Subgroups — #546×D₁₀₉ #28376473

Order 13952.

1900 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295673	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295672	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295671	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295670	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295669	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295668	C₂	1	2	yes	maximal, complemented
9	#20295667	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295666	C₂	1	2	yes	maximal, complemented
11	#20295665	C₂	1	2	yes	maximal, complemented
12	#20295664	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295663	C₂	1	2	yes	maximal, complemented
14	#124×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#123×D₁₀₉	C₂	1	2	yes	maximal, complemented
16	C₂²⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
17	#121×D₁₀₉	C₂	1	2	yes	maximal, complemented
18	#121×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
19	#120×D₁₀₉	C₂	1	2	yes	maximal, complemented
20	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×C₂²⋊C₄×D₁₀₉	C₂	1	2	yes	maximal, complemented
23	#546×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂⁴×D₁₀₉	C₂²	1	2	yes	—
25	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13182029	C₂²	1	2	yes	complemented
27	C₂×#13182029	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13182028	C₂²	1	1	yes	characteristic, complemented
29	C₂×#13182028	C₂²	1	2	yes	complemented
30	#41×D₁₀₉	—	2	8	no	—
31	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
32	C₂²×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
33	C₂²×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
34	C₂×D₄×D₁₀₉	—	2	8	no	—
35	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₁₀₉	C₂²	1	2	yes	—
37	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
38	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
40	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
41	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
43	C₂×D₄×D₁₀₉	C₂²	1	2	yes	complemented
44	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
46	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
47	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	complemented
48	#16812688	C₂²	1	1	yes	characteristic, complemented
49	#16812687	C₂²	1	1	yes	characteristic, complemented
50	#16812686	C₂²	1	1	yes	characteristic, complemented
51	#16812685	C₂²	1	2	yes	complemented
52	#16812685	C₂²	1	2	yes	complemented
53	#16812684	C₂²	1	2	yes	complemented
54	#16812684	C₂²	1	2	yes	complemented
55	#16812683	C₂²	1	2	yes	complemented
56	#16812682	C₂²	1	2	yes	complemented
57	#16812681	C₂²	1	2	yes	complemented
58	#16812681	C₂²	1	2	yes	complemented
59	#16812680	C₂²	1	2	yes	complemented
60	#16812679	C₂²	1	1	yes	characteristic, complemented
61	#16812678	C₂²	1	1	yes	characteristic, complemented
62	#16812677	C₂²	1	2	yes	complemented
63	#16812676	C₂²	1	2	yes	complemented
64	#16812675	C₂²	1	1	yes	characteristic, complemented
65	#16812674	C₂²	1	2	yes	complemented
66	#16812674	C₂²	1	1	yes	characteristic, complemented
67	#16812673	C₂²	1	2	yes	complemented
68	#16812673	C₂²	1	1	yes	characteristic, complemented
69	#16812672	C₂²	1	2	yes	complemented
70	#16812672	C₂²	1	2	yes	complemented
71	#16812672	C₂²	1	2	yes	complemented
72	#16812671	C₂²	1	2	yes	complemented
73	#16812671	C₂²	1	2	yes	complemented
74	#16812671	C₂²	1	2	yes	complemented
75	#16812670	C₂²	1	1	yes	characteristic, complemented
76	#16812670	C₂²	1	2	yes	complemented
77	#16812669	C₂²	1	2	yes	complemented
78	#16812669	C₂²	1	2	yes	complemented
79	#16812669	C₂²	1	2	yes	complemented
80	#16812668	C₂²	1	2	yes	complemented
81	#16812667	C₂²	1	2	yes	complemented
82	#16812667	C₂²	1	2	yes	complemented
83	#16812667	C₂²	1	2	yes	complemented
84	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
85	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
86	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
87	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
88	#16812661	C₂²	1	1	yes	characteristic, complemented
89	#16812661	C₂²	1	1	yes	characteristic, complemented
90	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
91	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	complemented
93	#16812659	C₂²	1	1	yes	characteristic, complemented
94	#16812659	C₂²	1	1	yes	characteristic, complemented
95	#16812659	C₂²	1	2	yes	complemented
96	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
97	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
98	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
99	C₂×C₂²⋊Dic₁₀₉	C₂²	1	2	yes	complemented
100	C₂×#13182006	C₂²	1	2	yes	complemented
101	C₂×#13182006	C₂²	1	2	yes	complemented
102	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
103	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
104	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
105	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
106	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
107	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
108	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
109	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
110	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
111	C₂²⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
112	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	complemented
113	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
114	C₂×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
115	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
116	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
117	#123×C₁₀₉	C₂²	1	2	yes	complemented
118	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
119	#121×C₁₀₉	C₂²	1	2	yes	complemented
120	#121×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
121	#120×C₁₀₉	C₂²	1	2	yes	complemented
122	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
123	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
124	C₂×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
125	C₂³×D₁₀₉	—	2	8	no	—
126	C₂³×D₁₀₉	—	2	8	no	—
127	C₂³×D₁₀₉	—	4	4	no	—
128	C₂³×D₁₀₉	C₂³	1	2	yes	—
129	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
130	C₂³×D₁₀₉	C₂³	1	2	yes	—
131	C₂³×D₁₀₉	C₂³	1	2	yes	—
132	C₂³×D₁₀₉	C₂³	1	2	yes	—
133	C₂³×D₁₀₉	C₂³	1	2	yes	—
134	C₂³×D₁₀₉	C₂³	1	1	yes	characteristic
135	#13182030	—	2	4	no	—
136	#13182029	—	2	8	no	—
137	#13182029	—	2	4	no	—
138	#13182028	—	2	4	no	—
139	#13182028	—	2	8	no	—
140	C₂×Dic₂₁₈	C₂³	1	2	yes	complemented
141	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic, complemented
142	Q₈×D₁₀₉	—	2	4	no	—
143	C₂×D₄₃₆	—	2	4	no	—
144	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
145	C₂×D₄₃₆	C₂³	1	2	yes	—
146	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
147	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
148	C₂×D₄₃₆	C₂³	1	2	yes	complemented
149	C₂×D₄₃₆	C₂³	1	2	yes	complemented
150	C₂×C₂²⋊D₁₀₉	—	2	8	no	—
151	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
152	C₂×C₂²⋊D₁₀₉	C₂³	1	1	yes	characteristic
153	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
158	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
159	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
160	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	complemented
161	D₄×D₁₀₉	—	2	8	no	—
162	D₄×D₁₀₉	—	2	8	no	—
163	D₄×D₁₀₉	—	2	4	no	—
164	D₄×D₁₀₉	—	2	4	no	—
165	D₄×D₁₀₉	—	2	8	no	—
166	D₄×D₁₀₉	—	2	4	no	—
167	D₄×D₁₀₉	—	2	4	no	—
168	D₄×D₁₀₉	—	4	4	no	—
169	D₄×D₁₀₉	D₄	1	8	yes	complemented
170	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
171	C₂²×Dic₁₀₉	C₂³	1	2	yes	complemented
172	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
173	C₂²×Dic₁₀₉	C₂³	1	2	yes	complemented
174	C₂×C₄×D₁₀₉	—	2	8	no	—
175	C₂×C₄×D₁₀₉	—	2	4	no	—
176	C₂×C₄×D₁₀₉	—	2	4	no	—
177	C₂×C₄×D₁₀₉	—	4	4	no	—
178	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
179	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
180	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
181	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
182	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
183	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
184	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
185	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
186	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
187	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
188	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
189	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic, complemented
190	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic, complemented
191	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
192	C₂×C₄×D₁₀₉	C₂³	1	2	yes	complemented
193	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
194	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
195	C₄⋊Dic₁₀₉	C₂³	1	2	yes	complemented
196	#13182008	C₂³	1	2	yes	complemented
197	#13182008	C₂³	1	1	yes	characteristic, complemented
198	#13182008	C₂³	1	1	yes	characteristic, complemented
199	#13182008	C₂³	1	2	yes	complemented
200	#13182008	C₂³	1	2	yes	complemented
201	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
202	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
203	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	complemented
204	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	complemented
205	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	complemented
206	C₂²⋊Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
207	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	complemented
208	#13182006	C₂³	1	1	yes	characteristic
209	#13182006	C₂³	1	1	yes	characteristic
210	#13182006	C₂³	1	2	yes	—
211	#13182006	C₂³	1	2	yes	—
212	#13182006	C₂³	1	2	yes	complemented
213	#13182006	C₂³	1	2	yes	complemented
214	#13182006	C₂³	1	2	yes	complemented
215	#13182006	C₂³	1	2	yes	complemented
216	#13182006	C₂³	1	2	yes	complemented
217	#13182006	C₂³	1	1	yes	characteristic, complemented
218	#13182006	C₂³	1	2	yes	complemented
219	#13182006	C₂³	1	1	yes	characteristic, complemented
220	#13182006	C₂³	1	2	yes	complemented
221	#13182006	C₂³	1	2	yes	complemented
222	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
223	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
224	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic, complemented
225	C₂⁴×C₁₀₉	C₂³	1	2	yes	—
226	#41×C₁₀₉	—	2	4	no	—
227	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
228	C₂×D₄×C₁₀₉	—	2	4	no	—
229	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
230	C₂×D₄×C₁₀₉	C₂³	1	2	yes	—
231	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
232	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
233	C₂×D₄×C₁₀₉	C₂³	1	2	yes	complemented
234	C₂×D₄×C₁₀₉	C₂³	1	2	yes	complemented
235	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
236	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	complemented
237	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
238	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	complemented
239	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
240	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
241	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
242	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
243	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
244	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
245	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
246	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
247	C₂²⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
248	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	complemented
249	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic, complemented
250	C₂³×C₁₀₉	—	2	4	no	—
251	C₂³×C₁₀₉	—	2	4	no	—
252	C₂³×C₁₀₉	—	4	2	no	—
253	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
254	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
255	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
256	C₂³×C₁₀₉	C₂⁴	1	1	yes	characteristic
257	C₂²×D₁₀₉	—	2	2	no	—
258	C₂²×D₁₀₉	—	2	4	no	—
259	C₂²×D₁₀₉	—	2	4	no	—
260	C₂²×D₁₀₉	—	2	2	no	—
261	C₂²×D₁₀₉	—	2	4	no	—
262	C₂²×D₁₀₉	—	2	4	no	—
263	C₂²×D₁₀₉	—	2	2	no	—
264	C₂²×D₁₀₉	—	2	4	no	—
265	C₂²×D₁₀₉	—	2	4	no	—
266	C₂²×D₁₀₉	—	2	4	no	—
267	C₂²×D₁₀₉	—	2	2	no	—
268	C₂²×D₁₀₉	—	2	4	no	—
269	C₂²×D₁₀₉	—	2	4	no	—
270	C₂²×D₁₀₉	—	2	4	no	—
271	C₂²×D₁₀₉	—	2	2	no	—
272	C₂²×D₁₀₉	—	2	4	no	—
273	C₂²×D₁₀₉	—	4	2	no	—
274	C₂²×D₁₀₉	—	4	2	no	—
275	C₂²×D₁₀₉	—	4	2	no	—
276	C₂²×D₁₀₉	—	4	32	no	—
277	C₂²×D₁₀₉	C₂×D₄	1	8	yes	—
278	C₂²×D₁₀₉	#41	1	4	yes	complemented
279	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
280	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
281	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
282	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
283	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
284	Q₈×C₁₀₉	—	2	2	no	—
285	D₄×C₁₀₉	—	2	4	no	—
286	D₄×C₁₀₉	—	2	4	no	—
287	D₄×C₁₀₉	—	2	2	no	—
288	D₄×C₁₀₉	—	2	2	no	—
289	D₄×C₁₀₉	—	4	2	no	—
290	D₄×C₁₀₉	C₂×D₄	1	4	yes	complemented
291	C₂×C₄×C₁₀₉	—	2	4	no	—
292	C₂×C₄×C₁₀₉	—	2	2	no	—
293	C₂×C₄×C₁₀₉	—	2	2	no	—
294	C₂×C₄×C₁₀₉	—	4	2	no	—
295	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
296	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
297	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
298	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
299	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
300	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
301	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
302	C₂²⋊D₁₀₉	—	2	4	no	—
303	C₂²⋊D₁₀₉	—	2	4	no	—
304	C₂²⋊D₁₀₉	—	2	2	no	—
305	C₂²⋊D₁₀₉	—	2	4	no	—
306	C₂²⋊D₁₀₉	—	2	4	no	—
307	C₂²⋊D₁₀₉	—	2	2	no	—
308	C₂²⋊D₁₀₉	—	2	4	no	—
309	C₂²⋊D₁₀₉	—	4	2	no	—
310	C₂²⋊D₁₀₉	—	4	2	no	—
311	C₂²⋊D₁₀₉	C₂×D₄	1	8	yes	complemented
312	C₂×Dic₁₀₉	—	2	4	no	—
313	C₂×Dic₁₀₉	—	2	2	no	—
314	C₂×Dic₁₀₉	—	2	2	no	—
315	C₂×Dic₁₀₉	—	4	2	no	—
316	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
317	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
318	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
319	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
320	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
321	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
322	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
323	D₄₃₆	—	2	4	no	—
324	D₄₃₆	—	2	4	no	—
325	D₄₃₆	—	2	2	no	—
326	D₄₃₆	—	2	2	no	—
327	D₄₃₆	—	4	2	no	—
328	D₄₃₆	C₂×D₄	1	4	yes	complemented
329	C₄×D₁₀₉	—	2	2	no	—
330	C₄×D₁₀₉	—	2	2	no	—
331	C₄×D₁₀₉	—	2	4	no	—
332	C₄×D₁₀₉	—	2	4	no	—
333	C₄×D₁₀₉	—	2	4	no	—
334	C₄×D₁₀₉	—	2	2	no	—
335	C₄×D₁₀₉	—	2	2	no	—
336	C₄×D₁₀₉	—	2	4	no	—
337	C₄×D₁₀₉	—	2	2	no	—
338	C₄×D₁₀₉	—	2	2	no	—
339	C₄×D₁₀₉	—	2	2	no	—
340	C₄×D₁₀₉	—	2	2	no	—
341	C₄×D₁₀₉	—	4	2	no	—
342	C₄×D₁₀₉	—	4	2	no	—
343	C₄×D₁₀₉	C₂×D₄	1	4	yes	—
344	Dic₂₁₈	—	2	2	no	—
345	Dic₂₁₈	—	2	4	no	—
346	C₂²×C₁₀₉	—	2	1	no	—
347	C₂²×C₁₀₉	—	2	2	no	—
348	C₂²×C₁₀₉	—	2	2	no	—
349	C₂²×C₁₀₉	—	2	1	no	—
350	C₂²×C₁₀₉	—	2	1	no	—
351	C₂²×C₁₀₉	—	2	2	no	—
352	C₂²×C₁₀₉	—	2	1	no	—
353	C₂²×C₁₀₉	—	2	2	no	—
354	C₂²×C₁₀₉	—	2	1	no	—
355	C₂²×C₁₀₉	—	2	2	no	—
356	C₂²×C₁₀₉	—	4	8	no	—
357	C₂²×C₁₀₉	C₂²×D₄	1	4	yes	—
358	C₂²×C₁₀₉	C₂×#41	1	2	yes	complemented
359	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
360	C₂×D₁₀₉	—	2	1	no	—
361	C₂×D₁₀₉	—	2	2	no	—
362	C₂×D₁₀₉	—	2	2	no	—
363	C₂×D₁₀₉	—	2	1	no	—
364	C₂×D₁₀₉	—	2	8	no	—
365	C₂×D₁₀₉	—	2	16	no	—
366	C₂×D₁₀₉	—	2	1	no	—
367	C₂×D₁₀₉	—	2	2	no	—
368	C₂×D₁₀₉	—	2	1	no	—
369	C₂×D₁₀₉	—	2	2	no	—
370	C₂×D₁₀₉	—	2	1	no	—
371	C₂×D₁₀₉	—	2	2	no	—
372	C₂×D₁₀₉	—	4	8	no	—
373	C₂×D₁₀₉	—	4	8	no	—
374	C₂×D₁₀₉	—	4	8	no	—
375	C₂×D₁₀₉	—	4	4	no	—
376	C₂×D₁₀₉	—	4	8	no	—
377	C₂×D₁₀₉	C₂²×D₄	1	4	yes	—
378	C₂×D₁₀₉	C₂²×D₄	1	2	yes	—
379	C₂×D₁₀₉	C₂×#41	1	2	yes	—
380	C₂×D₁₀₉	C₂×#41	1	2	yes	complemented
381	C₂×D₁₀₉	H(5,𝔽₂)	1	2	yes	—
382	C₄×C₁₀₉	—	2	2	no	—
383	C₄×C₁₀₉	—	2	1	no	—
384	C₄×C₁₀₉	—	2	1	no	—
385	C₄×C₁₀₉	—	2	1	no	—
386	C₄×C₁₀₉	—	2	1	no	—
387	C₄×C₁₀₉	—	2	2	no	—
388	C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
389	Dic₁₀₉	—	2	2	no	—
390	Dic₁₀₉	—	2	1	no	—
391	Dic₁₀₉	—	2	1	no	—
392	Dic₁₀₉	—	2	1	no	—
393	Dic₁₀₉	—	2	1	no	—
394	Dic₁₀₉	—	2	2	no	—
395	Dic₁₀₉	C₂²×D₄	1	2	yes	—
396	C₂×C₁₀₉	—	2	2	no	—
397	C₂×C₁₀₉	—	2	4	no	—
398	C₂×C₁₀₉	—	4	2	no	—
399	C₂×C₁₀₉	—	4	1	no	—
400	C₂×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
401	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
402	C₂×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
403	D₁₀₉	—	2	2	no	—
404	D₁₀₉	—	2	4	no	—
405	D₁₀₉	—	4	1	no	—
406	D₁₀₉	—	4	2	no	—
407	D₁₀₉	#546	1	4	yes	direct product factor
408	C₂×#546	—	109	1	no	maximal, Sylow
409	C₁₀₉	C₂×#546	1	1	yes	characteristic, complemented, Sylow
410	C₂²×#41	—	109	1	no	—
411	C₂³×D₄	—	109	1	no	—
412	#546	—	109	1	no	—
413	#546	—	109	1	no	—
414	#546	—	109	1	no	—
415	#546	—	109	2	no	—
416	#546	—	109	1	no	—
417	#546	—	109	2	no	—
418	#546	—	109	1	no	—
419	#546	—	109	2	no	—
420	#546	—	109	1	no	—
421	#546	—	109	1	no	—
422	#546	—	109	2	no	—
423	#546	D₁₀₉	1	1	yes	characteristic, direct product factor
424	C₂×#124	—	109	1	no	—
425	C₂×#123	—	109	2	no	—
426	C₂×C₂²⋊Q₈	—	109	1	no	—
427	C₂×#121	—	109	1	no	—
428	C₂×#121	—	109	2	no	—
429	C₂×#120	—	109	2	no	—
430	C₂×C₄×D₄	—	109	1	no	—
431	C₂×C₄×D₄	—	109	1	no	—
432	C₂²×C₂²⋊C₄	—	109	2	no	—
433	C₂⁵	—	109	2	no	—
434	C₂×#41	—	109	1	no	—
435	C₂×#41	—	109	1	no	—
436	C₂×#41	—	109	2	no	—
437	C₂×#41	—	109	1	no	—
438	C₂×#41	—	109	2	no	—
439	C₂×#41	—	218	8	no	—
440	C₂×#41	C₂×D₁₀₉	1	1	yes	characteristic, complemented
441	C₂²×Q₈	—	109	1	no	—
442	C₂²×D₄	—	109	1	no	—
443	C₂²×D₄	—	109	2	no	—
444	C₂²×D₄	—	109	2	no	—
445	C₂²×D₄	—	109	1	no	—
446	C₂²×D₄	—	109	2	no	—
447	C₂²×D₄	—	109	1	no	—
448	C₂²×D₄	—	109	2	no	—
449	C₂²×D₄	—	109	1	no	—
450	C₂²×D₄	—	109	1	no	—
451	C₂²×D₄	—	109	2	no	—
452	C₂²×D₄	—	109	1	no	—
453	C₂²×D₄	—	218	8	no	—
454	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
455	C₂³×C₄	—	109	2	no	—
456	C₂³×C₄	—	109	1	no	—
457	C₂³×C₄	—	109	2	no	—
458	C₂³×C₄	—	109	1	no	—
459	#124	—	109	1	no	—
460	#124	—	109	1	no	—
461	#124	—	109	2	no	—
462	#124	—	109	2	no	—
463	#124	—	109	1	no	—
464	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
465	#123	—	109	2	no	—
466	#123	—	109	2	no	—
467	#123	—	109	2	no	—
468	#123	—	109	2	no	—
469	#123	—	109	2	no	—
470	#123	—	109	2	no	—
471	#123	—	109	2	no	—
472	#123	C₂×D₁₀₉	1	2	yes	complemented
473	C₂²⋊Q₈	—	109	1	no	—
474	C₂²⋊Q₈	—	109	1	no	—
475	C₂²⋊Q₈	—	109	2	no	—
476	C₂²⋊Q₈	—	109	1	no	—
477	C₂²⋊Q₈	—	109	2	no	—
478	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
479	#121	—	109	1	no	—
480	#121	—	109	2	no	—
481	#121	—	109	2	no	—
482	#121	—	109	2	no	—
483	#121	—	109	2	no	—
484	#121	—	109	1	no	—
485	#121	—	109	2	no	—
486	#121	—	109	1	no	—
487	#121	—	109	2	no	—
488	#121	—	109	2	no	—
489	#121	—	109	2	no	—
490	#121	—	109	2	no	—
491	#121	C₂×D₁₀₉	1	1	yes	characteristic, complemented
492	#121	C₂×D₁₀₉	1	2	yes	complemented
493	#120	—	109	2	no	—
494	#120	—	109	2	no	—
495	#120	—	109	2	no	—
496	#120	—	109	2	no	—
497	#120	—	109	2	no	—
498	#120	—	109	2	no	—
499	#120	—	109	2	no	—
500	#120	C₂×D₁₀₉	1	2	yes	complemented
501	C₄×D₄	—	109	1	no	—
502	C₄×D₄	—	109	1	no	—
503	C₄×D₄	—	109	1	no	—
504	C₄×D₄	—	109	2	no	—
505	C₄×D₄	—	109	1	no	—
506	C₄×D₄	—	109	1	no	—
507	C₄×D₄	—	109	1	no	—
508	C₄×D₄	—	109	1	no	—
509	C₄×D₄	—	109	1	no	—
510	C₄×D₄	—	109	2	no	—
511	C₄×D₄	—	109	1	no	—
512	C₄×D₄	—	109	1	no	—
513	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
514	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
515	C₂×C₄⋊C₄	—	109	1	no	—
516	C₂×C₄⋊C₄	—	109	1	no	—
517	C₂×C₄⋊C₄	—	109	2	no	—
518	C₂×C₂²⋊C₄	—	109	2	no	—
519	C₂×C₂²⋊C₄	—	109	2	no	—
520	C₂×C₂²⋊C₄	—	109	2	no	—
521	C₂×C₂²⋊C₄	—	109	1	no	—
522	C₂×C₂²⋊C₄	—	109	2	no	—
523	C₂×C₂²⋊C₄	—	109	2	no	—
524	C₂×C₂²⋊C₄	—	109	2	no	—
525	C₂×C₂²⋊C₄	—	109	2	no	—
526	C₂×C₂²⋊C₄	—	109	2	no	—
527	C₂×C₂²⋊C₄	—	109	2	no	—
528	C₂×C₂²⋊C₄	—	109	2	no	—
529	C₂×C₂²⋊C₄	—	109	2	no	—
530	C₂×C₂²⋊C₄	—	109	1	no	—
531	C₂×C₂²⋊C₄	—	109	2	no	—
532	C₂×C₂²⋊C₄	C₂×D₁₀₉	1	2	yes	complemented
533	C₂×C₄²	—	109	1	no	—
534	C₂⁴	—	109	1	no	—
535	C₂⁴	—	109	2	no	—
536	C₂⁴	—	109	2	no	—
537	C₂⁴	—	109	2	no	—
538	C₂⁴	—	109	2	no	—
539	C₂⁴	—	109	2	no	—
540	C₂⁴	—	109	1	no	—
541	C₂⁴	—	436	4	no	—
542	C₂⁴	—	218	8	no	—
543	C₂⁴	—	218	8	no	—
544	C₂⁴	C₂²×D₁₀₉	1	2	yes	—
545	#41	—	2	4	no	—
546	#41	—	218	8	no	—
547	#41	—	218	4	no	—
548	#41	—	218	8	no	—
549	#41	—	218	4	no	—
550	#41	—	218	4	no	—
551	C₂×Q₈	—	109	2	no	—
552	C₂×Q₈	—	109	1	no	—
553	C₂×Q₈	—	218	4	no	—
554	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
555	C₂×D₄	—	2	4	no	—
556	C₂×D₄	—	109	2	no	—
557	C₂×D₄	—	109	8	no	—
558	C₂×D₄	—	109	2	no	—
559	C₂×D₄	—	109	2	no	—
560	C₂×D₄	—	109	1	no	—
561	C₂×D₄	—	109	1	no	—
562	C₂×D₄	—	109	2	no	—
563	C₂×D₄	—	109	2	no	—
564	C₂×D₄	—	109	2	no	—
565	C₂×D₄	—	109	2	no	—
566	C₂×D₄	—	109	2	no	—
567	C₂×D₄	—	109	1	no	—
568	C₂×D₄	—	109	2	no	—
569	C₂×D₄	—	109	1	no	—
570	C₂×D₄	—	109	2	no	—
571	C₂×D₄	—	109	1	no	—
572	C₂×D₄	—	109	2	no	—
573	C₂×D₄	—	436	4	no	—
574	C₂×D₄	—	218	4	no	—
575	C₂×D₄	—	218	4	no	—
576	C₂×D₄	—	218	8	no	—
577	C₂×D₄	—	218	4	no	—
578	C₂×D₄	—	218	4	no	—
579	C₂×D₄	—	218	8	no	—
580	C₂×D₄	—	218	8	no	—
581	C₂×D₄	—	218	8	no	—
582	C₂×D₄	—	218	4	no	—
583	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
584	C₂×D₄	C₂²×D₁₀₉	1	2	yes	—
585	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
586	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
587	C₂×D₄	C₂²×D₁₀₉	1	2	yes	complemented
588	C₂×D₄	C₂²×D₁₀₉	1	2	yes	complemented
589	C₂²×C₄	—	109	1	no	—
590	C₂²×C₄	—	109	2	no	—
591	C₂²×C₄	—	109	1	no	—
592	C₂²×C₄	—	109	2	no	—
593	C₂²×C₄	—	109	1	no	—
594	C₂²×C₄	—	109	2	no	—
595	C₂²×C₄	—	109	2	no	—
596	C₂²×C₄	—	109	1	no	—
597	C₂²×C₄	—	109	1	no	—
598	C₂²×C₄	—	109	2	no	—
599	C₂²×C₄	—	109	1	no	—
600	C₂²×C₄	—	109	2	no	—
601	C₂²×C₄	—	109	1	no	—
602	C₂²×C₄	—	109	1	no	—
603	C₂²×C₄	—	109	1	no	—
604	C₂²×C₄	—	109	2	no	—
605	C₂²×C₄	—	109	2	no	—
606	C₂²×C₄	—	109	1	no	—
607	C₂²×C₄	—	109	1	no	—
608	C₂²×C₄	—	436	4	no	—
609	C₂²×C₄	—	218	4	no	—
610	C₂²×C₄	—	218	4	no	—
611	C₂²×C₄	—	218	8	no	—
612	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
613	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	complemented
614	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
615	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	complemented
616	C₄⋊C₄	—	109	2	no	—
617	C₄⋊C₄	—	109	1	no	—
618	C₄⋊C₄	—	109	1	no	—
619	C₄⋊C₄	—	109	2	no	—
620	C₄⋊C₄	—	109	2	no	—
621	C₄⋊C₄	—	109	1	no	—
622	C₄⋊C₄	—	109	1	no	—
623	C₄⋊C₄	—	109	2	no	—
624	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
625	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
626	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
627	C₂²⋊C₄	—	109	1	no	—
628	C₂²⋊C₄	—	109	2	no	—
629	C₂²⋊C₄	—	109	2	no	—
630	C₂²⋊C₄	—	109	2	no	—
631	C₂²⋊C₄	—	109	2	no	—
632	C₂²⋊C₄	—	109	1	no	—
633	C₂²⋊C₄	—	109	2	no	—
634	C₂²⋊C₄	—	109	1	no	—
635	C₂²⋊C₄	—	109	1	no	—
636	C₂²⋊C₄	—	109	2	no	—
637	C₂²⋊C₄	—	109	2	no	—
638	C₂²⋊C₄	—	109	2	no	—
639	C₂²⋊C₄	—	109	2	no	—
640	C₂²⋊C₄	—	109	2	no	—
641	C₂²⋊C₄	—	109	2	no	—
642	C₂²⋊C₄	—	109	2	no	—
643	C₂²⋊C₄	—	109	2	no	—
644	C₂²⋊C₄	—	109	1	no	—
645	C₂²⋊C₄	—	109	1	no	—
646	C₂²⋊C₄	—	109	2	no	—
647	C₂²⋊C₄	—	109	2	no	—
648	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
649	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
650	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
651	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
652	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
653	C₂²⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
654	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	complemented
655	C₄²	—	109	1	no	—
656	C₄²	—	109	1	no	—
657	C₄²	—	109	1	no	—
658	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic, complemented
659	C₂³	—	2	4	no	—
660	C₂³	—	2	4	no	—
661	C₂³	—	4	2	no	—
662	C₂³	—	109	1	no	—
663	C₂³	—	109	8	no	—
664	C₂³	—	109	4	no	—
665	C₂³	—	109	1	no	—
666	C₂³	—	109	2	no	—
667	C₂³	—	109	2	no	—
668	C₂³	—	109	1	no	—
669	C₂³	—	436	2	no	—
670	C₂³	—	436	2	no	—
671	C₂³	—	436	2	no	—
672	C₂³	—	436	32	no	—
673	C₂³	—	218	2	no	—
674	C₂³	—	218	2	no	—
675	C₂³	—	218	4	no	—
676	C₂³	—	218	4	no	—
677	C₂³	—	218	4	no	—
678	C₂³	—	218	4	no	—
679	C₂³	—	218	2	no	—
680	C₂³	—	218	4	no	—
681	C₂³	—	218	4	no	—
682	C₂³	—	218	4	no	—
683	C₂³	—	218	4	no	—
684	C₂³	—	218	2	no	—
685	C₂³	—	218	2	no	—
686	C₂³	—	218	4	no	—
687	C₂³	—	218	4	no	—
688	C₂³	—	218	4	no	—
689	C₂³	C₂³×D₁₀₉	1	2	yes	—
690	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
691	C₂³	C₂³×D₁₀₉	1	2	yes	—
692	C₂³	C₂³×D₁₀₉	1	1	yes	characteristic
693	Q₈	—	2	2	no	—
694	Q₈	—	218	4	no	—
695	Q₈	—	218	2	no	—
696	D₄	—	2	4	no	—
697	D₄	—	2	4	no	—
698	D₄	—	2	2	no	—
699	D₄	—	2	2	no	—
700	D₄	—	4	2	no	—
701	D₄	—	109	8	no	—
702	D₄	—	109	4	no	—
703	D₄	—	436	2	no	—
704	D₄	—	436	2	no	—
705	D₄	—	436	2	no	—
706	D₄	—	218	4	no	—
707	D₄	—	218	4	no	—
708	D₄	—	218	2	no	—
709	D₄	—	218	4	no	—
710	D₄	—	218	4	no	—
711	D₄	—	218	4	no	—
712	D₄	—	218	2	no	—
713	D₄	—	218	4	no	—
714	D₄	—	218	4	no	—
715	D₄	—	218	2	no	—
716	D₄	—	218	2	no	—
717	D₄	D₄×D₁₀₉	1	4	yes	complemented
718	C₂×C₄	—	2	4	no	—
719	C₂×C₄	—	2	2	no	—
720	C₂×C₄	—	2	2	no	—
721	C₂×C₄	—	4	2	no	—
722	C₂×C₄	—	109	1	no	—
723	C₂×C₄	—	109	4	no	—
724	C₂×C₄	—	109	1	no	—
725	C₂×C₄	—	109	1	no	—
726	C₂×C₄	—	109	2	no	—
727	C₂×C₄	—	109	1	no	—
728	C₂×C₄	—	109	2	no	—
729	C₂×C₄	—	109	1	no	—
730	C₂×C₄	—	436	2	no	—
731	C₂×C₄	—	436	2	no	—
732	C₂×C₄	—	436	2	no	—
733	C₂×C₄	—	218	2	no	—
734	C₂×C₄	—	218	2	no	—
735	C₂×C₄	—	218	2	no	—
736	C₂×C₄	—	218	4	no	—
737	C₂×C₄	—	218	2	no	—
738	C₂×C₄	—	218	2	no	—
739	C₂×C₄	—	218	4	no	—
740	C₂×C₄	—	218	4	no	—
741	C₂×C₄	—	218	4	no	—
742	C₂×C₄	—	218	2	no	—
743	C₂×C₄	—	218	2	no	—
744	C₂×C₄	—	218	2	no	—
745	C₂×C₄	—	218	4	no	—
746	C₂×C₄	—	218	2	no	—
747	C₂×C₄	—	218	2	no	—
748	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
749	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
750	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
751	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
752	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
753	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
754	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
755	C₂²	—	2	1	no	—
756	C₂²	—	2	2	no	—
757	C₂²	—	2	2	no	—
758	C₂²	—	2	1	no	—
759	C₂²	—	2	1	no	—
760	C₂²	—	2	2	no	—
761	C₂²	—	2	1	no	—
762	C₂²	—	2	2	no	—
763	C₂²	—	2	1	no	—
764	C₂²	—	2	2	no	—
765	C₂²	—	4	8	no	—
766	C₂²	—	109	2	no	—
767	C₂²	—	109	2	no	—
768	C₂²	—	109	2	no	—
769	C₂²	—	109	4	no	—
770	C₂²	—	109	2	no	—
771	C₂²	—	436	8	no	—
772	C₂²	—	436	8	no	—
773	C₂²	—	436	8	no	—
774	C₂²	—	436	4	no	—
775	C₂²	—	436	8	no	—
776	C₂²	—	218	8	no	—
777	C₂²	—	218	16	no	—
778	C₂²	—	218	1	no	—
779	C₂²	—	218	2	no	—
780	C₂²	—	218	1	no	—
781	C₂²	—	218	2	no	—
782	C₂²	—	218	1	no	—
783	C₂²	—	218	2	no	—
784	C₂²	—	218	1	no	—
785	C₂²	—	218	2	no	—
786	C₂²	—	218	2	no	—
787	C₂²	—	218	1	no	—
788	C₂²	C₂×D₄×D₁₀₉	1	4	yes	—
789	C₂²	#41×D₁₀₉	1	2	yes	complemented
790	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
791	C₄	—	2	1	no	—
792	C₄	—	2	1	no	—
793	C₄	—	2	2	no	—
794	C₄	—	2	1	no	—
795	C₄	—	2	1	no	—
796	C₄	—	2	2	no	—
797	C₄	—	109	2	no	—
798	C₄	—	218	1	no	—
799	C₄	—	218	1	no	—
800	C₄	—	218	2	no	—
801	C₄	—	218	1	no	—
802	C₄	—	218	1	no	—
803	C₄	—	218	2	no	—
804	C₄	C₂×D₄×D₁₀₉	1	2	yes	—
805	C₂	—	2	2	no	—
806	C₂	—	2	4	no	—
807	C₂	—	4	2	no	—
808	C₂	—	4	1	no	—
809	C₂	—	109	4	no	—
810	C₂	—	436	2	no	—
811	C₂	—	436	1	no	—
812	C₂	—	218	2	no	—
813	C₂	—	218	4	no	—
814	C₂	C₂²×D₄×D₁₀₉	1	1	yes	characteristic
815	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
816	C₂	H(5,𝔽₂)×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#546×C₁₀₉	C₂
hypercenter	#546	D₁₀₉
hypocenter	C₁₀₉	C₂×#546
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #546

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₀₉	C₂	semidirect
2. C₂²×D₄×D₁₀₉	C₂	semidirect
3. #20295673	C₂	semidirect
4. #20295672	C₂	semidirect
5. #20295671	C₂	semidirect
6. #20295670	C₂	semidirect
7. #20295669	C₂	semidirect
8. #20295668	C₂	semidirect
9. #20295667	C₂	semidirect
10. #20295666	C₂	semidirect
11. #20295665	C₂	semidirect
12. #20295664	C₂	semidirect
13. #20295663	C₂	semidirect
14. #124×D₁₀₉	C₂	semidirect
15. #123×D₁₀₉	C₂	semidirect
16. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
17. #121×D₁₀₉	C₂	semidirect
18. #121×D₁₀₉	C₂	semidirect
19. #120×D₁₀₉	C₂	semidirect
20. C₄×D₄×D₁₀₉	C₂	semidirect
21. C₄×D₄×D₁₀₉	C₂	semidirect
22. C₂×C₂²⋊C₄×D₁₀₉	C₂	semidirect
23. #546×C₁₀₉	C₂	semidirect
25. C₂×#13182030	C₂²	semidirect
26. C₂×#13182029	C₂²	semidirect
27. C₂×#13182029	C₂²	semidirect
28. C₂×#13182028	C₂²	semidirect
29. C₂×#13182028	C₂²	semidirect
31. C₂×Q₈×D₁₀₉	C₂²	semidirect
32. C₂²×D₄₃₆	C₂²	semidirect
33. C₂²×C₂²⋊D₁₀₉	C₂²	semidirect
39. C₂×D₄×D₁₀₉	C₂²	semidirect
40. C₂×D₄×D₁₀₉	C₂²	semidirect
41. C₂×D₄×D₁₀₉	C₂²	semidirect
42. C₂×D₄×D₁₀₉	C₂²	semidirect
43. C₂×D₄×D₁₀₉	C₂²	semidirect
45. C₂²×C₄×D₁₀₉	C₂²	semidirect
46. C₂²×C₄×D₁₀₉	C₂²	semidirect
47. C₂²×C₄×D₁₀₉	C₂²	semidirect
48. #16812688	C₂²	semidirect
49. #16812687	C₂²	semidirect
50. #16812686	C₂²	semidirect
51. #16812685	C₂²	semidirect
52. #16812685	C₂²	semidirect
53. #16812684	C₂²	semidirect
54. #16812684	C₂²	semidirect
55. #16812683	C₂²	semidirect
56. #16812682	C₂²	semidirect
57. #16812681	C₂²	semidirect
58. #16812681	C₂²	semidirect
59. #16812680	C₂²	semidirect
60. #16812679	C₂²	semidirect
61. #16812678	C₂²	semidirect
62. #16812677	C₂²	semidirect
63. #16812676	C₂²	semidirect
64. #16812675	C₂²	semidirect
65. #16812674	C₂²	semidirect
66. #16812674	C₂²	semidirect
67. #16812673	C₂²	semidirect
68. #16812673	C₂²	semidirect
69. #16812672	C₂²	semidirect
70. #16812672	C₂²	semidirect
71. #16812672	C₂²	semidirect
72. #16812671	C₂²	semidirect
73. #16812671	C₂²	semidirect
74. #16812671	C₂²	semidirect
75. #16812670	C₂²	semidirect
76. #16812670	C₂²	semidirect
77. #16812669	C₂²	semidirect
78. #16812669	C₂²	semidirect
79. #16812669	C₂²	semidirect
80. #16812668	C₂²	semidirect
81. #16812667	C₂²	semidirect
82. #16812667	C₂²	semidirect
83. #16812667	C₂²	semidirect
84. C₄×D₄₃₆	C₂²	semidirect
85. C₄×D₄₃₆	C₂²	semidirect
86. D₄×Dic₁₀₉	C₂²	semidirect
87. D₄×Dic₁₀₉	C₂²	semidirect
88. #16812661	C₂²	semidirect
89. #16812661	C₂²	semidirect
90. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
91. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
92. C₄×C₂²⋊D₁₀₉	C₂²	semidirect
93. #16812659	C₂²	semidirect
94. #16812659	C₂²	semidirect
95. #16812659	C₂²	semidirect
96. C₄⋊C₄×D₁₀₉	C₂²	semidirect
97. C₄⋊C₄×D₁₀₉	C₂²	semidirect
98. C₄⋊C₄×D₁₀₉	C₂²	semidirect
99. C₂×C₂²⋊Dic₁₀₉	C₂²	semidirect
100. C₂×#13182006	C₂²	semidirect
101. C₂×#13182006	C₂²	semidirect
104. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
105. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
106. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
107. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
108. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
109. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
110. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
111. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
112. C₂²⋊C₄×D₁₀₉	C₂²	semidirect
113. C₄²×D₁₀₉	C₂²	semidirect
114. C₂×#41×C₁₀₉	C₂²	semidirect
115. C₂²×D₄×C₁₀₉	C₂²	semidirect
116. #124×C₁₀₉	C₂²	semidirect
117. #123×C₁₀₉	C₂²	semidirect
118. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
119. #121×C₁₀₉	C₂²	semidirect
120. #121×C₁₀₉	C₂²	semidirect
121. #120×C₁₀₉	C₂²	semidirect
122. C₄×D₄×C₁₀₉	C₂²	semidirect
123. C₄×D₄×C₁₀₉	C₂²	semidirect
124. C₂×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
140. C₂×Dic₂₁₈	C₂³	semidirect
141. C₂×Dic₂₁₈	C₂³	semidirect
148. C₂×D₄₃₆	C₂³	semidirect
149. C₂×D₄₃₆	C₂³	semidirect
157. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
158. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
159. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
160. C₂×C₂²⋊D₁₀₉	C₂³	semidirect
169. D₄×D₁₀₉	D₄	semidirect
171. C₂²×Dic₁₀₉	C₂³	semidirect
172. C₂²×Dic₁₀₉	C₂³	semidirect
173. C₂²×Dic₁₀₉	C₂³	semidirect
187. C₂×C₄×D₁₀₉	C₂³	semidirect
188. C₂×C₄×D₁₀₉	C₂³	semidirect
189. C₂×C₄×D₁₀₉	C₂³	semidirect
190. C₂×C₄×D₁₀₉	C₂³	semidirect
191. C₂×C₄×D₁₀₉	C₂³	semidirect
192. C₂×C₄×D₁₀₉	C₂³	semidirect
193. C₄⋊Dic₁₀₉	C₂³	semidirect
194. C₄⋊Dic₁₀₉	C₂³	semidirect
195. C₄⋊Dic₁₀₉	C₂³	semidirect
196. #13182008	C₂³	semidirect
197. #13182008	C₂³	semidirect
198. #13182008	C₂³	semidirect
199. #13182008	C₂³	semidirect
200. #13182008	C₂³	semidirect
203. C₂²⋊Dic₁₀₉	C₂³	semidirect
204. C₂²⋊Dic₁₀₉	C₂³	semidirect
205. C₂²⋊Dic₁₀₉	C₂³	semidirect
206. C₂²⋊Dic₁₀₉	C₂³	semidirect
207. C₂²⋊Dic₁₀₉	C₂³	semidirect
212. #13182006	C₂³	semidirect
213. #13182006	C₂³	semidirect
214. #13182006	C₂³	semidirect
215. #13182006	C₂³	semidirect
216. #13182006	C₂³	semidirect
217. #13182006	C₂³	semidirect
218. #13182006	C₂³	semidirect
219. #13182006	C₂³	semidirect
220. #13182006	C₂³	semidirect
221. #13182006	C₂³	semidirect
222. C₄×Dic₁₀₉	C₂³	semidirect
223. C₄×Dic₁₀₉	C₂³	semidirect
224. C₄×Dic₁₀₉	C₂³	semidirect
227. C₂×Q₈×C₁₀₉	C₂³	semidirect
233. C₂×D₄×C₁₀₉	C₂³	semidirect
234. C₂×D₄×C₁₀₉	C₂³	semidirect
236. C₂²×C₄×C₁₀₉	C₂³	semidirect
237. C₂²×C₄×C₁₀₉	C₂³	semidirect
238. C₂²×C₄×C₁₀₉	C₂³	semidirect
239. C₄⋊C₄×C₁₀₉	C₂³	semidirect
240. C₄⋊C₄×C₁₀₉	C₂³	semidirect
241. C₄⋊C₄×C₁₀₉	C₂³	semidirect
244. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
245. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
246. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
247. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
248. C₂²⋊C₄×C₁₀₉	C₂³	semidirect
249. C₄²×C₁₀₉	C₂³	semidirect
278. C₂²×D₁₀₉	#41	semidirect
290. D₄×C₁₀₉	C₂×D₄	semidirect
311. C₂²⋊D₁₀₉	C₂×D₄	semidirect
328. D₄₃₆	C₂×D₄	semidirect
358. C₂²×C₁₀₉	C₂×#41	semidirect
380. C₂×D₁₀₉	C₂×#41	semidirect
407. D₁₀₉	#546	direct (N × H)
409. C₁₀₉	C₂×#546	semidirect
423. #546	D₁₀₉	direct (N × H)
440. C₂×#41	C₂×D₁₀₉	semidirect
454. C₂²×D₄	C₂×D₁₀₉	semidirect
464. #124	C₂×D₁₀₉	semidirect
472. #123	C₂×D₁₀₉	semidirect
478. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
491. #121	C₂×D₁₀₉	semidirect
492. #121	C₂×D₁₀₉	semidirect
500. #120	C₂×D₁₀₉	semidirect
513. C₄×D₄	C₂×D₁₀₉	semidirect
514. C₄×D₄	C₂×D₁₀₉	semidirect
532. C₂×C₂²⋊C₄	C₂×D₁₀₉	semidirect
554. C₂×Q₈	C₂²×D₁₀₉	semidirect
587. C₂×D₄	C₂²×D₁₀₉	semidirect
588. C₂×D₄	C₂²×D₁₀₉	semidirect
613. C₂²×C₄	C₂²×D₁₀₉	semidirect
614. C₂²×C₄	C₂²×D₁₀₉	semidirect
615. C₂²×C₄	C₂²×D₁₀₉	semidirect
624. C₄⋊C₄	C₂²×D₁₀₉	semidirect
625. C₄⋊C₄	C₂²×D₁₀₉	semidirect
626. C₄⋊C₄	C₂²×D₁₀₉	semidirect
650. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
651. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
652. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
653. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
654. C₂²⋊C₄	C₂²×D₁₀₉	semidirect
658. C₄²	C₂²×D₁₀₉	semidirect
717. D₄	D₄×D₁₀₉	semidirect
789. C₂²	#41×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#41×D₁₀₉	2
C₂²×D₄×D₁₀₉	2
#20295673	2
#20295672	2
#20295671	2
#20295670	2
#20295669	2
#20295668	2
#20295667	2
#20295666	2
#20295665	2
#20295664	2
#20295663	2
#124×D₁₀₉	2
#123×D₁₀₉	2
C₂²⋊Q₈×D₁₀₉	2
#121×D₁₀₉	2
#120×D₁₀₉	2
C₄×D₄×D₁₀₉	2
C₂×C₂²⋊C₄×D₁₀₉	2
#546×C₁₀₉	2
C₂×#546	109

Subgroups — #546×D109 #28376473

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #546×D₁₀₉ #28376473