Subgroups — C₂×#13129241 #16770722

Order 3328.

8802 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13129241	C₂	1	32	yes	maximal, direct product factor
2	C₂×#11719388	C₂	1	4	yes	maximal, complemented
3	C₂×#11719439	C₂	1	2	yes	maximal, complemented
4	C₂×#11719268	C₂	1	4	yes	maximal, complemented
5	C₂×D₄×D₅₂	C₂	1	4	yes	maximal, complemented
6	C₂×#11719422	C₂	1	2	yes	maximal, complemented
7	C₂×#11719312	C₂	1	8	yes	maximal, complemented
8	C₂×#11719535	C₂	1	4	yes	maximal, complemented
9	C₂×#11719182	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₃×#532	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₁₃×#41	C₂²	1	2	yes	complemented
12	C₂²×D₄×D₁₃	C₂²	1	8	yes	complemented
13	C₂²×#6127	C₂²	1	4	yes	complemented
14	C₂³×D₅₂	C₂²	1	4	yes	complemented
15	C₁₃×#532	C₂²	1	16	yes	complemented
16	C₂×C₁₃×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₁₃×#127	C₂²	1	1	yes	characteristic
18	C₂×C₁₃×#124	C₂²	1	2	yes	complemented
19	C₂×C₁₃×#121	C₂²	1	4	yes	complemented
20	C₂×C₄×D₄×C₁₃	C₂²	1	4	yes	complemented
21	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
22	#11719535	C₂²	1	64	yes	complemented
23	C₂×#88201	C₂²	1	8	yes	complemented
24	C₂×#88194	C₂²	1	8	yes	complemented
25	C₂×#88192	C₂²	1	8	yes	complemented
26	C₂×#88191	C₂²	1	8	yes	complemented
27	C₂×#88191	C₂²	1	8	yes	complemented
28	C₂×#88184	C₂²	1	8	yes	complemented
29	C₂×#88184	C₂²	1	4	yes	complemented
30	C₂×#88184	C₂²	1	4	yes	complemented
31	C₂×#88180	C₂²	1	4	yes	complemented
32	#11719439	C₂²	1	32	yes	complemented
33	#11719422	C₂²	1	32	yes	complemented
34	#11719388	C₂²	1	64	yes	complemented
35	#11719312	C₂²	1	128	yes	complemented
36	#11719268	C₂²	1	64	yes	complemented
37	D₄×D₅₂	C₂²	1	64	yes	complemented
38	C₂×#88149	C₂²	1	8	yes	complemented
39	C₂×#88146	C₂²	1	8	yes	complemented
40	C₂×#88139	C₂²	1	16	yes	complemented
41	C₂×#88136	C₂²	1	16	yes	complemented
42	#11719182	C₂²	1	32	yes	complemented
43	C₂×#88129	C₂²	1	4	yes	complemented
44	C₂×#88128	C₂²	1	2	yes	—
45	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
46	C₂×C₄×D₅₂	C₂²	1	4	yes	complemented
47	C₂×#88123	C₂²	1	2	yes	complemented
48	C₂⁴×D₁₃	C₂³	1	8	yes	—
49	C₂×C₁₃×#41	—	4	8	no	—
50	C₂×C₁₃×#41	C₂³	1	16	yes	complemented
51	C₂²×Q₈×C₁₃	C₂³	1	2	yes	—
52	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
53	C₂²×D₄×C₁₃	C₂³	1	2	yes	—
54	C₂²×D₄×C₁₃	C₂³	1	4	yes	—
55	C₂³×C₄×C₁₃	C₂³	1	4	yes	—
56	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₁₃	C₂³	1	2	yes	—
58	C₂²×C₂²⋊D₁₃	C₂³	1	16	yes	—
59	C₂²×C₂²⋊D₁₃	C₂³	1	8	yes	—
60	C₂×D₄×D₁₃	—	4	32	no	—
61	C₂×D₄×D₁₃	C₂³	1	64	yes	complemented
62	C₂×#6127	—	4	16	no	—
63	C₂×#6127	C₂³	1	32	yes	complemented
64	C₂²×D₅₂	—	4	16	no	—
65	C₂²×D₅₂	C₂³	1	4	yes	—
66	C₂²×D₅₂	C₂³	1	4	yes	—
67	C₂²×D₅₂	C₂³	1	4	yes	—
68	C₂²×D₅₂	C₂³	1	8	yes	—
69	C₂²×D₅₂	C₂³	1	32	yes	complemented
70	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
71	C₂²×Dic₂₆	C₂³	1	4	yes	—
72	C₁₃×C₄⋊Q₈	C₂³	1	8	yes	complemented
73	C₁₃×#127	C₂³	1	8	yes	—
74	C₁₃×#124	C₂³	1	16	yes	complemented
75	C₁₃×#121	C₂³	1	32	yes	complemented
76	C₄×D₄×C₁₃	C₂³	1	32	yes	complemented
77	C₂×C₁₃×C₄⋊C₄	C₂³	1	4	yes	—
78	C₂×C₁₃×C₂²⋊C₄	C₂³	1	8	yes	—
79	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
80	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₁₃	C₂³	1	8	yes	complemented
83	C₂×C₂²⋊Dic₁₃	C₂³	1	8	yes	—
84	#88201	C₂³	1	64	yes	complemented
85	#88194	C₂³	1	64	yes	complemented
86	#88192	C₂³	1	64	yes	complemented
87	#88191	C₂³	1	64	yes	complemented
88	#88191	C₂³	1	64	yes	complemented
89	#88184	C₂³	1	32	yes	complemented
90	#88184	C₂³	1	32	yes	complemented
91	#88184	C₂³	1	64	yes	complemented
92	C₂×#6103	C₂³	1	8	yes	—
93	C₂×#6103	C₂³	1	8	yes	—
94	C₂×#6103	C₂³	1	16	yes	—
95	#88180	C₂³	1	32	yes	complemented
96	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
97	C₂×C₄⋊Dic₁₃	C₂³	1	4	yes	—
98	C₂×C₄×Dic₁₃	C₂³	1	8	yes	—
99	#88149	C₂³	1	64	yes	complemented
100	#88146	C₂³	1	64	yes	complemented
101	#88139	C₂³	1	128	yes	complemented
102	#88136	C₂³	1	128	yes	complemented
103	#88129	C₂³	1	32	yes	complemented
104	#88128	C₂³	1	16	yes	—
105	C₄×D₅₂	C₂³	1	32	yes	complemented
106	C₄×D₅₂	C₂³	1	32	yes	complemented
107	#88123	C₂³	1	16	yes	complemented
108	C₂×#3549	—	13	1	no	maximal, Sylow
109	C₂⁴×C₁₃	C₂⁴	1	4	yes	—
110	C₂⁴×C₁₃	C₂⁴	1	1	yes	characteristic
111	C₂³×D₁₃	—	4	16	no	—
112	C₂³×D₁₃	—	4	32	no	—
113	C₂³×D₁₃	C₂⁴	1	8	yes	—
114	C₂³×D₁₃	C₂⁴	1	32	yes	—
115	C₁₃×#41	—	4	32	no	—
116	C₂×Q₈×C₁₃	—	4	4	no	—
117	C₂×Q₈×C₁₃	C₂⁴	1	8	yes	—
118	C₂×D₄×C₁₃	—	2	16	no	—
119	C₂×D₄×C₁₃	—	4	8	no	—
120	C₂×D₄×C₁₃	—	4	4	no	—
121	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
122	C₂×D₄×C₁₃	C₂⁴	1	8	yes	—
123	C₂×D₄×C₁₃	C₂⁴	1	16	yes	—
124	C₂²×C₄×C₁₃	—	2	16	no	—
125	C₂²×C₄×C₁₃	—	2	8	no	—
126	C₂²×C₄×C₁₃	—	2	4	no	—
127	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
128	C₂²×C₄×C₁₃	C₂⁴	1	16	yes	—
129	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
130	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
131	C₂²×C₄×C₁₃	C₂⁴	1	4	yes	—
132	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
133	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
134	C₂²×C₄×C₁₃	C₂⁴	1	2	yes	—
135	C₂×C₂²⋊D₁₃	—	4	16	no	—
136	C₂×C₂²⋊D₁₃	—	4	32	no	—
137	C₂×C₂²⋊D₁₃	C₂⁴	1	64	yes	—
138	C₂×C₂²⋊D₁₃	C₂⁴	1	32	yes	—
139	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
140	D₄×D₁₃	—	4	128	no	—
141	#6127	—	4	64	no	—
142	C₂×D₅₂	—	2	16	no	—
143	C₂×D₅₂	—	2	16	no	—
144	C₂×D₅₂	—	4	64	no	—
145	C₂×D₅₂	—	4	16	no	—
146	C₂×D₅₂	—	4	8	no	—
147	C₂×D₅₂	C₂⁴	1	16	yes	—
148	C₂×D₅₂	C₂⁴	1	16	yes	—
149	C₂×D₅₂	C₂⁴	1	16	yes	—
150	C₂×D₅₂	C₂⁴	1	32	yes	—
151	C₂×C₄×D₁₃	—	2	32	no	—
152	C₂×C₄×D₁₃	C₂⁴	1	32	yes	—
153	C₂×Dic₂₆	—	4	8	no	—
154	C₂×Dic₂₆	C₂⁴	1	16	yes	—
155	C₁₃×C₄⋊C₄	C₂⁴	1	16	yes	—
156	C₁₃×C₂²⋊C₄	C₂⁴	1	32	yes	—
157	C₄²×C₁₃	C₂⁴	1	8	yes	—
158	C₄²×C₁₃	C₂⁴	1	4	yes	—
159	C₄²×C₁₃	C₂⁴	1	4	yes	—
160	C₂²⋊Dic₁₃	C₂⁴	1	32	yes	—
161	#6103	C₂⁴	1	32	yes	—
162	#6103	C₂⁴	1	32	yes	—
163	#6103	C₂⁴	1	64	yes	—
164	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
165	C₄⋊Dic₁₃	C₂⁴	1	16	yes	—
166	C₄×Dic₁₃	C₂⁴	1	32	yes	—
167	#3549	—	13	32	no	—
168	C₂×H(3,𝔽₄)	—	13	4	no	—
169	C₂×#555	—	13	2	no	—
170	C₂×#555	—	13	4	no	—
171	C₂×D₄²	—	13	2	no	—
172	C₂×D₄²	—	13	4	no	—
173	C₂×#535	—	13	4	no	—
174	C₂×#535	—	13	8	no	—
175	C₂×#532	—	13	2	no	—
176	C₂×#532	D₁₃	1	1	yes	characteristic, complemented
177	C₂³×C₁₃	—	2	4	no	—
178	C₂³×C₁₃	—	2	16	no	—
179	C₂³×C₁₃	—	2	2	no	—
180	C₂³×C₁₃	—	2	8	no	—
181	C₂³×C₁₃	C₂⁵	1	8	yes	—
182	C₂³×C₁₃	C₂⁵	1	2	yes	—
183	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
184	C₂²×D₁₃	—	2	16	no	—
185	C₂²×D₁₃	—	2	16	no	—
186	C₂²×D₁₃	—	2	16	no	—
187	C₂²×D₁₃	—	4	32	no	—
188	C₂²×D₁₃	—	4	64	no	—
189	C₂²×D₁₃	—	8	64	no	—
190	C₂²×D₁₃	C₂⁵	1	16	yes	—
191	Q₈×C₁₃	—	4	8	no	—
192	D₄×C₁₃	—	2	32	no	—
193	D₄×C₁₃	—	4	16	no	—
194	D₄×C₁₃	—	4	8	no	—
195	C₂×C₄×C₁₃	—	2	4	no	—
196	C₂×C₄×C₁₃	—	2	8	no	—
197	C₂×C₄×C₁₃	—	2	2	no	—
198	C₂×C₄×C₁₃	—	2	32	no	—
199	C₂×C₄×C₁₃	—	2	16	no	—
200	C₂×C₄×C₁₃	—	2	8	no	—
201	C₂×C₄×C₁₃	H(5,𝔽₂)	1	4	yes	—
202	C₂×C₄×C₁₃	H(5,𝔽₂)	1	8	yes	—
203	C₂×C₄×C₁₃	C₂⁵	1	8	yes	—
204	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
205	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
206	C₂×C₄×C₁₃	C₂⁵	1	2	yes	—
207	C₂×C₄×C₁₃	C₂⁵	1	4	yes	—
208	C₂²⋊D₁₃	—	4	32	no	—
209	C₂²⋊D₁₃	—	4	64	no	—
210	C₂×Dic₁₃	—	2	16	no	—
211	C₂×Dic₁₃	C₂⁵	1	16	yes	—
212	D₅₂	—	2	32	no	—
213	D₅₂	—	2	32	no	—
214	D₅₂	—	4	32	no	—
215	D₅₂	—	4	16	no	—
216	C₄×D₁₃	—	2	64	no	—
217	Dic₂₆	—	4	16	no	—
218	C₂²×#41	—	13	4	no	—
219	C₂²×#41	C₂×D₁₃	1	2	yes	complemented
220	C₂³×D₄	—	13	8	no	—
221	C₂³×D₄	—	13	4	no	—
222	H(3,𝔽₄)	—	13	64	no	—
223	#555	—	13	32	no	—
224	#555	—	13	64	no	—
225	D₄²	—	13	32	no	—
226	D₄²	—	13	64	no	—
227	#535	—	13	64	no	—
228	#535	—	13	128	no	—
229	#532	—	13	32	no	—
230	#532	C₂×D₁₃	1	16	yes	complemented
231	C₂×C₄⋊Q₈	—	13	2	no	—
232	C₂×C₄⋊Q₈	C₂×D₁₃	1	1	yes	characteristic, complemented
233	C₂×#127	—	13	8	no	—
234	C₂×#127	—	13	2	no	—
235	C₂×#127	C₂×D₁₃	1	1	yes	characteristic
236	C₂×#124	—	13	8	no	—
237	C₂×#124	—	13	16	no	—
238	C₂×#124	—	13	4	no	—
239	C₂×#124	C₂×D₁₃	1	2	yes	complemented
240	C₂×#121	—	13	8	no	—
241	C₂×#121	—	13	4	no	—
242	C₂×#121	—	13	4	no	—
243	C₂×#121	—	13	8	no	—
244	C₂×#121	—	13	8	no	—
245	C₂×#121	C₂×D₁₃	1	4	yes	complemented
246	C₂×#120	—	13	8	no	—
247	C₂×#120	—	13	8	no	—
248	C₂×#120	—	13	16	no	—
249	C₂×C₄×D₄	—	13	4	no	—
250	C₂×C₄×D₄	—	13	4	no	—
251	C₂×C₄×D₄	C₂×D₁₃	1	4	yes	complemented
252	C₂×#117	—	13	4	no	—
253	C₂×#117	—	13	8	no	—
254	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
255	C₂²×C₁₃	—	2	4	no	—
256	C₂²×C₁₃	—	2	16	no	—
257	C₂²×C₁₃	—	2	2	no	—
258	C₂²×C₁₃	—	2	8	no	—
259	C₂²×C₁₃	—	4	16	no	—
260	C₂²×C₁₃	—	4	4	no	—
261	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	2	yes	—
262	C₂²×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
263	C₂²×C₁₃	C₂⁶	1	1	yes	characteristic
264	C₂×D₁₃	—	2	16	no	—
265	C₂×D₁₃	—	2	16	no	—
266	C₂×D₁₃	—	2	16	no	—
267	C₂×D₁₃	—	4	32	no	—
268	C₂×D₁₃	—	8	64	no	—
269	C₄×C₁₃	—	2	4	no	—
270	C₄×C₁₃	—	2	8	no	—
271	C₄×C₁₃	—	2	2	no	—
272	C₄×C₁₃	C₂×H(5,𝔽₂)	1	4	yes	—
273	C₄×C₁₃	C₂×H(5,𝔽₂)	1	8	yes	—
274	Dic₁₃	—	2	16	no	—
275	C₂⁵	—	13	8	no	—
276	C₂×#41	—	4	8	no	—
277	C₂×#41	—	13	32	no	—
278	C₂×#41	—	52	16	no	—
279	C₂×#41	C₂²×D₁₃	1	16	yes	complemented
280	C₂²×Q₈	—	13	4	no	—
281	C₂²×Q₈	C₂²×D₁₃	1	2	yes	—
282	C₂²×D₄	—	13	16	no	—
283	C₂²×D₄	—	13	8	no	—
284	C₂²×D₄	—	13	64	no	—
285	C₂²×D₄	—	13	4	no	—
286	C₂²×D₄	—	13	4	no	—
287	C₂²×D₄	—	13	4	no	—
288	C₂²×D₄	—	13	8	no	—
289	C₂²×D₄	—	13	32	no	—
290	C₂²×D₄	—	52	16	no	—
291	C₂²×D₄	—	52	32	no	—
292	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
293	C₂²×D₄	C₂²×D₁₃	1	2	yes	—
294	C₂²×D₄	C₂²×D₁₃	1	4	yes	—
295	C₂³×C₄	—	13	8	no	—
296	C₂³×C₄	C₂²×D₁₃	1	4	yes	—
297	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
298	C₂³×C₄	C₂²×D₁₃	1	2	yes	—
299	C₄⋊Q₈	—	13	16	no	—
300	C₄⋊Q₈	C₂²×D₁₃	1	8	yes	complemented
301	#127	—	13	64	no	—
302	#127	—	13	16	no	—
303	#127	C₂²×D₁₃	1	8	yes	—
304	#124	—	13	64	no	—
305	#124	—	13	128	no	—
306	#124	—	13	32	no	—
307	#124	C₂²×D₁₃	1	16	yes	complemented
308	#121	—	13	64	no	—
309	#121	—	13	32	no	—
310	#121	—	13	32	no	—
311	#121	—	13	64	no	—
312	#121	—	13	64	no	—
313	#121	C₂²×D₁₃	1	32	yes	complemented
314	#120	—	13	64	no	—
315	#120	—	13	64	no	—
316	#120	—	13	128	no	—
317	C₄×D₄	—	13	32	no	—
318	C₄×D₄	—	13	32	no	—
319	C₄×D₄	C₂²×D₁₃	1	32	yes	complemented
320	#117	—	13	32	no	—
321	#117	—	13	64	no	—
322	C₂×C₄⋊C₄	—	13	4	no	—
323	C₂×C₄⋊C₄	—	13	4	no	—
324	C₂×C₄⋊C₄	C₂²×D₁₃	1	4	yes	—
325	C₂×C₂²⋊C₄	—	13	8	no	—
326	C₂×C₂²⋊C₄	—	13	16	no	—
327	C₂×C₂²⋊C₄	—	13	8	no	—
328	C₂×C₂²⋊C₄	—	13	8	no	—
329	C₂×C₂²⋊C₄	C₂²×D₁₃	1	8	yes	—
330	C₂×C₄²	—	13	8	no	—
331	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
332	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
333	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
334	C₂×C₄²	C₂²×D₁₃	1	8	yes	complemented
335	C₂×C₁₃	—	4	8	no	—
336	C₂×C₁₃	—	4	2	no	—
337	C₂×C₁₃	#3549	1	4	yes	complemented
338	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
339	C₂×C₁₃	C₂²×H(5,𝔽₂)	1	2	yes	—
340	D₁₃	—	4	16	no	—
341	C₂⁴	—	13	8	no	—
342	C₂⁴	—	13	32	no	—
343	C₂⁴	—	52	16	no	—
344	C₂⁴	—	52	32	no	—
345	C₂⁴	C₂³×D₁₃	1	4	yes	—
346	C₂⁴	C₂³×D₁₃	1	1	yes	characteristic
347	#41	—	4	32	no	—
348	#41	—	52	64	no	—
349	C₂×Q₈	—	4	4	no	—
350	C₂×Q₈	—	13	16	no	—
351	C₂×Q₈	—	52	8	no	—
352	C₂×Q₈	C₂³×D₁₃	1	8	yes	—
353	C₂×D₄	—	2	16	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	—	4	8	no	—
356	C₂×D₄	—	13	64	no	—
357	C₂×D₄	—	13	32	no	—
358	C₂×D₄	—	13	16	no	—
359	C₂×D₄	—	13	16	no	—
360	C₂×D₄	—	13	16	no	—
361	C₂×D₄	—	13	32	no	—
362	C₂×D₄	—	26	16	no	—
363	C₂×D₄	—	26	16	no	—
364	C₂×D₄	—	52	64	no	—
365	C₂×D₄	—	52	16	no	—
366	C₂×D₄	—	52	8	no	—
367	C₂×D₄	—	52	128	no	—
368	C₂×D₄	—	52	32	no	—
369	C₂×D₄	—	52	16	no	—
370	C₂×D₄	C₂³×D₁₃	1	16	yes	—
371	C₂×D₄	C₂³×D₁₃	1	8	yes	—
372	C₂×D₄	C₂³×D₁₃	1	16	yes	—
373	C₂²×C₄	—	2	16	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	8	no	—
376	C₂²×C₄	—	13	8	no	—
377	C₂²×C₄	—	13	32	no	—
378	C₂²×C₄	—	26	32	no	—
379	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
380	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
381	C₂²×C₄	C₂³×D₁₃	1	16	yes	—
382	C₂²×C₄	C₂³×D₁₃	1	4	yes	—
383	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
384	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
385	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
386	C₂²×C₄	C₂³×D₁₃	1	2	yes	—
387	C₄⋊C₄	—	13	16	no	—
388	C₄⋊C₄	—	13	16	no	—
389	C₄⋊C₄	C₂³×D₁₃	1	16	yes	—
390	C₂²⋊C₄	—	13	32	no	—
391	C₂²⋊C₄	—	13	64	no	—
392	C₂²⋊C₄	—	13	32	no	—
393	C₂²⋊C₄	—	13	32	no	—
394	C₂²⋊C₄	C₂³×D₁₃	1	32	yes	—
395	C₄²	—	13	32	no	—
396	C₄²	C₂³×D₁₃	1	4	yes	—
397	C₄²	C₂³×D₁₃	1	8	yes	—
398	C₄²	C₂³×D₁₃	1	4	yes	—
399	C₁₃	C₂×#3549	1	1	yes	characteristic, complemented, Sylow
400	C₂³	—	2	2	no	—
401	C₂³	—	2	8	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	16	no	—
404	C₂³	—	13	16	no	—
405	C₂³	—	26	16	no	—
406	C₂³	—	26	16	no	—
407	C₂³	—	26	16	no	—
408	C₂³	—	52	32	no	—
409	C₂³	—	52	64	no	—
410	C₂³	—	104	64	no	—
411	C₂³	C₂⁴×D₁₃	1	8	yes	—
412	C₂³	C₂⁴×D₁₃	1	2	yes	—
413	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
414	Q₈	—	4	8	no	—
415	Q₈	—	52	16	no	—
416	D₄	—	2	32	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	16	no	—
419	D₄	—	26	32	no	—
420	D₄	—	26	32	no	—
421	D₄	—	52	32	no	—
422	D₄	—	52	16	no	—
423	D₄	—	52	64	no	—
424	D₄	—	52	32	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	32	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	16	no	—
431	C₂×C₄	—	13	16	no	—
432	C₂×C₄	—	26	16	no	—
433	C₂×C₄	—	26	64	no	—
434	C₂×C₄	#88251	1	4	yes	—
435	C₂×C₄	#88256	1	8	yes	—
436	C₂×C₄	C₂⁴×D₁₃	1	8	yes	—
437	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
438	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
439	C₂×C₄	C₂⁴×D₁₃	1	2	yes	—
440	C₂×C₄	C₂⁴×D₁₃	1	4	yes	—
441	C₂²	—	2	2	no	—
442	C₂²	—	2	8	no	—
443	C₂²	—	2	4	no	—
444	C₂²	—	2	16	no	—
445	C₂²	—	4	4	no	—
446	C₂²	—	4	16	no	—
447	C₂²	—	26	16	no	—
448	C₂²	—	26	16	no	—
449	C₂²	—	26	16	no	—
450	C₂²	—	52	32	no	—
451	C₂²	—	104	64	no	—
452	C₂²	C₂×#88251	1	2	yes	—
453	C₂²	C₂×#88256	1	4	yes	—
454	C₂²	C₂⁵×D₁₃	1	1	yes	characteristic
455	C₄	—	2	2	no	—
456	C₄	—	2	8	no	—
457	C₄	—	2	4	no	—
458	C₄	—	26	16	no	—
459	C₄	C₂×#88251	1	4	yes	—
460	C₄	C₂×#88256	1	8	yes	—
461	C₂	—	4	8	no	—
462	C₂	—	4	2	no	—
463	C₂	—	52	16	no	—
464	C₂	#13129241	1	4	yes	direct product factor
465	C₂	C₂²×#88251	1	1	yes	characteristic
466	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×#532	C₂
socle	C₂³×C₁₃	C₂⁵
hypercenter	C₂×#532	D₁₃
hypocenter	C₁₃	C₂×#3549
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. #13129241	C₂	direct (N × H)
2. C₂×#11719388	C₂	semidirect
3. C₂×#11719439	C₂	semidirect
4. C₂×#11719268	C₂	semidirect
5. C₂×D₄×D₅₂	C₂	semidirect
6. C₂×#11719422	C₂	semidirect
7. C₂×#11719312	C₂	semidirect
8. C₂×#11719535	C₂	semidirect
9. C₂×#11719182	C₂	semidirect
10. C₂×C₁₃×#532	C₂	semidirect
11. C₂²×C₁₃×#41	C₂²	semidirect
12. C₂²×D₄×D₁₃	C₂²	semidirect
13. C₂²×#6127	C₂²	semidirect
14. C₂³×D₅₂	C₂²	semidirect
15. C₁₃×#532	C₂²	semidirect
16. C₂×C₁₃×C₄⋊Q₈	C₂²	semidirect
18. C₂×C₁₃×#124	C₂²	semidirect
19. C₂×C₁₃×#121	C₂²	semidirect
20. C₂×C₄×D₄×C₁₃	C₂²	semidirect
21. C₂²×C₄²×C₁₃	C₂²	semidirect
22. #11719535	C₂²	semidirect
23. C₂×#88201	C₂²	semidirect
24. C₂×#88194	C₂²	semidirect
25. C₂×#88192	C₂²	semidirect
26. C₂×#88191	C₂²	semidirect
27. C₂×#88191	C₂²	semidirect
28. C₂×#88184	C₂²	semidirect
29. C₂×#88184	C₂²	semidirect
30. C₂×#88184	C₂²	semidirect
31. C₂×#88180	C₂²	semidirect
32. #11719439	C₂²	semidirect
33. #11719422	C₂²	semidirect
34. #11719388	C₂²	semidirect
35. #11719312	C₂²	semidirect
36. #11719268	C₂²	semidirect
37. D₄×D₅₂	C₂²	semidirect
38. C₂×#88149	C₂²	semidirect
39. C₂×#88146	C₂²	semidirect
40. C₂×#88139	C₂²	semidirect
41. C₂×#88136	C₂²	semidirect
42. #11719182	C₂²	semidirect
43. C₂×#88129	C₂²	semidirect
45. C₂×C₄×D₅₂	C₂²	semidirect
46. C₂×C₄×D₅₂	C₂²	semidirect
47. C₂×#88123	C₂²	semidirect
50. C₂×C₁₃×#41	C₂³	semidirect
61. C₂×D₄×D₁₃	C₂³	semidirect
63. C₂×#6127	C₂³	semidirect
69. C₂²×D₅₂	C₂³	semidirect
72. C₁₃×C₄⋊Q₈	C₂³	semidirect
74. C₁₃×#124	C₂³	semidirect
75. C₁₃×#121	C₂³	semidirect
76. C₄×D₄×C₁₃	C₂³	semidirect
82. C₂×C₄²×C₁₃	C₂³	semidirect
84. #88201	C₂³	semidirect
85. #88194	C₂³	semidirect
86. #88192	C₂³	semidirect
87. #88191	C₂³	semidirect
88. #88191	C₂³	semidirect
89. #88184	C₂³	semidirect
90. #88184	C₂³	semidirect
91. #88184	C₂³	semidirect
95. #88180	C₂³	semidirect
99. #88149	C₂³	semidirect
100. #88146	C₂³	semidirect
101. #88139	C₂³	semidirect
102. #88136	C₂³	semidirect
103. #88129	C₂³	semidirect
105. C₄×D₅₂	C₂³	semidirect
106. C₄×D₅₂	C₂³	semidirect
107. #88123	C₂³	semidirect
176. C₂×#532	D₁₃	semidirect
219. C₂²×#41	C₂×D₁₃	semidirect
230. #532	C₂×D₁₃	semidirect
232. C₂×C₄⋊Q₈	C₂×D₁₃	semidirect
239. C₂×#124	C₂×D₁₃	semidirect
245. C₂×#121	C₂×D₁₃	semidirect
251. C₂×C₄×D₄	C₂×D₁₃	semidirect
254. C₂²×C₄²	C₂×D₁₃	semidirect
279. C₂×#41	C₂²×D₁₃	semidirect
300. C₄⋊Q₈	C₂²×D₁₃	semidirect
307. #124	C₂²×D₁₃	semidirect
313. #121	C₂²×D₁₃	semidirect
319. C₄×D₄	C₂²×D₁₃	semidirect
334. C₂×C₄²	C₂²×D₁₃	semidirect
337. C₂×C₁₃	#3549	semidirect
399. C₁₃	C₂×#3549	semidirect
464. C₂	#13129241	direct (N × H)

Maximal subgroups

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

subgroup	index
#13129241	2
C₂×#11719388	2
C₂×#11719439	2
C₂×#11719268	2
C₂×D₄×D₅₂	2
C₂×#11719422	2
C₂×#11719312	2
C₂×#11719535	2
C₂×#11719182	2
C₂×C₁₃×#532	2
C₂×#3549	13

Subgroups — C2×#13129241 #16770722

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129241 #16770722