Subgroups — C₄×#11719631 #16807461

Order 3328.

3698 conjugacy classes of subgroups.

The subgroup lattice has 550 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719631	C₂	1	2	yes	maximal
2	#13131276	C₂	1	2	yes	maximal, complemented
3	#13131275	C₂	1	6	yes	maximal, complemented
4	#13131273	C₂	1	6	yes	maximal, complemented
5	C₄×Q₈×#261	C₂	1	2	yes	maximal, complemented
6	C₄×D₄×#261	C₂	1	6	yes	maximal, complemented
7	C₄×#88237	C₂	1	3	yes	maximal, complemented
8	C₂×C₄×C₄⋊#261	C₂	1	3	yes	maximal, complemented
9	C₄×#41×D₁₃	C₂	1	1	yes	maximal, characteristic
10	C₂×#41×D₁₃	C₂²	1	1	yes	characteristic
11	#11719631	C₄	1	32	yes	direct product factor
12	C₂×Q₈×#261	C₂²	1	4	yes	—
13	C₂×D₄×#261	C₂²	1	12	yes	—
14	C₂×#88237	C₂²	1	6	yes	—
15	C₂²×C₄⋊#261	C₂²	1	6	yes	—
16	C₂²×C₄×#261	C₂²	1	6	yes	—
17	C₄×C₁₃×#41	C₄	1	1	yes	characteristic, complemented
18	#41×Dic₁₃	C₄	1	1	yes	characteristic, complemented
19	C₄×#6131	C₄	1	1	yes	characteristic, complemented
20	C₄×#6131	C₄	1	1	yes	characteristic, complemented
21	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
22	C₄×Q₈×D₁₃	C₂²	1	1	yes	characteristic
23	C₄×D₄×D₁₃	C₂²	1	3	yes	—
24	C₄×D₄×D₁₃	C₂²	1	3	yes	—
25	C₄×#6129	C₄	1	3	yes	complemented
26	C₄×#6129	C₄	1	3	yes	complemented
27	#11719227	C₄	1	3	yes	complemented
28	D₁₃×#117	C₂²	1	3	yes	—
29	C₄×#6127	C₄	1	3	yes	complemented
30	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
31	C₄×C₂²⋊#261	C₂²	1	6	yes	—
32	C₄×C₂²⋊#261	C₂²	1	6	yes	—
33	C₂×(C₂×#261)⋊C₄	C₂²	1	6	yes	—
34	C₄⋊C₄×#261	C₂²	1	12	yes	—
35	C₄⋊C₄×#261	C₂²	1	12	yes	—
36	C₂²⋊C₄×#261	C₂²	1	24	yes	—
37	C₄×C₄⋊#261	C₂²	1	3	yes	—
38	C₄×C₄⋊#261	C₂²	1	6	yes	—
39	C₄×C₄⋊#261	C₂²	1	6	yes	—
40	C₄×C₄⋊#261	C₂²	1	6	yes	—
41	C₄×C₄⋊#261	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊#261	C₂²	1	6	yes	—
43	#11719057	C₂²	1	6	yes	—
44	C₄²×#261	C₂²	1	6	yes	—
45	C₂³×#261	C₂³	1	12	yes	—
46	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
47	#41×D₁₃	C₂×C₄	1	16	yes	—
48	C₂×#6131	C₂×C₄	1	1	yes	characteristic
49	C₂×Q₈×D₁₃	C₂³	1	1	yes	characteristic
50	C₂×#6129	C₂×C₄	1	3	yes	—
51	C₂×D₄×D₁₃	C₂³	1	3	yes	—
52	C₂×#6127	C₂×C₄	1	3	yes	—
53	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
54	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
55	C₂²×C₄×D₁₃	C₂³	1	3	yes	—
56	C₂×C₂²⋊#261	C₂³	1	12	yes	—
57	Q₈×#261	C₂×C₄	1	32	yes	complemented
58	D₄×#261	C₂×C₄	1	96	yes	complemented
59	#88237	C₂×C₄	1	48	yes	complemented
60	C₂×C₄⋊#261	C₂×C₄	1	48	yes	complemented
61	C₂×C₄⋊#261	C₂³	1	6	yes	—
62	C₂×C₄⋊#261	C₂³	1	2	yes	—
63	C₂×C₄⋊#261	C₂³	1	12	yes	—
64	C₂×C₄×#261	—	4	12	no	—
65	C₂×C₄×#261	C₂³	1	2	yes	—
66	C₂×C₄×#261	C₂³	1	6	yes	—
67	C₂×C₄×#261	C₂³	1	12	yes	—
68	C₂×C₄×#261	C₂³	1	12	yes	—
69	C₂×C₄×#261	C₂³	1	12	yes	—
70	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
71	C₄×Q₈×C₁₃	C₂×C₄	1	1	yes	characteristic, complemented
72	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	complemented
73	C₄×D₄×C₁₃	C₂×C₄	1	3	yes	complemented
74	C₁₃×#117	C₂×C₄	1	3	yes	complemented
75	C₂×C₄²×C₁₃	C₂×C₄	1	3	yes	complemented
76	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
77	Q₈×Dic₁₃	C₂×C₄	1	1	yes	characteristic, complemented
78	D₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
79	D₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
80	C₄×C₂²⋊D₁₃	C₂×C₄	1	6	yes	complemented
81	C₄×C₂²⋊D₁₃	C₂×C₄	1	6	yes	complemented
82	#88180	C₂×C₄	1	3	yes	complemented
83	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
84	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
85	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	complemented
86	#88147	C₂×C₄	1	3	yes	complemented
87	#88147	C₂×C₄	1	3	yes	complemented
88	#88146	C₂×C₄	1	3	yes	complemented
89	#88146	C₂×C₄	1	3	yes	complemented
90	C₄⋊C₄×D₁₃	C₂³	1	3	yes	—
91	C₄⋊C₄×D₁₃	C₂³	1	3	yes	—
92	#88141	C₂×C₄	1	3	yes	complemented
93	#88141	C₂×C₄	1	3	yes	complemented
94	#88135	C₂×C₄	1	6	yes	complemented
95	#88135	C₂×C₄	1	6	yes	complemented
96	C₂²⋊C₄×D₁₃	C₂³	1	6	yes	—
97	#88131	C₂×C₄	1	6	yes	complemented
98	C₄×D₅₂	C₂×C₄	1	3	yes	complemented
99	C₄×D₅₂	C₂×C₄	1	3	yes	complemented
100	#88126	C₂×C₄	1	6	yes	complemented
101	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
102	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
103	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
104	C₄²×D₁₃	C₂×C₄	1	3	yes	complemented
105	C₄²×D₁₃	C₂³	1	1	yes	characteristic
106	C₄²×D₁₃	C₂³	1	3	yes	—
107	C₄²×D₁₃	C₂³	1	3	yes	—
108	C₄²×D₁₃	C₂³	1	3	yes	—
109	C₄×Dic₂₆	C₂×C₄	1	3	yes	complemented
110	C₄×Dic₂₆	C₂×C₄	1	3	yes	complemented
111	(C₂×#261)⋊C₄	C₂³	1	2	yes	—
112	(C₂×#261)⋊C₄	C₂³	1	6	yes	—
113	(C₂×#261)⋊C₄	C₂³	1	12	yes	—
114	(C₂×#261)⋊C₄	C₂³	1	12	yes	—
115	C₄×#520	—	13	1	no	maximal, Sylow
116	C₂³×D₁₃	C₂⁴	1	3	yes	—
117	C₂²×#261	—	4	12	no	—
118	C₂²×#261	—	4	12	no	—
119	C₂²×#261	C₂²×C₄	1	48	yes	—
120	C₂²×#261	C₂⁴	1	4	yes	—
121	C₂²×#261	C₂⁴	1	12	yes	—
122	C₁₃×#41	C₄²	1	8	yes	complemented
123	C₂×Q₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
124	C₂×D₄×C₁₃	C₂²×C₄	1	3	yes	—
125	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
126	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
127	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
128	C₂×C₂²⋊D₁₃	C₂²×C₄	1	6	yes	—
129	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
130	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
131	C₂²×Dic₁₃	C₂²×C₄	1	3	yes	—
132	#6131	C₄²	1	8	yes	complemented
133	Q₈×D₁₃	C₂²×C₄	1	8	yes	—
134	#6129	C₄²	1	24	yes	complemented
135	D₄×D₁₃	C₂²×C₄	1	24	yes	—
136	#6127	C₄²	1	24	yes	complemented
137	C₂×D₅₂	C₂²×C₄	1	3	yes	—
138	C₂×C₄×D₁₃	—	2	6	no	—
139	C₂×C₄×D₁₃	—	2	6	no	—
140	C₂×C₄×D₁₃	—	4	6	no	—
141	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
142	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
143	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
144	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
145	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
146	C₂×C₄×D₁₃	C₂²×C₄	1	3	yes	—
147	C₂×C₄×D₁₃	C₂²×C₄	1	24	yes	—
148	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
149	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
150	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
151	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
152	C₂×C₄×D₁₃	C₂⁴	1	3	yes	—
153	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
154	C₂×Dic₂₆	C₂²×C₄	1	3	yes	—
155	C₂²⋊#261	C₂²×C₄	1	48	yes	—
156	C₄⋊#261	C₂²×C₄	1	24	yes	—
157	C₄⋊#261	C₂²×C₄	1	48	yes	—
158	C₄⋊#261	C₂²×C₄	1	8	yes	—
159	C₄×#261	—	2	12	no	—
160	C₄×#261	—	2	4	no	—
161	C₄×#261	—	4	12	no	—
162	C₄×#261	—	4	12	no	—
163	C₄×#261	C₂²×C₄	1	48	yes	—
164	C₁₃×C₄⋊C₄	C₂²×C₄	1	3	yes	—
165	C₁₃×C₄⋊C₄	C₂²×C₄	1	3	yes	—
166	C₁₃×C₂²⋊C₄	C₂²×C₄	1	6	yes	—
167	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
168	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
169	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
170	C₄²×C₁₃	C₂²×C₄	1	3	yes	—
171	C₂²⋊Dic₁₃	C₂²×C₄	1	6	yes	—
172	#6103	C₂²×C₄	1	6	yes	—
173	#6103	C₂²×C₄	1	6	yes	—
174	C₄⋊Dic₁₃	C₂²×C₄	1	3	yes	—
175	C₄⋊Dic₁₃	C₂²×C₄	1	3	yes	—
176	#6101	C₂²×C₄	1	6	yes	—
177	#6101	C₂²×C₄	1	6	yes	—
178	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
179	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
180	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
181	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
182	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
183	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
184	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
185	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
186	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
187	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
188	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
189	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
190	C₂×#520	—	13	2	no	—
191	C₂×C₄×#41	—	13	1	no	—
192	#2276	—	13	2	no	—
193	#2275	—	13	6	no	—
194	#2274	—	13	6	no	—
195	C₄²×Q₈	—	13	2	no	—
196	C₄²×D₄	—	13	6	no	—
197	C₄×#117	—	13	3	no	—
198	C₂×C₄×C₄⋊C₄	—	13	3	no	—
199	C₂³×C₁₃	C₂³×C₄	1	3	yes	—
200	C₂²×D₁₃	—	2	3	no	—
201	C₂²×D₁₃	—	2	3	no	—
202	C₂²×D₁₃	—	2	6	no	—
203	C₂²×D₁₃	C₂³×C₄	1	12	yes	—
204	C₂²×D₁₃	C₂³×C₄	1	3	yes	—
205	C₂²×D₁₃	C₂⁵	1	1	yes	characteristic
206	C₂×#261	—	2	12	no	—
207	C₂×#261	—	2	4	no	—
208	C₂×#261	—	2	4	no	—
209	C₂×#261	—	2	12	no	—
210	C₂×#261	—	4	48	no	—
211	C₂×#261	C₂³×C₄	1	8	yes	—
212	C₂×#261	C₂³×C₄	1	24	yes	—
213	Q₈×C₁₃	C₂×C₄²	1	4	yes	complemented
214	D₄×C₁₃	C₂×C₄²	1	12	yes	complemented
215	C₂×C₄×C₁₃	—	2	6	no	—
216	C₂×C₄×C₁₃	—	4	3	no	—
217	C₂×C₄×C₁₃	C₂×C₄²	1	12	yes	complemented
218	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
219	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
220	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
221	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
223	C₂×C₄×C₁₃	C₂³×C₄	1	3	yes	—
224	C₂²⋊D₁₃	C₂×C₄²	1	24	yes	complemented
225	C₂×Dic₁₃	—	2	6	no	—
226	C₂×Dic₁₃	—	4	3	no	—
227	C₂×Dic₁₃	C₂×C₄²	1	12	yes	complemented
228	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
229	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
230	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
231	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
232	C₂×Dic₁₃	C₂³×C₄	1	1	yes	characteristic
233	C₂×Dic₁₃	C₂³×C₄	1	3	yes	—
234	D₅₂	C₂×C₄²	1	12	yes	complemented
235	C₄×D₁₃	—	2	3	no	—
236	C₄×D₁₃	—	2	3	no	—
237	C₄×D₁₃	—	2	6	no	—
238	C₄×D₁₃	—	2	2	no	—
239	C₄×D₁₃	—	2	6	no	—
240	C₄×D₁₃	—	2	6	no	—
241	C₄×D₁₃	—	4	3	no	—
242	C₄×D₁₃	—	4	3	no	—
243	C₄×D₁₃	C₂×C₄²	1	12	yes	complemented
244	C₄×D₁₃	C₂×C₄²	1	12	yes	complemented
245	C₄×D₁₃	C₂³×C₄	1	12	yes	—
246	C₄×D₁₃	C₂³×C₄	1	4	yes	—
247	C₄×D₁₃	H(5,𝔽₂)	1	2	yes	—
248	C₄×D₁₃	2₋¹⁺⁴	1	2	yes	—
249	Dic₂₆	C₂×C₄²	1	12	yes	complemented
250	C₂²×#41	—	13	1	no	—
251	#520	—	13	32	no	—
252	C₄×#41	—	13	1	no	—
253	C₄×#41	—	13	1	no	—
254	C₄×#41	—	13	1	no	—
255	C₄×#41	—	13	3	no	—
256	C₄×#41	—	13	3	no	—
257	C₄×#41	—	13	3	no	—
258	C₄×#41	—	13	3	no	—
259	C₄×#41	#261	1	1	yes	characteristic, complemented
260	C₂×C₄×Q₈	—	13	4	no	—
261	C₂×C₄×Q₈	—	13	1	no	—
262	C₂×C₄×Q₈	—	13	1	no	—
263	C₂×C₄×D₄	—	13	12	no	—
264	C₂×C₄×D₄	—	13	3	no	—
265	C₂×C₄×D₄	—	13	3	no	—
266	C₂×#117	—	13	6	no	—
267	C₂×#117	—	13	3	no	—
268	C₂²×C₄⋊C₄	—	13	6	no	—
269	C₂²×C₄²	—	13	3	no	—
270	C₂²×C₄²	—	13	6	no	—
271	C₄×C₄⋊C₄	—	13	3	no	—
272	C₄×C₄⋊C₄	—	13	6	no	—
273	C₄×C₄⋊C₄	—	13	6	no	—
274	C₄×C₄⋊C₄	—	13	6	no	—
275	C₄×C₄⋊C₄	—	13	1	no	—
276	C₄×C₄⋊C₄	—	13	6	no	—
277	C₄×C₄⋊C₄	—	13	12	no	—
278	C₄×C₄⋊C₄	—	13	12	no	—
279	C₄×C₂²⋊C₄	—	13	24	no	—
280	C₄×C₂²⋊C₄	—	13	6	no	—
281	C₄×C₂²⋊C₄	—	13	6	no	—
282	#376	—	13	6	no	—
283	C₂×#95	—	13	6	no	—
284	C₄³	—	13	6	no	—
285	C₂²×C₁₃	—	2	3	no	—
286	C₂²×C₁₃	—	2	3	no	—
287	C₂²×C₁₃	C₂²×C₄²	1	6	yes	—
288	C₂²×C₁₃	C₂⁴×C₄	1	1	yes	characteristic
289	C₂×D₁₃	—	2	3	no	—
290	C₂×D₁₃	—	2	3	no	—
291	C₂×D₁₃	—	2	12	no	—
292	C₂×D₁₃	—	2	12	no	—
293	C₂×D₁₃	C₂²×C₄²	1	6	yes	—
294	C₂×D₁₃	C₂⁴×C₄	1	2	yes	—
295	C₂×D₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
296	C₂×D₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
297	C₂×D₁₃	#585	1	2	yes	—
298	#261	—	2	24	no	—
299	#261	—	2	8	no	—
300	C₄×C₁₃	—	2	3	no	—
301	C₄×C₁₃	—	2	1	no	—
302	C₄×C₁₃	—	2	3	no	—
303	C₄×C₁₃	C₂²×C₄²	1	6	yes	—
304	C₄×C₁₃	C₂²×C₄²	1	2	yes	—
305	C₄×C₁₃	#520	1	2	yes	complemented
306	Dic₁₃	—	2	3	no	—
307	Dic₁₃	—	2	1	no	—
308	Dic₁₃	—	2	3	no	—
309	Dic₁₃	C₂²×C₄²	1	6	yes	—
310	Dic₁₃	C₂²×C₄²	1	2	yes	—
311	Dic₁₃	#520	1	2	yes	complemented
312	C₂×#41	—	13	16	no	—
313	C₂×#41	—	13	1	no	—
314	C₂×#41	—	13	3	no	—
315	C₂×#41	—	13	3	no	—
316	C₂×#41	C₂×#261	1	1	yes	characteristic
317	C₂²×Q₈	—	13	1	no	—
318	C₂²×D₄	—	13	3	no	—
319	C₂³×C₄	—	13	3	no	—
320	C₂³×C₄	—	13	12	no	—
321	C₂³×C₄	—	13	3	no	—
322	C₂³×C₄	—	13	3	no	—
323	C₄×Q₈	—	13	32	no	—
324	C₄×Q₈	—	13	1	no	—
325	C₄×Q₈	—	13	1	no	—
326	C₄×Q₈	—	13	3	no	—
327	C₄×Q₈	—	13	3	no	—
328	C₄×Q₈	—	13	3	no	—
329	C₄×Q₈	—	13	3	no	—
330	C₄×Q₈	C₂×#261	1	1	yes	characteristic, complemented
331	C₄×Q₈	C₂×#261	1	1	yes	characteristic, complemented
332	C₄×D₄	—	13	96	no	—
333	C₄×D₄	—	13	3	no	—
334	C₄×D₄	—	13	3	no	—
335	C₄×D₄	—	13	6	no	—
336	C₄×D₄	—	13	6	no	—
337	C₄×D₄	—	13	3	no	—
338	C₄×D₄	—	13	3	no	—
339	C₄×D₄	—	13	6	no	—
340	C₄×D₄	—	13	6	no	—
341	C₄×D₄	—	13	3	no	—
342	C₄×D₄	—	13	3	no	—
343	C₄×D₄	C₂×#261	1	3	yes	complemented
344	C₄×D₄	C₂×#261	1	3	yes	complemented
345	#117	—	13	48	no	—
346	#117	—	13	3	no	—
347	#117	—	13	3	no	—
348	#117	—	13	3	no	—
349	#117	—	13	6	no	—
350	#117	—	13	6	no	—
351	#117	C₂×#261	1	3	yes	complemented
352	C₂×C₄⋊C₄	—	13	6	no	—
353	C₂×C₄⋊C₄	—	13	12	no	—
354	C₂×C₄⋊C₄	—	13	48	no	—
355	C₂×C₄⋊C₄	—	13	2	no	—
356	C₂×C₄⋊C₄	—	13	3	no	—
357	C₂×C₄⋊C₄	—	13	3	no	—
358	C₂×C₂²⋊C₄	—	13	12	no	—
359	C₂×C₂²⋊C₄	—	13	6	no	—
360	C₂×C₄²	—	13	12	no	—
361	C₂×C₄²	—	13	3	no	—
362	C₂×C₄²	—	13	3	no	—
363	C₂×C₄²	—	13	3	no	—
364	C₂×C₄²	—	13	3	no	—
365	C₂×C₄²	—	13	3	no	—
366	C₂×C₄²	—	13	3	no	—
367	C₂×C₄²	—	13	3	no	—
368	C₂×C₄²	—	13	3	no	—
369	C₂×C₄²	—	13	3	no	—
370	C₂×C₄²	—	13	3	no	—
371	C₂×C₄²	—	13	1	no	—
372	C₂×C₄²	—	13	2	no	—
373	C₂×C₄²	—	13	6	no	—
374	C₂×C₄²	—	13	12	no	—
375	C₂×C₄²	—	13	12	no	—
376	C₂×C₄²	—	52	12	no	—
377	C₂×C₄²	C₂×#261	1	3	yes	complemented
378	#95	—	13	6	no	—
379	#95	—	13	12	no	—
380	#95	—	13	2	no	—
381	#95	—	13	12	no	—
382	C₂×C₁₃	—	2	6	no	—
383	C₂×C₁₃	C₂³×C₄²	1	1	yes	characteristic
384	C₂×C₁₃	C₂×#520	1	1	yes	characteristic
385	C₂×C₁₃	#3428	1	1	yes	characteristic
386	D₁₃	—	2	6	no	—
387	D₁₃	C₄×H(5,𝔽₂)	1	2	yes	—
388	D₁₃	C₄×2₋¹⁺⁴	1	2	yes	—
389	C₂⁴	—	13	3	no	—
390	#41	—	13	8	no	—
391	#41	—	13	24	no	—
392	#41	—	13	24	no	—
393	#41	C₄×#261	1	8	yes	complemented
394	C₂×Q₈	—	13	8	no	—
395	C₂×Q₈	—	13	3	no	—
396	C₂×Q₈	C₂²×#261	1	1	yes	characteristic
397	C₂×D₄	—	13	6	no	—
398	C₂×D₄	—	13	24	no	—
399	C₂×D₄	—	13	3	no	—
400	C₂×D₄	C₂²×#261	1	3	yes	—
401	C₂²×C₄	—	13	3	no	—
402	C₂²×C₄	—	13	24	no	—
403	C₂²×C₄	—	13	3	no	—
404	C₂²×C₄	—	13	1	no	—
405	C₂²×C₄	—	13	3	no	—
406	C₂²×C₄	—	13	3	no	—
407	C₂²×C₄	—	13	1	no	—
408	C₂²×C₄	—	13	4	no	—
409	C₂²×C₄	—	13	12	no	—
410	C₂²×C₄	—	13	3	no	—
411	C₂²×C₄	—	13	48	no	—
412	C₂²×C₄	—	13	3	no	—
413	C₂²×C₄	—	13	1	no	—
414	C₂²×C₄	—	13	3	no	—
415	C₂²×C₄	—	13	3	no	—
416	C₂²×C₄	—	13	3	no	—
417	C₂²×C₄	—	13	3	no	—
418	C₂²×C₄	—	13	3	no	—
419	C₂²×C₄	—	13	3	no	—
420	C₂²×C₄	—	26	6	no	—
421	C₂²×C₄	—	26	6	no	—
422	C₂²×C₄	—	52	6	no	—
423	C₂²×C₄	—	52	12	no	—
424	C₂²×C₄	—	52	12	no	—
425	C₂²×C₄	C₂²×#261	1	3	yes	—
426	C₂²×C₄	C₂²×#261	1	3	yes	—
427	C₂²×C₄	C₂²×#261	1	3	yes	—
428	C₄⋊C₄	—	13	24	no	—
429	C₄⋊C₄	—	13	48	no	—
430	C₄⋊C₄	—	13	8	no	—
431	C₄⋊C₄	—	13	6	no	—
432	C₄⋊C₄	—	13	6	no	—
433	C₄⋊C₄	—	13	3	no	—
434	C₄⋊C₄	—	13	3	no	—
435	C₄⋊C₄	C₂²×#261	1	3	yes	—
436	C₄⋊C₄	C₂²×#261	1	3	yes	—
437	C₂²⋊C₄	—	13	48	no	—
438	C₂²⋊C₄	—	13	6	no	—
439	C₂²⋊C₄	—	13	6	no	—
440	C₂²⋊C₄	—	13	6	no	—
441	C₂²⋊C₄	C₂²×#261	1	6	yes	—
442	C₄²	—	13	48	no	—
443	C₄²	—	13	1	no	—
444	C₄²	—	13	1	no	—
445	C₄²	—	13	3	no	—
446	C₄²	—	13	3	no	—
447	C₄²	—	13	3	no	—
448	C₄²	—	13	3	no	—
449	C₄²	—	13	3	no	—
450	C₄²	—	13	3	no	—
451	C₄²	—	13	3	no	—
452	C₄²	—	13	3	no	—
453	C₄²	—	13	1	no	—
454	C₄²	—	13	3	no	—
455	C₄²	—	26	12	no	—
456	C₄²	—	26	4	no	—
457	C₄²	—	52	12	no	—
458	C₄²	—	52	12	no	—
459	C₄²	C₂²×#261	1	3	yes	—
460	C₄²	C₂²×#261	1	3	yes	—
461	C₄²	C₂²×#261	1	1	yes	characteristic
462	C₄²	C₂²×#261	1	3	yes	—
463	C₁₃	C₄×#520	1	1	yes	characteristic, complemented, Sylow
464	C₂³	—	13	1	no	—
465	C₂³	—	13	12	no	—
466	C₂³	—	13	3	no	—
467	C₂³	—	26	3	no	—
468	C₂³	—	26	3	no	—
469	C₂³	—	26	6	no	—
470	C₂³	C₂³×#261	1	3	yes	—
471	Q₈	—	13	12	no	—
472	Q₈	C₂×C₄×#261	1	4	yes	complemented
473	D₄	—	13	24	no	—
474	D₄	—	13	12	no	—
475	D₄	C₂×C₄×#261	1	12	yes	complemented
476	C₂×C₄	—	2	6	no	—
477	C₂×C₄	—	4	3	no	—
478	C₂×C₄	—	13	12	no	—
479	C₂×C₄	—	13	1	no	—
480	C₂×C₄	—	13	1	no	—
481	C₂×C₄	—	13	3	no	—
482	C₂×C₄	—	13	12	no	—
483	C₂×C₄	—	13	4	no	—
484	C₂×C₄	—	13	12	no	—
485	C₂×C₄	—	13	12	no	—
486	C₂×C₄	—	13	2	no	—
487	C₂×C₄	—	13	2	no	—
488	C₂×C₄	—	13	8	no	—
489	C₂×C₄	—	13	24	no	—
490	C₂×C₄	—	13	1	no	—
491	C₂×C₄	—	13	3	no	—
492	C₂×C₄	—	13	3	no	—
493	C₂×C₄	—	26	6	no	—
494	C₂×C₄	—	26	3	no	—
495	C₂×C₄	—	26	6	no	—
496	C₂×C₄	—	26	3	no	—
497	C₂×C₄	—	26	2	no	—
498	C₂×C₄	—	26	6	no	—
499	C₂×C₄	—	26	12	no	—
500	C₂×C₄	—	26	4	no	—
501	C₂×C₄	—	26	4	no	—
502	C₂×C₄	—	26	12	no	—
503	C₂×C₄	—	26	6	no	—
504	C₂×C₄	—	52	3	no	—
505	C₂×C₄	—	52	3	no	—
506	C₂×C₄	—	52	3	no	—
507	C₂×C₄	—	52	48	no	—
508	C₂×C₄	C₂×C₄×#261	1	12	yes	complemented
509	C₂×C₄	C₂³×#261	1	1	yes	characteristic
510	C₂×C₄	C₂³×#261	1	3	yes	—
511	C₂×C₄	C₂³×#261	1	3	yes	—
512	C₂×C₄	C₂³×#261	1	1	yes	characteristic
513	C₂×C₄	C₂³×#261	1	3	yes	—
514	C₂×C₄	C₂³×#261	1	1	yes	characteristic
515	C₂²	—	2	3	no	—
516	C₂²	—	2	3	no	—
517	C₂²	—	13	2	no	—
518	C₂²	—	13	1	no	—
519	C₂²	—	13	1	no	—
520	C₂²	—	13	2	no	—
521	C₂²	—	13	6	no	—
522	C₂²	—	26	12	no	—
523	C₂²	—	26	12	no	—
524	C₂²	—	26	3	no	—
525	C₂²	—	26	3	no	—
526	C₂²	C₂²×C₄×#261	1	6	yes	—
527	C₂²	C₂⁴×#261	1	1	yes	characteristic
528	C₄	—	2	3	no	—
529	C₄	—	2	1	no	—
530	C₄	—	2	3	no	—
531	C₄	—	13	2	no	—
532	C₄	—	13	6	no	—
533	C₄	—	13	2	no	—
534	C₄	—	26	8	no	—
535	C₄	—	26	24	no	—
536	C₄	—	26	3	no	—
537	C₄	—	26	3	no	—
538	C₄	—	26	1	no	—
539	C₄	C₂²×C₄×#261	1	2	yes	—
540	C₄	C₂²×C₄×#261	1	6	yes	—
541	C₄	#11719631	1	2	yes	direct product factor
542	C₂	—	2	6	no	—
543	C₂	—	13	2	no	—
544	C₂	—	13	2	no	—
545	C₂	—	26	6	no	—
546	C₂	C₂³×C₄×#261	1	1	yes	characteristic
547	C₂	C₂×#11719631	1	1	yes	characteristic
548	C₂	#13131816	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×#261
commutator	C₂×C₁₃	C₂³×C₄²
Frattini	C₂²	C₂⁴×#261
Fitting	C₄×C₁₃×#41	C₄
socle	C₂²×C₁₃	C₂⁴×C₄
prime radical	C₂×#41×D₁₃	C₂²
cosocle	C₂²×D₁₃	C₂⁵
hypercenter	C₄×#41	#261
hypocenter	C₁₃	C₄×#520
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41

Complements

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

N	H ≅ G/N	type
2. #13131276	C₂	semidirect
3. #13131275	C₂	semidirect
4. #13131273	C₂	semidirect
5. C₄×Q₈×#261	C₂	semidirect
6. C₄×D₄×#261	C₂	semidirect
7. C₄×#88237	C₂	semidirect
8. C₂×C₄×C₄⋊#261	C₂	semidirect
11. #11719631	C₄	direct (N × H)
17. C₄×C₁₃×#41	C₄	semidirect
18. #41×Dic₁₃	C₄	semidirect
19. C₄×#6131	C₄	semidirect
20. C₄×#6131	C₄	semidirect
25. C₄×#6129	C₄	semidirect
26. C₄×#6129	C₄	semidirect
27. #11719227	C₄	semidirect
29. C₄×#6127	C₄	semidirect
57. Q₈×#261	C₂×C₄	semidirect
58. D₄×#261	C₂×C₄	semidirect
59. #88237	C₂×C₄	semidirect
60. C₂×C₄⋊#261	C₂×C₄	semidirect
70. C₄×Q₈×C₁₃	C₂×C₄	semidirect
71. C₄×Q₈×C₁₃	C₂×C₄	semidirect
72. C₄×D₄×C₁₃	C₂×C₄	semidirect
73. C₄×D₄×C₁₃	C₂×C₄	semidirect
74. C₁₃×#117	C₂×C₄	semidirect
75. C₂×C₄²×C₁₃	C₂×C₄	semidirect
76. Q₈×Dic₁₃	C₂×C₄	semidirect
77. Q₈×Dic₁₃	C₂×C₄	semidirect
78. D₄×Dic₁₃	C₂×C₄	semidirect
79. D₄×Dic₁₃	C₂×C₄	semidirect
80. C₄×C₂²⋊D₁₃	C₂×C₄	semidirect
81. C₄×C₂²⋊D₁₃	C₂×C₄	semidirect
82. #88180	C₂×C₄	semidirect
83. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
84. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
85. C₂×C₄×Dic₁₃	C₂×C₄	semidirect
86. #88147	C₂×C₄	semidirect
87. #88147	C₂×C₄	semidirect
88. #88146	C₂×C₄	semidirect
89. #88146	C₂×C₄	semidirect
92. #88141	C₂×C₄	semidirect
93. #88141	C₂×C₄	semidirect
94. #88135	C₂×C₄	semidirect
95. #88135	C₂×C₄	semidirect
97. #88131	C₂×C₄	semidirect
98. C₄×D₅₂	C₂×C₄	semidirect
99. C₄×D₅₂	C₂×C₄	semidirect
100. #88126	C₂×C₄	semidirect
101. C₄²×D₁₃	C₂×C₄	semidirect
102. C₄²×D₁₃	C₂×C₄	semidirect
103. C₄²×D₁₃	C₂×C₄	semidirect
104. C₄²×D₁₃	C₂×C₄	semidirect
109. C₄×Dic₂₆	C₂×C₄	semidirect
110. C₄×Dic₂₆	C₂×C₄	semidirect
122. C₁₃×#41	C₄²	semidirect
132. #6131	C₄²	semidirect
134. #6129	C₄²	semidirect
136. #6127	C₄²	semidirect
213. Q₈×C₁₃	C₂×C₄²	semidirect
214. D₄×C₁₃	C₂×C₄²	semidirect
217. C₂×C₄×C₁₃	C₂×C₄²	semidirect
224. C₂²⋊D₁₃	C₂×C₄²	semidirect
227. C₂×Dic₁₃	C₂×C₄²	semidirect
234. D₅₂	C₂×C₄²	semidirect
243. C₄×D₁₃	C₂×C₄²	semidirect
244. C₄×D₁₃	C₂×C₄²	semidirect
249. Dic₂₆	C₂×C₄²	semidirect
259. C₄×#41	#261	semidirect
305. C₄×C₁₃	#520	semidirect
311. Dic₁₃	#520	semidirect
330. C₄×Q₈	C₂×#261	semidirect
331. C₄×Q₈	C₂×#261	semidirect
343. C₄×D₄	C₂×#261	semidirect
344. C₄×D₄	C₂×#261	semidirect
351. #117	C₂×#261	semidirect
377. C₂×C₄²	C₂×#261	semidirect
393. #41	C₄×#261	semidirect
463. C₁₃	C₄×#520	semidirect
472. Q₈	C₂×C₄×#261	semidirect
475. D₄	C₂×C₄×#261	semidirect
508. C₂×C₄	C₂×C₄×#261	semidirect
541. C₄	#11719631	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×#11719631	2
#13131276	2
#13131275	2
#13131273	2
C₄×Q₈×#261	2
C₄×D₄×#261	2
C₄×#88237	2
C₂×C₄×C₄⋊#261	2
C₄×#41×D₁₃	2
C₄×#520	13

Subgroups — C4×#11719631 #16807461

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11719631 #16807461