Subgroups — C₁₀₉×#35031 #42153025

Order 27904.

2966 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2854	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#2848	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₉×#2847	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₀₉×#2622	C₂	1	2	yes	maximal, complemented
8	C₁₀₉×#2613	C₂	1	2	yes	maximal, complemented
9	C₁₀₉×#2602	C₂	1	4	yes	maximal, complemented
10	C₁₀₉×#2600	C₂	1	4	yes	maximal, complemented
11	C₁₀₉×#2485	C₂	1	2	yes	maximal, complemented
12	C₁₀₉×#2415	C₂	1	2	yes	maximal, complemented
13	C₁₀₉×#2414	C₂	1	2	yes	maximal, complemented
14	C₁₀₉×#2407	C₂	1	2	yes	maximal, complemented
15	C₁₀₉×#2322	C₂	1	2	yes	maximal, complemented
16	C₁₀₉×#2321	C₂	1	2	yes	maximal, complemented
17	C₁₀₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#41×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
19	C₂³×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
22	#525×C₁₀₉	—	2	8	no	—
23	C₂×#123×C₁₀₉	C₂²	1	2	yes	—
24	C₂×#123×C₁₀₉	C₂²	1	2	yes	complemented
25	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
28	C₂×#121×C₁₀₉	C₂²	1	1	yes	characteristic
29	C₂×#121×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
30	C₂×#121×C₁₀₉	C₂²	1	2	yes	complemented
31	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
32	C₂×#120×C₁₀₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₁₀₉	—	2	8	no	—
34	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
38	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	—
39	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
40	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
41	C₂×#117×C₁₀₉	C₂²	1	2	yes	complemented
42	C₂²×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
46	#397×C₁₀₉	C₂²	1	4	yes	complemented
47	#397×C₁₀₉	C₂²	1	4	yes	complemented
48	#394×C₁₀₉	C₂²	1	4	yes	—
49	#394×C₁₀₉	C₂²	1	4	yes	—
50	#394×C₁₀₉	C₂²	1	4	yes	complemented
51	#394×C₁₀₉	C₂²	1	4	yes	complemented
52	#392×C₁₀₉	C₂²	1	4	yes	—
53	#392×C₁₀₉	C₂²	1	4	yes	—
54	#391×C₁₀₉	C₂²	1	2	yes	complemented
55	#390×C₁₀₉	C₂²	1	4	yes	complemented
56	#390×C₁₀₉	C₂²	1	2	yes	complemented
57	#389×C₁₀₉	C₂²	1	2	yes	complemented
58	#389×C₁₀₉	C₂²	1	2	yes	complemented
59	#389×C₁₀₉	C₂²	1	4	yes	complemented
60	#388×C₁₀₉	C₂²	1	4	yes	complemented
61	#388×C₁₀₉	C₂²	1	4	yes	complemented
62	#388×C₁₀₉	C₂²	1	4	yes	complemented
63	#388×C₁₀₉	C₂²	1	4	yes	complemented
64	#387×C₁₀₉	C₂²	1	4	yes	complemented
65	#387×C₁₀₉	C₂²	1	4	yes	complemented
66	#386×C₁₀₉	C₂²	1	2	yes	—
67	#386×C₁₀₉	C₂²	1	2	yes	—
68	#386×C₁₀₉	C₂²	1	4	yes	complemented
69	#386×C₁₀₉	C₂²	1	4	yes	complemented
70	#385×C₁₀₉	C₂²	1	2	yes	—
71	#385×C₁₀₉	C₂²	1	2	yes	—
72	#385×C₁₀₉	C₂²	1	4	yes	complemented
73	#385×C₁₀₉	C₂²	1	4	yes	complemented
74	#381×C₁₀₉	C₂²	1	2	yes	—
75	#381×C₁₀₉	C₂²	1	2	yes	complemented
76	#380×C₁₀₉	C₂²	1	1	yes	characteristic
77	#380×C₁₀₉	C₂²	1	1	yes	characteristic
78	#380×C₁₀₉	C₂²	1	2	yes	complemented
79	#380×C₁₀₉	C₂²	1	2	yes	complemented
80	#380×C₁₀₉	C₂²	1	2	yes	complemented
81	#379×C₁₀₉	C₂²	1	2	yes	—
82	#379×C₁₀₉	C₂²	1	2	yes	—
83	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
84	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
85	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
86	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
87	C₂×#41×C₁₀₉	—	2	4	no	—
88	C₂×#41×C₁₀₉	—	4	4	no	—
89	C₂²×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
90	C₂²×D₄×C₁₀₉	—	2	4	no	—
91	C₂²×D₄×C₁₀₉	—	2	4	no	—
92	C₂²×D₄×C₁₀₉	—	2	4	no	—
93	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
94	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
95	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
96	C₂²×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
98	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
99	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
100	C₂³×C₄×C₁₀₉	—	2	4	no	—
101	C₂³×C₄×C₁₀₉	—	4	4	no	—
102	C₂³×C₄×C₁₀₉	—	4	4	no	—
103	C₂³×C₄×C₁₀₉	D₄	1	8	yes	complemented
104	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
105	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
112	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
113	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	#123×C₁₀₉	—	2	8	no	—
117	#123×C₁₀₉	—	2	8	no	—
118	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
119	C₂²⋊Q₈×C₁₀₉	—	2	4	no	—
120	C₂²⋊Q₈×C₁₀₉	—	4	4	no	—
121	#121×C₁₀₉	—	2	4	no	—
122	#121×C₁₀₉	—	2	4	no	—
123	#121×C₁₀₉	—	4	4	no	—
124	#120×C₁₀₉	—	2	8	no	—
125	#120×C₁₀₉	—	2	8	no	—
126	C₄×D₄×C₁₀₉	—	2	8	no	—
127	C₄×D₄×C₁₀₉	—	2	8	no	—
128	C₄×D₄×C₁₀₉	—	2	8	no	—
129	C₄×D₄×C₁₀₉	—	2	8	no	—
130	C₄×D₄×C₁₀₉	—	2	8	no	—
131	C₄×D₄×C₁₀₉	—	2	8	no	—
132	#117×C₁₀₉	—	2	4	no	—
133	#117×C₁₀₉	—	4	4	no	—
134	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
135	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
137	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
139	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
140	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
141	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
144	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
145	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
147	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
148	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
149	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
150	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
151	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
153	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
159	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
161	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
162	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
163	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
164	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
165	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
167	C₂×C₄²×C₁₀₉	—	2	4	no	—
168	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
169	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
170	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
171	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
172	#95×C₁₀₉	C₂³	1	4	yes	—
173	#95×C₁₀₉	C₂³	1	2	yes	—
174	#95×C₁₀₉	C₂³	1	2	yes	—
175	#95×C₁₀₉	C₂³	1	4	yes	—
176	#95×C₁₀₉	C₂³	1	4	yes	—
177	#95×C₁₀₉	C₂³	1	4	yes	—
178	#95×C₁₀₉	C₂³	1	4	yes	—
179	#95×C₁₀₉	C₂³	1	4	yes	—
180	#95×C₁₀₉	C₂³	1	4	yes	—
181	C₂⁴×C₁₀₉	—	2	2	no	—
182	C₂⁴×C₁₀₉	—	2	2	no	—
183	C₂⁴×C₁₀₉	—	2	2	no	—
184	C₂⁴×C₁₀₉	—	2	2	no	—
185	C₂⁴×C₁₀₉	—	4	2	no	—
186	C₂⁴×C₁₀₉	—	4	2	no	—
187	C₂⁴×C₁₀₉	—	4	2	no	—
188	C₂⁴×C₁₀₉	—	4	2	no	—
189	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
190	C₂⁴×C₁₀₉	#41	1	4	yes	complemented
191	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
192	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
193	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
194	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
195	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
196	#41×C₁₀₉	—	4	16	no	—
197	C₂×Q₈×C₁₀₉	—	2	2	no	—
198	C₂×Q₈×C₁₀₉	—	2	4	no	—
199	C₂×D₄×C₁₀₉	—	2	32	no	—
200	C₂×D₄×C₁₀₉	—	2	4	no	—
201	C₂×D₄×C₁₀₉	—	2	4	no	—
202	C₂×D₄×C₁₀₉	—	2	4	no	—
203	C₂×D₄×C₁₀₉	—	2	4	no	—
204	C₂×D₄×C₁₀₉	—	2	4	no	—
205	C₂×D₄×C₁₀₉	—	2	4	no	—
206	C₂×D₄×C₁₀₉	—	2	4	no	—
207	C₂×D₄×C₁₀₉	—	2	4	no	—
208	C₂×D₄×C₁₀₉	—	2	4	no	—
209	C₂×D₄×C₁₀₉	—	2	8	no	—
210	C₂×D₄×C₁₀₉	—	2	2	no	—
211	C₂×D₄×C₁₀₉	—	2	4	no	—
212	C₂×D₄×C₁₀₉	—	2	4	no	—
213	C₂×D₄×C₁₀₉	—	2	4	no	—
214	C₂×D₄×C₁₀₉	—	4	4	no	—
215	C₂×D₄×C₁₀₉	—	4	4	no	—
216	C₂×D₄×C₁₀₉	—	4	4	no	—
217	C₂×D₄×C₁₀₉	—	4	4	no	—
218	C₂²×C₄×C₁₀₉	—	2	2	no	—
219	C₂²×C₄×C₁₀₉	—	2	2	no	—
220	C₂²×C₄×C₁₀₉	—	2	4	no	—
221	C₂²×C₄×C₁₀₉	—	2	4	no	—
222	C₂²×C₄×C₁₀₉	—	2	4	no	—
223	C₂²×C₄×C₁₀₉	—	2	2	no	—
224	C₂²×C₄×C₁₀₉	—	2	2	no	—
225	C₂²×C₄×C₁₀₉	—	2	4	no	—
226	C₂²×C₄×C₁₀₉	—	2	4	no	—
227	C₂²×C₄×C₁₀₉	—	2	4	no	—
228	C₂²×C₄×C₁₀₉	—	2	4	no	—
229	C₂²×C₄×C₁₀₉	—	2	4	no	—
230	C₂²×C₄×C₁₀₉	—	4	16	no	—
231	C₂²×C₄×C₁₀₉	—	4	2	no	—
232	C₂²×C₄×C₁₀₉	—	4	2	no	—
233	C₂²×C₄×C₁₀₉	—	4	2	no	—
234	C₂²×C₄×C₁₀₉	—	4	2	no	—
235	C₂²×C₄×C₁₀₉	—	4	2	no	—
236	C₂²×C₄×C₁₀₉	—	4	2	no	—
237	C₂²×C₄×C₁₀₉	—	4	2	no	—
238	C₂²×C₄×C₁₀₉	—	4	4	no	—
239	C₂²×C₄×C₁₀₉	—	4	16	no	—
240	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
242	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
243	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
244	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₁₀₉	#41	1	4	yes	complemented
247	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
248	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
250	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
251	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
255	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
256	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
257	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
259	C₄⋊C₄×C₁₀₉	—	2	4	no	—
260	C₄⋊C₄×C₁₀₉	—	2	4	no	—
261	C₄⋊C₄×C₁₀₉	—	2	2	no	—
262	C₄⋊C₄×C₁₀₉	—	2	2	no	—
263	C₄⋊C₄×C₁₀₉	—	2	4	no	—
264	C₄⋊C₄×C₁₀₉	—	2	4	no	—
265	C₄⋊C₄×C₁₀₉	—	2	8	no	—
266	C₄⋊C₄×C₁₀₉	—	2	4	no	—
267	C₄⋊C₄×C₁₀₉	—	2	4	no	—
268	C₄⋊C₄×C₁₀₉	—	4	4	no	—
269	C₄⋊C₄×C₁₀₉	—	4	4	no	—
270	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
271	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
272	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
273	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
274	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
275	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
276	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
277	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
278	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
279	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
280	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
281	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
282	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
283	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
284	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
285	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
286	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
287	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
288	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
289	C₄²×C₁₀₉	—	2	4	no	—
290	C₄²×C₁₀₉	—	2	4	no	—
291	C₄²×C₁₀₉	—	2	4	no	—
292	C₄²×C₁₀₉	—	4	4	no	—
293	C₂³×C₁₀₉	—	2	2	no	—
294	C₂³×C₁₀₉	—	2	2	no	—
295	C₂³×C₁₀₉	—	2	8	no	—
296	C₂³×C₁₀₉	—	2	8	no	—
297	C₂³×C₁₀₉	—	2	2	no	—
298	C₂³×C₁₀₉	—	2	1	no	—
299	C₂³×C₁₀₉	—	2	1	no	—
300	C₂³×C₁₀₉	—	2	1	no	—
301	C₂³×C₁₀₉	—	2	1	no	—
302	C₂³×C₁₀₉	—	2	2	no	—
303	C₂³×C₁₀₉	—	2	2	no	—
304	C₂³×C₁₀₉	—	2	2	no	—
305	C₂³×C₁₀₉	—	2	2	no	—
306	C₂³×C₁₀₉	—	2	2	no	—
307	C₂³×C₁₀₉	—	2	2	no	—
308	C₂³×C₁₀₉	—	2	2	no	—
309	C₂³×C₁₀₉	—	2	2	no	—
310	C₂³×C₁₀₉	—	2	2	no	—
311	C₂³×C₁₀₉	—	2	2	no	—
312	C₂³×C₁₀₉	—	2	2	no	—
313	C₂³×C₁₀₉	—	2	2	no	—
314	C₂³×C₁₀₉	—	2	4	no	—
315	C₂³×C₁₀₉	—	2	4	no	—
316	C₂³×C₁₀₉	—	4	4	no	—
317	C₂³×C₁₀₉	—	4	4	no	—
318	C₂³×C₁₀₉	—	4	8	no	—
319	C₂³×C₁₀₉	—	4	4	no	—
320	C₂³×C₁₀₉	—	4	4	no	—
321	C₂³×C₁₀₉	—	4	8	no	—
322	C₂³×C₁₀₉	—	4	8	no	—
323	C₂³×C₁₀₉	—	4	8	no	—
324	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
325	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
326	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
327	C₂³×C₁₀₉	C₂×#41	1	4	yes	—
328	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
329	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
330	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
331	Q₈×C₁₀₉	—	4	4	no	—
332	D₄×C₁₀₉	—	2	16	no	—
333	D₄×C₁₀₉	—	2	16	no	—
334	D₄×C₁₀₉	—	4	8	no	—
335	D₄×C₁₀₉	—	4	8	no	—
336	D₄×C₁₀₉	—	4	8	no	—
337	D₄×C₁₀₉	—	4	4	no	—
338	D₄×C₁₀₉	—	8	8	no	—
339	C₂×C₄×C₁₀₉	—	2	8	no	—
340	C₂×C₄×C₁₀₉	—	2	2	no	—
341	C₂×C₄×C₁₀₉	—	2	2	no	—
342	C₂×C₄×C₁₀₉	—	2	2	no	—
343	C₂×C₄×C₁₀₉	—	2	2	no	—
344	C₂×C₄×C₁₀₉	—	2	2	no	—
345	C₂×C₄×C₁₀₉	—	2	8	no	—
346	C₂×C₄×C₁₀₉	—	2	8	no	—
347	C₂×C₄×C₁₀₉	—	2	8	no	—
348	C₂×C₄×C₁₀₉	—	2	2	no	—
349	C₂×C₄×C₁₀₉	—	2	2	no	—
350	C₂×C₄×C₁₀₉	—	2	2	no	—
351	C₂×C₄×C₁₀₉	—	2	2	no	—
352	C₂×C₄×C₁₀₉	—	2	2	no	—
353	C₂×C₄×C₁₀₉	—	2	4	no	—
354	C₂×C₄×C₁₀₉	—	2	2	no	—
355	C₂×C₄×C₁₀₉	—	2	4	no	—
356	C₂×C₄×C₁₀₉	—	2	2	no	—
357	C₂×C₄×C₁₀₉	—	2	4	no	—
358	C₂×C₄×C₁₀₉	—	2	4	no	—
359	C₂×C₄×C₁₀₉	—	2	2	no	—
360	C₂×C₄×C₁₀₉	—	2	4	no	—
361	C₂×C₄×C₁₀₉	—	2	2	no	—
362	C₂×C₄×C₁₀₉	—	2	4	no	—
363	C₂×C₄×C₁₀₉	—	2	2	no	—
364	C₂×C₄×C₁₀₉	—	2	4	no	—
365	C₂×C₄×C₁₀₉	—	2	4	no	—
366	C₂×C₄×C₁₀₉	—	2	2	no	—
367	C₂×C₄×C₁₀₉	—	4	4	no	—
368	C₂×C₄×C₁₀₉	—	4	4	no	—
369	C₂×C₄×C₁₀₉	—	4	4	no	—
370	C₂×C₄×C₁₀₉	—	4	8	no	—
371	C₂×C₄×C₁₀₉	—	4	8	no	—
372	C₂×C₄×C₁₀₉	—	4	4	no	—
373	C₂×C₄×C₁₀₉	—	4	4	no	—
374	C₂×C₄×C₁₀₉	—	4	8	no	—
375	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
376	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
377	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
378	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
379	C₂×C₄×C₁₀₉	C₂×#41	1	4	yes	—
380	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	4	yes	—
381	C₂²×C₁₀₉	—	2	2	no	—
382	C₂²×C₁₀₉	—	2	2	no	—
383	C₂²×C₁₀₉	—	2	4	no	—
384	C₂²×C₁₀₉	—	2	4	no	—
385	C₂²×C₁₀₉	—	2	2	no	—
386	C₂²×C₁₀₉	—	2	2	no	—
387	C₂²×C₁₀₉	—	2	4	no	—
388	C₂²×C₁₀₉	—	2	2	no	—
389	C₂²×C₁₀₉	—	2	2	no	—
390	C₂²×C₁₀₉	—	2	2	no	—
391	C₂²×C₁₀₉	—	2	2	no	—
392	C₂²×C₁₀₉	—	2	4	no	—
393	C₂²×C₁₀₉	—	2	4	no	—
394	C₂²×C₁₀₉	—	4	16	no	—
395	C₂²×C₁₀₉	—	4	16	no	—
396	C₂²×C₁₀₉	—	4	2	no	—
397	C₂²×C₁₀₉	—	4	2	no	—
398	C₂²×C₁₀₉	—	4	2	no	—
399	C₂²×C₁₀₉	—	4	2	no	—
400	C₂²×C₁₀₉	—	4	2	no	—
401	C₂²×C₁₀₉	—	4	2	no	—
402	C₂²×C₁₀₉	—	4	2	no	—
403	C₂²×C₁₀₉	—	4	2	no	—
404	C₂²×C₁₀₉	—	4	2	no	—
405	C₂²×C₁₀₉	—	4	2	no	—
406	C₂²×C₁₀₉	—	4	2	no	—
407	C₂²×C₁₀₉	—	4	4	no	—
408	C₂²×C₁₀₉	—	4	4	no	—
409	C₂²×C₁₀₉	#525	1	4	yes	—
410	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
411	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
413	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	2	yes	—
414	C₂²×C₁₀₉	#585	1	2	yes	—
415	C₄×C₁₀₉	—	2	4	no	—
416	C₄×C₁₀₉	—	2	2	no	—
417	C₄×C₁₀₉	—	2	2	no	—
418	C₄×C₁₀₉	—	2	2	no	—
419	C₄×C₁₀₉	—	4	2	no	—
420	C₄×C₁₀₉	—	4	2	no	—
421	C₄×C₁₀₉	—	4	2	no	—
422	C₄×C₁₀₉	—	4	2	no	—
423	C₄×C₁₀₉	—	4	2	no	—
424	C₄×C₁₀₉	—	4	4	no	—
425	C₄×C₁₀₉	—	4	4	no	—
426	C₄×C₁₀₉	#534	1	4	yes	—
427	#35031	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
428	C₂×C₁₀₉	—	2	4	no	—
429	C₂×C₁₀₉	—	4	2	no	—
430	C₂×C₁₀₉	—	4	2	no	—
431	C₂×C₁₀₉	—	4	4	no	—
432	C₂×C₁₀₉	—	8	2	no	—
433	C₂×C₁₀₉	C₂×#525	1	1	yes	characteristic
434	C₂×C₁₀₉	C₂×#534	1	1	yes	characteristic
435	C₂×C₁₀₉	#3449	1	1	yes	characteristic
436	C₂×C₁₀₉	#3505	1	2	yes	—
437	C₂×C₁₀₉	#3506	1	2	yes	—
438	C₂×#525	C₂×C₁₀₉	1	1	yes	characteristic, complemented
439	C₂²×C₄×D₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
440	#2855	C₂×C₁₀₉	1	1	yes	characteristic, complemented
441	#2854	C₂×C₁₀₉	1	1	yes	characteristic, complemented
442	#2848	C₂×C₁₀₉	1	1	yes	characteristic, complemented
443	#2847	C₂×C₁₀₉	1	1	yes	characteristic, complemented
444	#2622	C₂×C₁₀₉	1	2	yes	complemented
445	#2613	C₂×C₁₀₉	1	2	yes	complemented
446	#2602	C₂×C₁₀₉	1	4	yes	complemented
447	#2600	C₂×C₁₀₉	1	4	yes	complemented
448	#2485	C₂×C₁₀₉	1	2	yes	complemented
449	#2415	C₂×C₁₀₉	1	2	yes	complemented
450	#2414	C₂×C₁₀₉	1	2	yes	complemented
451	#2407	C₂×C₁₀₉	1	2	yes	complemented
452	#2322	C₂×C₁₀₉	1	2	yes	complemented
453	#2321	C₂×C₁₀₉	1	2	yes	complemented
454	#2280	C₂×C₁₀₉	1	1	yes	characteristic, complemented
455	C₁₀₉	#35031	1	1	yes	characteristic, direct product factor, Sylow
456	C₂²×#41	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
457	C₂³×D₄	C₂²×C₁₀₉	1	1	yes	characteristic
458	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
459	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
460	#525	—	2	8	no	—
461	C₂×#123	C₂²×C₁₀₉	1	2	yes	—
462	C₂×#123	C₂²×C₁₀₉	1	2	yes	complemented
463	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
464	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
465	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	complemented
466	C₂×#121	C₂²×C₁₀₉	1	1	yes	characteristic
467	C₂×#121	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
468	C₂×#121	C₂²×C₁₀₉	1	2	yes	complemented
469	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
470	C₂×#120	C₂²×C₁₀₉	1	2	yes	—
471	C₂×C₄×D₄	—	2	8	no	—
472	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
473	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
474	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
475	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
476	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	—
477	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
478	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
479	C₂×#117	C₂²×C₁₀₉	1	2	yes	complemented
480	C₂²×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
483	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
484	#397	C₂²×C₁₀₉	1	4	yes	complemented
485	#397	C₂²×C₁₀₉	1	4	yes	complemented
486	#394	C₂²×C₁₀₉	1	4	yes	—
487	#394	C₂²×C₁₀₉	1	4	yes	—
488	#394	C₂²×C₁₀₉	1	4	yes	complemented
489	#394	C₂²×C₁₀₉	1	4	yes	complemented
490	#392	C₂²×C₁₀₉	1	4	yes	—
491	#392	C₂²×C₁₀₉	1	4	yes	—
492	#391	C₂²×C₁₀₉	1	2	yes	complemented
493	#390	C₂²×C₁₀₉	1	4	yes	complemented
494	#390	C₂²×C₁₀₉	1	2	yes	complemented
495	#389	C₂²×C₁₀₉	1	4	yes	complemented
496	#389	C₂²×C₁₀₉	1	2	yes	complemented
497	#389	C₂²×C₁₀₉	1	2	yes	complemented
498	#388	C₂²×C₁₀₉	1	4	yes	complemented
499	#388	C₂²×C₁₀₉	1	4	yes	complemented
500	#388	C₂²×C₁₀₉	1	4	yes	complemented
501	#388	C₂²×C₁₀₉	1	4	yes	complemented
502	#387	C₂²×C₁₀₉	1	4	yes	complemented
503	#387	C₂²×C₁₀₉	1	4	yes	complemented
504	#386	C₂²×C₁₀₉	1	2	yes	—
505	#386	C₂²×C₁₀₉	1	2	yes	—
506	#386	C₂²×C₁₀₉	1	4	yes	complemented
507	#386	C₂²×C₁₀₉	1	4	yes	complemented
508	#385	C₂²×C₁₀₉	1	2	yes	—
509	#385	C₂²×C₁₀₉	1	2	yes	—
510	#385	C₂²×C₁₀₉	1	4	yes	complemented
511	#385	C₂²×C₁₀₉	1	4	yes	complemented
512	#381	C₂²×C₁₀₉	1	2	yes	—
513	#381	C₂²×C₁₀₉	1	2	yes	complemented
514	#380	C₂²×C₁₀₉	1	1	yes	characteristic
515	#380	C₂²×C₁₀₉	1	1	yes	characteristic
516	#380	C₂²×C₁₀₉	1	2	yes	complemented
517	#380	C₂²×C₁₀₉	1	2	yes	complemented
518	#380	C₂²×C₁₀₉	1	2	yes	complemented
519	#379	C₂²×C₁₀₉	1	2	yes	—
520	#379	C₂²×C₁₀₉	1	2	yes	—
521	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
522	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
523	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
524	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
525	C₂×#41	—	2	4	no	—
526	C₂×#41	—	4	4	no	—
527	C₂²×Q₈	C₂³×C₁₀₉	1	1	yes	characteristic
528	C₂²×D₄	—	2	4	no	—
529	C₂²×D₄	—	2	4	no	—
530	C₂²×D₄	—	2	4	no	—
531	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
532	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
533	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
534	C₂²×D₄	C₂³×C₁₀₉	1	1	yes	characteristic
535	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
536	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
537	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
538	C₂³×C₄	—	2	4	no	—
539	C₂³×C₄	—	4	4	no	—
540	C₂³×C₄	—	4	4	no	—
541	C₂³×C₄	D₄×C₁₀₉	1	8	yes	complemented
542	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
543	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
544	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
545	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
546	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
547	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
548	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
550	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
551	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
554	#123	—	2	8	no	—
555	#123	—	2	8	no	—
556	C₂²⋊Q₈	—	2	4	no	—
557	C₂²⋊Q₈	—	2	4	no	—
558	C₂²⋊Q₈	—	4	4	no	—
559	#121	—	2	4	no	—
560	#121	—	2	4	no	—
561	#121	—	4	4	no	—
562	#120	—	2	8	no	—
563	#120	—	2	8	no	—
564	C₄×D₄	—	2	8	no	—
565	C₄×D₄	—	2	8	no	—
566	C₄×D₄	—	2	8	no	—
567	C₄×D₄	—	2	8	no	—
568	C₄×D₄	—	2	8	no	—
569	C₄×D₄	—	2	8	no	—
570	#117	—	2	4	no	—
571	#117	—	4	4	no	—
572	C₂×C₄⋊C₄	—	2	4	no	—
573	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
574	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
575	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
576	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	1	yes	characteristic
577	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
578	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
579	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
580	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
581	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
582	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
583	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
584	C₂×C₂²⋊C₄	—	2	4	no	—
585	C₂×C₂²⋊C₄	—	2	4	no	—
586	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
587	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
588	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
589	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
590	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
591	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
592	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
593	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
605	C₂×C₄²	—	2	4	no	—
606	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
607	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
608	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
609	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
610	#95	C₂³×C₁₀₉	1	4	yes	—
611	#95	C₂³×C₁₀₉	1	2	yes	—
612	#95	C₂³×C₁₀₉	1	2	yes	—
613	#95	C₂³×C₁₀₉	1	4	yes	—
614	#95	C₂³×C₁₀₉	1	4	yes	—
615	#95	C₂³×C₁₀₉	1	4	yes	—
616	#95	C₂³×C₁₀₉	1	4	yes	—
617	#95	C₂³×C₁₀₉	1	4	yes	—
618	#95	C₂³×C₁₀₉	1	4	yes	—
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	2	2	no	—
623	C₂⁴	—	4	2	no	—
624	C₂⁴	—	4	2	no	—
625	C₂⁴	—	4	2	no	—
626	C₂⁴	—	4	2	no	—
627	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
628	C₂⁴	#41×C₁₀₉	1	4	yes	complemented
629	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
630	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
631	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
632	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
633	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
634	#41	—	4	16	no	—
635	C₂×Q₈	—	2	2	no	—
636	C₂×Q₈	—	2	4	no	—
637	C₂×D₄	—	2	32	no	—
638	C₂×D₄	—	2	4	no	—
639	C₂×D₄	—	2	4	no	—
640	C₂×D₄	—	2	4	no	—
641	C₂×D₄	—	2	4	no	—
642	C₂×D₄	—	2	4	no	—
643	C₂×D₄	—	2	4	no	—
644	C₂×D₄	—	2	4	no	—
645	C₂×D₄	—	2	4	no	—
646	C₂×D₄	—	2	4	no	—
647	C₂×D₄	—	2	8	no	—
648	C₂×D₄	—	2	2	no	—
649	C₂×D₄	—	2	4	no	—
650	C₂×D₄	—	2	4	no	—
651	C₂×D₄	—	2	4	no	—
652	C₂×D₄	—	4	4	no	—
653	C₂×D₄	—	4	4	no	—
654	C₂×D₄	—	4	4	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	4	no	—
659	C₂²×C₄	—	2	4	no	—
660	C₂²×C₄	—	2	4	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	4	no	—
664	C₂²×C₄	—	2	4	no	—
665	C₂²×C₄	—	2	4	no	—
666	C₂²×C₄	—	2	4	no	—
667	C₂²×C₄	—	2	4	no	—
668	C₂²×C₄	—	4	16	no	—
669	C₂²×C₄	—	4	2	no	—
670	C₂²×C₄	—	4	2	no	—
671	C₂²×C₄	—	4	2	no	—
672	C₂²×C₄	—	4	2	no	—
673	C₂²×C₄	—	4	2	no	—
674	C₂²×C₄	—	4	2	no	—
675	C₂²×C₄	—	4	2	no	—
676	C₂²×C₄	—	4	4	no	—
677	C₂²×C₄	—	4	16	no	—
678	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
679	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
680	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
681	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
682	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
683	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
684	C₂²×C₄	#41×C₁₀₉	1	4	yes	complemented
685	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
686	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
688	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
689	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
690	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
691	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
692	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
693	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
694	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
695	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
696	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
697	C₄⋊C₄	—	2	4	no	—
698	C₄⋊C₄	—	2	4	no	—
699	C₄⋊C₄	—	2	2	no	—
700	C₄⋊C₄	—	2	2	no	—
701	C₄⋊C₄	—	2	4	no	—
702	C₄⋊C₄	—	2	4	no	—
703	C₄⋊C₄	—	2	8	no	—
704	C₄⋊C₄	—	2	4	no	—
705	C₄⋊C₄	—	2	4	no	—
706	C₄⋊C₄	—	4	4	no	—
707	C₄⋊C₄	—	4	4	no	—
708	C₂²⋊C₄	—	2	4	no	—
709	C₂²⋊C₄	—	2	4	no	—
710	C₂²⋊C₄	—	2	4	no	—
711	C₂²⋊C₄	—	2	4	no	—
712	C₂²⋊C₄	—	2	4	no	—
713	C₂²⋊C₄	—	2	8	no	—
714	C₂²⋊C₄	—	2	4	no	—
715	C₂²⋊C₄	—	2	4	no	—
716	C₂²⋊C₄	—	2	4	no	—
717	C₂²⋊C₄	—	2	4	no	—
718	C₂²⋊C₄	—	2	4	no	—
719	C₂²⋊C₄	—	2	4	no	—
720	C₂²⋊C₄	—	2	8	no	—
721	C₂²⋊C₄	—	4	4	no	—
722	C₂²⋊C₄	—	4	4	no	—
723	C₂²⋊C₄	—	4	4	no	—
724	C₂²⋊C₄	—	4	4	no	—
725	C₂²⋊C₄	—	4	4	no	—
726	C₂²⋊C₄	—	4	4	no	—
727	C₄²	—	2	4	no	—
728	C₄²	—	2	4	no	—
729	C₄²	—	2	4	no	—
730	C₄²	—	4	4	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	8	no	—
734	C₂³	—	2	8	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	2	1	no	—
737	C₂³	—	2	1	no	—
738	C₂³	—	2	1	no	—
739	C₂³	—	2	1	no	—
740	C₂³	—	2	2	no	—
741	C₂³	—	2	2	no	—
742	C₂³	—	2	2	no	—
743	C₂³	—	2	2	no	—
744	C₂³	—	2	2	no	—
745	C₂³	—	2	2	no	—
746	C₂³	—	2	2	no	—
747	C₂³	—	2	2	no	—
748	C₂³	—	2	2	no	—
749	C₂³	—	2	2	no	—
750	C₂³	—	2	2	no	—
751	C₂³	—	2	2	no	—
752	C₂³	—	2	4	no	—
753	C₂³	—	2	4	no	—
754	C₂³	—	4	4	no	—
755	C₂³	—	4	4	no	—
756	C₂³	—	4	8	no	—
757	C₂³	—	4	4	no	—
758	C₂³	—	4	8	no	—
759	C₂³	—	4	8	no	—
760	C₂³	—	4	8	no	—
761	C₂³	—	4	4	no	—
762	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
763	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
764	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
765	C₂³	C₂×#41×C₁₀₉	1	4	yes	—
766	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
767	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
768	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
769	Q₈	—	4	4	no	—
770	D₄	—	2	16	no	—
771	D₄	—	2	16	no	—
772	D₄	—	4	8	no	—
773	D₄	—	4	8	no	—
774	D₄	—	4	8	no	—
775	D₄	—	4	4	no	—
776	D₄	—	8	8	no	—
777	C₂×C₄	—	2	8	no	—
778	C₂×C₄	—	2	2	no	—
779	C₂×C₄	—	2	2	no	—
780	C₂×C₄	—	2	2	no	—
781	C₂×C₄	—	2	2	no	—
782	C₂×C₄	—	2	2	no	—
783	C₂×C₄	—	2	8	no	—
784	C₂×C₄	—	2	8	no	—
785	C₂×C₄	—	2	8	no	—
786	C₂×C₄	—	2	2	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	4	no	—
792	C₂×C₄	—	2	4	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	4	no	—
796	C₂×C₄	—	2	4	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	4	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	4	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	4	no	—
803	C₂×C₄	—	2	4	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	8	no	—
809	C₂×C₄	—	4	8	no	—
810	C₂×C₄	—	4	4	no	—
811	C₂×C₄	—	4	4	no	—
812	C₂×C₄	—	4	8	no	—
813	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
814	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
815	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
816	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
817	C₂×C₄	C₂×#41×C₁₀₉	1	4	yes	—
818	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	4	yes	—
819	C₂²	—	2	4	no	—
820	C₂²	—	2	4	no	—
821	C₂²	—	2	2	no	—
822	C₂²	—	2	2	no	—
823	C₂²	—	2	4	no	—
824	C₂²	—	2	4	no	—
825	C₂²	—	2	2	no	—
826	C₂²	—	2	2	no	—
827	C₂²	—	2	4	no	—
828	C₂²	—	2	2	no	—
829	C₂²	—	2	2	no	—
830	C₂²	—	2	2	no	—
831	C₂²	—	2	2	no	—
832	C₂²	—	4	16	no	—
833	C₂²	—	4	16	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	4	2	no	—
838	C₂²	—	4	2	no	—
839	C₂²	—	4	2	no	—
840	C₂²	—	4	2	no	—
841	C₂²	—	4	2	no	—
842	C₂²	—	4	4	no	—
843	C₂²	—	4	4	no	—
844	C₂²	—	4	2	no	—
845	C₂²	—	4	2	no	—
846	C₂²	—	4	2	no	—
847	C₂²	#525×C₁₀₉	1	4	yes	—
848	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
849	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
850	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
851	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	2	yes	—
852	C₂²	#585×C₁₀₉	1	2	yes	—
853	C₄	—	2	4	no	—
854	C₄	—	2	2	no	—
855	C₄	—	2	2	no	—
856	C₄	—	2	2	no	—
857	C₄	—	4	4	no	—
858	C₄	—	4	4	no	—
859	C₄	—	4	2	no	—
860	C₄	—	4	2	no	—
861	C₄	—	4	2	no	—
862	C₄	—	4	2	no	—
863	C₄	—	4	2	no	—
864	C₄	#534×C₁₀₉	1	4	yes	—
865	C₂	—	2	4	no	—
866	C₂	—	4	4	no	—
867	C₂	—	4	2	no	—
868	C₂	—	4	2	no	—
869	C₂	—	8	2	no	—
870	C₂	C₂×#525×C₁₀₉	1	1	yes	characteristic
871	C₂	C₂×#534×C₁₀₉	1	1	yes	characteristic
872	C₂	C₁₀₉×#3449	1	1	yes	characteristic
873	C₂	C₁₀₉×#3505	1	2	yes	—
874	C₂	C₁₀₉×#3506	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₁₀₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₁₀₉
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#525×C₁₀₉	C₂	semidirect
2. C₂²×C₄×D₄×C₁₀₉	C₂	semidirect
3. C₁₀₉×#2855	C₂	semidirect
4. C₁₀₉×#2854	C₂	semidirect
5. C₁₀₉×#2848	C₂	semidirect
6. C₁₀₉×#2847	C₂	semidirect
7. C₁₀₉×#2622	C₂	semidirect
8. C₁₀₉×#2613	C₂	semidirect
9. C₁₀₉×#2602	C₂	semidirect
10. C₁₀₉×#2600	C₂	semidirect
11. C₁₀₉×#2485	C₂	semidirect
12. C₁₀₉×#2415	C₂	semidirect
13. C₁₀₉×#2414	C₂	semidirect
14. C₁₀₉×#2407	C₂	semidirect
15. C₁₀₉×#2322	C₂	semidirect
16. C₁₀₉×#2321	C₂	semidirect
17. C₁₀₉×#2280	C₂	semidirect
18. C₂²×#41×C₁₀₉	C₂²	semidirect
24. C₂×#123×C₁₀₉	C₂²	semidirect
26. C₂×C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
27. C₂×C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
29. C₂×#121×C₁₀₉	C₂²	semidirect
30. C₂×#121×C₁₀₉	C₂²	semidirect
39. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
40. C₂×#117×C₁₀₉	C₂²	semidirect
41. C₂×#117×C₁₀₉	C₂²	semidirect
46. #397×C₁₀₉	C₂²	semidirect
47. #397×C₁₀₉	C₂²	semidirect
50. #394×C₁₀₉	C₂²	semidirect
51. #394×C₁₀₉	C₂²	semidirect
54. #391×C₁₀₉	C₂²	semidirect
55. #390×C₁₀₉	C₂²	semidirect
56. #390×C₁₀₉	C₂²	semidirect
57. #389×C₁₀₉	C₂²	semidirect
58. #389×C₁₀₉	C₂²	semidirect
59. #389×C₁₀₉	C₂²	semidirect
60. #388×C₁₀₉	C₂²	semidirect
61. #388×C₁₀₉	C₂²	semidirect
62. #388×C₁₀₉	C₂²	semidirect
63. #388×C₁₀₉	C₂²	semidirect
64. #387×C₁₀₉	C₂²	semidirect
65. #387×C₁₀₉	C₂²	semidirect
68. #386×C₁₀₉	C₂²	semidirect
69. #386×C₁₀₉	C₂²	semidirect
72. #385×C₁₀₉	C₂²	semidirect
73. #385×C₁₀₉	C₂²	semidirect
75. #381×C₁₀₉	C₂²	semidirect
78. #380×C₁₀₉	C₂²	semidirect
79. #380×C₁₀₉	C₂²	semidirect
80. #380×C₁₀₉	C₂²	semidirect
84. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
103. C₂³×C₄×C₁₀₉	D₄	semidirect
190. C₂⁴×C₁₀₉	#41	semidirect
246. C₂²×C₄×C₁₀₉	#41	semidirect
427. #35031	C₁₀₉	direct (N × H)
438. C₂×#525	C₂×C₁₀₉	semidirect
439. C₂²×C₄×D₄	C₂×C₁₀₉	semidirect
440. #2855	C₂×C₁₀₉	semidirect
441. #2854	C₂×C₁₀₉	semidirect
442. #2848	C₂×C₁₀₉	semidirect
443. #2847	C₂×C₁₀₉	semidirect
444. #2622	C₂×C₁₀₉	semidirect
445. #2613	C₂×C₁₀₉	semidirect
446. #2602	C₂×C₁₀₉	semidirect
447. #2600	C₂×C₁₀₉	semidirect
448. #2485	C₂×C₁₀₉	semidirect
449. #2415	C₂×C₁₀₉	semidirect
450. #2414	C₂×C₁₀₉	semidirect
451. #2407	C₂×C₁₀₉	semidirect
452. #2322	C₂×C₁₀₉	semidirect
453. #2321	C₂×C₁₀₉	semidirect
454. #2280	C₂×C₁₀₉	semidirect
455. C₁₀₉	#35031	direct (N × H)
456. C₂²×#41	C₂²×C₁₀₉	semidirect
462. C₂×#123	C₂²×C₁₀₉	semidirect
464. C₂×C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
465. C₂×C₂²⋊Q₈	C₂²×C₁₀₉	semidirect
467. C₂×#121	C₂²×C₁₀₉	semidirect
468. C₂×#121	C₂²×C₁₀₉	semidirect
477. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
478. C₂×#117	C₂²×C₁₀₉	semidirect
479. C₂×#117	C₂²×C₁₀₉	semidirect
484. #397	C₂²×C₁₀₉	semidirect
485. #397	C₂²×C₁₀₉	semidirect
488. #394	C₂²×C₁₀₉	semidirect
489. #394	C₂²×C₁₀₉	semidirect
492. #391	C₂²×C₁₀₉	semidirect
493. #390	C₂²×C₁₀₉	semidirect
494. #390	C₂²×C₁₀₉	semidirect
495. #389	C₂²×C₁₀₉	semidirect
496. #389	C₂²×C₁₀₉	semidirect
497. #389	C₂²×C₁₀₉	semidirect
498. #388	C₂²×C₁₀₉	semidirect
499. #388	C₂²×C₁₀₉	semidirect
500. #388	C₂²×C₁₀₉	semidirect
501. #388	C₂²×C₁₀₉	semidirect
502. #387	C₂²×C₁₀₉	semidirect
503. #387	C₂²×C₁₀₉	semidirect
506. #386	C₂²×C₁₀₉	semidirect
507. #386	C₂²×C₁₀₉	semidirect
510. #385	C₂²×C₁₀₉	semidirect
511. #385	C₂²×C₁₀₉	semidirect
513. #381	C₂²×C₁₀₉	semidirect
516. #380	C₂²×C₁₀₉	semidirect
517. #380	C₂²×C₁₀₉	semidirect
518. #380	C₂²×C₁₀₉	semidirect
522. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
541. C₂³×C₄	D₄×C₁₀₉	semidirect
628. C₂⁴	#41×C₁₀₉	semidirect
684. C₂²×C₄	#41×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₁₀₉	2
C₂²×C₄×D₄×C₁₀₉	2
C₁₀₉×#2855	2
C₁₀₉×#2854	2
C₁₀₉×#2848	2
C₁₀₉×#2847	2
C₁₀₉×#2622	2
C₁₀₉×#2613	2
C₁₀₉×#2602	2
C₁₀₉×#2600	2
C₁₀₉×#2485	2
C₁₀₉×#2415	2
C₁₀₉×#2414	2
C₁₀₉×#2407	2
C₁₀₉×#2322	2
C₁₀₉×#2321	2
C₁₀₉×#2280	2
#35031	109

Subgroups — C109×#35031 #42153025

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#35031 #42153025