Subgroups — C₂×#13128685 #16770867

Order 3328.

7994 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13128685	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719386	C₂	1	4	yes	maximal, complemented
3	C₂×#11719437	C₂	1	2	yes	maximal, complemented
4	C₂×#11719268	C₂	1	2	yes	maximal, complemented
5	C₂×#11719270	C₂	1	4	yes	maximal, complemented
6	C₂×#11719423	C₂	1	2	yes	maximal, complemented
7	C₂×#11719260	C₂	1	2	yes	maximal, complemented
8	C₂×#11719322	C₂	1	4	yes	maximal, complemented
9	C₂×#11719535	C₂	1	2	yes	maximal, complemented
10	C₂×#11719175	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#11719311	C₂	1	4	yes	maximal, complemented
12	C₂×#11719532	C₂	1	2	yes	maximal, complemented
13	C₂²×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₁₃×#41	C₂²	1	2	yes	—
16	C₂²×#6129	C₂²	1	4	yes	complemented
17	C₂³×D₅₂	C₂²	1	1	yes	characteristic
18	C₂³×C₄×D₁₃	C₂²	1	2	yes	—
19	C₁₃×#532	C₂²	1	16	yes	complemented
20	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
23	C₂×C₁₃×#121	C₂²	1	2	yes	—
24	C₂×C₁₃×#121	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
26	C₂×C₄×D₄×C₁₃	C₂²	1	2	yes	complemented
27	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
28	#11719535	C₂²	1	32	yes	complemented
29	#11719532	C₂²	1	32	yes	complemented
30	C₂×#88201	C₂²	1	4	yes	—
31	C₂×Q₈×Dic₁₃	C₂²	1	4	yes	complemented
32	C₂×#88194	C₂²	1	4	yes	—
33	C₂×#88193	C₂²	1	8	yes	complemented
34	C₂×#88192	C₂²	1	4	yes	complemented
35	C₂×#88191	C₂²	1	8	yes	—
36	C₂×D₄×Dic₁₃	C₂²	1	8	yes	—
37	C₂×D₄×Dic₁₃	C₂²	1	4	yes	complemented
38	C₂×#88184	C₂²	1	4	yes	—
39	C₂×#88184	C₂²	1	4	yes	—
40	C₂²×#6103	C₂²	1	2	yes	—
41	C₂×#88180	C₂²	1	2	yes	—
42	C₂×#88180	C₂²	1	4	yes	complemented
43	C₂²×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic
44	C₂²×C₄⋊Dic₁₃	C₂²	1	4	yes	complemented
45	C₂×#88178	C₂²	1	2	yes	—
46	C₂×#88178	C₂²	1	2	yes	—
47	#11719437	C₂²	1	32	yes	complemented
48	#11719423	C₂²	1	32	yes	complemented
49	#11719386	C₂²	1	64	yes	complemented
50	#11719322	C₂²	1	64	yes	complemented
51	#11719311	C₂²	1	64	yes	complemented
52	#11719270	C₂²	1	64	yes	complemented
53	#11719268	C₂²	1	32	yes	complemented
54	#11719260	C₂²	1	32	yes	complemented
55	C₂×#88152	C₂²	1	8	yes	complemented
56	C₂×#88151	C₂²	1	4	yes	complemented
57	C₂×#88146	C₂²	1	4	yes	complemented
58	C₂×#88140	C₂²	1	8	yes	complemented
59	C₂×#88139	C₂²	1	8	yes	complemented
60	C₂×#88137	C₂²	1	8	yes	complemented
61	C₂×#88135	C₂²	1	8	yes	complemented
62	C₂×C₄×D₅₂	C₂²	1	2	yes	—
63	C₂×C₄×D₅₂	C₂²	1	2	yes	—
64	C₂×C₄×D₅₂	C₂²	1	2	yes	—
65	C₂×C₄×D₅₂	C₂²	1	2	yes	—
66	C₂×C₄×D₅₂	C₂²	1	16	yes	complemented
67	#11719175	C₂²	1	16	yes	complemented
68	C₂×#88124	C₂²	1	2	yes	complemented
69	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
70	C₂×#88123	C₂²	1	1	yes	characteristic, complemented
71	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
72	C₂×C₄×Dic₂₆	C₂²	1	2	yes	complemented
73	C₂⁴×D₁₃	C₂³	1	2	yes	—
74	C₂×C₁₃×#41	—	2	16	no	—
75	C₂×C₁₃×#41	C₂³	1	16	yes	—
76	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
77	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
78	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
79	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
81	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
83	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
84	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
85	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
86	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
87	C₂³×Dic₁₃	C₂³	1	8	yes	—
88	C₂³×Dic₁₃	C₂³	1	2	yes	—
89	C₂×#6129	—	4	16	no	—
90	C₂×#6129	C₂³	1	32	yes	complemented
91	C₂²×D₅₂	—	2	8	no	—
92	C₂²×D₅₂	C₂³	1	2	yes	—
93	C₂²×D₅₂	C₂³	1	2	yes	—
94	C₂²×D₅₂	C₂³	1	8	yes	—
95	C₂²×C₄×D₁₃	—	4	8	no	—
96	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
97	C₂²×C₄×D₁₃	C₂³	1	4	yes	—
98	C₂²×C₄×D₁₃	C₂³	1	16	yes	—
99	C₂²×Dic₂₆	C₂³	1	2	yes	—
100	C₂²×Dic₂₆	C₂³	1	2	yes	—
101	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
102	C₁₃×#127	C₂³	1	8	yes	complemented
103	C₁₃×#124	C₂³	1	16	yes	complemented
104	C₁₃×#121	C₂³	1	16	yes	—
105	C₁₃×#121	C₂³	1	16	yes	—
106	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
107	C₄×D₄×C₁₃	C₂³	1	16	yes	complemented
108	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
109	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
110	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
111	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₁₃	C₂³	1	8	yes	—
117	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
118	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
119	#88201	C₂³	1	32	yes	—
120	Q₈×Dic₁₃	C₂³	1	32	yes	complemented
121	#88194	C₂³	1	32	yes	—
122	#88193	C₂³	1	64	yes	complemented
123	#88192	C₂³	1	32	yes	complemented
124	#88191	C₂³	1	64	yes	—
125	D₄×Dic₁₃	C₂³	1	64	yes	—
126	D₄×Dic₁₃	C₂³	1	32	yes	complemented
127	#88184	C₂³	1	32	yes	—
128	#88184	C₂³	1	32	yes	—
129	C₂×#6103	C₂³	1	4	yes	—
130	C₂×#6103	C₂³	1	4	yes	—
131	C₂×#6103	C₂³	1	16	yes	—
132	C₂×#6103	C₂³	1	8	yes	—
133	C₂×#6103	C₂³	1	8	yes	—
134	#88180	C₂³	1	16	yes	—
135	#88180	C₂³	1	32	yes	complemented
136	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
137	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
138	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
139	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
140	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
141	C₂×C₄⋊Dic₁₃	C₂³	1	2	yes	—
142	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
143	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
144	C₂×C₄⋊Dic₁₃	C₂³	1	32	yes	complemented
145	#88178	C₂³	1	16	yes	—
146	#88178	C₂³	1	16	yes	—
147	C₂×#6101	C₂³	1	4	yes	—
148	C₂×#6101	C₂³	1	4	yes	—
149	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
150	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
151	#88152	C₂³	1	64	yes	complemented
152	#88151	C₂³	1	32	yes	complemented
153	#88146	C₂³	1	32	yes	complemented
154	#88140	C₂³	1	64	yes	complemented
155	#88139	C₂³	1	64	yes	complemented
156	#88137	C₂³	1	64	yes	complemented
157	#88135	C₂³	1	64	yes	complemented
158	C₄×D₅₂	C₂³	1	16	yes	—
159	C₄×D₅₂	C₂³	1	16	yes	—
160	C₄×D₅₂	C₂³	1	16	yes	—
161	C₄×D₅₂	C₂³	1	16	yes	—
162	#88124	C₂³	1	16	yes	complemented
163	#88123	C₂³	1	8	yes	complemented
164	#88123	C₂³	1	8	yes	complemented
165	C₄×Dic₂₆	C₂³	1	16	yes	complemented
166	C₄×Dic₂₆	C₂³	1	16	yes	complemented
167	C₂×#3506	—	13	1	no	maximal, Sylow
168	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
169	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
170	C₂³×D₁₃	—	2	8	no	—
171	C₂³×D₁₃	—	4	4	no	—
172	C₂³×D₁₃	—	4	4	no	—
173	C₂³×D₁₃	C₂⁴	1	4	yes	—
174	C₂³×D₁₃	C₂⁴	1	8	yes	—
175	C₁₃×#41	—	2	64	no	—
176	C₂×Q₈×C₁₃	—	2	8	no	—
177	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
178	C₂×D₄×C₁₃	—	2	16	no	—
179	C₂×D₄×C₁₃	—	2	8	no	—
180	C₂×D₄×C₁₃	—	2	8	no	—
181	C₂×D₄×C₁₃	—	4	4	no	—
182	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
183	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
184	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
185	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
186	C₂²×C₄×C₁₃	—	2	16	no	—
187	C₂²×C₄×C₁₃	—	2	4	no	—
188	C₂²×C₄×C₁₃	—	4	2	no	—
189	C₂²×C₄×C₁₃	#41	1	8	yes	complemented
190	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
191	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
192	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
193	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
196	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
197	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
198	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
199	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
200	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₃	—	4	16	no	—
202	C₂×C₂²⋊D₁₃	—	4	16	no	—
203	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
204	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
205	C₂²×Dic₁₃	—	4	4	no	—
206	C₂²×Dic₁₃	—	4	16	no	—
207	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
208	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
209	C₂²×Dic₁₃	C₂⁴	1	4	yes	—
210	C₂²×Dic₁₃	C₂⁴	1	32	yes	—
211	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
212	#6129	—	4	64	no	—
213	C₂×D₅₂	—	2	8	no	—
214	C₂×D₅₂	—	2	8	no	—
215	C₂×D₅₂	—	2	32	no	—
216	C₂×D₅₂	C₂⁴	1	8	yes	—
217	C₂×D₅₂	C₂⁴	1	8	yes	—
218	C₂×C₄×D₁₃	—	2	16	no	—
219	C₂×C₄×D₁₃	—	4	32	no	—
220	C₂×C₄×D₁₃	—	4	8	no	—
221	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
222	C₂×C₄×D₁₃	C₂⁴	1	16	yes	—
223	C₂×Dic₂₆	—	2	8	no	—
224	C₂×Dic₂₆	—	4	4	no	—
225	C₂×Dic₂₆	C₂⁴	1	8	yes	—
226	C₂×Dic₂₆	C₂⁴	1	8	yes	—
227	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
228	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
229	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
230	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
231	C₄²×C₁₃	C₂⁴	1	4	yes	—
232	C₄²×C₁₃	C₂⁴	1	4	yes	—
233	C₄²×C₁₃	C₂⁴	1	4	yes	—
234	C₄²×C₁₃	C₂⁴	1	4	yes	—
235	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
236	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
237	#6103	C₂⁴	1	16	yes	—
238	#6103	C₂⁴	1	16	yes	—
239	#6103	C₂⁴	1	32	yes	—
240	#6103	C₂⁴	1	32	yes	—
241	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
242	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
243	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
244	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
245	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
246	C₄⋊Dic₁₃	C₂⁴	1	8	yes	—
247	C₄⋊Dic₁₃	C₂⁴	1	32	yes	—
248	#6101	C₂⁴	1	16	yes	—
249	#6101	C₂⁴	1	16	yes	—
250	C₄×Dic₁₃	C₂⁴	1	16	yes	—
251	C₄×Dic₁₃	C₂⁴	1	32	yes	—
252	#3506	—	13	32	no	—
253	C₂×#559	—	13	4	no	—
254	C₂×#556	—	13	2	no	—
255	C₂×#555	—	13	2	no	—
256	C₂×#553	—	13	4	no	—
257	C₂×#550	—	13	2	no	—
258	C₂×#547	—	13	2	no	—
259	C₂×#538	—	13	4	no	—
260	C₂×#535	—	13	2	no	—
261	C₂×#533	—	13	1	no	—
262	C₂×#532	D₁₃	1	1	yes	characteristic, complemented
263	C₂×#525	—	13	4	no	—
264	C₂×#520	—	13	2	no	—
265	C₂²×C₄×D₄	—	13	1	no	—
266	C₂³×C₁₃	—	2	2	no	—
267	C₂³×C₁₃	—	2	2	no	—
268	C₂³×C₁₃	—	2	8	no	—
269	C₂³×C₁₃	—	2	8	no	—
270	C₂³×C₁₃	—	2	8	no	—
271	C₂³×C₁₃	C₂×#41	1	4	yes	—
272	C₂³×C₁₃	C₂⁵	1	8	yes	—
273	C₂³×C₁₃	C₂⁵	1	2	yes	—
274	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
275	C₂²×D₁₃	—	2	16	no	—
276	C₂²×D₁₃	—	2	8	no	—
277	C₂²×D₁₃	—	2	8	no	—
278	C₂²×D₁₃	—	2	8	no	—
279	C₂²×D₁₃	—	4	8	no	—
280	C₂²×D₁₃	—	4	8	no	—
281	C₂²×D₁₃	—	4	32	no	—
282	C₂²×D₁₃	C₂⁵	1	8	yes	—
283	Q₈×C₁₃	—	2	16	no	—
284	D₄×C₁₃	—	2	32	no	—
285	D₄×C₁₃	—	2	16	no	—
286	D₄×C₁₃	—	2	16	no	—
287	D₄×C₁₃	—	4	8	no	—
288	C₂×C₄×C₁₃	—	2	8	no	—
289	C₂×C₄×C₁₃	—	2	2	no	—
290	C₂×C₄×C₁₃	—	2	2	no	—
291	C₂×C₄×C₁₃	—	2	2	no	—
292	C₂×C₄×C₁₃	—	2	32	no	—
293	C₂×C₄×C₁₃	—	2	8	no	—
294	C₂×C₄×C₁₃	—	4	4	no	—
295	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
296	C₂×C₄×C₁₃	C₂×#41	1	4	yes	—
297	C₂×C₄×C₁₃	C₂×#41	1	16	yes	complemented
298	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
299	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
300	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
301	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
302	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
303	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
304	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
305	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
306	C₂²⋊D₁₃	—	4	32	no	—
307	C₂²⋊D₁₃	—	4	32	no	—
308	C₂×Dic₁₃	—	2	8	no	—
309	C₂×Dic₁₃	—	2	8	no	—
310	C₂×Dic₁₃	—	2	8	no	—
311	C₂×Dic₁₃	—	4	8	no	—
312	C₂×Dic₁₃	—	4	32	no	—
313	C₂×Dic₁₃	C₂⁵	1	8	yes	—
314	C₂×Dic₁₃	C₂⁵	1	8	yes	—
315	C₂×Dic₁₃	C₂⁵	1	8	yes	—
316	D₅₂	—	2	16	no	—
317	D₅₂	—	2	16	no	—
318	C₄×D₁₃	—	2	32	no	—
319	C₄×D₁₃	—	4	16	no	—
320	Dic₂₆	—	2	16	no	—
321	Dic₂₆	—	4	8	no	—
322	C₂²×#41	—	13	4	no	—
323	C₂²×#41	C₂×D₁₃	1	2	yes	—
324	C₂³×D₄	—	13	1	no	—
325	C₂⁴×C₄	—	13	2	no	—
326	#559	—	13	64	no	—
327	#556	—	13	32	no	—
328	#555	—	13	32	no	—
329	#553	—	13	64	no	—
330	#550	—	13	32	no	—
331	#547	—	13	32	no	—
332	#538	—	13	64	no	—
333	#535	—	13	32	no	—
334	#533	—	13	16	no	—
335	#532	C₂×D₁₃	1	16	yes	complemented
336	C₂×C₄⋊Q₈	—	13	1	no	—
337	C₂×C₄⋊Q₈	—	13	1	no	—
338	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
339	C₂×#127	—	13	4	no	—
340	C₂×#127	C₂×D₁₃	1	1	yes	characteristic, complemented
341	C₂×#126	—	13	8	no	—
342	C₂×#125	—	13	2	no	—
343	C₂×#124	—	13	4	no	—
344	C₂×#124	—	13	8	no	—
345	C₂×#124	C₂×D₁₃	1	2	yes	complemented
346	#525	—	13	64	no	—
347	C₂×#123	—	13	8	no	—
348	C₂×#123	—	13	8	no	—
349	C₂×C₂²⋊Q₈	—	13	2	no	—
350	C₂×C₂²⋊Q₈	—	13	2	no	—
351	C₂×C₂²⋊Q₈	—	13	4	no	—
352	C₂×#121	—	13	4	no	—
353	C₂×#121	—	13	8	no	—
354	C₂×#121	—	13	4	no	—
355	C₂×#121	—	13	4	no	—
356	C₂×#121	C₂×D₁₃	1	2	yes	—
357	C₂×#121	C₂×D₁₃	1	2	yes	—
358	C₂×#120	—	13	8	no	—
359	#520	—	13	32	no	—
360	C₂×C₄×Q₈	—	13	4	no	—
361	C₂×C₄×Q₈	—	13	2	no	—
362	C₂×C₄×Q₈	—	13	2	no	—
363	C₂×C₄×D₄	—	13	8	no	—
364	C₂×C₄×D₄	—	13	4	no	—
365	C₂×C₄×D₄	—	13	8	no	—
366	C₂×C₄×D₄	—	13	2	no	—
367	C₂×C₄×D₄	—	13	2	no	—
368	C₂×C₄×D₄	—	13	2	no	—
369	C₂×C₄×D₄	—	13	2	no	—
370	C₂×C₄×D₄	—	13	16	no	—
371	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
372	C₂×C₄×D₄	C₂×D₁₃	1	2	yes	complemented
373	C₂×#117	—	13	2	no	—
374	C₂×#117	—	13	4	no	—
375	C₂×#117	—	13	4	no	—
376	C₂²×C₄⋊C₄	—	13	1	no	—
377	C₂²×C₄⋊C₄	—	13	4	no	—
378	C₂²×C₂²⋊C₄	—	13	2	no	—
379	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
380	C₂²×C₁₃	—	2	2	no	—
381	C₂²×C₁₃	—	2	2	no	—
382	C₂²×C₁₃	—	2	8	no	—
383	C₂²×C₁₃	—	2	8	no	—
384	C₂²×C₁₃	—	2	8	no	—
385	C₂²×C₁₃	—	2	8	no	—
386	C₂²×C₁₃	—	4	16	no	—
387	C₂²×C₁₃	C₂²×#41	1	4	yes	—
388	C₂²×C₁₃	C₂²×#41	1	2	yes	—
389	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
390	C₂²×C₁₃	#585	1	2	yes	—
391	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
392	C₂×D₁₃	—	2	8	no	—
393	C₂×D₁₃	—	2	8	no	—
394	C₂×D₁₃	—	2	8	no	—
395	C₂×D₁₃	—	4	32	no	—
396	C₂×D₁₃	—	4	16	no	—
397	C₄×C₁₃	—	2	8	no	—
398	C₄×C₁₃	—	2	2	no	—
399	C₄×C₁₃	—	2	2	no	—
400	C₄×C₁₃	—	2	2	no	—
401	C₄×C₁₃	C₂²×#41	1	4	yes	—
402	C₄×C₁₃	C₂²×#41	1	4	yes	—
403	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
404	Dic₁₃	—	2	8	no	—
405	Dic₁₃	—	2	8	no	—
406	Dic₁₃	—	2	8	no	—
407	C₂⁵	—	13	2	no	—
408	C₂×#41	—	2	16	no	—
409	C₂×#41	—	13	32	no	—
410	C₂×#41	—	52	16	no	—
411	C₂×#41	C₂²×D₁₃	1	16	yes	—
412	C₂²×Q₈	—	13	2	no	—
413	C₂²×Q₈	—	13	2	no	—
414	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
415	C₂²×D₄	—	13	8	no	—
416	C₂²×D₄	—	13	8	no	—
417	C₂²×D₄	—	13	2	no	—
418	C₂²×D₄	—	13	2	no	—
419	C₂²×D₄	—	13	8	no	—
420	C₂²×D₄	—	26	8	no	—
421	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
422	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
423	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
424	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
425	C₂³×C₄	—	13	2	no	—
426	C₂³×C₄	—	13	8	no	—
427	C₂³×C₄	—	13	4	no	—
428	C₂³×C₄	—	13	4	no	—
429	C₂³×C₄	—	13	16	no	—
430	C₂³×C₄	—	52	8	no	—
431	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
432	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
433	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
434	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
435	C₄⋊Q₈	—	13	8	no	—
436	C₄⋊Q₈	—	13	8	no	—
437	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
438	#127	—	13	32	no	—
439	#127	C₂²×D₁₃	1	8	yes	complemented
440	#126	—	13	64	no	—
441	#125	—	13	16	no	—
442	#124	—	13	32	no	—
443	#124	—	13	64	no	—
444	#124	C₂²×D₁₃	1	16	yes	complemented
445	#123	—	13	64	no	—
446	#123	—	13	64	no	—
447	C₂²⋊Q₈	—	13	16	no	—
448	C₂²⋊Q₈	—	13	16	no	—
449	C₂²⋊Q₈	—	13	32	no	—
450	#121	—	13	32	no	—
451	#121	—	13	64	no	—
452	#121	—	13	32	no	—
453	#121	—	13	32	no	—
454	#121	C₂²×D₁₃	1	16	yes	—
455	#121	C₂²×D₁₃	1	16	yes	—
456	#120	—	13	64	no	—
457	C₄×Q₈	—	13	32	no	—
458	C₄×Q₈	—	13	16	no	—
459	C₄×Q₈	—	13	16	no	—
460	C₄×D₄	—	13	64	no	—
461	C₄×D₄	—	13	32	no	—
462	C₄×D₄	—	13	64	no	—
463	C₄×D₄	—	13	16	no	—
464	C₄×D₄	—	13	16	no	—
465	C₄×D₄	—	13	16	no	—
466	C₄×D₄	—	13	16	no	—
467	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
468	C₄×D₄	C₂²×D₁₃	1	16	yes	complemented
469	#117	—	13	16	no	—
470	#117	—	13	32	no	—
471	#117	—	13	32	no	—
472	C₂×C₄⋊C₄	—	13	2	no	—
473	C₂×C₄⋊C₄	—	13	2	no	—
474	C₂×C₄⋊C₄	—	13	2	no	—
475	C₂×C₄⋊C₄	—	13	8	no	—
476	C₂×C₄⋊C₄	—	13	8	no	—
477	C₂×C₄⋊C₄	—	13	32	no	—
478	C₂×C₄⋊C₄	—	13	2	no	—
479	C₂×C₄⋊C₄	—	13	2	no	—
480	C₂×C₄⋊C₄	—	13	4	no	—
481	C₂×C₄⋊C₄	—	13	4	no	—
482	C₂×C₄⋊C₄	—	13	2	no	—
483	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
484	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
485	C₂×C₂²⋊C₄	—	13	4	no	—
486	C₂×C₂²⋊C₄	—	13	8	no	—
487	C₂×C₂²⋊C₄	—	13	4	no	—
488	C₂×C₂²⋊C₄	—	13	4	no	—
489	C₂×C₂²⋊C₄	—	13	16	no	—
490	C₂×C₂²⋊C₄	—	13	8	no	—
491	C₂×C₂²⋊C₄	—	13	8	no	—
492	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
493	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
494	C₂×C₄²	—	13	8	no	—
495	C₂×C₄²	—	13	4	no	—
496	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
497	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
498	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
499	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
500	C₂×C₄²	C₂²×D₁₃	1	8	yes	—
501	C₂×C₁₃	—	2	4	no	—
502	C₂×C₁₃	—	4	8	no	—
503	C₂×C₁₃	#3506	1	4	yes	complemented
504	C₂×C₁₃	C₂³×#41	1	1	yes	characteristic
505	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
506	C₂×C₁₃	C₂×#585	1	1	yes	characteristic
507	D₁₃	—	4	8	no	—
508	C₂⁴	—	13	4	no	—
509	C₂⁴	—	13	8	no	—
510	C₂⁴	—	26	8	no	—
511	C₂⁴	—	52	4	no	—
512	C₂⁴	—	52	4	no	—
513	C₂⁴	C₂³×D₁₃	1	4	yes	—
514	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
515	#41	—	2	64	no	—
516	#41	—	52	64	no	—
517	C₂×Q₈	—	2	8	no	—
518	C₂×Q₈	—	13	8	no	—
519	C₂×Q₈	—	13	8	no	—
520	C₂×Q₈	—	26	8	no	—
521	C₂×Q₈	—	52	4	no	—
522	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
523	C₂×D₄	—	2	16	no	—
524	C₂×D₄	—	2	8	no	—
525	C₂×D₄	—	2	8	no	—
526	C₂×D₄	—	4	4	no	—
527	C₂×D₄	—	13	32	no	—
528	C₂×D₄	—	13	32	no	—
529	C₂×D₄	—	13	8	no	—
530	C₂×D₄	—	13	8	no	—
531	C₂×D₄	—	26	8	no	—
532	C₂×D₄	—	26	8	no	—
533	C₂×D₄	—	26	32	no	—
534	C₂×D₄	—	52	16	no	—
535	C₂×D₄	—	52	16	no	—
536	C₂×D₄	C₂³×D₁₃	1	16	yes	—
537	C₂×D₄	C₂³×D₁₃	1	8	yes	—
538	C₂×D₄	C₂³×D₁₃	1	8	yes	—
539	C₂×D₄	C₂³×D₁₃	1	8	yes	—
540	C₂²×C₄	—	2	16	no	—
541	C₂²×C₄	—	2	4	no	—
542	C₂²×C₄	—	4	2	no	—
543	C₂²×C₄	—	13	4	no	—
544	C₂²×C₄	—	13	4	no	—
545	C₂²×C₄	—	13	4	no	—
546	C₂²×C₄	—	13	8	no	—
547	C₂²×C₄	—	13	32	no	—
548	C₂²×C₄	—	13	16	no	—
549	C₂²×C₄	—	13	16	no	—
550	C₂²×C₄	—	26	16	no	—
551	C₂²×C₄	—	52	32	no	—
552	C₂²×C₄	—	52	8	no	—
553	C₂²×C₄	—	52	4	no	—
554	C₂²×C₄	—	52	16	no	—
555	C₂²×C₄	#6129	1	8	yes	complemented
556	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
557	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
558	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
559	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
560	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
561	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
562	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
563	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
564	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
565	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
566	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
567	C₄⋊C₄	—	13	8	no	—
568	C₄⋊C₄	—	13	8	no	—
569	C₄⋊C₄	—	13	8	no	—
570	C₄⋊C₄	—	13	32	no	—
571	C₄⋊C₄	—	13	8	no	—
572	C₄⋊C₄	—	13	8	no	—
573	C₄⋊C₄	—	13	16	no	—
574	C₄⋊C₄	—	13	16	no	—
575	C₄⋊C₄	—	13	8	no	—
576	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
577	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
578	C₂²⋊C₄	—	13	16	no	—
579	C₂²⋊C₄	—	13	32	no	—
580	C₂²⋊C₄	—	13	16	no	—
581	C₂²⋊C₄	—	13	16	no	—
582	C₂²⋊C₄	—	13	32	no	—
583	C₂²⋊C₄	—	13	32	no	—
584	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
585	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
586	C₄²	—	13	32	no	—
587	C₄²	—	13	16	no	—
588	C₄²	C₂³×D₁₃	1	4	yes	—
589	C₄²	C₂³×D₁₃	1	4	yes	—
590	C₄²	C₂³×D₁₃	1	4	yes	—
591	C₄²	C₂³×D₁₃	1	4	yes	—
592	C₁₃	C₂×#3506	1	1	yes	characteristic, complemented, Sylow
593	C₂³	—	2	2	no	—
594	C₂³	—	2	2	no	—
595	C₂³	—	2	8	no	—
596	C₂³	—	2	8	no	—
597	C₂³	—	2	8	no	—
598	C₂³	—	13	8	no	—
599	C₂³	—	26	16	no	—
600	C₂³	—	26	8	no	—
601	C₂³	—	26	8	no	—
602	C₂³	—	26	8	no	—
603	C₂³	—	52	8	no	—
604	C₂³	—	52	8	no	—
605	C₂³	—	52	32	no	—
606	C₂³	C₂×#6129	1	4	yes	—
607	C₂³	C₂⁴×D₁₃	1	8	yes	—
608	C₂³	C₂⁴×D₁₃	1	2	yes	—
609	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
610	Q₈	—	2	16	no	—
611	Q₈	—	26	16	no	—
612	Q₈	—	52	8	no	—
613	D₄	—	2	32	no	—
614	D₄	—	2	16	no	—
615	D₄	—	2	16	no	—
616	D₄	—	4	8	no	—
617	D₄	—	26	16	no	—
618	D₄	—	26	16	no	—
619	D₄	—	52	32	no	—
620	D₄	—	52	32	no	—
621	C₂×C₄	—	2	8	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	2	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	32	no	—
626	C₂×C₄	—	2	8	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	13	8	no	—
629	C₂×C₄	—	13	8	no	—
630	C₂×C₄	—	13	8	no	—
631	C₂×C₄	—	26	8	no	—
632	C₂×C₄	—	26	8	no	—
633	C₂×C₄	—	26	8	no	—
634	C₂×C₄	—	26	32	no	—
635	C₂×C₄	—	52	16	no	—
636	C₂×C₄	—	52	8	no	—
637	C₂×C₄	—	52	32	no	—
638	C₂×C₄	C₂×#6129	1	4	yes	—
639	C₂×C₄	C₂×#6129	1	4	yes	—
640	C₂×C₄	C₂×#6129	1	16	yes	complemented
641	C₂×C₄	#88256	1	4	yes	—
642	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
643	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
644	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
645	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
646	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
647	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
648	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	2	8	no	—
652	C₂²	—	2	8	no	—
653	C₂²	—	2	8	no	—
654	C₂²	—	2	8	no	—
655	C₂²	—	4	16	no	—
656	C₂²	—	26	8	no	—
657	C₂²	—	26	8	no	—
658	C₂²	—	26	8	no	—
659	C₂²	—	52	32	no	—
660	C₂²	—	52	16	no	—
661	C₂²	C₂²×#6129	1	4	yes	—
662	C₂²	C₂²×#6129	1	2	yes	—
663	C₂²	C₂×#88256	1	2	yes	—
664	C₂²	#11719648	1	2	yes	—
665	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
666	C₄	—	2	8	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	2	no	—
669	C₄	—	2	2	no	—
670	C₄	—	26	8	no	—
671	C₄	—	26	8	no	—
672	C₄	—	26	8	no	—
673	C₄	C₂²×#6129	1	4	yes	—
674	C₄	C₂²×#6129	1	4	yes	—
675	C₄	C₂×#88256	1	4	yes	—
676	C₂	—	2	4	no	—
677	C₂	—	4	8	no	—
678	C₂	—	52	8	no	—
679	C₂	#13128685	1	4	yes	direct product factor
680	C₂	C₂³×#6129	1	1	yes	characteristic
681	C₂	C₂²×#88256	1	1	yes	characteristic
682	C₂	C₂×#11719648	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#532	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#532	D₁₃
hypocenter	C₁₃	C₂×#3506
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #13128685	C₂	direct (N × H)
2. C₂×#11719386	C₂	semidirect
3. C₂×#11719437	C₂	semidirect
4. C₂×#11719268	C₂	semidirect
5. C₂×#11719270	C₂	semidirect
6. C₂×#11719423	C₂	semidirect
7. C₂×#11719260	C₂	semidirect
8. C₂×#11719322	C₂	semidirect
9. C₂×#11719535	C₂	semidirect
10. C₂×#11719175	C₂	semidirect
11. C₂×#11719311	C₂	semidirect
12. C₂×#11719532	C₂	semidirect
13. C₂²×C₄×D₅₂	C₂	semidirect
14. C₂×C₁₃×#532	C₂	semidirect
16. C₂²×#6129	C₂²	semidirect
19. C₁₃×#532	C₂²	semidirect
20. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#127	C₂²	semidirect
22. C₂×C₁₃×#124	C₂²	semidirect
25. C₂×C₄×D₄×C₁₃	C₂²	semidirect
26. C₂×C₄×D₄×C₁₃	C₂²	semidirect
28. #11719535	C₂²	semidirect
29. #11719532	C₂²	semidirect
31. C₂×Q₈×Dic₁₃	C₂²	semidirect
33. C₂×#88193	C₂²	semidirect
34. C₂×#88192	C₂²	semidirect
37. C₂×D₄×Dic₁₃	C₂²	semidirect
42. C₂×#88180	C₂²	semidirect
44. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
47. #11719437	C₂²	semidirect
48. #11719423	C₂²	semidirect
49. #11719386	C₂²	semidirect
50. #11719322	C₂²	semidirect
51. #11719311	C₂²	semidirect
52. #11719270	C₂²	semidirect
53. #11719268	C₂²	semidirect
54. #11719260	C₂²	semidirect
55. C₂×#88152	C₂²	semidirect
56. C₂×#88151	C₂²	semidirect
57. C₂×#88146	C₂²	semidirect
58. C₂×#88140	C₂²	semidirect
59. C₂×#88139	C₂²	semidirect
60. C₂×#88137	C₂²	semidirect
61. C₂×#88135	C₂²	semidirect
66. C₂×C₄×D₅₂	C₂²	semidirect
67. #11719175	C₂²	semidirect
68. C₂×#88124	C₂²	semidirect
69. C₂×#88123	C₂²	semidirect
70. C₂×#88123	C₂²	semidirect
71. C₂×C₄×Dic₂₆	C₂²	semidirect
72. C₂×C₄×Dic₂₆	C₂²	semidirect
90. C₂×#6129	C₂³	semidirect
101. C₁₃×C₄⋊Q₈	C₂³	semidirect
102. C₁₃×#127	C₂³	semidirect
103. C₁₃×#124	C₂³	semidirect
106. C₄×D₄×C₁₃	C₂³	semidirect
107. C₄×D₄×C₁₃	C₂³	semidirect
120. Q₈×Dic₁₃	C₂³	semidirect
122. #88193	C₂³	semidirect
123. #88192	C₂³	semidirect
126. D₄×Dic₁₃	C₂³	semidirect
135. #88180	C₂³	semidirect
144. C₂×C₄⋊Dic₁₃	C₂³	semidirect
151. #88152	C₂³	semidirect
152. #88151	C₂³	semidirect
153. #88146	C₂³	semidirect
154. #88140	C₂³	semidirect
155. #88139	C₂³	semidirect
156. #88137	C₂³	semidirect
157. #88135	C₂³	semidirect
162. #88124	C₂³	semidirect
163. #88123	C₂³	semidirect
164. #88123	C₂³	semidirect
165. C₄×Dic₂₆	C₂³	semidirect
166. C₄×Dic₂₆	C₂³	semidirect
189. C₂²×C₄×C₁₃	#41	semidirect
262. C₂×#532	D₁₃	semidirect
297. C₂×C₄×C₁₃	C₂×#41	semidirect
335. #532	C₂×D₁₃	semidirect
338. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
340. C₂×#127	C₂×D₁₃	semidirect
345. C₂×#124	C₂×D₁₃	semidirect
371. C₂×C₄×D₄	C₂×D₁₃	semidirect
372. C₂×C₄×D₄	C₂×D₁₃	semidirect
437. C₄⋊Q₈	C₂²×D₁₃	semidirect
439. #127	C₂²×D₁₃	semidirect
444. #124	C₂²×D₁₃	semidirect
467. C₄×D₄	C₂²×D₁₃	semidirect
468. C₄×D₄	C₂²×D₁₃	semidirect
503. C₂×C₁₃	#3506	semidirect
555. C₂²×C₄	#6129	semidirect
592. C₁₃	C₂×#3506	semidirect
640. C₂×C₄	C₂×#6129	semidirect
679. C₂	#13128685	direct (N × H)

Maximal subgroups

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

subgroup	index
#13128685	2
C₂×#11719386	2
C₂×#11719437	2
C₂×#11719268	2
C₂×#11719270	2
C₂×#11719423	2
C₂×#11719260	2
C₂×#11719322	2
C₂×#11719535	2
C₂×#11719175	2
C₂×#11719311	2
C₂×#11719532	2
C₂²×C₄×D₅₂	2
C₂×C₁₃×#532	2
C₂×#3506	13

Subgroups — C2×#13128685 #16770867

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13128685 #16770867