Subgroups — C₂×#13129075 #16770154

Order 3328.

8890 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129075	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719371	C₂	1	4	yes	maximal, complemented
3	C₂×#11719270	C₂	1	4	yes	maximal, complemented
4	C₂×D₄×D₅₂	C₂	1	4	yes	maximal, complemented
5	C₂×#11719295	C₂	1	4	yes	maximal, complemented
6	C₂×#11719240	C₂	1	2	yes	maximal, complemented
7	C₂×#11719349	C₂	1	4	yes	maximal, complemented
8	C₂×#11719535	C₂	1	2	yes	maximal, complemented
9	C₂×#11719310	C₂	1	4	yes	maximal, complemented
10	C₂²×#88184	C₂	1	2	yes	maximal, complemented
11	C₂×C₁₃×#525	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₁₃×#41	C₂²	1	1	yes	characteristic, complemented
13	C₂⁴×C₄×C₁₃	C₂²	1	1	yes	characteristic, complemented
14	C₂³×C₂²⋊D₁₃	C₂²	1	4	yes	complemented
15	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
16	C₂³×D₅₂	C₂²	1	2	yes	complemented
17	C₂³×D₅₂	C₂²	1	2	yes	complemented
18	C₁₃×#525	C₂²	1	16	yes	complemented
19	C₂×C₁₃×#123	C₂²	1	2	yes	complemented
20	C₂×C₁₃×C₂²⋊Q₈	C₂²	1	2	yes	complemented
21	C₂×C₁₃×#121	C₂²	1	2	yes	complemented
22	C₂×C₁₃×#120	C₂²	1	2	yes	complemented
23	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
24	C₂×C₁₃×#117	C₂²	1	1	yes	characteristic, complemented
25	#11719535	C₂²	1	32	yes	complemented
26	C₂×#88201	C₂²	1	4	yes	complemented
27	C₂×#88194	C₂²	1	4	yes	complemented
28	C₂×#88193	C₂²	1	8	yes	complemented
29	C₂×#88191	C₂²	1	4	yes	complemented
30	C₂×#88191	C₂²	1	4	yes	complemented
31	C₂×#88184	C₂²	1	4	yes	complemented
32	C₂×#88184	C₂²	1	4	yes	complemented
33	C₂×#88184	C₂²	1	4	yes	complemented
34	C₂×#88184	C₂²	1	4	yes	complemented
35	C₂×#88184	C₂²	1	4	yes	complemented
36	C₂×#88184	C₂²	1	32	yes	complemented
37	C₂²×#6103	C₂²	1	4	yes	complemented
38	C₂×#88180	C₂²	1	2	yes	complemented
39	C₂²×C₄⋊Dic₁₃	C₂²	1	2	yes	complemented
40	#11719371	C₂²	1	64	yes	complemented
41	#11719349	C₂²	1	64	yes	complemented
42	#11719310	C₂²	1	64	yes	complemented
43	#11719295	C₂²	1	64	yes	complemented
44	#11719270	C₂²	1	64	yes	complemented
45	D₄×D₅₂	C₂²	1	64	yes	complemented
46	#11719240	C₂²	1	32	yes	complemented
47	C₂×#88152	C₂²	1	8	yes	complemented
48	C₂×#88149	C₂²	1	8	yes	complemented
49	C₂×#88148	C₂²	1	8	yes	complemented
50	C₂×#88138	C₂²	1	8	yes	complemented
51	C₂×#88137	C₂²	1	8	yes	complemented
52	C₂×#88136	C₂²	1	8	yes	complemented
53	C₂×#88136	C₂²	1	8	yes	complemented
54	C₂×#88135	C₂²	1	8	yes	complemented
55	C₂×#88128	C₂²	1	2	yes	complemented
56	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
57	C₂×#88124	C₂²	1	2	yes	complemented
58	C₂⁵×C₁₃	C₂³	1	1	yes	characteristic
59	C₂⁴×D₁₃	C₂³	1	4	yes	—
60	C₂⁴×D₁₃	C₂³	1	4	yes	—
61	C₂×C₁₃×#41	—	4	4	no	—
62	C₂×C₁₃×#41	C₂³	1	8	yes	complemented
63	C₂²×Q₈×C₁₃	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
65	C₂²×D₄×C₁₃	C₂³	1	1	yes	characteristic
66	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
67	C₂³×C₄×C₁₃	—	4	4	no	—
68	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
69	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
70	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
72	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₁₃	C₂³	1	8	yes	complemented
74	C₂²×C₂²⋊D₁₃	—	4	16	no	—
75	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
76	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
77	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
78	C₂²×C₂²⋊D₁₃	C₂³	1	32	yes	complemented
79	C₂³×Dic₁₃	C₂³	1	4	yes	—
80	C₂×D₄×D₁₃	—	4	32	no	—
81	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
82	C₂²×D₅₂	—	4	8	no	—
83	C₂²×D₅₂	—	4	8	no	—
84	C₂²×D₅₂	C₂³	1	4	yes	—
85	C₂²×D₅₂	C₂³	1	8	yes	—
86	C₂²×D₅₂	C₂³	1	4	yes	—
87	C₂²×D₅₂	C₂³	1	4	yes	—
88	C₂²×D₅₂	C₂³	1	16	yes	complemented
89	C₂²×D₅₂	C₂³	1	16	yes	complemented
90	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
91	C₁₃×#123	C₂³	1	16	yes	complemented
92	C₁₃×C₂²⋊Q₈	C₂³	1	16	yes	complemented
93	C₁₃×#121	C₂³	1	16	yes	complemented
94	C₁₃×#120	C₂³	1	16	yes	complemented
95	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
96	C₁₃×#117	C₂³	1	8	yes	complemented
97	C₂×C₁₃×C₄⋊C₄	C₂³	1	2	yes	—
98	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
99	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
100	C₂×C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
101	C₂×C₁₃×C₂²⋊C₄	C₂³	1	2	yes	—
102	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
103	C₂×C₂²⋊Dic₁₃	C₂³	1	4	yes	—
104	#88201	C₂³	1	32	yes	complemented
105	#88194	C₂³	1	32	yes	complemented
106	#88193	C₂³	1	64	yes	complemented
107	#88191	C₂³	1	32	yes	complemented
108	#88191	C₂³	1	32	yes	complemented
109	#88184	C₂³	1	32	yes	complemented
110	#88184	C₂³	1	32	yes	complemented
111	#88184	C₂³	1	32	yes	complemented
112	#88184	C₂³	1	32	yes	complemented
113	#88184	C₂³	1	32	yes	complemented
114	C₂×#6103	C₂³	1	8	yes	—
115	C₂×#6103	C₂³	1	8	yes	—
116	C₂×#6103	C₂³	1	8	yes	—
117	C₂×#6103	C₂³	1	8	yes	—
118	C₂×#6103	C₂³	1	32	yes	complemented
119	#88180	C₂³	1	16	yes	complemented
120	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
121	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
122	C₂×C₄⋊Dic₁₃	C₂³	1	16	yes	complemented
123	C₂×#6101	C₂³	1	8	yes	—
124	C₂×C₄×Dic₁₃	C₂³	1	4	yes	—
125	#88152	C₂³	1	64	yes	complemented
126	#88149	C₂³	1	64	yes	complemented
127	#88148	C₂³	1	64	yes	complemented
128	#88138	C₂³	1	64	yes	complemented
129	#88137	C₂³	1	64	yes	complemented
130	#88136	C₂³	1	64	yes	complemented
131	#88136	C₂³	1	64	yes	complemented
132	#88135	C₂³	1	64	yes	complemented
133	#88128	C₂³	1	16	yes	complemented
134	C₄×D₅₂	C₂³	1	32	yes	complemented
135	#88124	C₂³	1	16	yes	complemented
136	C₂×#3537	—	13	1	no	maximal, Sylow
137	C₂⁴×C₁₃	—	2	8	no	—
138	C₂⁴×C₁₃	—	4	2	no	—
139	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
140	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
141	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
142	C₂⁴×C₁₃	C₂⁴	1	2	yes	—
143	C₂³×D₁₃	—	2	16	no	—
144	C₂³×D₁₃	—	4	8	no	—
145	C₂³×D₁₃	—	4	8	no	—
146	C₂³×D₁₃	—	4	16	no	—
147	C₂³×D₁₃	—	4	8	no	—
148	C₂³×D₁₃	C₂⁴	1	8	yes	—
149	C₂³×D₁₃	C₂⁴	1	16	yes	—
150	C₂³×D₁₃	C₂⁴	1	16	yes	—
151	C₁₃×#41	—	4	16	no	—
152	C₂×Q₈×C₁₃	—	4	2	no	—
153	C₂×Q₈×C₁₃	C₂⁴	1	4	yes	—
154	C₂×D₄×C₁₃	—	2	16	no	—
155	C₂×D₄×C₁₃	—	4	4	no	—
156	C₂×D₄×C₁₃	—	4	2	no	—
157	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
158	C₂×D₄×C₁₃	C₂⁴	1	4	yes	—
159	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
160	C₂²×C₄×C₁₃	—	2	8	no	—
161	C₂²×C₄×C₁₃	—	2	8	no	—
162	C₂²×C₄×C₁₃	—	2	4	no	—
163	C₂²×C₄×C₁₃	—	4	16	no	—
164	C₂²×C₄×C₁₃	—	4	2	no	—
165	C₂²×C₄×C₁₃	—	4	4	no	—
166	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
169	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
170	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
171	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
174	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
176	C₂×C₂²⋊D₁₃	—	2	32	no	—
177	C₂×C₂²⋊D₁₃	—	4	16	no	—
178	C₂×C₂²⋊D₁₃	—	4	16	no	—
179	C₂×C₂²⋊D₁₃	—	4	64	no	—
180	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
181	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
182	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
183	C₂²×Dic₁₃	—	4	8	no	—
184	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
185	C₂²×Dic₁₃	C₂⁴	1	16	yes	—
186	D₄×D₁₃	—	4	128	no	—
187	C₂×D₅₂	—	2	16	no	—
188	C₂×D₅₂	—	4	32	no	—
189	C₂×D₅₂	—	4	32	no	—
190	C₂×D₅₂	—	4	8	no	—
191	C₂×D₅₂	—	4	8	no	—
192	C₂×D₅₂	—	4	16	no	—
193	C₂×D₅₂	C₂⁴	1	16	yes	—
194	C₂×D₅₂	C₂⁴	1	32	yes	—
195	C₂×D₅₂	C₂⁴	1	16	yes	—
196	C₂×D₅₂	C₂⁴	1	16	yes	—
197	C₂×C₄×D₁₃	—	4	16	no	—
198	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
199	C₁₃×C₄⋊C₄	C₂⁴	1	8	yes	—
200	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
201	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
202	C₁₃×C₂²⋊C₄	C₂⁴	1	16	yes	—
203	C₁₃×C₂²⋊C₄	C₂⁴	1	8	yes	—
204	C₄²×C₁₃	C₂⁴	1	8	yes	—
205	C₂²⋊Dic₁₃	C₂⁴	1	16	yes	—
206	#6103	C₂⁴	1	32	yes	—
207	#6103	C₂⁴	1	32	yes	—
208	#6103	C₂⁴	1	32	yes	—
209	#6103	C₂⁴	1	32	yes	—
210	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
211	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
212	#6101	C₂⁴	1	32	yes	—
213	C₄×Dic₁₃	C₂⁴	1	16	yes	—
214	#3537	—	13	32	no	—
215	C₂×#560	—	13	4	no	—
216	C₂×#553	—	13	4	no	—
217	C₂×D₄²	—	13	4	no	—
218	C₂×D₄²	—	13	4	no	—
219	C₂×#540	—	13	2	no	—
220	C₂×#538	—	13	4	no	—
221	C₂×#535	—	13	2	no	—
222	C₂×#534	—	13	4	no	—
223	C₂×#525	D₁₃	1	1	yes	characteristic, complemented
224	C₂²×#121	—	13	2	no	—
225	C₂³×C₁₃	—	2	4	no	—
226	C₂³×C₁₃	—	2	4	no	—
227	C₂³×C₁₃	—	2	16	no	—
228	C₂³×C₁₃	—	2	4	no	—
229	C₂³×C₁₃	—	2	8	no	—
230	C₂³×C₁₃	—	2	2	no	—
231	C₂³×C₁₃	—	2	4	no	—
232	C₂³×C₁₃	—	4	4	no	—
233	C₂³×C₁₃	—	4	16	no	—
234	C₂³×C₁₃	H(5,𝔽₂)	1	8	yes	—
235	C₂³×C₁₃	C₂⁵	1	4	yes	—
236	C₂³×C₁₃	C₂⁵	1	2	yes	—
237	C₂³×C₁₃	C₂⁵	1	4	yes	—
238	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
239	C₂²×D₁₃	—	2	16	no	—
240	C₂²×D₁₃	—	2	16	no	—
241	C₂²×D₁₃	—	2	16	no	—
242	C₂²×D₁₃	—	2	32	no	—
243	C₂²×D₁₃	—	4	16	no	—
244	C₂²×D₁₃	—	4	16	no	—
245	C₂²×D₁₃	—	4	32	no	—
246	C₂²×D₁₃	—	4	16	no	—
247	C₂²×D₁₃	—	8	32	no	—
248	C₂²×D₁₃	—	8	32	no	—
249	C₂²×D₁₃	C₂⁵	1	16	yes	—
250	Q₈×C₁₃	—	4	4	no	—
251	D₄×C₁₃	—	2	32	no	—
252	D₄×C₁₃	—	4	8	no	—
253	D₄×C₁₃	—	4	4	no	—
254	C₂×C₄×C₁₃	—	2	8	no	—
255	C₂×C₄×C₁₃	—	2	4	no	—
256	C₂×C₄×C₁₃	—	2	4	no	—
257	C₂×C₄×C₁₃	—	2	2	no	—
258	C₂×C₄×C₁₃	—	2	16	no	—
259	C₂×C₄×C₁₃	—	2	16	no	—
260	C₂×C₄×C₁₃	—	2	8	no	—
261	C₂×C₄×C₁₃	—	4	4	no	—
262	C₂×C₄×C₁₃	—	4	8	no	—
263	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
264	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
265	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
266	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
267	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
268	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
269	C₂²⋊D₁₃	—	2	64	no	—
270	C₂²⋊D₁₃	—	4	32	no	—
271	C₂²⋊D₁₃	—	4	32	no	—
272	C₂×Dic₁₃	—	2	16	no	—
273	C₂×Dic₁₃	—	4	16	no	—
274	C₂×Dic₁₃	C₂⁵	1	16	yes	—
275	D₅₂	—	2	32	no	—
276	D₅₂	—	4	16	no	—
277	D₅₂	—	4	16	no	—
278	D₅₂	—	4	32	no	—
279	C₄×D₁₃	—	4	32	no	—
280	C₂²×#41	C₂×D₁₃	1	1	yes	characteristic, complemented
281	C₂³×D₄	—	13	4	no	—
282	C₂³×D₄	—	13	8	no	—
283	C₂³×D₄	—	13	2	no	—
284	C₂³×D₄	—	13	2	no	—
285	C₂⁴×C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
286	#560	—	13	64	no	—
287	#553	—	13	64	no	—
288	D₄²	—	13	64	no	—
289	D₄²	—	13	64	no	—
290	#540	—	13	32	no	—
291	#538	—	13	64	no	—
292	#535	—	13	32	no	—
293	#534	—	13	64	no	—
294	C₂×#127	—	13	4	no	—
295	C₂×#127	—	13	2	no	—
296	C₂×#126	—	13	8	no	—
297	C₂×#125	—	13	2	no	—
298	C₂×#124	—	13	4	no	—
299	#525	C₂×D₁₃	1	16	yes	complemented
300	C₂×#123	—	13	8	no	—
301	C₂×#123	—	13	8	no	—
302	C₂×#123	C₂×D₁₃	1	2	yes	complemented
303	C₂×C₂²⋊Q₈	C₂×D₁₃	1	2	yes	complemented
304	C₂×#121	—	13	8	no	—
305	C₂×#121	—	13	4	no	—
306	C₂×#121	—	13	4	no	—
307	C₂×#121	—	13	4	no	—
308	C₂×#121	—	13	4	no	—
309	C₂×#121	—	13	4	no	—
310	C₂×#121	—	13	32	no	—
311	C₂×#121	—	13	8	no	—
312	C₂×#121	—	13	8	no	—
313	C₂×#121	C₂×D₁₃	1	2	yes	complemented
314	C₂×#120	—	13	4	no	—
315	C₂×#120	—	13	4	no	—
316	C₂×#120	—	13	8	no	—
317	C₂×#120	—	13	8	no	—
318	C₂×#120	C₂×D₁₃	1	2	yes	complemented
319	C₂×C₄×D₄	—	13	8	no	—
320	C₂×C₄×D₄	—	13	4	no	—
321	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
322	C₂×#117	—	13	2	no	—
323	C₂×#117	C₂×D₁₃	1	1	yes	characteristic, complemented
324	C₂²×C₄⋊C₄	—	13	2	no	—
325	C₂²×C₂²⋊C₄	—	13	4	no	—
326	C₂²×C₁₃	—	2	4	no	—
327	C₂²×C₁₃	—	2	4	no	—
328	C₂²×C₁₃	—	2	16	no	—
329	C₂²×C₁₃	—	2	4	no	—
330	C₂²×C₁₃	—	2	8	no	—
331	C₂²×C₁₃	—	2	2	no	—
332	C₂²×C₁₃	—	2	4	no	—
333	C₂²×C₁₃	—	4	16	no	—
334	C₂²×C₁₃	—	4	8	no	—
335	C₂²×C₁₃	—	4	4	no	—
336	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
337	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
338	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
339	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
340	C₂×D₁₃	—	2	16	no	—
341	C₂×D₁₃	—	2	16	no	—
342	C₂×D₁₃	—	2	16	no	—
343	C₂×D₁₃	—	4	32	no	—
344	C₂×D₁₃	—	8	32	no	—
345	C₂×D₁₃	—	8	32	no	—
346	C₄×C₁₃	—	2	8	no	—
347	C₄×C₁₃	—	2	4	no	—
348	C₄×C₁₃	—	2	4	no	—
349	C₄×C₁₃	—	2	2	no	—
350	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
351	Dic₁₃	—	2	16	no	—
352	C₂⁵	—	13	4	no	—
353	C₂⁵	—	13	4	no	—
354	C₂⁵	C₂²×D₁₃	1	1	yes	characteristic
355	C₂×#41	—	4	4	no	—
356	C₂×#41	C₂²×D₁₃	1	8	yes	complemented
357	C₂²×Q₈	C₂²×D₁₃	1	1	yes	characteristic
358	C₂²×D₄	—	13	8	no	—
359	C₂²×D₄	—	13	8	no	—
360	C₂²×D₄	—	13	8	no	—
361	C₂²×D₄	—	13	32	no	—
362	C₂²×D₄	—	13	64	no	—
363	C₂²×D₄	—	13	4	no	—
364	C₂²×D₄	—	13	4	no	—
365	C₂²×D₄	—	13	8	no	—
366	C₂²×D₄	—	13	4	no	—
367	C₂²×D₄	—	13	16	no	—
368	C₂²×D₄	—	13	16	no	—
369	C₂²×D₄	—	52	8	no	—
370	C₂²×D₄	—	52	8	no	—
371	C₂²×D₄	—	52	32	no	—
372	C₂²×D₄	—	52	16	no	—
373	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
374	C₂²×D₄	C₂²×D₁₃	1	1	yes	characteristic
375	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
376	C₂³×C₄	—	4	4	no	—
377	C₂³×C₄	—	13	4	no	—
378	C₂³×C₄	—	13	8	no	—
379	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
380	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
381	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
382	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
383	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
384	C₂³×C₄	C₂²×D₁₃	1	8	yes	complemented
385	#127	—	13	32	no	—
386	#127	—	13	16	no	—
387	#126	—	13	64	no	—
388	#125	—	13	16	no	—
389	#124	—	13	32	no	—
390	#123	—	13	64	no	—
391	#123	—	13	64	no	—
392	#123	C₂²×D₁₃	1	16	yes	complemented
393	C₂²⋊Q₈	C₂²×D₁₃	1	16	yes	complemented
394	#121	—	13	64	no	—
395	#121	—	13	32	no	—
396	#121	—	13	32	no	—
397	#121	—	13	32	no	—
398	#121	—	13	32	no	—
399	#121	—	13	32	no	—
400	#121	—	13	64	no	—
401	#121	—	13	64	no	—
402	#121	C₂²×D₁₃	1	16	yes	complemented
403	#120	—	13	32	no	—
404	#120	—	13	32	no	—
405	#120	—	13	64	no	—
406	#120	—	13	64	no	—
407	#120	C₂²×D₁₃	1	16	yes	complemented
408	C₄×D₄	—	13	64	no	—
409	C₄×D₄	—	13	32	no	—
410	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
411	#117	—	13	16	no	—
412	#117	C₂²×D₁₃	1	8	yes	complemented
413	C₂×C₄⋊C₄	—	13	4	no	—
414	C₂×C₄⋊C₄	—	13	4	no	—
415	C₂×C₄⋊C₄	—	13	16	no	—
416	C₂×C₄⋊C₄	—	13	8	no	—
417	C₂×C₄⋊C₄	C₂²×D₁₃	1	2	yes	—
418	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
419	C₂×C₂²⋊C₄	—	13	4	no	—
420	C₂×C₂²⋊C₄	—	13	8	no	—
421	C₂×C₂²⋊C₄	—	13	8	no	—
422	C₂×C₂²⋊C₄	—	13	32	no	—
423	C₂×C₂²⋊C₄	—	13	8	no	—
424	C₂×C₂²⋊C₄	—	13	8	no	—
425	C₂×C₂²⋊C₄	C₂²×D₁₃	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
428	C₂×C₄²	—	13	4	no	—
429	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
430	C₂×C₁₃	—	2	8	no	—
431	C₂×C₁₃	—	4	4	no	—
432	C₂×C₁₃	—	4	2	no	—
433	C₂×C₁₃	#3537	1	4	yes	complemented
434	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
436	D₁₃	—	4	16	no	—
437	C₂⁴	—	2	8	no	—
438	C₂⁴	—	4	2	no	—
439	C₂⁴	—	13	8	no	—
440	C₂⁴	—	13	16	no	—
441	C₂⁴	—	13	16	no	—
442	C₂⁴	—	26	16	no	—
443	C₂⁴	—	52	8	no	—
444	C₂⁴	—	52	8	no	—
445	C₂⁴	—	52	8	no	—
446	C₂⁴	—	52	16	no	—
447	C₂⁴	C₂³×D₁₃	1	2	yes	—
448	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
449	C₂⁴	C₂³×D₁₃	1	4	yes	—
450	C₂⁴	C₂³×D₁₃	1	2	yes	—
451	#41	—	4	16	no	—
452	C₂×Q₈	—	4	2	no	—
453	C₂×Q₈	C₂³×D₁₃	1	4	yes	—
454	C₂×D₄	—	2	16	no	—
455	C₂×D₄	—	4	2	no	—
456	C₂×D₄	—	4	4	no	—
457	C₂×D₄	—	13	32	no	—
458	C₂×D₄	—	13	32	no	—
459	C₂×D₄	—	13	32	no	—
460	C₂×D₄	—	13	16	no	—
461	C₂×D₄	—	13	16	no	—
462	C₂×D₄	—	13	32	no	—
463	C₂×D₄	—	13	16	no	—
464	C₂×D₄	—	26	32	no	—
465	C₂×D₄	—	26	16	no	—
466	C₂×D₄	—	52	32	no	—
467	C₂×D₄	—	52	32	no	—
468	C₂×D₄	—	52	8	no	—
469	C₂×D₄	—	52	8	no	—
470	C₂×D₄	—	52	16	no	—
471	C₂×D₄	—	52	16	no	—
472	C₂×D₄	—	52	16	no	—
473	C₂×D₄	—	52	128	no	—
474	C₂×D₄	—	52	64	no	—
475	C₂×D₄	C₂³×D₁₃	1	16	yes	—
476	C₂×D₄	C₂³×D₁₃	1	4	yes	—
477	C₂×D₄	C₂³×D₁₃	1	8	yes	—
478	C₂²×C₄	—	2	8	no	—
479	C₂²×C₄	—	2	4	no	—
480	C₂²×C₄	—	2	8	no	—
481	C₂²×C₄	—	4	16	no	—
482	C₂²×C₄	—	4	4	no	—
483	C₂²×C₄	—	4	2	no	—
484	C₂²×C₄	—	13	8	no	—
485	C₂²×C₄	—	13	16	no	—
486	C₂²×C₄	—	13	32	no	—
487	C₂²×C₄	—	52	16	no	—
488	C₂²×C₄	—	52	8	no	—
489	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
490	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
491	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
492	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
493	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
494	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
495	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
496	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
497	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
498	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
499	C₄⋊C₄	—	13	16	no	—
500	C₄⋊C₄	—	13	16	no	—
501	C₄⋊C₄	—	13	32	no	—
502	C₄⋊C₄	C₂³×D₁₃	1	8	yes	—
503	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
504	C₂²⋊C₄	—	13	16	no	—
505	C₂²⋊C₄	—	13	32	no	—
506	C₂²⋊C₄	—	13	32	no	—
507	C₂²⋊C₄	—	13	32	no	—
508	C₂²⋊C₄	—	13	32	no	—
509	C₂²⋊C₄	C₂³×D₁₃	1	8	yes	—
510	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
511	C₂²⋊C₄	C₂³×D₁₃	1	16	yes	—
512	C₄²	—	13	16	no	—
513	C₄²	C₂³×D₁₃	1	8	yes	—
514	C₁₃	C₂×#3537	1	1	yes	characteristic, complemented, Sylow
515	C₂³	—	2	4	no	—
516	C₂³	—	2	4	no	—
517	C₂³	—	2	2	no	—
518	C₂³	—	2	4	no	—
519	C₂³	—	2	8	no	—
520	C₂³	—	2	16	no	—
521	C₂³	—	2	4	no	—
522	C₂³	—	4	4	no	—
523	C₂³	—	4	16	no	—
524	C₂³	—	13	16	no	—
525	C₂³	—	26	16	no	—
526	C₂³	—	26	16	no	—
527	C₂³	—	26	16	no	—
528	C₂³	—	26	32	no	—
529	C₂³	—	52	16	no	—
530	C₂³	—	52	16	no	—
531	C₂³	—	52	16	no	—
532	C₂³	—	52	32	no	—
533	C₂³	—	104	32	no	—
534	C₂³	—	104	32	no	—
535	C₂³	#88256	1	8	yes	—
536	C₂³	C₂⁴×D₁₃	1	4	yes	—
537	C₂³	C₂⁴×D₁₃	1	2	yes	—
538	C₂³	C₂⁴×D₁₃	1	4	yes	—
539	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
540	Q₈	—	4	4	no	—
541	D₄	—	2	32	no	—
542	D₄	—	4	4	no	—
543	D₄	—	4	8	no	—
544	D₄	—	26	64	no	—
545	D₄	—	26	32	no	—
546	D₄	—	52	16	no	—
547	D₄	—	52	16	no	—
548	D₄	—	52	32	no	—
549	D₄	—	52	32	no	—
550	D₄	—	52	32	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	4	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	16	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	16	no	—
558	C₂×C₄	—	4	8	no	—
559	C₂×C₄	—	4	4	no	—
560	C₂×C₄	—	13	16	no	—
561	C₂×C₄	—	26	16	no	—
562	C₂×C₄	—	52	32	no	—
563	C₂×C₄	—	52	16	no	—
564	C₂×C₄	#88251	1	4	yes	—
565	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
566	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
567	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
568	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
569	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
570	C₂²	—	2	16	no	—
571	C₂²	—	2	4	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	2	no	—
574	C₂²	—	2	4	no	—
575	C₂²	—	2	8	no	—
576	C₂²	—	2	4	no	—
577	C₂²	—	4	16	no	—
578	C₂²	—	4	4	no	—
579	C₂²	—	4	8	no	—
580	C₂²	—	26	16	no	—
581	C₂²	—	26	16	no	—
582	C₂²	—	26	16	no	—
583	C₂²	—	52	32	no	—
584	C₂²	—	104	32	no	—
585	C₂²	—	104	32	no	—
586	C₂²	C₂×#88251	1	2	yes	—
587	C₂²	C₂×#88256	1	8	yes	—
588	C₂²	C₂×#88256	1	4	yes	—
589	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	4	no	—
593	C₄	—	2	8	no	—
594	C₄	—	26	16	no	—
595	C₄	C₂×#88251	1	4	yes	—
596	C₂	—	2	8	no	—
597	C₂	—	4	2	no	—
598	C₂	—	4	4	no	—
599	C₂	—	52	16	no	—
600	C₂	#13129075	1	4	yes	direct product factor
601	C₂	C₂²×#88251	1	1	yes	characteristic
602	C₂	C₂²×#88256	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁶
Frattini	C₂²	C₂⁵×D₁₃
Fitting	C₂×C₁₃×#525	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#525	D₁₃
hypocenter	C₁₃	C₂×#3537
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#525

Complements

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

N	H ≅ G/N	type
1. #13129075	C₂	direct (N × H)
2. C₂×#11719371	C₂	semidirect
3. C₂×#11719270	C₂	semidirect
4. C₂×D₄×D₅₂	C₂	semidirect
5. C₂×#11719295	C₂	semidirect
6. C₂×#11719240	C₂	semidirect
7. C₂×#11719349	C₂	semidirect
8. C₂×#11719535	C₂	semidirect
9. C₂×#11719310	C₂	semidirect
10. C₂²×#88184	C₂	semidirect
11. C₂×C₁₃×#525	C₂	semidirect
12. C₂²×C₁₃×#41	C₂²	semidirect
13. C₂⁴×C₄×C₁₃	C₂²	semidirect
14. C₂³×C₂²⋊D₁₃	C₂²	semidirect
15. C₂²×D₄×D₁₃	C₂²	semidirect
16. C₂³×D₅₂	C₂²	semidirect
17. C₂³×D₅₂	C₂²	semidirect
18. C₁₃×#525	C₂²	semidirect
19. C₂×C₁₃×#123	C₂²	semidirect
20. C₂×C₁₃×C₂²⋊Q₈	C₂²	semidirect
21. C₂×C₁₃×#121	C₂²	semidirect
22. C₂×C₁₃×#120	C₂²	semidirect
23. C₂×C₄×D₄×C₁₃	C₂²	semidirect
24. C₂×C₁₃×#117	C₂²	semidirect
25. #11719535	C₂²	semidirect
26. C₂×#88201	C₂²	semidirect
27. C₂×#88194	C₂²	semidirect
28. C₂×#88193	C₂²	semidirect
29. C₂×#88191	C₂²	semidirect
30. C₂×#88191	C₂²	semidirect
31. C₂×#88184	C₂²	semidirect
32. C₂×#88184	C₂²	semidirect
33. C₂×#88184	C₂²	semidirect
34. C₂×#88184	C₂²	semidirect
35. C₂×#88184	C₂²	semidirect
36. C₂×#88184	C₂²	semidirect
37. C₂²×#6103	C₂²	semidirect
38. C₂×#88180	C₂²	semidirect
39. C₂²×C₄⋊Dic₁₃	C₂²	semidirect
40. #11719371	C₂²	semidirect
41. #11719349	C₂²	semidirect
42. #11719310	C₂²	semidirect
43. #11719295	C₂²	semidirect
44. #11719270	C₂²	semidirect
45. D₄×D₅₂	C₂²	semidirect
46. #11719240	C₂²	semidirect
47. C₂×#88152	C₂²	semidirect
48. C₂×#88149	C₂²	semidirect
49. C₂×#88148	C₂²	semidirect
50. C₂×#88138	C₂²	semidirect
51. C₂×#88137	C₂²	semidirect
52. C₂×#88136	C₂²	semidirect
53. C₂×#88136	C₂²	semidirect
54. C₂×#88135	C₂²	semidirect
55. C₂×#88128	C₂²	semidirect
56. C₂×C₄×D₅₂	C₂²	semidirect
57. C₂×#88124	C₂²	semidirect
62. C₂×C₁₃×#41	C₂³	semidirect
73. C₂³×C₄×C₁₃	C₂³	semidirect
78. C₂²×C₂²⋊D₁₃	C₂³	semidirect
81. C₂×D₄×D₁₃	C₂³	semidirect
88. C₂²×D₅₂	C₂³	semidirect
89. C₂²×D₅₂	C₂³	semidirect
91. C₁₃×#123	C₂³	semidirect
92. C₁₃×C₂²⋊Q₈	C₂³	semidirect
93. C₁₃×#121	C₂³	semidirect
94. C₁₃×#120	C₂³	semidirect
95. C₄×D₄×C₁₃	C₂³	semidirect
96. C₁₃×#117	C₂³	semidirect
104. #88201	C₂³	semidirect
105. #88194	C₂³	semidirect
106. #88193	C₂³	semidirect
107. #88191	C₂³	semidirect
108. #88191	C₂³	semidirect
109. #88184	C₂³	semidirect
110. #88184	C₂³	semidirect
111. #88184	C₂³	semidirect
112. #88184	C₂³	semidirect
113. #88184	C₂³	semidirect
118. C₂×#6103	C₂³	semidirect
119. #88180	C₂³	semidirect
122. C₂×C₄⋊Dic₁₃	C₂³	semidirect
125. #88152	C₂³	semidirect
126. #88149	C₂³	semidirect
127. #88148	C₂³	semidirect
128. #88138	C₂³	semidirect
129. #88137	C₂³	semidirect
130. #88136	C₂³	semidirect
131. #88136	C₂³	semidirect
132. #88135	C₂³	semidirect
133. #88128	C₂³	semidirect
134. C₄×D₅₂	C₂³	semidirect
135. #88124	C₂³	semidirect
223. C₂×#525	D₁₃	semidirect
280. C₂²×#41	C₂×D₁₃	semidirect
285. C₂⁴×C₄	C₂×D₁₃	semidirect
299. #525	C₂×D₁₃	semidirect
302. C₂×#123	C₂×D₁₃	semidirect
303. C₂×C₂²⋊Q₈	C₂×D₁₃	semidirect
313. C₂×#121	C₂×D₁₃	semidirect
318. C₂×#120	C₂×D₁₃	semidirect
321. C₂×C₄×D₄	C₂×D₁₃	semidirect
323. C₂×#117	C₂×D₁₃	semidirect
356. C₂×#41	C₂²×D₁₃	semidirect
384. C₂³×C₄	C₂²×D₁₃	semidirect
392. #123	C₂²×D₁₃	semidirect
393. C₂²⋊Q₈	C₂²×D₁₃	semidirect
402. #121	C₂²×D₁₃	semidirect
407. #120	C₂²×D₁₃	semidirect
410. C₄×D₄	C₂²×D₁₃	semidirect
412. #117	C₂²×D₁₃	semidirect
433. C₂×C₁₃	#3537	semidirect
514. C₁₃	C₂×#3537	semidirect
600. C₂	#13129075	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129075	2
C₂×#11719371	2
C₂×#11719270	2
C₂×D₄×D₅₂	2
C₂×#11719295	2
C₂×#11719240	2
C₂×#11719349	2
C₂×#11719535	2
C₂×#11719310	2
C₂²×#88184	2
C₂×C₁₃×#525	2
C₂×#3537	13

Subgroups — C2×#13129075 #16770154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129075 #16770154