Subgroups — #16797222

Order 3328.

994 conjugacy classes of subgroups.

The subgroup lattice has 504 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	#13131399	C₂	1	2	yes	maximal
3	C₂×#11719089	C₂	1	1	yes	maximal, characteristic
4	#13130657	C₂	1	4	yes	maximal, complemented
5	#108×#261	C₂	1	4	yes	maximal, complemented
6	#13130529	C₂	1	2	yes	maximal
7	C₂×D₁₃×#108	C₂	1	1	yes	maximal, characteristic
8	C₂×#88237	C₂²	1	1	yes	characteristic
9	C₂×D₁₃⋊M₁₆	C₂²	1	2	yes	—
10	C₂×D₁₃⋊M₁₆	C₂²	1	1	yes	characteristic
11	C₂×M₁₆×D₁₃	C₂²	1	2	yes	—
12	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	#11719099	—	2	4	no	—
14	M₁₆×#261	C₂²	1	8	yes	—
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	#11719089	—	2	4	no	—
22	#11719089	C₄	1	2	yes	—
23	#11719089	C₄	1	2	yes	—
24	#11719089	C₄	1	2	yes	—
25	#11719089	C₄	1	2	yes	—
26	C₂×#88100	C₂²	1	2	yes	—
27	C₂×C₈×#261	C₂²	1	2	yes	—
28	C₂×C₁₃×#108	C₄	1	1	yes	characteristic, complemented
29	C₂×#88062	C₄	1	2	yes	complemented
30	C₂×#88059	C₄	1	1	yes	characteristic, complemented
31	D₁₃×#108	C₄	1	2	yes	complemented
32	D₁₃×#108	C₄	1	2	yes	complemented
33	D₁₃×#108	C₂²	1	2	yes	—
34	D₁₃×#108	C₂²	1	2	yes	—
35	#11718273	C₂²	1	8	yes	—
36	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
37	C₂×C₂²⋊#261	Q₈	1	2	yes	—
38	C₂×#6122	—	2	2	no	—
39	C₂×#6122	—	2	1	no	—
40	#88237	C₂×C₄	1	2	yes	—
41	#88237	C₂×C₄	1	2	yes	—
42	#88237	D₄	1	2	yes	—
43	#88237	D₄	1	2	yes	—
44	C₂×C₄⋊#261	Q₈	1	2	yes	—
45	C₂×C₄×#261	C₂³	1	2	yes	—
46	D₁₃⋊M₁₆	—	2	2	no	—
47	D₁₃⋊M₁₆	—	2	2	no	—
48	D₁₃⋊M₁₆	—	2	1	no	—
49	D₁₃⋊M₁₆	—	2	1	no	—
50	D₁₃⋊M₁₆	C₂×C₄	1	4	yes	—
51	D₁₃⋊M₁₆	C₂×C₄	1	2	yes	—
52	D₁₃⋊M₁₆	C₂×C₄	1	2	yes	—
53	D₁₃⋊M₁₆	C₂³	1	4	yes	—
54	C₂×#6118	—	2	1	no	—
55	C₂×#6118	C₂×C₄	1	4	yes	—
56	C₂×D₁₃⋊C₈	—	2	2	no	—
57	C₂×D₁₃⋊C₈	C₂³	1	2	yes	—
58	C₂×C₁₃×M₁₆	C₂×C₄	1	2	yes	—
59	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
60	C₂×#6099	C₂×C₄	1	2	yes	—
61	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
62	M₁₆×D₁₃	—	2	2	no	—
63	M₁₆×D₁₃	—	2	2	no	—
64	M₁₆×D₁₃	C₂×C₄	1	4	yes	—
65	M₁₆×D₁₃	C₂³	1	4	yes	—
66	C₂×#6094	—	2	2	no	—
67	C₂×C₈×D₁₃	—	2	2	no	—
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	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₈×D₁₃	C₂×C₄	1	1	yes	characteristic
78	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₁₃	C₂³	1	1	yes	characteristic
80	#88104	C₂×C₄	1	4	yes	—
81	#88104	C₂×C₄	1	4	yes	—
82	#88103	C₂×C₄	1	4	yes	—
83	#88103	C₂×C₄	1	4	yes	—
84	#88100	—	2	8	no	—
85	#88100	C₂×C₄	1	4	yes	—
86	#88100	C₂×C₄	1	4	yes	—
87	C₈×#261	—	2	8	no	—
88	C₈×#261	C₂×C₄	1	4	yes	—
89	C₈×#261	C₂×C₄	1	4	yes	—
90	C₁₃×#108	C₂×C₄	1	2	yes	—
91	C₁₃×#108	C₂×C₄	1	2	yes	—
92	#88062	C₂×C₄	1	4	yes	—
93	#88062	C₂×C₄	1	4	yes	—
94	#88059	C₂×C₄	1	2	yes	—
95	#88059	C₂×C₄	1	2	yes	—
96	#20460	—	13	1	no	maximal, Sylow
97	C₂³×D₁₃	C₂×Q₈	1	1	yes	characteristic
98	C₂²×#261	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
100	C₂²×Dic₁₃	#41	1	1	yes	characteristic
101	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
102	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
103	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₁₃	C₂²×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×D₄	1	1	yes	characteristic
108	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
109	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
110	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
111	C₂×C₄×D₁₃	#41	1	1	yes	characteristic
112	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
113	C₂²⋊#261	C₄⋊C₄	1	4	yes	—
114	C₂²⋊#261	C₄⋊C₄	1	4	yes	—
115	#6122	—	2	2	no	—
116	#6122	—	2	2	no	—
117	#6122	—	2	4	no	—
118	#6122	—	2	4	no	—
119	C₂×#1057	—	2	4	no	—
120	C₂×#1057	—	2	2	no	—
121	C₄⋊#261	C₄⋊C₄	1	4	yes	—
122	C₄⋊#261	C₄⋊C₄	1	4	yes	—
123	C₄×#261	C₂²×C₄	1	4	yes	—
124	C₄×#261	C₂×D₄	1	4	yes	—
125	#6118	—	2	2	no	—
126	#6118	—	2	2	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	D₁₃⋊C₈	—	2	2	no	—
132	D₁₃⋊C₈	C₂²×C₄	1	4	yes	—
133	C₁₃×M₁₆	—	2	2	no	—
134	C₁₃×M₁₆	C₂²×C₄	1	4	yes	—
135	C₂×C₈×C₁₃	—	2	2	no	—
136	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
137	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
138	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
139	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
140	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
142	#6099	—	2	2	no	—
143	#6099	C₂²×C₄	1	4	yes	—
144	C₂×#1055	—	2	2	no	—
145	C₂×#1055	C₄²	1	1	yes	characteristic
146	C₂×#1055	C₄²	1	1	yes	characteristic
147	C₂×#1055	C₄²	1	1	yes	characteristic
148	C₂×#1055	C₄²	1	1	yes	characteristic
149	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
150	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
151	#6094	—	2	4	no	—
152	#6094	—	2	4	no	—
153	C₈×D₁₃	—	2	4	no	—
154	C₈×D₁₃	—	2	4	no	—
155	C₈×D₁₃	C₄²	1	1	yes	characteristic
156	C₈×D₁₃	C₄²	1	1	yes	characteristic
157	C₈×D₁₃	C₄²	1	1	yes	characteristic
158	C₈×D₁₃	C₄²	1	1	yes	characteristic
159	C₈×D₁₃	C₄²	1	1	yes	characteristic
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	C₂²×C₄	1	1	yes	characteristic
164	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
165	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
166	C₈×D₁₃	C₂²×C₄	1	1	yes	characteristic
167	C₈×D₁₃	C₂²×C₄	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	C₂²×#108	—	13	1	no	—
172	C₂²×#108	—	13	1	no	—
173	#2873	—	13	2	no	—
174	C₂×#405	—	13	1	no	—
175	#1778	—	13	4	no	—
176	C₄×#108	—	13	4	no	—
177	#1738	—	13	2	no	—
178	C₂³×C₁₃	C₄×Q₈	1	1	yes	characteristic
179	C₂²×D₁₃	—	4	2	no	—
180	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
181	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
182	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
183	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
184	C₂²×D₁₃	C₄×Q₈	1	1	yes	characteristic
185	C₂²×D₁₃	C₂²×Q₈	1	1	yes	characteristic
186	C₂×#261	—	4	4	no	—
187	C₂×#261	C₂×C₄⋊C₄	1	8	yes	—
188	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
189	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
190	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
194	C₂×Dic₁₃	#117	1	1	yes	characteristic
195	C₂×Dic₁₃	#117	1	1	yes	characteristic
196	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
197	C₂×Dic₁₃	C₄×D₄	1	1	yes	characteristic
198	C₂×Dic₁₃	C₄×Q₈	1	1	yes	characteristic
199	C₂×Dic₁₃	C₂×#41	1	1	yes	characteristic
200	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
201	C₄×D₁₃	C₂×C₄²	1	1	yes	characteristic
202	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
203	C₄×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
204	C₄×D₁₃	#117	1	1	yes	characteristic
205	C₄×D₁₃	#117	1	1	yes	characteristic
206	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
207	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
208	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
209	C₄×D₁₃	C₄×D₄	1	1	yes	characteristic
210	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
211	C₄×D₁₃	C₄×Q₈	1	1	yes	characteristic
212	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
213	C₄×D₁₃	C₂³×C₄	1	1	yes	characteristic
214	C₄×D₁₃	C₂²×D₄	1	1	yes	characteristic
215	C₄×D₁₃	C₂×#41	1	1	yes	characteristic
216	#1057	—	2	4	no	—
217	#1057	—	2	8	no	—
218	C₈×C₁₃	—	2	4	no	—
219	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
220	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
221	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
222	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
223	#1055	—	2	4	no	—
224	#1055	C₂×C₄²	1	1	yes	characteristic
225	#1055	C₂×C₄²	1	1	yes	characteristic
226	#1055	C₂×C₄²	1	1	yes	characteristic
227	#1055	C₂×C₄²	1	1	yes	characteristic
228	C₂²×M₁₆	—	13	1	no	—
229	C₂²×M₁₆	—	13	2	no	—
230	C₂²×M₁₆	—	13	2	no	—
231	C₂³×C₈	—	13	1	no	—
232	C₂×#117	—	13	1	no	—
233	C₂×#108	—	13	2	no	—
234	C₂×#108	—	13	2	no	—
235	C₂×#108	—	13	2	no	—
236	C₂×#108	—	13	2	no	—
237	C₂×#108	—	13	2	no	—
238	C₂×#108	—	13	2	no	—
239	C₂×#108	—	13	2	no	—
240	C₂×#108	—	13	1	no	—
241	C₂×#108	—	13	2	no	—
242	C₂×#108	—	13	2	no	—
243	C₂×#108	—	13	2	no	—
244	C₂×#108	—	13	2	no	—
245	C₂×#108	#261	1	1	yes	characteristic, complemented
246	#405	—	13	2	no	—
247	#405	—	13	2	no	—
248	#405	—	13	2	no	—
249	#405	—	13	2	no	—
250	#405	—	26	4	no	—
251	#405	—	26	4	no	—
252	C₄×M₁₆	—	13	8	no	—
253	C₂×#97	—	13	2	no	—
254	C₂×C₄×C₈	—	13	2	no	—
255	#341	—	13	8	no	—
256	C₂²×C₁₃	—	4	1	no	—
257	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
258	C₂²×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
259	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
260	C₂×D₁₃	—	2	2	no	—
261	C₂×D₁₃	—	2	2	no	—
262	C₂×D₁₃	—	2	2	no	—
263	C₂×D₁₃	—	4	1	no	—
264	C₂×D₁₃	—	4	1	no	—
265	C₂×D₁₃	—	4	1	no	—
266	C₂×D₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
267	C₂×D₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
268	C₂×D₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
269	C₂×D₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
270	#261	—	2	8	no	—
271	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
272	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
273	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
274	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
275	Dic₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
276	Dic₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
277	Dic₁₃	C₂×#117	1	1	yes	characteristic
278	Dic₁₃	C₂×C₄×D₄	1	1	yes	characteristic
279	C₂³×C₄	—	13	1	no	—
280	C₂×M₁₆	—	13	2	no	—
281	C₂×M₁₆	—	13	2	no	—
282	C₂×M₁₆	—	13	4	no	—
283	C₂×M₁₆	—	13	4	no	—
284	C₂×M₁₆	—	13	4	no	—
285	C₂×M₁₆	—	13	2	no	—
286	C₂×M₁₆	—	13	4	no	—
287	C₂×M₁₆	—	13	4	no	—
288	C₂×M₁₆	—	26	2	no	—
289	C₂×M₁₆	—	26	2	no	—
290	C₂×M₁₆	—	26	2	no	—
291	C₂×M₁₆	—	26	2	no	—
292	C₂×M₁₆	—	26	1	no	—
293	C₂×M₁₆	—	26	1	no	—
294	C₂×M₁₆	—	26	1	no	—
295	C₂×M₁₆	—	26	2	no	—
296	C₂×M₁₆	—	26	1	no	—
297	C₂×M₁₆	—	26	2	no	—
298	C₂×M₁₆	C₂×#261	1	2	yes	—
299	C₂²×C₈	—	13	1	no	—
300	C₂²×C₈	—	13	1	no	—
301	C₂²×C₈	—	13	1	no	—
302	C₂²×C₈	—	13	1	no	—
303	C₂²×C₈	—	13	1	no	—
304	C₂²×C₈	—	13	1	no	—
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	2	no	—
313	C₂²×C₈	—	26	2	no	—
314	C₂²×C₈	—	26	2	no	—
315	C₂²×C₈	C₂×#261	1	1	yes	characteristic
316	#117	—	13	2	no	—
317	#117	—	13	2	no	—
318	#117	—	13	2	no	—
319	#117	—	13	2	no	—
320	C₂×C₄⋊C₄	—	13	2	no	—
321	C₂×C₂²⋊C₄	—	13	2	no	—
322	C₂×C₄²	—	13	2	no	—
323	#108	—	13	4	no	—
324	#108	—	13	4	no	—
325	#108	—	13	4	no	—
326	#108	—	13	4	no	—
327	#108	—	13	4	no	—
328	#108	—	13	4	no	—
329	#108	—	13	2	no	—
330	#108	—	13	2	no	—
331	#108	C₂×#261	1	2	yes	—
332	#108	C₂×#261	1	2	yes	—
333	#97	—	13	4	no	—
334	#97	—	13	4	no	—
335	#97	—	26	8	no	—
336	C₄×C₈	—	13	4	no	—
337	C₄×C₈	—	13	4	no	—
338	C₄×C₈	—	26	8	no	—
339	C₂×C₁₃	—	2	1	no	—
340	C₂×C₁₃	—	2	1	no	—
341	C₂×C₁₃	—	2	1	no	—
342	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
343	D₁₃	—	2	1	no	—
344	D₁₃	—	2	1	no	—
345	D₁₃	—	2	1	no	—
346	D₁₃	#2916	1	2	yes	—
347	C₂⁴	—	13	1	no	—
348	C₂²×C₄	—	13	1	no	—
349	C₂²×C₄	—	13	1	no	—
350	C₂²×C₄	—	13	1	no	—
351	C₂²×C₄	—	13	1	no	—
352	C₂²×C₄	—	13	1	no	—
353	C₂²×C₄	—	13	1	no	—
354	C₂²×C₄	—	13	1	no	—
355	C₂²×C₄	—	13	1	no	—
356	C₂²×C₄	—	13	1	no	—
357	C₂²×C₄	—	13	1	no	—
358	C₂²×C₄	—	13	1	no	—
359	C₂²×C₄	—	13	1	no	—
360	C₂²×C₄	—	13	1	no	—
361	C₂²×C₄	—	13	4	no	—
362	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
363	M₁₆	—	2	2	no	—
364	M₁₆	—	13	8	no	—
365	M₁₆	—	13	4	no	—
366	M₁₆	—	26	4	no	—
367	M₁₆	—	26	4	no	—
368	M₁₆	—	26	2	no	—
369	M₁₆	—	26	2	no	—
370	M₁₆	—	26	4	no	—
371	M₁₆	—	26	2	no	—
372	M₁₆	—	26	2	no	—
373	M₁₆	—	26	4	no	—
374	M₁₆	—	26	4	no	—
375	M₁₆	—	26	2	no	—
376	M₁₆	C₂²×#261	1	4	yes	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	13	1	no	—
379	C₂×C₈	—	13	1	no	—
380	C₂×C₈	—	13	1	no	—
381	C₂×C₈	—	13	1	no	—
382	C₂×C₈	—	13	1	no	—
383	C₂×C₈	—	13	1	no	—
384	C₂×C₈	—	13	1	no	—
385	C₂×C₈	—	13	1	no	—
386	C₂×C₈	—	13	1	no	—
387	C₂×C₈	—	13	1	no	—
388	C₂×C₈	—	13	1	no	—
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	1	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	4	no	—
401	C₂×C₈	—	26	4	no	—
402	C₂×C₈	—	26	4	no	—
403	C₂×C₈	—	26	4	no	—
404	C₂×C₈	—	26	2	no	—
405	C₂×C₈	—	26	2	no	—
406	C₂×C₈	—	26	4	no	—
407	C₂×C₈	—	26	4	no	—
408	C₂×C₈	—	26	2	no	—
409	C₂×C₈	C₄×#261	1	1	yes	characteristic
410	C₂×C₈	C₄×#261	1	1	yes	characteristic
411	C₂×C₈	C₄×#261	1	1	yes	characteristic
412	C₂×C₈	C₄×#261	1	1	yes	characteristic
413	C₂×C₈	C₂²×#261	1	1	yes	characteristic
414	C₂×C₈	C₂²×#261	1	1	yes	characteristic
415	C₄⋊C₄	—	13	4	no	—
416	C₄⋊C₄	—	13	4	no	—
417	C₂²⋊C₄	—	13	4	no	—
418	C₂²⋊C₄	—	13	4	no	—
419	C₄²	—	13	4	no	—
420	C₄²	—	13	4	no	—
421	C₁₃	#20460	1	1	yes	characteristic, complemented, Sylow
422	C₂³	—	13	1	no	—
423	C₂³	—	13	1	no	—
424	C₂³	—	13	1	no	—
425	C₂³	—	13	1	no	—
426	C₂³	—	13	1	no	—
427	C₂³	—	13	1	no	—
428	C₂³	—	52	2	no	—
429	C₂³	Q₈×#261	1	1	yes	characteristic
430	C₂×C₄	—	13	1	no	—
431	C₂×C₄	—	13	1	no	—
432	C₂×C₄	—	13	1	no	—
433	C₂×C₄	—	13	1	no	—
434	C₂×C₄	—	13	1	no	—
435	C₂×C₄	—	13	1	no	—
436	C₂×C₄	—	13	1	no	—
437	C₂×C₄	—	13	1	no	—
438	C₂×C₄	—	13	1	no	—
439	C₂×C₄	—	13	1	no	—
440	C₂×C₄	—	13	1	no	—
441	C₂×C₄	—	13	1	no	—
442	C₂×C₄	—	13	1	no	—
443	C₂×C₄	—	13	1	no	—
444	C₂×C₄	—	13	1	no	—
445	C₂×C₄	—	13	1	no	—
446	C₂×C₄	—	13	1	no	—
447	C₂×C₄	—	13	1	no	—
448	C₂×C₄	—	13	1	no	—
449	C₂×C₄	—	13	1	no	—
450	C₂×C₄	—	13	1	no	—
451	C₂×C₄	—	13	1	no	—
452	C₂×C₄	—	13	8	no	—
453	C₂×C₄	—	52	4	no	—
454	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
455	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
456	C₂×C₄	D₄×#261	1	1	yes	characteristic
457	C₂×C₄	D₄×#261	1	1	yes	characteristic
458	C₂×C₄	Q₈×#261	1	1	yes	characteristic
459	C₂×C₄	C₂³×#261	1	1	yes	characteristic
460	C₈	—	2	4	no	—
461	C₈	—	13	1	no	—
462	C₈	—	13	1	no	—
463	C₈	—	13	1	no	—
464	C₈	—	13	1	no	—
465	C₈	—	26	4	no	—
466	C₈	—	26	8	no	—
467	C₈	—	26	4	no	—
468	C₈	C₂×C₄×#261	1	1	yes	characteristic
469	C₈	C₂×C₄×#261	1	1	yes	characteristic
470	C₈	C₂×C₄×#261	1	1	yes	characteristic
471	C₈	C₂×C₄×#261	1	1	yes	characteristic
472	C₂²	—	4	1	no	—
473	C₂²	—	13	1	no	—
474	C₂²	—	13	1	no	—
475	C₂²	—	13	1	no	—
476	C₂²	—	13	1	no	—
477	C₂²	—	26	2	no	—
478	C₂²	—	26	2	no	—
479	C₂²	—	26	2	no	—
480	C₂²	—	52	1	no	—
481	C₂²	—	52	1	no	—
482	C₂²	—	52	1	no	—
483	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
484	C₂²	C₄⋊C₄×#261	1	1	yes	characteristic
485	C₂²	C₂×Q₈×#261	1	1	yes	characteristic
486	C₄	—	13	1	no	—
487	C₄	—	13	1	no	—
488	C₄	—	13	1	no	—
489	C₄	—	13	1	no	—
490	C₄	—	26	8	no	—
491	C₄	C₄⋊C₄×#261	1	1	yes	characteristic
492	C₄	C₄⋊C₄×#261	1	1	yes	characteristic
493	C₄	C₂²×C₄×#261	1	1	yes	characteristic
494	C₄	C₂×D₄×#261	1	1	yes	characteristic
495	C₂	—	2	1	no	—
496	C₂	—	2	1	no	—
497	C₂	—	2	1	no	—
498	C₂	—	13	2	no	—
499	C₂	—	26	1	no	—
500	C₂	—	26	1	no	—
501	C₂	—	26	1	no	—
502	C₂	C₂×C₄⋊C₄×#261	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₁₃×#108	C₄
socle	C₂×C₁₃	C₂×C₄×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×#108	#261
hypocenter	C₁₃	#20460
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #13130657	C₂	semidirect
5. #108×#261	C₂	semidirect
15. D₁₃⋊#108	C₄	semidirect
16. D₁₃⋊#108	C₄	semidirect
19. C₂×#88104	C₄	semidirect
20. C₂×#88103	C₄	semidirect
28. C₂×C₁₃×#108	C₄	semidirect
29. C₂×#88062	C₄	semidirect
30. C₂×#88059	C₄	semidirect
31. D₁₃×#108	C₄	semidirect
32. D₁₃×#108	C₄	semidirect
245. C₂×#108	#261	semidirect
421. C₁₃	#20460	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
#13131399	2
C₂×#11719089	2
#13130657	2
#108×#261	2
#13130529	2
C₂×D₁₃×#108	2
#20460	13