Subgroups — C₂×#11719232 #13128331

Order 1664.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₃×#117	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#88183	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#6103	C₂	1	1	yes	maximal, characteristic, complemented
4	#11719232	C₂	1	16	yes	maximal, direct product factor
5	C₂×#88152	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#88150	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#88148	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#88148	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#88136	C₂	1	1	yes	maximal, characteristic
10	C₂×#88135	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₂²⋊C₄×D₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#88132	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#88130	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#88129	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄×D₅₂	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#88126	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂⁴×D₁₃	C₂²	1	1	yes	characteristic
18	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
19	C₂²×C₂²⋊D₁₃	C₂²	1	1	yes	characteristic
20	C₂³×Dic₁₃	C₂²	1	1	yes	characteristic
21	C₂²×D₅₂	C₂²	1	1	yes	characteristic
22	C₂²×D₅₂	C₂²	1	1	yes	characteristic
23	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₁₃	C₂²	1	1	yes	characteristic, complemented
26	C₂²×Dic₂₆	C₂²	1	1	yes	characteristic, complemented
27	C₁₃×#117	C₂²	1	8	yes	complemented
28	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₁₃×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄²×C₁₃	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₂²⋊Dic₁₃	C₂²	1	1	yes	characteristic
35	#88183	C₂²	1	8	yes	complemented
36	C₂×#6103	C₂²	1	1	yes	characteristic
37	C₂×#6103	C₂²	1	1	yes	characteristic
38	C₂×#6103	C₂²	1	1	yes	characteristic
39	C₂×#6103	C₂²	1	1	yes	characteristic
40	C₂×#6103	C₂²	1	1	yes	characteristic
41	C₂×#6103	C₂²	1	1	yes	characteristic
42	C₂×#6103	C₂²	1	1	yes	characteristic
43	C₂×#6103	C₂²	1	1	yes	characteristic
44	C₂×#6103	C₂²	1	8	yes	complemented
45	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
46	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
47	C₂×#6103	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄⋊Dic₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
50	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
51	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
52	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
53	C₂×#6101	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄×Dic₁₃	C₂²	1	1	yes	characteristic, complemented
55	#88152	C₂²	1	8	yes	complemented
56	#88150	C₂²	1	8	yes	complemented
57	#88148	C₂²	1	8	yes	complemented
58	#88148	C₂²	1	8	yes	complemented
59	#88136	C₂²	1	8	yes	—
60	#88135	C₂²	1	8	yes	complemented
61	C₂²⋊C₄×D₁₃	C₂²	1	8	yes	complemented
62	#88132	C₂²	1	8	yes	complemented
63	#88130	C₂²	1	8	yes	complemented
64	#88129	C₂²	1	8	yes	complemented
65	C₄×D₅₂	C₂²	1	8	yes	complemented
66	#88126	C₂²	1	8	yes	complemented
67	C₂⁴×C₁₃	C₂³	1	1	yes	characteristic
68	C₂³×D₁₃	—	2	4	no	—
69	C₂³×D₁₃	—	2	4	no	—
70	C₂³×D₁₃	—	4	2	no	—
71	C₂³×D₁₃	C₂³	1	1	yes	characteristic
72	C₂³×D₁₃	C₂³	1	1	yes	characteristic
73	C₂³×D₁₃	C₂³	1	4	yes	—
74	C₂³×D₁₃	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₁₃	—	2	4	no	—
76	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₁₃	C₂³	1	4	yes	—
83	C₂×C₂²⋊D₁₃	—	2	4	no	—
84	C₂×C₂²⋊D₁₃	C₂³	1	4	yes	—
85	C₂²×Dic₁₃	—	4	2	no	—
86	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
87	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
88	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
89	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
90	C₂²×Dic₁₃	C₂³	1	1	yes	characteristic
91	C₂²×Dic₁₃	C₂³	1	4	yes	—
92	C₂×D₅₂	—	2	4	no	—
93	C₂×D₅₂	—	4	2	no	—
94	C₂×D₅₂	C₂³	1	4	yes	—
95	C₂×D₅₂	C₂³	1	4	yes	—
96	C₂×C₄×D₁₃	—	2	4	no	—
97	C₂×C₄×D₁₃	—	4	2	no	—
98	C₂×C₄×D₁₃	—	4	2	no	—
99	C₂×C₄×D₁₃	C₂³	1	4	yes	—
100	C₂×C₄×D₁₃	C₂³	1	4	yes	—
101	C₂×C₄×D₁₃	C₂³	1	4	yes	complemented
102	C₂×Dic₂₆	—	4	2	no	—
103	C₂×Dic₂₆	C₂³	1	4	yes	complemented
104	C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
105	C₁₃×C₄⋊C₄	C₂³	1	4	yes	complemented
106	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
107	C₁₃×C₂²⋊C₄	C₂³	1	4	yes	—
108	C₄²×C₁₃	C₂³	1	4	yes	complemented
109	C₄²×C₁₃	C₂³	1	4	yes	complemented
110	C₂²⋊Dic₁₃	C₂³	1	4	yes	—
111	#6103	C₂³	1	4	yes	—
112	#6103	C₂³	1	4	yes	—
113	#6103	C₂³	1	4	yes	—
114	#6103	C₂³	1	4	yes	—
115	#6103	C₂³	1	4	yes	—
116	#6103	C₂³	1	4	yes	—
117	#6103	C₂³	1	4	yes	—
118	#6103	C₂³	1	4	yes	—
119	#6103	C₂³	1	4	yes	complemented
120	#6103	C₂³	1	4	yes	complemented
121	#6103	C₂³	1	4	yes	complemented
122	C₄⋊Dic₁₃	C₂³	1	4	yes	complemented
123	#6101	C₂³	1	4	yes	complemented
124	#6101	C₂³	1	4	yes	complemented
125	#6101	C₂³	1	4	yes	complemented
126	#6101	C₂³	1	4	yes	complemented
127	#6101	C₂³	1	4	yes	complemented
128	C₄×Dic₁₃	C₂³	1	4	yes	complemented
129	C₂×#551	—	13	1	no	maximal, Sylow
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	—	2	2	no	—
132	C₂³×C₁₃	#41	1	4	yes	—
133	C₂³×C₁₃	C₂⁴	1	2	yes	—
134	C₂³×C₁₃	C₂⁴	1	1	yes	characteristic
135	C₂²×D₁₃	—	2	2	no	—
136	C₂²×D₁₃	—	2	2	no	—
137	C₂²×D₁₃	—	2	2	no	—
138	C₂²×D₁₃	—	2	2	no	—
139	C₂²×D₁₃	—	2	8	no	—
140	C₂²×D₁₃	—	2	2	no	—
141	C₂²×D₁₃	—	2	2	no	—
142	C₂²×D₁₃	—	2	2	no	—
143	C₂²×D₁₃	—	2	2	no	—
144	C₂²×D₁₃	—	2	8	no	—
145	C₂²×D₁₃	—	4	4	no	—
146	C₂²×D₁₃	—	4	16	no	—
147	C₂²×D₁₃	#41	1	4	yes	—
148	C₂²×D₁₃	C₂⁴	1	2	yes	—
149	C₂²×D₁₃	C₂⁴	1	2	yes	—
150	C₂²×D₁₃	C₂⁴	1	2	yes	—
151	C₂×C₄×C₁₃	—	2	2	no	—
152	C₂×C₄×C₁₃	—	2	2	no	—
153	C₂×C₄×C₁₃	—	2	8	no	—
154	C₂×C₄×C₁₃	—	2	2	no	—
155	C₂×C₄×C₁₃	—	2	2	no	—
156	C₂×C₄×C₁₃	—	2	2	no	—
157	C₂×C₄×C₁₃	—	2	2	no	—
158	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
159	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
160	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
161	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
162	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₃	C₂⁴	1	2	yes	—
164	C₂²⋊D₁₃	—	2	8	no	—
165	C₂×Dic₁₃	—	2	2	no	—
166	C₂×Dic₁₃	—	2	2	no	—
167	C₂×Dic₁₃	—	2	2	no	—
168	C₂×Dic₁₃	—	2	2	no	—
169	C₂×Dic₁₃	—	2	2	no	—
170	C₂×Dic₁₃	—	4	4	no	—
171	C₂×Dic₁₃	C₂⁴	1	2	yes	—
172	C₂×Dic₁₃	C₂⁴	1	2	yes	—
173	C₂×Dic₁₃	C₂⁴	1	2	yes	—
174	C₂×Dic₁₃	C₂⁴	1	2	yes	—
175	C₂×Dic₁₃	C₂⁴	1	2	yes	—
176	D₅₂	—	2	8	no	—
177	D₅₂	—	4	4	no	—
178	C₄×D₁₃	—	2	8	no	—
179	C₄×D₁₃	—	4	4	no	—
180	C₄×D₁₃	—	4	4	no	—
181	Dic₂₆	—	4	4	no	—
182	#551	—	13	16	no	—
183	C₂×#126	—	13	1	no	—
184	C₂×#126	—	13	1	no	—
185	C₂×#124	—	13	1	no	—
186	C₂×#123	—	13	1	no	—
187	C₂×#123	—	13	1	no	—
188	C₂×#123	—	13	1	no	—
189	C₂×C₂²⋊Q₈	—	13	1	no	—
190	C₂×C₂²⋊Q₈	—	13	1	no	—
191	C₂×#120	—	13	1	no	—
192	C₂×C₄×D₄	—	13	1	no	—
193	C₂×C₄×D₄	—	13	1	no	—
194	C₂×#117	—	13	1	no	—
195	C₂×#117	D₁₃	1	1	yes	characteristic, complemented
196	C₂²×C₂²⋊C₄	—	13	1	no	—
197	C₂²×C₂²⋊C₄	—	13	1	no	—
198	C₂²×C₁₃	—	2	8	no	—
199	C₂²×C₁₃	—	2	2	no	—
200	C₂²×C₁₃	—	2	2	no	—
201	C₂²×C₁₃	C₂×#41	1	4	yes	—
202	C₂²×C₁₃	C₂×#41	1	2	yes	—
203	C₂²×C₁₃	C₂×#41	1	2	yes	—
204	C₂²×C₁₃	H(5,𝔽₂)	1	2	yes	—
205	C₂²×C₁₃	C₂⁵	1	1	yes	characteristic
206	C₂×D₁₃	—	2	8	no	—
207	C₂×D₁₃	—	2	2	no	—
208	C₂×D₁₃	—	2	2	no	—
209	C₂×D₁₃	—	2	2	no	—
210	C₂×D₁₃	—	2	2	no	—
211	C₂×D₁₃	—	2	2	no	—
212	C₂×D₁₃	—	2	2	no	—
213	C₂×D₁₃	—	2	2	no	—
214	C₂×D₁₃	—	2	2	no	—
215	C₂×D₁₃	—	4	16	no	—
216	C₂×D₁₃	—	4	4	no	—
217	C₂×D₁₃	—	4	4	no	—
218	C₂×D₁₃	C₂×#41	1	4	yes	—
219	C₄×C₁₃	—	2	2	no	—
220	C₄×C₁₃	—	2	2	no	—
221	C₄×C₁₃	—	2	2	no	—
222	C₄×C₁₃	—	2	2	no	—
223	C₄×C₁₃	—	2	2	no	—
224	C₄×C₁₃	—	2	2	no	—
225	Dic₁₃	—	2	2	no	—
226	Dic₁₃	—	2	2	no	—
227	Dic₁₃	—	2	2	no	—
228	Dic₁₃	—	2	2	no	—
229	Dic₁₃	—	2	2	no	—
230	C₂⁵	—	13	1	no	—
231	C₂²×Q₈	—	13	1	no	—
232	C₂²×D₄	—	13	1	no	—
233	C₂²×D₄	—	13	1	no	—
234	C₂²×D₄	—	13	1	no	—
235	C₂³×C₄	—	13	1	no	—
236	C₂³×C₄	—	13	1	no	—
237	C₂³×C₄	—	13	1	no	—
238	C₂³×C₄	—	13	1	no	—
239	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
240	#126	—	13	8	no	—
241	#126	—	13	8	no	—
242	#124	—	13	8	no	—
243	#123	—	13	8	no	—
244	#123	—	13	8	no	—
245	#123	—	13	8	no	—
246	C₂²⋊Q₈	—	13	8	no	—
247	C₂²⋊Q₈	—	13	8	no	—
248	#120	—	13	8	no	—
249	C₄×D₄	—	13	8	no	—
250	C₄×D₄	—	13	8	no	—
251	#117	—	13	8	no	—
252	#117	C₂×D₁₃	1	8	yes	complemented
253	C₂×C₄⋊C₄	—	13	1	no	—
254	C₂×C₄⋊C₄	—	13	1	no	—
255	C₂×C₄⋊C₄	—	13	1	no	—
256	C₂×C₄⋊C₄	—	13	1	no	—
257	C₂×C₄⋊C₄	—	13	1	no	—
258	C₂×C₄⋊C₄	—	13	1	no	—
259	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
260	C₂×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic, complemented
261	C₂×C₂²⋊C₄	—	13	1	no	—
262	C₂×C₂²⋊C₄	—	13	1	no	—
263	C₂×C₂²⋊C₄	—	13	1	no	—
264	C₂×C₂²⋊C₄	—	13	1	no	—
265	C₂×C₂²⋊C₄	—	13	1	no	—
266	C₂×C₂²⋊C₄	—	13	1	no	—
267	C₂×C₂²⋊C₄	—	13	1	no	—
268	C₂×C₂²⋊C₄	—	13	8	no	—
269	C₂×C₂²⋊C₄	—	13	1	no	—
270	C₂×C₂²⋊C₄	—	13	1	no	—
271	C₂×C₂²⋊C₄	—	13	1	no	—
272	C₂×C₂²⋊C₄	—	13	1	no	—
273	C₂×C₂²⋊C₄	—	13	1	no	—
274	C₂×C₂²⋊C₄	—	13	8	no	—
275	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂×D₁₃	1	1	yes	characteristic
277	C₂×C₄²	—	13	1	no	—
278	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
279	C₂×C₄²	C₂×D₁₃	1	1	yes	characteristic, complemented
280	C₂×C₁₃	—	2	4	no	—
281	C₂×C₁₃	#551	1	4	yes	complemented
282	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
283	C₂×C₁₃	C₂²×#41	1	1	yes	characteristic
284	C₂×C₁₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
285	D₁₃	—	2	4	no	—
286	D₁₃	—	4	2	no	—
287	D₁₃	—	4	2	no	—
288	C₂⁴	—	13	1	no	—
289	C₂⁴	—	13	1	no	—
290	C₂⁴	—	13	1	no	—
291	C₂⁴	—	13	4	no	—
292	C₂⁴	—	26	4	no	—
293	C₂⁴	—	26	4	no	—
294	C₂⁴	—	52	2	no	—
295	C₂⁴	C₂²×D₁₃	1	1	yes	characteristic
296	C₂×Q₈	—	13	4	no	—
297	C₂×Q₈	—	52	2	no	—
298	C₂×D₄	—	13	4	no	—
299	C₂×D₄	—	13	4	no	—
300	C₂×D₄	—	13	4	no	—
301	C₂×D₄	—	26	4	no	—
302	C₂×D₄	—	26	4	no	—
303	C₂×D₄	—	52	2	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	—	13	1	no	—
306	C₂²×C₄	—	13	1	no	—
307	C₂²×C₄	—	13	1	no	—
308	C₂²×C₄	—	13	1	no	—
309	C₂²×C₄	—	13	1	no	—
310	C₂²×C₄	—	13	4	no	—
311	C₂²×C₄	—	13	4	no	—
312	C₂²×C₄	—	13	4	no	—
313	C₂²×C₄	—	13	4	no	—
314	C₂²×C₄	—	26	4	no	—
315	C₂²×C₄	—	52	2	no	—
316	C₂²×C₄	—	52	2	no	—
317	C₂²×C₄	—	52	2	no	—
318	C₂²×C₄	C₂²×D₁₃	1	4	yes	—
319	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
320	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
321	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
322	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
323	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
324	C₂²×C₄	C₂²×D₁₃	1	1	yes	characteristic
325	C₄⋊C₄	—	13	4	no	—
326	C₄⋊C₄	—	13	4	no	—
327	C₄⋊C₄	—	13	4	no	—
328	C₄⋊C₄	—	13	4	no	—
329	C₄⋊C₄	—	13	4	no	—
330	C₄⋊C₄	—	13	4	no	—
331	C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
332	C₄⋊C₄	C₂²×D₁₃	1	4	yes	complemented
333	C₂²⋊C₄	—	13	4	no	—
334	C₂²⋊C₄	—	13	4	no	—
335	C₂²⋊C₄	—	13	4	no	—
336	C₂²⋊C₄	—	13	4	no	—
337	C₂²⋊C₄	—	13	4	no	—
338	C₂²⋊C₄	—	13	4	no	—
339	C₂²⋊C₄	—	13	4	no	—
340	C₂²⋊C₄	—	13	4	no	—
341	C₂²⋊C₄	—	13	4	no	—
342	C₂²⋊C₄	—	13	4	no	—
343	C₂²⋊C₄	—	13	4	no	—
344	C₂²⋊C₄	—	13	4	no	—
345	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
346	C₂²⋊C₄	C₂²×D₁₃	1	4	yes	—
347	C₄²	—	13	4	no	—
348	C₄²	C₂²×D₁₃	1	4	yes	complemented
349	C₄²	C₂²×D₁₃	1	4	yes	complemented
350	C₁₃	C₂×#551	1	1	yes	characteristic, complemented, Sylow
351	C₂³	—	2	2	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	13	4	no	—
354	C₂³	—	13	2	no	—
355	C₂³	—	13	2	no	—
356	C₂³	—	13	2	no	—
357	C₂³	—	26	8	no	—
358	C₂³	—	26	2	no	—
359	C₂³	—	26	2	no	—
360	C₂³	—	26	2	no	—
361	C₂³	—	26	8	no	—
362	C₂³	—	26	2	no	—
363	C₂³	—	26	2	no	—
364	C₂³	—	26	2	no	—
365	C₂³	—	26	2	no	—
366	C₂³	—	26	2	no	—
367	C₂³	—	52	4	no	—
368	C₂³	—	52	16	no	—
369	C₂³	#6127	1	4	yes	—
370	C₂³	C₂³×D₁₃	1	2	yes	—
371	C₂³	C₂³×D₁₃	1	1	yes	characteristic
372	Q₈	—	52	4	no	—
373	D₄	—	26	8	no	—
374	D₄	—	26	8	no	—
375	D₄	—	52	4	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	13	2	no	—
384	C₂×C₄	—	13	2	no	—
385	C₂×C₄	—	13	2	no	—
386	C₂×C₄	—	13	2	no	—
387	C₂×C₄	—	13	2	no	—
388	C₂×C₄	—	26	8	no	—
389	C₂×C₄	—	26	2	no	—
390	C₂×C₄	—	26	2	no	—
391	C₂×C₄	—	26	2	no	—
392	C₂×C₄	—	26	2	no	—
393	C₂×C₄	—	26	2	no	—
394	C₂×C₄	—	52	4	no	—
395	C₂×C₄	—	52	4	no	—
396	C₂×C₄	—	52	4	no	—
397	C₂×C₄	C₂³×D₁₃	1	2	yes	—
398	C₂×C₄	C₂³×D₁₃	1	2	yes	—
399	C₂×C₄	C₂³×D₁₃	1	2	yes	—
400	C₂×C₄	C₂³×D₁₃	1	2	yes	—
401	C₂×C₄	C₂³×D₁₃	1	2	yes	—
402	C₂×C₄	C₂³×D₁₃	1	2	yes	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	13	4	no	—
407	C₂²	—	26	8	no	—
408	C₂²	—	26	2	no	—
409	C₂²	—	26	2	no	—
410	C₂²	—	26	2	no	—
411	C₂²	—	26	2	no	—
412	C₂²	—	26	2	no	—
413	C₂²	—	26	2	no	—
414	C₂²	—	26	2	no	—
415	C₂²	—	26	2	no	—
416	C₂²	—	52	16	no	—
417	C₂²	—	52	4	no	—
418	C₂²	—	52	4	no	—
419	C₂²	C₂×#6127	1	4	yes	—
420	C₂²	C₂×#6127	1	2	yes	—
421	C₂²	#41×D₁₃	1	2	yes	—
422	C₂²	#88256	1	2	yes	—
423	C₂²	C₂⁴×D₁₃	1	1	yes	characteristic
424	C₄	—	2	2	no	—
425	C₄	—	2	2	no	—
426	C₄	—	2	2	no	—
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	2	no	—
430	C₄	—	26	2	no	—
431	C₄	—	26	2	no	—
432	C₄	—	26	2	no	—
433	C₄	—	26	2	no	—
434	C₄	—	26	2	no	—
435	C₂	—	2	4	no	—
436	C₂	—	26	4	no	—
437	C₂	—	52	2	no	—
438	C₂	—	52	2	no	—
439	C₂	#11719232	1	4	yes	direct product factor
440	C₂	C₂²×#6127	1	1	yes	characteristic
441	C₂	C₂×#41×D₁₃	1	1	yes	characteristic
442	C₂	C₂×#88256	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₁₃
commutator, cosocle	C₂²×C₁₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₃
Fitting	C₂×C₁₃×#117	C₂
socle	C₂³×C₁₃	C₂⁴
prime radical	C₂×#88136	C₂
hypercenter	C₂×#117	D₁₃
hypocenter	C₁₃	C₂×#551
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×#117

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₃×#117	C₂	semidirect
2. C₂×#88183	C₂	semidirect
3. C₂²×#6103	C₂	semidirect
4. #11719232	C₂	direct (N × H)
5. C₂×#88152	C₂	semidirect
6. C₂×#88150	C₂	semidirect
7. C₂×#88148	C₂	semidirect
8. C₂×#88148	C₂	semidirect
10. C₂×#88135	C₂	semidirect
11. C₂×C₂²⋊C₄×D₁₃	C₂	semidirect
12. C₂×#88132	C₂	semidirect
13. C₂×#88130	C₂	semidirect
14. C₂×#88129	C₂	semidirect
15. C₂×C₄×D₅₂	C₂	semidirect
16. C₂×#88126	C₂	semidirect
25. C₂²×C₄×D₁₃	C₂²	semidirect
26. C₂²×Dic₂₆	C₂²	semidirect
27. C₁₃×#117	C₂²	semidirect
28. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
29. C₂×C₁₃×C₄⋊C₄	C₂²	semidirect
32. C₂×C₄²×C₁₃	C₂²	semidirect
33. C₂×C₄²×C₁₃	C₂²	semidirect
35. #88183	C₂²	semidirect
44. C₂×#6103	C₂²	semidirect
45. C₂×#6103	C₂²	semidirect
46. C₂×#6103	C₂²	semidirect
47. C₂×#6103	C₂²	semidirect
48. C₂×C₄⋊Dic₁₃	C₂²	semidirect
49. C₂×#6101	C₂²	semidirect
50. C₂×#6101	C₂²	semidirect
51. C₂×#6101	C₂²	semidirect
52. C₂×#6101	C₂²	semidirect
53. C₂×#6101	C₂²	semidirect
54. C₂×C₄×Dic₁₃	C₂²	semidirect
55. #88152	C₂²	semidirect
56. #88150	C₂²	semidirect
57. #88148	C₂²	semidirect
58. #88148	C₂²	semidirect
60. #88135	C₂²	semidirect
61. C₂²⋊C₄×D₁₃	C₂²	semidirect
62. #88132	C₂²	semidirect
63. #88130	C₂²	semidirect
64. #88129	C₂²	semidirect
65. C₄×D₅₂	C₂²	semidirect
66. #88126	C₂²	semidirect
101. C₂×C₄×D₁₃	C₂³	semidirect
103. C₂×Dic₂₆	C₂³	semidirect
104. C₁₃×C₄⋊C₄	C₂³	semidirect
105. C₁₃×C₄⋊C₄	C₂³	semidirect
108. C₄²×C₁₃	C₂³	semidirect
109. C₄²×C₁₃	C₂³	semidirect
119. #6103	C₂³	semidirect
120. #6103	C₂³	semidirect
121. #6103	C₂³	semidirect
122. C₄⋊Dic₁₃	C₂³	semidirect
123. #6101	C₂³	semidirect
124. #6101	C₂³	semidirect
125. #6101	C₂³	semidirect
126. #6101	C₂³	semidirect
127. #6101	C₂³	semidirect
128. C₄×Dic₁₃	C₂³	semidirect
195. C₂×#117	D₁₃	semidirect
252. #117	C₂×D₁₃	semidirect
259. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
260. C₂×C₄⋊C₄	C₂×D₁₃	semidirect
278. C₂×C₄²	C₂×D₁₃	semidirect
279. C₂×C₄²	C₂×D₁₃	semidirect
281. C₂×C₁₃	#551	semidirect
331. C₄⋊C₄	C₂²×D₁₃	semidirect
332. C₄⋊C₄	C₂²×D₁₃	semidirect
348. C₄²	C₂²×D₁₃	semidirect
349. C₄²	C₂²×D₁₃	semidirect
350. C₁₃	C₂×#551	semidirect
439. C₂	#11719232	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×C₁₃×#117	2
C₂×#88183	2
C₂²×#6103	2
#11719232	2
C₂×#88152	2
C₂×#88150	2
C₂×#88148	2
C₂×#88136	2
C₂×#88135	2
C₂×C₂²⋊C₄×D₁₃	2
C₂×#88132	2
C₂×#88130	2
C₂×#88129	2
C₂×C₄×D₅₂	2
C₂×#88126	2
C₂×#551	13

Subgroups — C2×#11719232 #13128331

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11719232 #13128331