Subgroups — C₁₀₉×#22649 #42140643

Order 27904.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#436×C₁₀₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#435×C₁₀₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#424×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#423×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#2290	C₂	1	1	yes	maximal, characteristic
6	C₁₀₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₉×#1939	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₀₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₀₉×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₀₉×#1850	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₀₉×#1843	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₀₉×#1798	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₀₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₀₉×#1768	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
18	C₂²×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
19	C₂³×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
23	#436×C₁₀₉	—	2	4	no	—
24	#435×C₁₀₉	—	2	4	no	—
25	#424×C₁₀₉	—	2	4	no	—
26	#423×C₁₀₉	—	2	4	no	—
27	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
43	C₂×#97×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
45	#388×C₁₀₉	C₄	1	1	yes	characteristic
46	#388×C₁₀₉	C₄	1	1	yes	characteristic
47	#387×C₁₀₉	C₄	1	1	yes	characteristic
48	#387×C₁₀₉	C₄	1	1	yes	characteristic
49	#386×C₁₀₉	C₄	1	1	yes	characteristic
50	#386×C₁₀₉	C₄	1	1	yes	characteristic
51	#385×C₁₀₉	C₄	1	1	yes	characteristic
52	#385×C₁₀₉	C₄	1	1	yes	characteristic
53	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
56	#376×C₁₀₉	C₂²	1	1	yes	characteristic
57	#336×C₁₀₉	C₂²	1	1	yes	characteristic
58	#336×C₁₀₉	C₂²	1	1	yes	characteristic
59	#336×C₁₀₉	C₂²	1	1	yes	characteristic
60	#336×C₁₀₉	C₂²	1	1	yes	characteristic
61	#336×C₁₀₉	C₂²	1	1	yes	characteristic
62	#336×C₁₀₉	C₂²	1	1	yes	characteristic
63	C₂²×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
66	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
68	C₂×M₁₆×C₁₀₉	—	2	2	no	—
69	C₂×M₁₆×C₁₀₉	—	2	2	no	—
70	C₂×M₁₆×C₁₀₉	—	2	2	no	—
71	C₂×M₁₆×C₁₀₉	—	2	2	no	—
72	C₂×M₁₆×C₁₀₉	—	2	2	no	—
73	C₂×M₁₆×C₁₀₉	—	2	2	no	—
74	C₂×M₁₆×C₁₀₉	—	4	1	no	—
75	C₂×M₁₆×C₁₀₉	—	4	1	no	—
76	C₂×M₁₆×C₁₀₉	—	4	1	no	—
77	C₂²×C₈×C₁₀₉	—	2	2	no	—
78	C₂²×C₈×C₁₀₉	—	2	2	no	—
79	C₂²×C₈×C₁₀₉	—	4	1	no	—
80	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
84	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
88	C₄×D₄×C₁₀₉	D₄	1	4	yes	—
89	C₄×D₄×C₁₀₉	Q₈	1	4	yes	—
90	#117×C₁₀₉	—	2	2	no	—
91	#117×C₁₀₉	—	2	2	no	—
92	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
97	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
98	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
99	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
102	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₀₉	—	2	2	no	—
106	C₂×C₄²×C₁₀₉	—	2	2	no	—
107	C₂×C₄²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄²×C₁₀₉	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₈×C₁₀₉	—	2	2	no	—
115	C₄⋊C₈×C₁₀₉	—	2	2	no	—
116	C₄⋊C₈×C₁₀₉	—	2	2	no	—
117	C₄⋊C₈×C₁₀₉	—	2	2	no	—
118	C₄⋊C₈×C₁₀₉	—	2	2	no	—
119	C₄⋊C₈×C₁₀₉	—	2	2	no	—
120	C₄⋊C₈×C₁₀₉	—	2	2	no	—
121	C₄⋊C₈×C₁₀₉	—	2	2	no	—
122	C₄⋊C₈×C₁₀₉	—	2	2	no	—
123	C₄⋊C₈×C₁₀₉	—	4	1	no	—
124	C₄⋊C₈×C₁₀₉	—	4	1	no	—
125	C₄⋊C₈×C₁₀₉	D₄	1	4	yes	complemented
126	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
127	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
128	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
129	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
130	#97×C₁₀₉	—	2	2	no	—
131	C₄×C₈×C₁₀₉	—	2	2	no	—
132	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
133	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
134	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
135	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
136	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
137	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
138	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
139	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
140	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
141	#95×C₁₀₉	C₂×C₄	1	1	yes	characteristic
142	C₂⁴×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
143	C₂⁴×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
144	C₂×D₄×C₁₀₉	—	4	1	no	—
145	C₂×D₄×C₁₀₉	—	4	1	no	—
146	C₂×D₄×C₁₀₉	C₄⋊C₄	1	4	yes	—
147	C₂²×C₄×C₁₀₉	—	2	1	no	—
148	C₂²×C₄×C₁₀₉	—	2	1	no	—
149	C₂²×C₄×C₁₀₉	—	2	1	no	—
150	C₂²×C₄×C₁₀₉	—	2	1	no	—
151	C₂²×C₄×C₁₀₉	—	2	1	no	—
152	C₂²×C₄×C₁₀₉	—	2	1	no	—
153	C₂²×C₄×C₁₀₉	—	2	1	no	—
154	C₂²×C₄×C₁₀₉	—	2	1	no	—
155	C₂²×C₄×C₁₀₉	—	2	2	no	—
156	C₂²×C₄×C₁₀₉	—	2	2	no	—
157	C₂²×C₄×C₁₀₉	—	2	2	no	—
158	C₂²×C₄×C₁₀₉	—	4	1	no	—
159	C₂²×C₄×C₁₀₉	—	4	1	no	—
160	C₂²×C₄×C₁₀₉	—	4	1	no	—
161	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
165	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
166	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
172	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
173	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₁₀₉	C₂×Q₈	1	2	yes	—
176	C₂²×C₄×C₁₀₉	C₂×Q₈	1	2	yes	—
177	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
178	M₁₆×C₁₀₉	—	4	4	no	—
179	M₁₆×C₁₀₉	—	4	4	no	—
180	M₁₆×C₁₀₉	—	4	4	no	—
181	C₂×C₈×C₁₀₉	—	2	1	no	—
182	C₂×C₈×C₁₀₉	—	2	1	no	—
183	C₂×C₈×C₁₀₉	—	2	1	no	—
184	C₂×C₈×C₁₀₉	—	2	1	no	—
185	C₂×C₈×C₁₀₉	—	2	1	no	—
186	C₂×C₈×C₁₀₉	—	2	1	no	—
187	C₂×C₈×C₁₀₉	—	2	1	no	—
188	C₂×C₈×C₁₀₉	—	2	1	no	—
189	C₂×C₈×C₁₀₉	—	2	1	no	—
190	C₂×C₈×C₁₀₉	—	2	1	no	—
191	C₂×C₈×C₁₀₉	—	2	1	no	—
192	C₂×C₈×C₁₀₉	—	2	1	no	—
193	C₂×C₈×C₁₀₉	—	2	1	no	—
194	C₂×C₈×C₁₀₉	—	2	1	no	—
195	C₂×C₈×C₁₀₉	—	2	1	no	—
196	C₂×C₈×C₁₀₉	—	2	1	no	—
197	C₂×C₈×C₁₀₉	—	2	1	no	—
198	C₂×C₈×C₁₀₉	—	2	1	no	—
199	C₂×C₈×C₁₀₉	—	2	1	no	—
200	C₂×C₈×C₁₀₉	—	2	1	no	—
201	C₂×C₈×C₁₀₉	—	2	1	no	—
202	C₂×C₈×C₁₀₉	—	2	1	no	—
203	C₂×C₈×C₁₀₉	—	4	4	no	—
204	C₂×C₈×C₁₀₉	C₂×D₄	1	2	yes	—
205	C₂×C₈×C₁₀₉	C₂×D₄	1	2	yes	—
206	C₄⋊C₄×C₁₀₉	—	2	2	no	—
207	C₄⋊C₄×C₁₀₉	—	2	2	no	—
208	C₄⋊C₄×C₁₀₉	—	2	2	no	—
209	C₄⋊C₄×C₁₀₉	—	4	1	no	—
210	C₄⋊C₄×C₁₀₉	C₄⋊C₄	1	4	yes	—
211	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
212	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
213	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
214	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
215	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
216	C₂²⋊C₄×C₁₀₉	—	4	1	no	—
217	C₂²⋊C₄×C₁₀₉	C₄⋊C₄	1	4	yes	—
218	C₂²⋊C₄×C₁₀₉	C₄⋊C₄	1	4	yes	—
219	C₄²×C₁₀₉	—	2	2	no	—
220	C₄²×C₁₀₉	—	2	2	no	—
221	C₄²×C₁₀₉	—	2	1	no	—
222	C₄²×C₁₀₉	—	2	1	no	—
223	C₄²×C₁₀₉	—	2	1	no	—
224	C₄²×C₁₀₉	—	2	1	no	—
225	C₄²×C₁₀₉	—	2	1	no	—
226	C₄²×C₁₀₉	—	2	1	no	—
227	C₄²×C₁₀₉	C₂×D₄	1	2	yes	—
228	C₄²×C₁₀₉	C₂×D₄	1	2	yes	—
229	C₄²×C₁₀₉	C₂×Q₈	1	2	yes	—
230	C₄²×C₁₀₉	#41	1	2	yes	—
231	C₂³×C₁₀₉	—	2	1	no	—
232	C₂³×C₁₀₉	—	2	1	no	—
233	C₂³×C₁₀₉	—	2	1	no	—
234	C₂³×C₁₀₉	—	2	1	no	—
235	C₂³×C₁₀₉	—	2	1	no	—
236	C₂³×C₁₀₉	—	2	1	no	—
237	C₂³×C₁₀₉	—	2	1	no	—
238	C₂³×C₁₀₉	—	2	1	no	—
239	C₂³×C₁₀₉	—	2	1	no	—
240	C₂³×C₁₀₉	—	2	1	no	—
241	C₂³×C₁₀₉	—	2	1	no	—
242	C₂³×C₁₀₉	—	2	1	no	—
243	C₂³×C₁₀₉	C₂×C₄⋊C₄	1	2	yes	—
244	C₂³×C₁₀₉	C₂×C₄⋊C₄	1	2	yes	—
245	C₂³×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
246	D₄×C₁₀₉	—	4	4	no	—
247	C₂×C₄×C₁₀₉	—	2	1	no	—
248	C₂×C₄×C₁₀₉	—	2	1	no	—
249	C₂×C₄×C₁₀₉	—	2	1	no	—
250	C₂×C₄×C₁₀₉	—	2	1	no	—
251	C₂×C₄×C₁₀₉	—	2	1	no	—
252	C₂×C₄×C₁₀₉	—	2	1	no	—
253	C₂×C₄×C₁₀₉	—	2	1	no	—
254	C₂×C₄×C₁₀₉	—	2	1	no	—
255	C₂×C₄×C₁₀₉	—	2	1	no	—
256	C₂×C₄×C₁₀₉	—	2	1	no	—
257	C₂×C₄×C₁₀₉	—	2	1	no	—
258	C₂×C₄×C₁₀₉	—	2	1	no	—
259	C₂×C₄×C₁₀₉	—	2	1	no	—
260	C₂×C₄×C₁₀₉	—	2	1	no	—
261	C₂×C₄×C₁₀₉	—	2	2	no	—
262	C₂×C₄×C₁₀₉	—	2	2	no	—
263	C₂×C₄×C₁₀₉	—	2	2	no	—
264	C₂×C₄×C₁₀₉	—	2	2	no	—
265	C₂×C₄×C₁₀₉	—	2	2	no	—
266	C₂×C₄×C₁₀₉	—	2	2	no	—
267	C₂×C₄×C₁₀₉	—	2	2	no	—
268	C₂×C₄×C₁₀₉	—	2	2	no	—
269	C₂×C₄×C₁₀₉	—	2	1	no	—
270	C₂×C₄×C₁₀₉	—	2	1	no	—
271	C₂×C₄×C₁₀₉	—	2	1	no	—
272	C₂×C₄×C₁₀₉	—	2	1	no	—
273	C₂×C₄×C₁₀₉	—	2	1	no	—
274	C₂×C₄×C₁₀₉	—	2	1	no	—
275	C₂×C₄×C₁₀₉	—	2	1	no	—
276	C₂×C₄×C₁₀₉	—	2	1	no	—
277	C₂×C₄×C₁₀₉	—	2	1	no	—
278	C₂×C₄×C₁₀₉	—	2	1	no	—
279	C₂×C₄×C₁₀₉	—	2	1	no	—
280	C₂×C₄×C₁₀₉	—	2	1	no	—
281	C₂×C₄×C₁₀₉	—	2	1	no	—
282	C₂×C₄×C₁₀₉	—	2	1	no	—
283	C₂×C₄×C₁₀₉	—	2	1	no	—
284	C₂×C₄×C₁₀₉	—	4	4	no	—
285	C₂×C₄×C₁₀₉	—	4	4	no	—
286	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	2	yes	—
287	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	2	yes	—
288	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	2	yes	—
289	C₂×C₄×C₁₀₉	C₂×C₄⋊C₄	1	2	yes	—
290	C₂×C₄×C₁₀₉	C₄×D₄	1	2	yes	—
291	C₂×C₄×C₁₀₉	C₄×D₄	1	2	yes	—
292	C₂×C₄×C₁₀₉	#131	1	2	yes	—
293	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
294	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
295	C₂×C₄×C₁₀₉	C₂²×Q₈	1	1	yes	characteristic
296	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
297	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
298	C₂×C₄×C₁₀₉	2₋¹⁺⁴	1	1	yes	characteristic
299	C₈×C₁₀₉	—	2	2	no	—
300	C₈×C₁₀₉	—	2	2	no	—
301	C₈×C₁₀₉	—	4	1	no	—
302	C₈×C₁₀₉	—	4	1	no	—
303	C₈×C₁₀₉	—	4	1	no	—
304	C₈×C₁₀₉	—	4	1	no	—
305	C₈×C₁₀₉	—	4	1	no	—
306	C₈×C₁₀₉	—	4	1	no	—
307	C₂²×C₁₀₉	—	2	2	no	—
308	C₂²×C₁₀₉	—	2	2	no	—
309	C₂²×C₁₀₉	—	2	2	no	—
310	C₂²×C₁₀₉	—	2	2	no	—
311	C₂²×C₁₀₉	—	2	2	no	—
312	C₂²×C₁₀₉	—	2	2	no	—
313	C₂²×C₁₀₉	—	4	1	no	—
314	C₂²×C₁₀₉	—	4	1	no	—
315	C₂²×C₁₀₉	—	4	1	no	—
316	C₂²×C₁₀₉	—	4	1	no	—
317	C₂²×C₁₀₉	—	4	1	no	—
318	C₂²×C₁₀₉	—	4	1	no	—
319	C₂²×C₁₀₉	—	4	1	no	—
320	C₂²×C₁₀₉	—	4	1	no	—
321	C₂²×C₁₀₉	C₂²×C₄⋊C₄	1	1	yes	characteristic
322	C₂²×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
323	C₂²×C₁₀₉	#520	1	1	yes	characteristic
324	C₂²×C₁₀₉	C₂×#131	1	1	yes	characteristic
325	C₂²×C₁₀₉	#568	1	1	yes	characteristic
326	C₂²×C₁₀₉	#568	1	1	yes	characteristic
327	C₂²×C₁₀₉	#568	1	1	yes	characteristic
328	C₄×C₁₀₉	—	2	2	no	—
329	C₄×C₁₀₉	—	2	2	no	—
330	C₄×C₁₀₉	—	2	2	no	—
331	C₄×C₁₀₉	—	2	2	no	—
332	C₄×C₁₀₉	—	2	2	no	—
333	C₄×C₁₀₉	—	2	2	no	—
334	C₄×C₁₀₉	—	2	2	no	—
335	C₄×C₁₀₉	—	4	1	no	—
336	C₄×C₁₀₉	—	4	1	no	—
337	C₄×C₁₀₉	—	4	1	no	—
338	C₄×C₁₀₉	—	4	1	no	—
339	C₄×C₁₀₉	—	4	1	no	—
340	C₄×C₁₀₉	D₄²	1	1	yes	characteristic
341	C₄×C₁₀₉	#547	1	1	yes	characteristic
342	C₄×C₁₀₉	D₄×Q₈	1	1	yes	characteristic
343	C₄×C₁₀₉	#554	1	1	yes	characteristic
344	#22649	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
345	C₂×C₁₀₉	—	4	2	no	—
346	C₂×C₁₀₉	—	4	2	no	—
347	C₂×C₁₀₉	D₄×C₄⋊C₄	1	1	yes	characteristic
348	C₂×C₁₀₉	#2905	1	1	yes	characteristic
349	C₂×C₁₀₉	#2906	1	1	yes	characteristic
350	C₂×C₁₀₉	#2930	1	1	yes	characteristic
351	C₂×C₁₀₉	#2933	1	1	yes	characteristic
352	C₂×C₁₀₉	#2993	1	1	yes	characteristic
353	C₂×C₁₀₉	#2995	1	1	yes	characteristic
354	C₂×#436	C₂×C₁₀₉	1	1	yes	characteristic
355	C₂×#435	C₂×C₁₀₉	1	1	yes	characteristic
356	C₂×#424	C₂×C₁₀₉	1	1	yes	characteristic, complemented
357	C₂×#423	C₂×C₁₀₉	1	1	yes	characteristic, complemented
358	#2290	C₂×C₁₀₉	1	1	yes	characteristic
359	#1940	C₂×C₁₀₉	1	1	yes	characteristic, complemented
360	#1939	C₂×C₁₀₉	1	1	yes	characteristic, complemented
361	#1851	C₂×C₁₀₉	1	1	yes	characteristic, complemented
362	#1851	C₂×C₁₀₉	1	1	yes	characteristic, complemented
363	#1851	C₂×C₁₀₉	1	1	yes	characteristic, complemented
364	#1850	C₂×C₁₀₉	1	1	yes	characteristic, complemented
365	#1843	C₂×C₁₀₉	1	1	yes	characteristic, complemented
366	#1798	C₂×C₁₀₉	1	1	yes	characteristic, complemented
367	#1797	C₂×C₁₀₉	1	1	yes	characteristic, complemented
368	#1768	C₂×C₁₀₉	1	1	yes	characteristic, complemented
369	C₁₀₉	#22649	1	1	yes	characteristic, direct product factor, Sylow
370	C₂²×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
371	C₂²×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
372	C₂²×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
373	C₂³×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
374	C₂×C₄×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
375	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
376	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
377	#436	—	2	4	no	—
378	#435	—	2	4	no	—
379	#424	—	2	4	no	—
380	#423	—	2	4	no	—
381	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
382	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
383	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
384	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
385	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
386	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
387	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
388	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
389	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
390	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
391	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
392	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
394	C₂×C₂²⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
395	C₂×C₂²⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
396	C₂×C₂²⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
397	C₂×#97	C₂²×C₁₀₉	1	1	yes	characteristic
398	C₂×C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
399	#388	C₄×C₁₀₉	1	1	yes	characteristic
400	#388	C₄×C₁₀₉	1	1	yes	characteristic
401	#387	C₄×C₁₀₉	1	1	yes	characteristic
402	#387	C₄×C₁₀₉	1	1	yes	characteristic
403	#386	C₄×C₁₀₉	1	1	yes	characteristic
404	#386	C₄×C₁₀₉	1	1	yes	characteristic
405	#385	C₄×C₁₀₉	1	1	yes	characteristic
406	#385	C₄×C₁₀₉	1	1	yes	characteristic
407	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
408	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
409	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
410	#376	C₂²×C₁₀₉	1	1	yes	characteristic
411	#336	C₂²×C₁₀₉	1	1	yes	characteristic
412	#336	C₂²×C₁₀₉	1	1	yes	characteristic
413	#336	C₂²×C₁₀₉	1	1	yes	characteristic
414	#336	C₂²×C₁₀₉	1	1	yes	characteristic
415	#336	C₂²×C₁₀₉	1	1	yes	characteristic
416	#336	C₂²×C₁₀₉	1	1	yes	characteristic
417	C₂²×D₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
418	C₂³×C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
419	C₂³×C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
420	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
421	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
422	C₂×M₁₆	—	2	2	no	—
423	C₂×M₁₆	—	2	2	no	—
424	C₂×M₁₆	—	2	2	no	—
425	C₂×M₁₆	—	2	2	no	—
426	C₂×M₁₆	—	2	2	no	—
427	C₂×M₁₆	—	2	2	no	—
428	C₂×M₁₆	—	4	1	no	—
429	C₂×M₁₆	—	4	1	no	—
430	C₂×M₁₆	—	4	1	no	—
431	C₂²×C₈	—	2	2	no	—
432	C₂²×C₈	—	2	2	no	—
433	C₂²×C₈	—	4	1	no	—
434	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
435	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
436	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
437	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
438	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
439	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
440	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
441	C₂²×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
442	C₄×D₄	D₄×C₁₀₉	1	4	yes	—
443	C₄×D₄	Q₈×C₁₀₉	1	4	yes	—
444	#117	—	2	2	no	—
445	#117	—	2	2	no	—
446	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
447	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
449	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
452	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
453	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
454	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
455	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
456	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
457	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
458	C₂×C₂²⋊C₄	C₂×C₄×C₁₀₉	1	1	yes	characteristic
459	C₂×C₄²	—	2	2	no	—
460	C₂×C₄²	—	2	2	no	—
461	C₂×C₄²	C₂×C₄×C₁₀₉	1	1	yes	characteristic
462	C₂×C₄²	C₂×C₄×C₁₀₉	1	1	yes	characteristic
463	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
464	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
465	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
466	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
467	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
468	C₄⋊C₈	—	2	2	no	—
469	C₄⋊C₈	—	2	2	no	—
470	C₄⋊C₈	—	2	2	no	—
471	C₄⋊C₈	—	2	2	no	—
472	C₄⋊C₈	—	2	2	no	—
473	C₄⋊C₈	—	2	2	no	—
474	C₄⋊C₈	—	2	2	no	—
475	C₄⋊C₈	—	2	2	no	—
476	C₄⋊C₈	—	2	2	no	—
477	C₄⋊C₈	—	4	1	no	—
478	C₄⋊C₈	—	4	1	no	—
479	C₄⋊C₈	D₄×C₁₀₉	1	4	yes	complemented
480	C₂²⋊C₈	—	2	2	no	—
481	C₂²⋊C₈	—	2	2	no	—
482	C₂²⋊C₈	—	2	2	no	—
483	C₂²⋊C₈	—	2	2	no	—
484	#97	—	2	2	no	—
485	C₄×C₈	—	2	2	no	—
486	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
487	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
488	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
489	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
490	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
491	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
492	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
493	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
494	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
495	#95	C₂×C₄×C₁₀₉	1	1	yes	characteristic
496	C₂⁴	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
497	C₂⁴	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
498	C₂×D₄	—	4	1	no	—
499	C₂×D₄	—	4	1	no	—
500	C₂×D₄	C₄⋊C₄×C₁₀₉	1	4	yes	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	2	1	no	—
508	C₂²×C₄	—	2	1	no	—
509	C₂²×C₄	—	2	2	no	—
510	C₂²×C₄	—	2	2	no	—
511	C₂²×C₄	—	2	2	no	—
512	C₂²×C₄	—	4	1	no	—
513	C₂²×C₄	—	4	1	no	—
514	C₂²×C₄	—	4	1	no	—
515	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
516	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
517	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
518	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
519	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
520	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
521	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
522	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
523	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
524	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
525	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
526	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
527	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
528	C₂²×C₄	C₂×D₄×C₁₀₉	1	2	yes	—
529	C₂²×C₄	C₂×Q₈×C₁₀₉	1	2	yes	—
530	C₂²×C₄	C₂×Q₈×C₁₀₉	1	2	yes	—
531	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
532	M₁₆	—	4	4	no	—
533	M₁₆	—	4	4	no	—
534	M₁₆	—	4	4	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	2	1	no	—
547	C₂×C₈	—	2	1	no	—
548	C₂×C₈	—	2	1	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	4	4	no	—
558	C₂×C₈	C₂×D₄×C₁₀₉	1	2	yes	—
559	C₂×C₈	C₂×D₄×C₁₀₉	1	2	yes	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	2	2	no	—
563	C₄⋊C₄	—	4	1	no	—
564	C₄⋊C₄	C₄⋊C₄×C₁₀₉	1	4	yes	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	2	no	—
568	C₂²⋊C₄	—	4	1	no	—
569	C₂²⋊C₄	—	4	1	no	—
570	C₂²⋊C₄	—	4	1	no	—
571	C₂²⋊C₄	C₄⋊C₄×C₁₀₉	1	4	yes	—
572	C₂²⋊C₄	C₄⋊C₄×C₁₀₉	1	4	yes	—
573	C₄²	—	2	2	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	1	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	C₂×D₄×C₁₀₉	1	2	yes	—
582	C₄²	C₂×D₄×C₁₀₉	1	2	yes	—
583	C₄²	C₂×Q₈×C₁₀₉	1	2	yes	—
584	C₄²	#41×C₁₀₉	1	2	yes	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	—	2	1	no	—
596	C₂³	—	2	1	no	—
597	C₂³	C₂×C₄⋊C₄×C₁₀₉	1	2	yes	—
598	C₂³	C₂×C₄⋊C₄×C₁₀₉	1	2	yes	—
599	C₂³	C₂³×C₄×C₁₀₉	1	1	yes	characteristic
600	D₄	—	4	4	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	2	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	2	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	2	2	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	2	1	no	—
637	C₂×C₄	—	2	1	no	—
638	C₂×C₄	—	4	4	no	—
639	C₂×C₄	—	4	4	no	—
640	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	2	yes	—
641	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	2	yes	—
642	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	2	yes	—
643	C₂×C₄	C₂×C₄⋊C₄×C₁₀₉	1	2	yes	—
644	C₂×C₄	C₄×D₄×C₁₀₉	1	2	yes	—
645	C₂×C₄	C₄×D₄×C₁₀₉	1	2	yes	—
646	C₂×C₄	#131×C₁₀₉	1	2	yes	—
647	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
648	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
649	C₂×C₄	C₂²×Q₈×C₁₀₉	1	1	yes	characteristic
650	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
651	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
652	C₂×C₄	2₋¹⁺⁴×C₁₀₉	1	1	yes	characteristic
653	C₈	—	2	2	no	—
654	C₈	—	2	2	no	—
655	C₈	—	4	1	no	—
656	C₈	—	4	1	no	—
657	C₈	—	4	1	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	4	1	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	2	2	no	—
664	C₂²	—	2	2	no	—
665	C₂²	—	2	2	no	—
666	C₂²	—	2	2	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	—	4	1	no	—
672	C₂²	—	4	1	no	—
673	C₂²	—	4	1	no	—
674	C₂²	—	4	1	no	—
675	C₂²	C₂²×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
676	C₂²	C₂×C₄×D₄×C₁₀₉	1	1	yes	characteristic
677	C₂²	#520×C₁₀₉	1	1	yes	characteristic
678	C₂²	C₂×#131×C₁₀₉	1	1	yes	characteristic
679	C₂²	#568×C₁₀₉	1	1	yes	characteristic
680	C₂²	#568×C₁₀₉	1	1	yes	characteristic
681	C₂²	#568×C₁₀₉	1	1	yes	characteristic
682	C₄	—	2	2	no	—
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	2	no	—
688	C₄	—	2	2	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	1	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	D₄²×C₁₀₉	1	1	yes	characteristic
695	C₄	#547×C₁₀₉	1	1	yes	characteristic
696	C₄	D₄×Q₈×C₁₀₉	1	1	yes	characteristic
697	C₄	#554×C₁₀₉	1	1	yes	characteristic
698	C₂	—	4	2	no	—
699	C₂	—	4	2	no	—
700	C₂	D₄×C₄⋊C₄×C₁₀₉	1	1	yes	characteristic
701	C₂	C₁₀₉×#2905	1	1	yes	characteristic
702	C₂	C₁₀₉×#2906	1	1	yes	characteristic
703	C₂	C₁₀₉×#2930	1	1	yes	characteristic
704	C₂	C₁₀₉×#2933	1	1	yes	characteristic
705	C₂	C₁₀₉×#2993	1	1	yes	characteristic
706	C₂	C₁₀₉×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₀₉	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₀₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₉
socle	C₂³×C₁₀₉	C₂³×C₄
prime radical	C₂²×D₄×C₁₀₉	C₂×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×#424×C₁₀₉	C₂	semidirect
4. C₂×#423×C₁₀₉	C₂	semidirect
6. C₁₀₉×#1940	C₂	semidirect
7. C₁₀₉×#1939	C₂	semidirect
8. C₁₀₉×#1851	C₂	semidirect
9. C₁₀₉×#1851	C₂	semidirect
10. C₁₀₉×#1851	C₂	semidirect
11. C₁₀₉×#1850	C₂	semidirect
12. C₁₀₉×#1843	C₂	semidirect
13. C₁₀₉×#1798	C₂	semidirect
14. C₁₀₉×#1797	C₂	semidirect
15. C₁₀₉×#1768	C₂	semidirect
125. C₄⋊C₈×C₁₀₉	D₄	semidirect
344. #22649	C₁₀₉	direct (N × H)
356. C₂×#424	C₂×C₁₀₉	semidirect
357. C₂×#423	C₂×C₁₀₉	semidirect
359. #1940	C₂×C₁₀₉	semidirect
360. #1939	C₂×C₁₀₉	semidirect
361. #1851	C₂×C₁₀₉	semidirect
362. #1851	C₂×C₁₀₉	semidirect
363. #1851	C₂×C₁₀₉	semidirect
364. #1850	C₂×C₁₀₉	semidirect
365. #1843	C₂×C₁₀₉	semidirect
366. #1798	C₂×C₁₀₉	semidirect
367. #1797	C₂×C₁₀₉	semidirect
368. #1768	C₂×C₁₀₉	semidirect
369. C₁₀₉	#22649	direct (N × H)
479. C₄⋊C₈	D₄×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#436×C₁₀₉	2
C₂×#435×C₁₀₉	2
C₂×#424×C₁₀₉	2
C₂×#423×C₁₀₉	2
C₁₀₉×#2290	2
C₁₀₉×#1940	2
C₁₀₉×#1939	2
C₁₀₉×#1851	2
C₁₀₉×#1850	2
C₁₀₉×#1843	2
C₁₀₉×#1798	2
C₁₀₉×#1797	2
C₁₀₉×#1768	2
#22649	109

Subgroups — C109×#22649 #42140643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#22649 #42140643