₂×C₈×C₁₃	—	2	2	no	—
117	C₂×C₈×C₁₃	—	2	2	no	—
118	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
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	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
123	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
124	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
125	C₄²×C₁₃	C₂²×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	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	C₂²×C₄	1	1	yes	characteristic
133	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
134	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
135	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
138	C₂×#1055	—	2	2	no	—
139	C₂×#1055	—	2	2	no	—
140	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
141	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
142	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
143	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
144	C₈×D₁₃	—	2	2	no	—
145	C₈×D₁₃	—	2	2	no	—
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	#41	1	4	yes	—
151	C₈×D₁₃	#41	1	4	yes	—
152	#2920	—	13	2	no	—
153	C₂²×C₄×C₈	—	13	1	no	—
154	#1848	—	13	2	no	—
155	#1837	—	13	2	no	—
156	#1810	—	13	2	no	—
157	#1810	—	13	2	no	—
158	C₄×#108	—	13	2	no	—
159	C₄×#108	—	13	2	no	—
160	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×D₁₃	—	2	2	no	—
162	C₂²×D₁₃	—	2	2	no	—
163	C₂²×D₁₃	—	2	2	no	—
164	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
165	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
166	C₂×C₄×C₁₃	—	2	2	no	—
167	C₂×C₄×C₁₃	—	2	1	no	—
168	C₂×C₄×C₁₃	—	2	1	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×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
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	#108	1	4	yes	complemented
179	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
180	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
183	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
184	C₂×Dic₁₃	C₂²×D₄	1	1	yes	characteristic
185	C₄×D₁₃	—	2	2	no	—
186	C₄×D₁₃	—	2	2	no	—
187	C₄×D₁₃	—	2	1	no	—
188	C₄×D₁₃	—	2	1	no	—
189	C₄×D₁₃	—	2	2	no	—
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	#108	1	4	yes	complemented
197	C₄×D₁₃	C₂×#41	1	2	yes	—
198	C₄×D₁₃	C₂×#41	1	2	yes	—
199	#1057	—	4	8	no	—
200	C₈×C₁₃	—	2	1	no	—
201	C₈×C₁₃	—	2	1	no	—
202	C₈×C₁₃	#117	1	2	yes	—
203	C₈×C₁₃	#117	1	2	yes	—
204	#1055	—	2	1	no	—
205	#1055	—	2	1	no	—
206	#1055	#117	1	2	yes	—
207	#1055	#117	1	2	yes	—
208	C₂³×C₈	—	13	1	no	—
209	C₂³×C₈	—	13	1	no	—
210	C₂²×C₄²	—	13	1	no	—
211	#432	—	26	2	no	—
212	#432	—	26	2	no	—
213	#431	—	26	2	no	—
214	#431	—	26	2	no	—
215	C₂×#108	—	13	4	no	—
216	C₂×#108	—	13	4	no	—
217	#423	—	13	4	no	—
218	#407	—	13	4	no	—
219	C₄×M₁₆	—	13	4	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	—	13	1	no	—
229	C₂×C₄×C₈	—	13	1	no	—
230	C₂×C₄×C₈	—	13	1	no	—
231	C₂×C₄×C₈	#261	1	1	yes	characteristic
232	#341	—	13	4	no	—
233	#341	—	13	4	no	—
234	C₂²×C₁₃	—	2	1	no	—
235	C₂²×C₁₃	—	2	1	no	—
236	C₂²×C₁₃	C₂×#108	1	2	yes	—
237	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
238	C₂×D₁₃	—	2	8	no	—
239	C₂×D₁₃	—	2	1	no	—
240	C₂×D₁₃	—	2	1	no	—
241	C₂×D₁₃	—	2	1	no	—
242	C₂×D₁₃	—	2	1	no	—
243	C₂×D₁₃	C₂×#108	1	2	yes	—
244	C₂×D₁₃	#533	1	2	yes	—
245	C₄×C₁₃	—	2	1	no	—
246	C₄×C₁₃	—	2	1	no	—
247	C₄×C₁₃	—	2	1	no	—
248	C₄×C₁₃	—	2	1	no	—
249	C₄×C₁₃	C₂×#108	1	2	yes	—
250	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
251	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
252	Dic₁₃	—	2	1	no	—
253	Dic₁₃	—	2	1	no	—
254	Dic₁₃	C₂×#108	1	2	yes	—
255	Dic₁₃	C₂×#108	1	2	yes	—
256	Dic₁₃	C₂×#108	1	2	yes	—
257	Dic₁₃	#532	1	2	yes	—
258	C₂³×C₄	—	13	1	no	—
259	C₂³×C₄	—	13	1	no	—
260	C₂³×C₄	—	13	1	no	—
261	C₂×M₁₆	—	13	8	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	—	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	—	26	4	no	—
273	C₂²×C₈	—	26	4	no	—
274	C₂²×C₈	C₂×#261	1	1	yes	characteristic
275	C₂²×C₈	C₂×#261	1	1	yes	characteristic
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	C₂×C₄²	—	13	1	no	—
286	C₂×C₄²	—	13	1	no	—
287	C₂×C₄²	C₂×#261	1	1	yes	characteristic
288	#108	—	26	8	no	—
289	#108	—	26	8	no	—
290	C₄⋊C₈	—	26	4	no	—
291	C₄⋊C₈	—	26	4	no	—
292	C₂²⋊C₈	—	26	4	no	—
293	C₂²⋊C₈	—	26	4	no	—
294	#97	—	26	4	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	—	13	1	no	—
307	C₄×C₈	—	26	4	no	—
308	C₄×C₈	C₂×#261	1	1	yes	characteristic
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	C₂×C₁₃	—	2	2	no	—
313	C₂×C₁₃	#2285	1	1	yes	characteristic
314	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
315	C₂×C₁₃	C₂²×#108	1	1	yes	characteristic
316	D₁₃	—	2	2	no	—
317	D₁₃	—	2	2	no	—
318	C₂⁴	—	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	—	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	—	26	2	no	—
335	C₂²×C₄	—	26	2	no	—
336	C₂²×C₄	—	26	4	no	—
337	C₂²×C₄	—	26	4	no	—
338	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
339	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
340	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
341	M₁₆	—	26	8	no	—
342	M₁₆	—	26	8	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	13	1	no	—
346	C₂×C₈	—	13	1	no	—
347	C₂×C₈	—	13	4	no	—
348	C₂×C₈	—	13	4	no	—
349	C₂×C₈	—	13	1	no	—
350	C₂×C₈	—	13	1	no	—
351	C₂×C₈	—	26	2	no	—
352	C₂×C₈	—	26	2	no	—
353	C₂×C₈	—	26	2	no	—
354	C₂×C₈	—	26	2	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	8	no	—
360	C₂×C₈	C₂²×#261	1	1	yes	characteristic
361	C₂×C₈	C₂²×#261	1	1	yes	characteristic
362	C₂×C₈	C₂²×#261	1	1	yes	characteristic
363	C₂×C₈	C₂²×#261	1	1	yes	characteristic
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	C₄²	—	13	1	no	—
375	C₄²	—	13	1	no	—
376	C₄²	C₄⋊#261	1	1	yes	characteristic
377	C₄²	C₄⋊#261	1	1	yes	characteristic
378	C₄²	C₂²×#261	1	1	yes	characteristic
379	C₄²	C₂²×#261	1	1	yes	characteristic
380	C₁₃	#20826	1	1	yes	characteristic, complemented, Sylow
381	C₂³	—	13	1	no	—
382	C₂³	—	13	1	no	—
383	C₂³	—	26	2	no	—
384	C₂³	—	26	2	no	—
385	C₂³	—	26	2	no	—
386	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	13	4	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	4	no	—
397	C₂×C₄	—	13	2	no	—
398	C₂×C₄	—	13	2	no	—
399	C₂×C₄	—	13	1	no	—
400	C₂×C₄	—	13	1	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	—	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	1	no	—
413	C₂×C₄	—	26	1	no	—
414	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
415	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
418	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
419	C₂×C₄	C₂³×#261	1	1	yes	characteristic
420	C₈	—	2	1	no	—
421	C₈	—	2	1	no	—
422	C₈	—	13	2	no	—
423	C₈	—	13	2	no	—
424	C₈	—	26	1	no	—
425	C₈	—	26	1	no	—
426	C₈	—	52	8	no	—
427	C₈	#88237	1	2	yes	—
428	C₈	#88237	1	2	yes	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	13	2	no	—
432	C₂²	—	13	2	no	—
433	C₂²	—	26	8	no	—
434	C₂²	—	26	1	no	—
435	C₂²	—	26	1	no	—
436	C₂²	—	26	1	no	—
437	C₂²	—	26	1	no	—
438	C₂²	D₁₃⋊#108	1	2	yes	—
439	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
440	C₄	—	2	1	no	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	13	2	no	—
445	C₄	—	13	2	no	—
446	C₄	—	13	2	no	—
447	C₄	—	13	2	no	—
448	C₄	—	26	1	no	—
449	C₄	—	26	1	no	—
450	C₄	D₁₃⋊#108	1	2	yes	—
451	C₄	C₂×#88237	1	1	yes	characteristic
452	C₄	C₂×#88237	1	1	yes	characteristic
453	C₂	—	2	2	no	—
454	C₂	—	26	2	no	—
455	C₂	—	26	2	no	—
456	C₂	#13131285	1	1	yes	characteristic
457	C₂	C₂×D₁₃⋊#108	1	1	yes	characteristic
458	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	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	#20826
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. #13130776	C₂	semidirect
3. #13130761	C₂	semidirect
6. C₄×#88104	C₂	semidirect
7. C₄×#88103	C₂	semidirect
178. C₂×Dic₁₃	#108	semidirect
196. C₄×D₁₃	#108	semidirect
380. C₁₃	#20826	semidirect

Maximal subgroups

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

subgroup	index
#13131515	2
#13130776	2
#13130761	2
#13130716	2
#13130715	2
C₄×#88104	2
C₄×#88103	2
C₂×C₄×C₈×D₁₃	2
#20826	13