Subgroups — D₄×C₁₁×#135 #14638241

Order 2816.

2822 conjugacy classes of subgroups.

The subgroup lattice has 858 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₁×#135	C₂	1	2	yes	maximal, complemented
2	D₄×C₁₁×#41	C₂	1	2	yes	maximal, complemented
3	C₁₁×#3287	C₂	1	1	yes	maximal, characteristic, complemented
4	D₄×C₁₁×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₁×#3285	C₂	1	2	yes	maximal, complemented
6	C₁₁×#3284	C₂	1	2	yes	maximal, complemented
7	C₁₁×#3283	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₁×#3282	C₂	1	4	yes	maximal, complemented
9	D₄×C₁₁×SD₁₆	C₂	1	2	yes	maximal, complemented
10	C₁₁×#3280	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₁×D₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₁×#3147	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₁×#3050	C₂	1	2	yes	maximal, complemented
14	C₁₁×#3035	C₂	1	2	yes	maximal, complemented
15	C₁₁×#3002	C₂	1	4	yes	maximal, complemented
16	C₄×C₁₁×#135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₈×D₄×C₁₁	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×C₁₁×#41	C₂²	1	4	yes	complemented
19	C₂×C₁₁×#135	—	2	16	no	—
20	C₂×C₁₁×#135	C₂²	1	1	yes	characteristic
21	C₂×C₁₁×#135	C₂²	1	2	yes	complemented
22	C₂×C₁₁×#135	C₂²	1	4	yes	complemented
23	C₂×C₁₁×#135	C₂²	1	2	yes	complemented
24	C₂×C₁₁×#135	C₂²	1	4	yes	complemented
25	C₂×C₁₁×#135	C₂²	1	2	yes	complemented
26	C₂×C₁₁×#135	C₂²	1	2	yes	complemented
27	C₂²×C₁₁×Q₁₆	C₂²	1	2	yes	complemented
28	C₂²×C₁₁×SD₁₆	C₂²	1	4	yes	complemented
29	C₂²×C₁₁×D₈	C₂²	1	2	yes	complemented
30	C₂³×C₈×C₁₁	C₂²	1	2	yes	complemented
31	C₁₁×#550	C₂²	1	2	yes	complemented
32	D₄×Q₈×C₁₁	C₂²	1	2	yes	—
33	C₁₁×#548	C₂²	1	4	yes	complemented
34	C₁₁×#547	—	2	2	no	—
35	C₁₁×#547	C₂²	1	2	yes	complemented
36	C₁₁×#546	—	2	4	no	—
37	C₁₁×#546	C₂²	1	4	yes	complemented
38	D₄²×C₁₁	—	2	2	no	—
39	D₄²×C₁₁	C₂²	1	2	yes	—
40	C₁₁×#532	—	2	2	no	—
41	C₁₁×#532	C₂²	1	2	yes	complemented
42	C₁₁×#525	—	2	4	no	—
43	C₁₁×#525	C₂²	1	4	yes	complemented
44	C₄×C₁₁×#41	C₂²	1	2	yes	complemented
45	C₂×C₄×D₄×C₁₁	—	2	2	no	—
46	C₂×C₄×D₄×C₁₁	C₂²	1	1	yes	characteristic
47	C₁₁×#495	C₂²	1	2	yes	complemented
48	C₁₁×#495	C₂²	1	2	yes	complemented
49	C₁₁×#494	C₂²	1	1	yes	characteristic, complemented
50	C₁₁×#493	C₂²	1	1	yes	characteristic, complemented
51	C₁₁×#492	C₂²	1	2	yes	complemented
52	C₁₁×#467	C₂²	1	2	yes	complemented
53	C₁₁×#467	C₂²	1	2	yes	complemented
54	C₁₁×#466	C₂²	1	2	yes	complemented
55	C₁₁×#466	C₂²	1	2	yes	complemented
56	C₁₁×#465	C₂²	1	4	yes	complemented
57	C₁₁×#465	C₂²	1	4	yes	complemented
58	C₁₁×#464	C₂²	1	4	yes	complemented
59	C₁₁×#463	C₂²	1	4	yes	complemented
60	C₁₁×#462	C₂²	1	2	yes	complemented
61	C₁₁×#461	C₂²	1	2	yes	complemented
62	C₁₁×#460	C₂²	1	2	yes	complemented
63	C₁₁×#459	C₂²	1	2	yes	complemented
64	C₁₁×#452	C₂²	1	4	yes	complemented
65	C₁₁×#452	C₂²	1	4	yes	complemented
66	C₁₁×#451	C₂²	1	4	yes	complemented
67	C₁₁×#450	C₂²	1	4	yes	complemented
68	C₁₁×#449	C₂²	1	4	yes	complemented
69	C₁₁×#449	C₂²	1	4	yes	complemented
70	C₁₁×#448	C₂²	1	4	yes	complemented
71	C₁₁×#447	C₂²	1	4	yes	complemented
72	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₁₁×Q₁₆	C₂²	1	1	yes	characteristic, complemented
74	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
75	C₄×C₁₁×SD₁₆	C₂²	1	2	yes	complemented
76	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₁₁×D₈	C₂²	1	1	yes	characteristic, complemented
78	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₁₁	C₂²	1	2	yes	complemented
81	C₈×D₄×C₁₁	C₂²	1	2	yes	complemented
82	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
83	C₈×D₄×C₁₁	C₂²	1	1	yes	characteristic, complemented
84	C₁₁×#427	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₁₁×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	C₁₁×#416	C₂²	1	2	yes	complemented
87	C₁₁×#416	C₂²	1	4	yes	complemented
88	C₂×C₁₁×C₂²⋊C₈	C₂²	1	2	yes	complemented
89	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₁₁×#41	—	2	4	no	—
91	C₂×C₁₁×#41	—	2	4	no	—
92	C₂×C₁₁×#41	—	2	16	no	—
93	C₂×C₁₁×#41	—	4	8	no	—
94	C₂×C₁₁×#41	C₂³	1	4	yes	—
95	C₂×C₁₁×#41	C₂³	1	4	yes	—
96	C₂×C₁₁×#41	C₂³	1	4	yes	—
97	C₂×C₁₁×#41	C₂³	1	2	yes	—
98	C₂²×Q₈×C₁₁	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₁	—	2	4	no	—
100	C₂²×D₄×C₁₁	—	2	2	no	—
101	C₂²×D₄×C₁₁	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₁₁	C₂³	1	4	yes	—
103	C₂³×C₄×C₁₁	—	2	4	no	—
104	C₂³×C₄×C₁₁	C₂³	1	2	yes	—
105	C₁₁×#135	—	2	16	no	—
106	C₁₁×#135	—	2	8	no	—
107	C₁₁×#135	—	2	16	no	—
108	C₁₁×#135	—	2	8	no	—
109	C₁₁×#135	—	2	8	no	—
110	C₁₁×#135	—	4	4	no	—
111	C₁₁×#135	D₄	1	8	yes	direct product factor
112	C₂×C₁₁×Q₁₆	—	2	8	no	—
113	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
114	C₂×C₁₁×Q₁₆	C₂³	1	4	yes	—
115	C₂×C₁₁×Q₁₆	C₂³	1	2	yes	—
116	C₂×C₁₁×Q₁₆	C₂³	1	1	yes	characteristic
117	C₂×C₁₁×SD₁₆	—	2	16	no	—
118	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
119	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
120	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
121	C₂×C₁₁×SD₁₆	C₂³	1	4	yes	—
122	C₂×C₁₁×SD₁₆	C₂³	1	2	yes	—
123	C₂×C₁₁×D₈	—	2	8	no	—
124	C₂×C₁₁×D₈	C₂³	1	2	yes	—
125	C₂×C₁₁×D₈	C₂³	1	4	yes	—
126	C₂×C₁₁×D₈	C₂³	1	2	yes	—
127	C₂×C₁₁×D₈	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₁₁	—	2	8	no	—
129	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
131	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
132	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
133	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
134	C₂²×C₈×C₁₁	C₂³	1	2	yes	—
135	C₂²×C₈×C₁₁	C₂³	1	1	yes	characteristic
136	C₁₁×C₄⋊Q₈	—	2	2	no	—
137	C₁₁×C₄⋊Q₈	C₂³	1	2	yes	—
138	C₁₁×#127	—	2	2	no	—
139	C₁₁×#127	C₂³	1	2	yes	—
140	C₁₁×#124	—	2	4	no	—
141	C₁₁×#124	C₂³	1	4	yes	—
142	C₁₁×#123	—	2	4	no	—
143	C₁₁×#123	—	2	4	no	—
144	C₁₁×#123	—	2	4	no	—
145	C₁₁×C₂²⋊Q₈	—	2	4	no	—
146	C₁₁×C₂²⋊Q₈	—	2	4	no	—
147	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
148	C₁₁×C₂²⋊Q₈	C₂³	1	4	yes	—
149	C₁₁×#121	—	2	4	no	—
150	C₁₁×#121	—	2	2	no	—
151	C₁₁×#121	—	2	2	no	—
152	C₁₁×#121	—	2	2	no	—
153	C₁₁×#121	—	2	2	no	—
154	C₁₁×#121	—	2	4	no	—
155	C₁₁×#121	—	2	4	no	—
156	C₁₁×#121	C₂³	1	4	yes	—
157	C₁₁×#121	C₂³	1	4	yes	—
158	C₁₁×#120	—	2	4	no	—
159	C₁₁×#120	—	2	4	no	—
160	C₁₁×#120	—	2	4	no	—
161	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
162	C₄×Q₈×C₁₁	C₂³	1	2	yes	—
163	C₄×D₄×C₁₁	—	2	2	no	—
164	C₄×D₄×C₁₁	—	2	4	no	—
165	C₄×D₄×C₁₁	—	2	2	no	—
166	C₄×D₄×C₁₁	—	2	2	no	—
167	C₄×D₄×C₁₁	—	2	4	no	—
168	C₄×D₄×C₁₁	—	2	2	no	—
169	C₄×D₄×C₁₁	—	2	4	no	—
170	C₄×D₄×C₁₁	—	2	2	no	—
171	C₄×D₄×C₁₁	—	2	2	no	—
172	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
173	C₄×D₄×C₁₁	D₄	1	2	yes	—
174	C₄×D₄×C₁₁	D₄	1	1	yes	characteristic
175	C₄×D₄×C₁₁	C₂³	1	2	yes	—
176	C₄×D₄×C₁₁	C₂³	1	2	yes	—
177	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
178	C₄×D₄×C₁₁	C₂³	1	2	yes	—
179	C₄×D₄×C₁₁	C₂³	1	1	yes	characteristic
180	C₁₁×#117	—	2	2	no	—
181	C₁₁×#117	C₂³	1	2	yes	—
182	C₂×C₁₁×C₄⋊C₄	—	2	2	no	—
183	C₂×C₁₁×C₄⋊C₄	D₄	1	1	yes	characteristic
184	C₂×C₁₁×C₂²⋊C₄	—	2	4	no	—
185	C₂×C₁₁×C₂²⋊C₄	D₄	1	2	yes	—
186	C₂×C₄²×C₁₁	—	2	2	no	—
187	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
188	C₁₁×#107	C₂³	1	1	yes	characteristic
189	C₁₁×#107	C₂³	1	1	yes	characteristic
190	C₁₁×#106	C₂³	1	2	yes	—
191	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
192	C₁₁×C₄⋊C₈	C₂³	1	1	yes	characteristic
193	C₁₁×C₄⋊C₈	C₂³	1	2	yes	—
194	C₁₁×#103	C₂³	1	2	yes	—
195	C₁₁×#103	C₂³	1	2	yes	—
196	C₁₁×#103	C₂³	1	4	yes	—
197	C₁₁×#103	C₂³	1	4	yes	—
198	C₁₁×#102	C₂³	1	2	yes	—
199	C₁₁×#102	C₂³	1	2	yes	—
200	C₁₁×#102	C₂³	1	4	yes	—
201	C₁₁×#102	C₂³	1	4	yes	—
202	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
203	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
204	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
205	C₁₁×C₂²⋊C₈	C₂³	1	2	yes	—
206	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
207	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
208	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
209	C₄×C₈×C₁₁	C₂³	1	1	yes	characteristic
210	D₄×#135	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂⁴×C₁₁	—	2	4	no	—
212	C₂⁴×C₁₁	C₂×D₄	1	2	yes	—
213	C₁₁×#41	—	2	4	no	—
214	C₁₁×#41	—	2	8	no	—
215	C₁₁×#41	—	2	8	no	—
216	C₁₁×#41	—	2	8	no	—
217	C₁₁×#41	—	2	8	no	—
218	C₁₁×#41	—	4	16	no	—
219	C₁₁×#41	—	4	4	no	—
220	C₁₁×#41	—	4	4	no	—
221	C₁₁×#41	—	4	16	no	—
222	C₁₁×#41	C₂×D₄	1	8	yes	complemented
223	C₂×Q₈×C₁₁	—	2	4	no	—
224	C₂×Q₈×C₁₁	—	2	8	no	—
225	C₂×Q₈×C₁₁	—	4	4	no	—
226	C₂×Q₈×C₁₁	C₂⁴	1	4	yes	—
227	C₂×Q₈×C₁₁	C₂⁴	1	2	yes	—
228	C₂×D₄×C₁₁	—	2	2	no	—
229	C₂×D₄×C₁₁	—	2	4	no	—
230	C₂×D₄×C₁₁	—	2	8	no	—
231	C₂×D₄×C₁₁	—	2	4	no	—
232	C₂×D₄×C₁₁	—	2	4	no	—
233	C₂×D₄×C₁₁	—	2	4	no	—
234	C₂×D₄×C₁₁	—	2	4	no	—
235	C₂×D₄×C₁₁	—	2	4	no	—
236	C₂×D₄×C₁₁	—	2	2	no	—
237	C₂×D₄×C₁₁	—	2	4	no	—
238	C₂×D₄×C₁₁	—	2	2	no	—
239	C₂×D₄×C₁₁	—	4	4	no	—
240	C₂×D₄×C₁₁	—	4	16	no	—
241	C₂×D₄×C₁₁	—	4	8	no	—
242	C₂×D₄×C₁₁	C₂×D₄	1	2	yes	—
243	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
244	C₂×D₄×C₁₁	C₂×D₄	1	1	yes	characteristic
245	C₂×D₄×C₁₁	C₂⁴	1	4	yes	—
246	C₂×D₄×C₁₁	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₁₁	—	2	4	no	—
248	C₂²×C₄×C₁₁	—	2	2	no	—
249	C₂²×C₄×C₁₁	—	2	4	no	—
250	C₂²×C₄×C₁₁	—	2	4	no	—
251	C₂²×C₄×C₁₁	—	2	2	no	—
252	C₂²×C₄×C₁₁	—	2	4	no	—
253	C₂²×C₄×C₁₁	—	2	4	no	—
254	C₂²×C₄×C₁₁	—	2	4	no	—
255	C₂²×C₄×C₁₁	—	2	2	no	—
256	C₂²×C₄×C₁₁	—	4	16	no	—
257	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
258	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
259	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
260	C₂²×C₄×C₁₁	C₂×D₄	1	2	yes	—
261	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
262	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
263	C₂²×C₄×C₁₁	C₂⁴	1	2	yes	—
264	C₂²×C₄×C₁₁	C₂⁴	1	1	yes	characteristic
265	C₁₁×Q₁₆	—	2	4	no	—
266	C₁₁×Q₁₆	—	2	8	no	—
267	C₁₁×Q₁₆	—	4	2	no	—
268	C₁₁×Q₁₆	C₂×D₄	1	4	yes	complemented
269	C₁₁×SD₁₆	—	2	8	no	—
270	C₁₁×SD₁₆	—	2	8	no	—
271	C₁₁×SD₁₆	—	2	8	no	—
272	C₁₁×SD₁₆	—	4	4	no	—
273	C₁₁×SD₁₆	C₂×D₄	1	8	yes	complemented
274	C₁₁×D₈	—	2	4	no	—
275	C₁₁×D₈	—	2	8	no	—
276	C₁₁×D₈	—	4	2	no	—
277	C₁₁×D₈	C₂×D₄	1	4	yes	complemented
278	C₂×C₈×C₁₁	—	2	4	no	—
279	C₂×C₈×C₁₁	—	2	4	no	—
280	C₂×C₈×C₁₁	—	2	4	no	—
281	C₂×C₈×C₁₁	—	2	4	no	—
282	C₂×C₈×C₁₁	—	2	4	no	—
283	C₂×C₈×C₁₁	—	2	2	no	—
284	C₂×C₈×C₁₁	C₂×D₄	1	4	yes	complemented
285	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
286	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
287	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
288	C₂×C₈×C₁₁	C₂⁴	1	2	yes	—
289	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
290	C₂×C₈×C₁₁	C₂⁴	1	1	yes	characteristic
291	C₁₁×C₄⋊C₄	—	2	2	no	—
292	C₁₁×C₄⋊C₄	—	2	4	no	—
293	C₁₁×C₄⋊C₄	—	2	2	no	—
294	C₁₁×C₄⋊C₄	—	2	2	no	—
295	C₁₁×C₄⋊C₄	—	2	2	no	—
296	C₁₁×C₄⋊C₄	—	2	4	no	—
297	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
298	C₁₁×C₄⋊C₄	C₂×D₄	1	1	yes	characteristic
299	C₁₁×C₄⋊C₄	C₂×D₄	1	2	yes	—
300	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
301	C₁₁×C₄⋊C₄	C₂⁴	1	2	yes	—
302	C₁₁×C₂²⋊C₄	—	2	4	no	—
303	C₁₁×C₂²⋊C₄	—	2	2	no	—
304	C₁₁×C₂²⋊C₄	—	2	4	no	—
305	C₁₁×C₂²⋊C₄	—	2	4	no	—
306	C₁₁×C₂²⋊C₄	—	2	4	no	—
307	C₁₁×C₂²⋊C₄	—	2	2	no	—
308	C₁₁×C₂²⋊C₄	—	2	2	no	—
309	C₁₁×C₂²⋊C₄	—	2	4	no	—
310	C₁₁×C₂²⋊C₄	—	2	4	no	—
311	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
312	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
313	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
314	C₁₁×C₂²⋊C₄	C₂×D₄	1	2	yes	—
315	C₄²×C₁₁	—	2	2	no	—
316	C₄²×C₁₁	—	2	2	no	—
317	C₄²×C₁₁	—	2	2	no	—
318	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
319	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
320	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
321	C₄²×C₁₁	C₂⁴	1	1	yes	characteristic
322	C₂²×#135	C₂×C₁₁	1	2	yes	complemented
323	D₄×#41	C₂×C₁₁	1	2	yes	complemented
324	#3287	C₂×C₁₁	1	1	yes	characteristic, complemented
325	D₄×Q₁₆	C₂×C₁₁	1	1	yes	characteristic, complemented
326	#3285	C₂×C₁₁	1	2	yes	complemented
327	#3284	C₂×C₁₁	1	2	yes	complemented
328	#3283	C₂×C₁₁	1	1	yes	characteristic, complemented
329	#3282	C₂×C₁₁	1	4	yes	complemented
330	D₄×SD₁₆	C₂×C₁₁	1	2	yes	complemented
331	#3280	C₂×C₁₁	1	2	yes	complemented
332	D₄×D₈	C₂×C₁₁	1	1	yes	characteristic, complemented
333	#3147	C₂×C₁₁	1	1	yes	characteristic, complemented
334	#3050	C₂×C₁₁	1	2	yes	complemented
335	#3035	C₂×C₁₁	1	2	yes	complemented
336	#3002	C₂×C₁₁	1	4	yes	complemented
337	C₄×#135	C₂×C₁₁	1	1	yes	characteristic, complemented
338	C₂×C₈×D₄	C₂×C₁₁	1	1	yes	characteristic, complemented
339	C₂³×C₁₁	—	2	4	no	—
340	C₂³×C₁₁	—	2	4	no	—
341	C₂³×C₁₁	—	2	2	no	—
342	C₂³×C₁₁	—	2	4	no	—
343	C₂³×C₁₁	—	4	2	no	—
344	C₂³×C₁₁	—	4	8	no	—
345	C₂³×C₁₁	—	4	8	no	—
346	C₂³×C₁₁	—	8	4	no	—
347	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
348	C₂³×C₁₁	C₂²×D₄	1	1	yes	characteristic
349	C₂³×C₁₁	C₂²×D₄	1	2	yes	—
350	Q₈×C₁₁	—	2	2	no	—
351	Q₈×C₁₁	—	2	4	no	—
352	Q₈×C₁₁	—	2	4	no	—
353	Q₈×C₁₁	—	4	8	no	—
354	Q₈×C₁₁	C₂²×D₄	1	4	yes	—
355	D₄×C₁₁	—	2	8	no	—
356	D₄×C₁₁	—	2	4	no	—
357	D₄×C₁₁	—	2	2	no	—
358	D₄×C₁₁	—	2	4	no	—
359	D₄×C₁₁	—	2	2	no	—
360	D₄×C₁₁	—	2	4	no	—
361	D₄×C₁₁	—	4	8	no	—
362	D₄×C₁₁	—	4	8	no	—
363	D₄×C₁₁	—	4	8	no	—
364	D₄×C₁₁	—	4	8	no	—
365	D₄×C₁₁	—	4	8	no	—
366	D₄×C₁₁	—	4	4	no	—
367	D₄×C₁₁	—	8	2	no	—
368	D₄×C₁₁	—	8	4	no	—
369	D₄×C₁₁	#135	1	4	yes	direct product factor
370	D₄×C₁₁	C₂²×D₄	1	4	yes	—
371	C₂×C₄×C₁₁	—	2	4	no	—
372	C₂×C₄×C₁₁	—	2	2	no	—
373	C₂×C₄×C₁₁	—	2	4	no	—
374	C₂×C₄×C₁₁	—	2	4	no	—
375	C₂×C₄×C₁₁	—	2	8	no	—
376	C₂×C₄×C₁₁	—	2	2	no	—
377	C₂×C₄×C₁₁	—	2	2	no	—
378	C₂×C₄×C₁₁	—	2	2	no	—
379	C₂×C₄×C₁₁	—	2	2	no	—
380	C₂×C₄×C₁₁	—	2	2	no	—
381	C₂×C₄×C₁₁	—	2	2	no	—
382	C₂×C₄×C₁₁	—	2	2	no	—
383	C₂×C₄×C₁₁	—	2	4	no	—
384	C₂×C₄×C₁₁	—	4	1	no	—
385	C₂×C₄×C₁₁	—	4	8	no	—
386	C₂×C₄×C₁₁	—	4	8	no	—
387	C₂×C₄×C₁₁	—	4	8	no	—
388	C₂×C₄×C₁₁	—	4	8	no	—
389	C₂×C₄×C₁₁	—	4	4	no	—
390	C₂×C₄×C₁₁	—	8	2	no	—
391	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
392	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
393	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
394	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
395	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
396	C₂×C₄×C₁₁	C₂²×D₄	1	2	yes	—
397	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
398	C₂×C₄×C₁₁	C₂²×D₄	1	1	yes	characteristic
399	C₂×C₄×C₁₁	H(5,𝔽₂)	1	2	yes	—
400	C₂×C₄×C₁₁	C₂⁵	1	1	yes	characteristic
401	C₈×C₁₁	—	2	2	no	—
402	C₈×C₁₁	—	2	2	no	—
403	C₈×C₁₁	—	2	1	no	—
404	C₈×C₁₁	—	2	1	no	—
405	C₈×C₁₁	C₂²×D₄	1	2	yes	—
406	C₈×C₁₁	C₂²×D₄	1	2	yes	—
407	C₂²×#41	C₂²×C₁₁	1	4	yes	complemented
408	C₂×#135	—	2	16	no	—
409	C₂×#135	C₂²×C₁₁	1	1	yes	characteristic
410	C₂×#135	C₂²×C₁₁	1	2	yes	complemented
411	C₂×#135	C₂²×C₁₁	1	4	yes	complemented
412	C₂×#135	C₂²×C₁₁	1	2	yes	complemented
413	C₂×#135	C₂²×C₁₁	1	4	yes	complemented
414	C₂×#135	C₂²×C₁₁	1	2	yes	complemented
415	C₂×#135	C₂²×C₁₁	1	2	yes	complemented
416	C₂²×Q₁₆	C₂²×C₁₁	1	2	yes	complemented
417	C₂²×SD₁₆	C₂²×C₁₁	1	4	yes	complemented
418	C₂²×D₈	C₂²×C₁₁	1	2	yes	complemented
419	C₂³×C₈	C₂²×C₁₁	1	2	yes	complemented
420	#550	C₂²×C₁₁	1	2	yes	complemented
421	D₄×Q₈	C₂²×C₁₁	1	2	yes	—
422	#548	C₂²×C₁₁	1	4	yes	complemented
423	#547	—	2	2	no	—
424	#547	C₂²×C₁₁	1	2	yes	complemented
425	#546	—	2	4	no	—
426	#546	C₂²×C₁₁	1	4	yes	complemented
427	D₄²	—	2	2	no	—
428	D₄²	C₂²×C₁₁	1	2	yes	—
429	#532	—	2	2	no	—
430	#532	C₂²×C₁₁	1	2	yes	complemented
431	#525	—	2	4	no	—
432	#525	C₂²×C₁₁	1	4	yes	complemented
433	C₄×#41	C₂²×C₁₁	1	2	yes	complemented
434	C₂×C₄×D₄	—	2	2	no	—
435	C₂×C₄×D₄	C₂²×C₁₁	1	1	yes	characteristic
436	#495	C₂²×C₁₁	1	2	yes	complemented
437	#495	C₂²×C₁₁	1	2	yes	complemented
438	#494	C₂²×C₁₁	1	1	yes	characteristic, complemented
439	#493	C₂²×C₁₁	1	1	yes	characteristic, complemented
440	#492	C₂²×C₁₁	1	2	yes	complemented
441	#467	C₂²×C₁₁	1	2	yes	complemented
442	#467	C₂²×C₁₁	1	2	yes	complemented
443	#466	C₂²×C₁₁	1	2	yes	complemented
444	#466	C₂²×C₁₁	1	2	yes	complemented
445	#465	C₂²×C₁₁	1	4	yes	complemented
446	#465	C₂²×C₁₁	1	4	yes	complemented
447	#464	C₂²×C₁₁	1	4	yes	complemented
448	#463	C₂²×C₁₁	1	4	yes	complemented
449	#462	C₂²×C₁₁	1	2	yes	complemented
450	#461	C₂²×C₁₁	1	2	yes	complemented
451	#460	C₂²×C₁₁	1	2	yes	complemented
452	#459	C₂²×C₁₁	1	2	yes	complemented
453	#452	C₂²×C₁₁	1	4	yes	complemented
454	#452	C₂²×C₁₁	1	4	yes	complemented
455	#451	C₂²×C₁₁	1	4	yes	complemented
456	#450	C₂²×C₁₁	1	4	yes	complemented
457	#449	C₂²×C₁₁	1	4	yes	complemented
458	#449	C₂²×C₁₁	1	4	yes	complemented
459	#448	C₂²×C₁₁	1	4	yes	complemented
460	#447	C₂²×C₁₁	1	4	yes	complemented
461	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
462	C₄×Q₁₆	C₂²×C₁₁	1	1	yes	characteristic, complemented
463	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
464	C₄×SD₁₆	C₂²×C₁₁	1	2	yes	complemented
465	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
466	C₄×D₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
467	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic
468	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic
469	C₈×D₄	C₂²×C₁₁	1	2	yes	complemented
470	C₈×D₄	C₂²×C₁₁	1	2	yes	complemented
471	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
472	C₈×D₄	C₂²×C₁₁	1	1	yes	characteristic, complemented
473	#427	C₂²×C₁₁	1	1	yes	characteristic, complemented
474	C₂×C₄⋊C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
475	#416	C₂²×C₁₁	1	2	yes	complemented
476	#416	C₂²×C₁₁	1	4	yes	complemented
477	C₂×C₂²⋊C₈	C₂²×C₁₁	1	2	yes	complemented
478	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic, complemented
479	C₂²×C₁₁	—	2	1	no	—
480	C₂²×C₁₁	—	2	2	no	—
481	C₂²×C₁₁	—	2	2	no	—
482	C₂²×C₁₁	—	2	1	no	—
483	C₂²×C₁₁	—	2	2	no	—
484	C₂²×C₁₁	—	2	2	no	—
485	C₂²×C₁₁	—	2	4	no	—
486	C₂²×C₁₁	—	2	2	no	—
487	C₂²×C₁₁	—	4	8	no	—
488	C₂²×C₁₁	—	4	2	no	—
489	C₂²×C₁₁	—	4	2	no	—
490	C₂²×C₁₁	—	4	4	no	—
491	C₂²×C₁₁	—	4	4	no	—
492	C₂²×C₁₁	—	4	4	no	—
493	C₂²×C₁₁	—	8	16	no	—
494	C₂²×C₁₁	D₄²	1	2	yes	—
495	C₂²×C₁₁	C₂×#135	1	4	yes	complemented
496	C₂²×C₁₁	C₂³×D₄	1	1	yes	characteristic
497	C₄×C₁₁	—	2	1	no	—
498	C₄×C₁₁	—	2	1	no	—
499	C₄×C₁₁	—	2	2	no	—
500	C₄×C₁₁	—	2	2	no	—
501	C₄×C₁₁	—	2	4	no	—
502	C₄×C₁₁	—	2	1	no	—
503	C₄×C₁₁	—	4	2	no	—
504	C₄×C₁₁	—	4	4	no	—
505	C₄×C₁₁	—	4	2	no	—
506	C₄×C₁₁	D₄²	1	2	yes	—
507	C₄×C₁₁	C₂×#135	1	2	yes	complemented
508	C₄×C₁₁	C₂³×D₄	1	1	yes	characteristic
509	C₄×C₁₁	C₂×H(5,𝔽₂)	1	1	yes	characteristic
510	C₂×#41	—	2	4	no	—
511	C₂×#41	—	2	4	no	—
512	C₂×#41	—	2	16	no	—
513	C₂×#41	—	4	8	no	—
514	C₂×#41	C₂³×C₁₁	1	4	yes	—
515	C₂×#41	C₂³×C₁₁	1	4	yes	—
516	C₂×#41	C₂³×C₁₁	1	4	yes	—
517	C₂×#41	C₂³×C₁₁	1	2	yes	—
518	C₂²×Q₈	C₂³×C₁₁	1	4	yes	—
519	C₂²×D₄	—	2	4	no	—
520	C₂²×D₄	—	2	2	no	—
521	C₂²×D₄	D₄×C₁₁	1	1	yes	characteristic
522	C₂²×D₄	C₂³×C₁₁	1	4	yes	—
523	C₂³×C₄	—	2	4	no	—
524	C₂³×C₄	C₂³×C₁₁	1	2	yes	—
525	#135	—	2	16	no	—
526	#135	—	2	8	no	—
527	#135	—	2	16	no	—
528	#135	—	2	8	no	—
529	#135	—	2	8	no	—
530	#135	—	4	4	no	—
531	#135	D₄×C₁₁	1	8	yes	direct product factor
532	C₂×Q₁₆	—	2	8	no	—
533	C₂×Q₁₆	C₂³×C₁₁	1	4	yes	—
534	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
535	C₂×Q₁₆	C₂³×C₁₁	1	2	yes	—
536	C₂×Q₁₆	C₂³×C₁₁	1	1	yes	characteristic
537	C₂×SD₁₆	—	2	16	no	—
538	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
539	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
540	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
541	C₂×SD₁₆	C₂³×C₁₁	1	4	yes	—
542	C₂×SD₁₆	C₂³×C₁₁	1	2	yes	—
543	C₂×D₈	—	2	8	no	—
544	C₂×D₈	C₂³×C₁₁	1	4	yes	—
545	C₂×D₈	C₂³×C₁₁	1	2	yes	—
546	C₂×D₈	C₂³×C₁₁	1	2	yes	—
547	C₂×D₈	C₂³×C₁₁	1	1	yes	characteristic
548	C₂²×C₈	—	2	8	no	—
549	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
550	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
551	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
552	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
553	C₂²×C₈	C₂³×C₁₁	1	2	yes	—
554	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
555	C₂²×C₈	C₂³×C₁₁	1	1	yes	characteristic
556	C₄⋊Q₈	—	2	2	no	—
557	C₄⋊Q₈	C₂³×C₁₁	1	2	yes	—
558	#127	—	2	2	no	—
559	#127	C₂³×C₁₁	1	2	yes	—
560	#124	—	2	4	no	—
561	#124	C₂³×C₁₁	1	4	yes	—
562	#123	—	2	4	no	—
563	#123	—	2	4	no	—
564	#123	—	2	4	no	—
565	C₂²⋊Q₈	—	2	4	no	—
566	C₂²⋊Q₈	—	2	4	no	—
567	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
568	C₂²⋊Q₈	C₂³×C₁₁	1	4	yes	—
569	#121	—	2	4	no	—
570	#121	—	2	2	no	—
571	#121	—	2	2	no	—
572	#121	—	2	2	no	—
573	#121	—	2	2	no	—
574	#121	—	2	4	no	—
575	#121	—	2	4	no	—
576	#121	C₂³×C₁₁	1	4	yes	—
577	#121	C₂³×C₁₁	1	4	yes	—
578	#120	—	2	4	no	—
579	#120	—	2	4	no	—
580	#120	—	2	4	no	—
581	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
582	C₄×Q₈	C₂³×C₁₁	1	2	yes	—
583	C₄×D₄	—	2	2	no	—
584	C₄×D₄	—	2	4	no	—
585	C₄×D₄	—	2	2	no	—
586	C₄×D₄	—	2	2	no	—
587	C₄×D₄	—	2	4	no	—
588	C₄×D₄	—	2	2	no	—
589	C₄×D₄	—	2	4	no	—
590	C₄×D₄	—	2	2	no	—
591	C₄×D₄	—	2	2	no	—
592	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
593	C₄×D₄	D₄×C₁₁	1	2	yes	—
594	C₄×D₄	D₄×C₁₁	1	1	yes	characteristic
595	C₄×D₄	C₂³×C₁₁	1	2	yes	—
596	C₄×D₄	C₂³×C₁₁	1	2	yes	—
597	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
598	C₄×D₄	C₂³×C₁₁	1	2	yes	—
599	C₄×D₄	C₂³×C₁₁	1	1	yes	characteristic
600	#117	—	2	2	no	—
601	#117	C₂³×C₁₁	1	2	yes	—
602	C₂×C₄⋊C₄	—	2	2	no	—
603	C₂×C₄⋊C₄	D₄×C₁₁	1	1	yes	characteristic
604	C₂×C₂²⋊C₄	—	2	4	no	—
605	C₂×C₂²⋊C₄	D₄×C₁₁	1	2	yes	—
606	C₂×C₄²	—	2	2	no	—
607	C₂×C₄²	C₂³×C₁₁	1	1	yes	characteristic
608	#107	C₂³×C₁₁	1	1	yes	characteristic
609	#107	C₂³×C₁₁	1	1	yes	characteristic
610	#106	C₂³×C₁₁	1	2	yes	—
611	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
612	C₄⋊C₈	C₂³×C₁₁	1	1	yes	characteristic
613	C₄⋊C₈	C₂³×C₁₁	1	2	yes	—
614	#103	C₂³×C₁₁	1	2	yes	—
615	#103	C₂³×C₁₁	1	2	yes	—
616	#103	C₂³×C₁₁	1	4	yes	—
617	#103	C₂³×C₁₁	1	4	yes	—
618	#102	C₂³×C₁₁	1	2	yes	—
619	#102	C₂³×C₁₁	1	2	yes	—
620	#102	C₂³×C₁₁	1	4	yes	—
621	#102	C₂³×C₁₁	1	4	yes	—
622	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
623	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
624	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
625	C₂²⋊C₈	C₂³×C₁₁	1	2	yes	—
626	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
627	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
628	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
629	C₄×C₈	C₂³×C₁₁	1	1	yes	characteristic
630	C₂×C₁₁	—	2	2	no	—
631	C₂×C₁₁	—	2	4	no	—
632	C₂×C₁₁	—	4	2	no	—
633	C₂×C₁₁	—	4	4	no	—
634	C₂×C₁₁	—	8	4	no	—
635	C₂×C₁₁	C₂×D₄²	1	1	yes	characteristic
636	C₂×C₁₁	C₂²×#135	1	1	yes	characteristic
637	C₂×C₁₁	#3584	1	1	yes	characteristic
638	C₂⁴	—	2	4	no	—
639	C₂⁴	C₂×D₄×C₁₁	1	2	yes	—
640	#41	—	2	4	no	—
641	#41	—	2	8	no	—
642	#41	—	2	8	no	—
643	#41	—	2	8	no	—
644	#41	—	2	8	no	—
645	#41	—	4	16	no	—
646	#41	—	4	4	no	—
647	#41	—	4	4	no	—
648	#41	—	4	16	no	—
649	#41	C₂×D₄×C₁₁	1	8	yes	complemented
650	C₂×Q₈	—	2	4	no	—
651	C₂×Q₈	—	2	8	no	—
652	C₂×Q₈	—	4	4	no	—
653	C₂×Q₈	C₂⁴×C₁₁	1	4	yes	—
654	C₂×Q₈	C₂⁴×C₁₁	1	2	yes	—
655	C₂×D₄	—	2	2	no	—
656	C₂×D₄	—	2	4	no	—
657	C₂×D₄	—	2	8	no	—
658	C₂×D₄	—	2	4	no	—
659	C₂×D₄	—	2	4	no	—
660	C₂×D₄	—	2	4	no	—
661	C₂×D₄	—	2	4	no	—
662	C₂×D₄	—	2	4	no	—
663	C₂×D₄	—	2	2	no	—
664	C₂×D₄	—	2	4	no	—
665	C₂×D₄	—	2	2	no	—
666	C₂×D₄	—	4	4	no	—
667	C₂×D₄	—	4	16	no	—
668	C₂×D₄	—	4	8	no	—
669	C₂×D₄	C₂×D₄×C₁₁	1	2	yes	—
670	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
671	C₂×D₄	C₂×D₄×C₁₁	1	1	yes	characteristic
672	C₂×D₄	C₂⁴×C₁₁	1	4	yes	—
673	C₂×D₄	C₂⁴×C₁₁	1	2	yes	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	4	no	—
676	C₂²×C₄	—	2	4	no	—
677	C₂²×C₄	—	2	4	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	4	no	—
680	C₂²×C₄	—	2	4	no	—
681	C₂²×C₄	—	2	4	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	4	16	no	—
684	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
685	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
686	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
687	C₂²×C₄	C₂×D₄×C₁₁	1	2	yes	—
688	C₂²×C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
689	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₁	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₁	1	1	yes	characteristic
692	Q₁₆	—	2	8	no	—
693	Q₁₆	—	2	4	no	—
694	Q₁₆	—	4	2	no	—
695	Q₁₆	C₂×D₄×C₁₁	1	4	yes	complemented
696	SD₁₆	—	2	8	no	—
697	SD₁₆	—	2	8	no	—
698	SD₁₆	—	2	8	no	—
699	SD₁₆	—	4	4	no	—
700	SD₁₆	C₂×D₄×C₁₁	1	8	yes	complemented
701	D₈	—	2	8	no	—
702	D₈	—	2	4	no	—
703	D₈	—	4	2	no	—
704	D₈	C₂×D₄×C₁₁	1	4	yes	complemented
705	C₂×C₈	—	2	4	no	—
706	C₂×C₈	—	2	2	no	—
707	C₂×C₈	—	2	4	no	—
708	C₂×C₈	—	2	4	no	—
709	C₂×C₈	—	2	4	no	—
710	C₂×C₈	—	2	4	no	—
711	C₂×C₈	C₂×D₄×C₁₁	1	4	yes	complemented
712	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
713	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
714	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
715	C₂×C₈	C₂⁴×C₁₁	1	2	yes	—
716	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
717	C₂×C₈	C₂⁴×C₁₁	1	1	yes	characteristic
718	C₄⋊C₄	—	2	2	no	—
719	C₄⋊C₄	—	2	4	no	—
720	C₄⋊C₄	—	2	2	no	—
721	C₄⋊C₄	—	2	2	no	—
722	C₄⋊C₄	—	2	2	no	—
723	C₄⋊C₄	—	2	4	no	—
724	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
725	C₄⋊C₄	C₂×D₄×C₁₁	1	1	yes	characteristic
726	C₄⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
727	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
728	C₄⋊C₄	C₂⁴×C₁₁	1	2	yes	—
729	C₂²⋊C₄	—	2	4	no	—
730	C₂²⋊C₄	—	2	2	no	—
731	C₂²⋊C₄	—	2	4	no	—
732	C₂²⋊C₄	—	2	4	no	—
733	C₂²⋊C₄	—	2	4	no	—
734	C₂²⋊C₄	—	2	2	no	—
735	C₂²⋊C₄	—	2	2	no	—
736	C₂²⋊C₄	—	2	4	no	—
737	C₂²⋊C₄	—	2	4	no	—
738	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
739	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
740	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
741	C₂²⋊C₄	C₂×D₄×C₁₁	1	2	yes	—
742	C₄²	—	2	2	no	—
743	C₄²	—	2	2	no	—
744	C₄²	—	2	2	no	—
745	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
746	C₄²	C₂×D₄×C₁₁	1	1	yes	characteristic
747	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
748	C₄²	C₂⁴×C₁₁	1	1	yes	characteristic
749	C₁₁	D₄×#135	1	1	yes	characteristic, direct product factor, Sylow
750	C₂³	—	2	4	no	—
751	C₂³	—	2	4	no	—
752	C₂³	—	2	2	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	4	2	no	—
755	C₂³	—	4	8	no	—
756	C₂³	—	4	8	no	—
757	C₂³	—	8	4	no	—
758	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
759	C₂³	C₂²×D₄×C₁₁	1	1	yes	characteristic
760	C₂³	C₂²×D₄×C₁₁	1	2	yes	—
761	Q₈	—	2	2	no	—
762	Q₈	—	2	4	no	—
763	Q₈	—	2	4	no	—
764	Q₈	—	4	8	no	—
765	Q₈	C₂²×D₄×C₁₁	1	4	yes	—
766	D₄	—	2	8	no	—
767	D₄	—	2	4	no	—
768	D₄	—	2	2	no	—
769	D₄	—	2	4	no	—
770	D₄	—	2	2	no	—
771	D₄	—	2	4	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	8	no	—
776	D₄	—	4	8	no	—
777	D₄	—	4	4	no	—
778	D₄	—	8	2	no	—
779	D₄	—	8	4	no	—
780	D₄	C₁₁×#135	1	4	yes	direct product factor
781	D₄	C₂²×D₄×C₁₁	1	4	yes	—
782	C₂×C₄	—	2	4	no	—
783	C₂×C₄	—	2	2	no	—
784	C₂×C₄	—	2	4	no	—
785	C₂×C₄	—	2	4	no	—
786	C₂×C₄	—	2	8	no	—
787	C₂×C₄	—	2	2	no	—
788	C₂×C₄	—	2	2	no	—
789	C₂×C₄	—	2	2	no	—
790	C₂×C₄	—	2	2	no	—
791	C₂×C₄	—	2	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	4	no	—
795	C₂×C₄	—	4	1	no	—
796	C₂×C₄	—	4	8	no	—
797	C₂×C₄	—	4	8	no	—
798	C₂×C₄	—	4	8	no	—
799	C₂×C₄	—	4	8	no	—
800	C₂×C₄	—	4	4	no	—
801	C₂×C₄	—	8	2	no	—
802	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
803	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
804	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
805	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
806	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
807	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
808	C₂×C₄	C₂²×D₄×C₁₁	1	2	yes	—
809	C₂×C₄	C₂²×D₄×C₁₁	1	1	yes	characteristic
810	C₂×C₄	C₁₁×H(5,𝔽₂)	1	2	yes	—
811	C₂×C₄	C₂⁵×C₁₁	1	1	yes	characteristic
812	C₈	—	2	2	no	—
813	C₈	—	2	2	no	—
814	C₈	—	2	1	no	—
815	C₈	—	2	1	no	—
816	C₈	C₂²×D₄×C₁₁	1	2	yes	—
817	C₈	C₂²×D₄×C₁₁	1	2	yes	—
818	C₂²	—	2	2	no	—
819	C₂²	—	2	1	no	—
820	C₂²	—	2	1	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	2	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	4	8	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	4	no	—
830	C₂²	—	4	4	no	—
831	C₂²	—	4	4	no	—
832	C₂²	—	8	16	no	—
833	C₂²	D₄²×C₁₁	1	2	yes	—
834	C₂²	C₂×C₁₁×#135	1	4	yes	complemented
835	C₂²	C₂³×D₄×C₁₁	1	1	yes	characteristic
836	C₄	—	2	2	no	—
837	C₄	—	2	2	no	—
838	C₄	—	2	4	no	—
839	C₄	—	2	1	no	—
840	C₄	—	2	1	no	—
841	C₄	—	2	1	no	—
842	C₄	—	4	4	no	—
843	C₄	—	4	2	no	—
844	C₄	—	4	2	no	—
845	C₄	D₄²×C₁₁	1	2	yes	—
846	C₄	C₂×C₁₁×#135	1	2	yes	complemented
847	C₄	C₂³×D₄×C₁₁	1	1	yes	characteristic
848	C₄	C₂×C₁₁×H(5,𝔽₂)	1	1	yes	characteristic
849	C₂	—	2	2	no	—
850	C₂	—	2	4	no	—
851	C₂	—	4	2	no	—
852	C₂	—	4	4	no	—
853	C₂	—	8	4	no	—
854	C₂	C₂×D₄²×C₁₁	1	1	yes	characteristic
855	C₂	C₂²×C₁₁×#135	1	1	yes	characteristic
856	C₂	C₁₁×#3584	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₁	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₁
socle	C₂²×C₁₁	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₁ ◁ C₂×C₄×D₄×C₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₁×#135	C₂	semidirect
2. D₄×C₁₁×#41	C₂	semidirect
3. C₁₁×#3287	C₂	semidirect
4. D₄×C₁₁×Q₁₆	C₂	semidirect
5. C₁₁×#3285	C₂	semidirect
6. C₁₁×#3284	C₂	semidirect
7. C₁₁×#3283	C₂	semidirect
8. C₁₁×#3282	C₂	semidirect
9. D₄×C₁₁×SD₁₆	C₂	semidirect
10. C₁₁×#3280	C₂	semidirect
11. D₄×C₁₁×D₈	C₂	semidirect
12. C₁₁×#3147	C₂	semidirect
13. C₁₁×#3050	C₂	semidirect
14. C₁₁×#3035	C₂	semidirect
15. C₁₁×#3002	C₂	semidirect
16. C₄×C₁₁×#135	C₂	semidirect
17. C₂×C₈×D₄×C₁₁	C₂	semidirect
18. C₂²×C₁₁×#41	C₂²	semidirect
21. C₂×C₁₁×#135	C₂²	semidirect
22. C₂×C₁₁×#135	C₂²	semidirect
23. C₂×C₁₁×#135	C₂²	semidirect
24. C₂×C₁₁×#135	C₂²	semidirect
25. C₂×C₁₁×#135	C₂²	semidirect
26. C₂×C₁₁×#135	C₂²	semidirect
27. C₂²×C₁₁×Q₁₆	C₂²	semidirect
28. C₂²×C₁₁×SD₁₆	C₂²	semidirect
29. C₂²×C₁₁×D₈	C₂²	semidirect
30. C₂³×C₈×C₁₁	C₂²	semidirect
31. C₁₁×#550	C₂²	semidirect
33. C₁₁×#548	C₂²	semidirect
35. C₁₁×#547	C₂²	semidirect
37. C₁₁×#546	C₂²	semidirect
41. C₁₁×#532	C₂²	semidirect
43. C₁₁×#525	C₂²	semidirect
44. C₄×C₁₁×#41	C₂²	semidirect
47. C₁₁×#495	C₂²	semidirect
48. C₁₁×#495	C₂²	semidirect
49. C₁₁×#494	C₂²	semidirect
50. C₁₁×#493	C₂²	semidirect
51. C₁₁×#492	C₂²	semidirect
52. C₁₁×#467	C₂²	semidirect
53. C₁₁×#467	C₂²	semidirect
54. C₁₁×#466	C₂²	semidirect
55. C₁₁×#466	C₂²	semidirect
56. C₁₁×#465	C₂²	semidirect
57. C₁₁×#465	C₂²	semidirect
58. C₁₁×#464	C₂²	semidirect
59. C₁₁×#463	C₂²	semidirect
60. C₁₁×#462	C₂²	semidirect
61. C₁₁×#461	C₂²	semidirect
62. C₁₁×#460	C₂²	semidirect
63. C₁₁×#459	C₂²	semidirect
64. C₁₁×#452	C₂²	semidirect
65. C₁₁×#452	C₂²	semidirect
66. C₁₁×#451	C₂²	semidirect
67. C₁₁×#450	C₂²	semidirect
68. C₁₁×#449	C₂²	semidirect
69. C₁₁×#449	C₂²	semidirect
70. C₁₁×#448	C₂²	semidirect
71. C₁₁×#447	C₂²	semidirect
72. C₄×C₁₁×Q₁₆	C₂²	semidirect
73. C₄×C₁₁×Q₁₆	C₂²	semidirect
74. C₄×C₁₁×SD₁₆	C₂²	semidirect
75. C₄×C₁₁×SD₁₆	C₂²	semidirect
76. C₄×C₁₁×D₈	C₂²	semidirect
77. C₄×C₁₁×D₈	C₂²	semidirect
80. C₈×D₄×C₁₁	C₂²	semidirect
81. C₈×D₄×C₁₁	C₂²	semidirect
82. C₈×D₄×C₁₁	C₂²	semidirect
83. C₈×D₄×C₁₁	C₂²	semidirect
84. C₁₁×#427	C₂²	semidirect
85. C₂×C₁₁×C₄⋊C₈	C₂²	semidirect
86. C₁₁×#416	C₂²	semidirect
87. C₁₁×#416	C₂²	semidirect
88. C₂×C₁₁×C₂²⋊C₈	C₂²	semidirect
89. C₂×C₄×C₈×C₁₁	C₂²	semidirect
111. C₁₁×#135	D₄	direct (N × H)
210. D₄×#135	C₁₁	direct (N × H)
222. C₁₁×#41	C₂×D₄	semidirect
268. C₁₁×Q₁₆	C₂×D₄	semidirect
273. C₁₁×SD₁₆	C₂×D₄	semidirect
277. C₁₁×D₈	C₂×D₄	semidirect
284. C₂×C₈×C₁₁	C₂×D₄	semidirect
322. C₂²×#135	C₂×C₁₁	semidirect
323. D₄×#41	C₂×C₁₁	semidirect
324. #3287	C₂×C₁₁	semidirect
325. D₄×Q₁₆	C₂×C₁₁	semidirect
326. #3285	C₂×C₁₁	semidirect
327. #3284	C₂×C₁₁	semidirect
328. #3283	C₂×C₁₁	semidirect
329. #3282	C₂×C₁₁	semidirect
330. D₄×SD₁₆	C₂×C₁₁	semidirect
331. #3280	C₂×C₁₁	semidirect
332. D₄×D₈	C₂×C₁₁	semidirect
333. #3147	C₂×C₁₁	semidirect
334. #3050	C₂×C₁₁	semidirect
335. #3035	C₂×C₁₁	semidirect
336. #3002	C₂×C₁₁	semidirect
337. C₄×#135	C₂×C₁₁	semidirect
338. C₂×C₈×D₄	C₂×C₁₁	semidirect
369. D₄×C₁₁	#135	direct (N × H)
407. C₂²×#41	C₂²×C₁₁	semidirect
410. C₂×#135	C₂²×C₁₁	semidirect
411. C₂×#135	C₂²×C₁₁	semidirect
412. C₂×#135	C₂²×C₁₁	semidirect
413. C₂×#135	C₂²×C₁₁	semidirect
414. C₂×#135	C₂²×C₁₁	semidirect
415. C₂×#135	C₂²×C₁₁	semidirect
416. C₂²×Q₁₆	C₂²×C₁₁	semidirect
417. C₂²×SD₁₆	C₂²×C₁₁	semidirect
418. C₂²×D₈	C₂²×C₁₁	semidirect
419. C₂³×C₈	C₂²×C₁₁	semidirect
420. #550	C₂²×C₁₁	semidirect
422. #548	C₂²×C₁₁	semidirect
424. #547	C₂²×C₁₁	semidirect
426. #546	C₂²×C₁₁	semidirect
430. #532	C₂²×C₁₁	semidirect
432. #525	C₂²×C₁₁	semidirect
433. C₄×#41	C₂²×C₁₁	semidirect
436. #495	C₂²×C₁₁	semidirect
437. #495	C₂²×C₁₁	semidirect
438. #494	C₂²×C₁₁	semidirect
439. #493	C₂²×C₁₁	semidirect
440. #492	C₂²×C₁₁	semidirect
441. #467	C₂²×C₁₁	semidirect
442. #467	C₂²×C₁₁	semidirect
443. #466	C₂²×C₁₁	semidirect
444. #466	C₂²×C₁₁	semidirect
445. #465	C₂²×C₁₁	semidirect
446. #465	C₂²×C₁₁	semidirect
447. #464	C₂²×C₁₁	semidirect
448. #463	C₂²×C₁₁	semidirect
449. #462	C₂²×C₁₁	semidirect
450. #461	C₂²×C₁₁	semidirect
451. #460	C₂²×C₁₁	semidirect
452. #459	C₂²×C₁₁	semidirect
453. #452	C₂²×C₁₁	semidirect
454. #452	C₂²×C₁₁	semidirect
455. #451	C₂²×C₁₁	semidirect
456. #450	C₂²×C₁₁	semidirect
457. #449	C₂²×C₁₁	semidirect
458. #449	C₂²×C₁₁	semidirect
459. #448	C₂²×C₁₁	semidirect
460. #447	C₂²×C₁₁	semidirect
461. C₄×Q₁₆	C₂²×C₁₁	semidirect
462. C₄×Q₁₆	C₂²×C₁₁	semidirect
463. C₄×SD₁₆	C₂²×C₁₁	semidirect
464. C₄×SD₁₆	C₂²×C₁₁	semidirect
465. C₄×D₈	C₂²×C₁₁	semidirect
466. C₄×D₈	C₂²×C₁₁	semidirect
469. C₈×D₄	C₂²×C₁₁	semidirect
470. C₈×D₄	C₂²×C₁₁	semidirect
471. C₈×D₄	C₂²×C₁₁	semidirect
472. C₈×D₄	C₂²×C₁₁	semidirect
473. #427	C₂²×C₁₁	semidirect
474. C₂×C₄⋊C₈	C₂²×C₁₁	semidirect
475. #416	C₂²×C₁₁	semidirect
476. #416	C₂²×C₁₁	semidirect
477. C₂×C₂²⋊C₈	C₂²×C₁₁	semidirect
478. C₂×C₄×C₈	C₂²×C₁₁	semidirect
495. C₂²×C₁₁	C₂×#135	semidirect
507. C₄×C₁₁	C₂×#135	semidirect
531. #135	D₄×C₁₁	direct (N × H)
649. #41	C₂×D₄×C₁₁	semidirect
695. Q₁₆	C₂×D₄×C₁₁	semidirect
700. SD₁₆	C₂×D₄×C₁₁	semidirect
704. D₈	C₂×D₄×C₁₁	semidirect
711. C₂×C₈	C₂×D₄×C₁₁	semidirect
749. C₁₁	D₄×#135	direct (N × H)
780. D₄	C₁₁×#135	direct (N × H)
834. C₂²	C₂×C₁₁×#135	semidirect
846. C₄	C₂×C₁₁×#135	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₁₁×#135	2
D₄×C₁₁×#41	2
C₁₁×#3287	2
D₄×C₁₁×Q₁₆	2
C₁₁×#3285	2
C₁₁×#3284	2
C₁₁×#3283	2
C₁₁×#3282	2
D₄×C₁₁×SD₁₆	2
C₁₁×#3280	2
D₄×C₁₁×D₈	2
C₁₁×#3147	2
C₁₁×#3050	2
C₁₁×#3035	2
C₁₁×#3002	2
C₄×C₁₁×#135	2
C₂×C₈×D₄×C₁₁	2
D₄×#135	11

Subgroups — D4×C11×#135 #14638241

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄×C₁₁×#135 #14638241