Subgroups — C₁₀₉×#35005 #42152999

Order 27904.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#538×C₁₀₉	C₂	1	2	yes	maximal, complemented
2	C₁₀₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₉×#2856	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2847	C₂	1	2	yes	maximal, complemented
5	C₁₀₉×#2639	C₂	1	2	yes	maximal, complemented
6	C₁₀₉×#2617	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#2559	C₂	1	4	yes	maximal, complemented
8	C₁₀₉×#2557	C₂	1	4	yes	maximal, complemented
9	C₁₀₉×#2496	C₂	1	2	yes	maximal, complemented
10	C₁₀₉×#2491	C₂	1	2	yes	maximal, complemented
11	C₁₀₉×#2428	C₂	1	2	yes	maximal, complemented
12	C₁₀₉×#2422	C₂	1	2	yes	maximal, complemented
13	C₁₀₉×#2325	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₁₀₉	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁴×C₄×C₁₀₉	C₂²	1	1	yes	characteristic
17	#538×C₁₀₉	—	2	16	no	—
18	C₂×C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×#127×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×#126×C₁₀₉	C₂²	1	4	yes	—
21	C₂×#124×C₁₀₉	C₂²	1	4	yes	—
22	C₂×#123×C₁₀₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	—
24	C₂×#121×C₁₀₉	C₂²	1	4	yes	—
25	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
26	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
27	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
28	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
29	C₂×#121×C₁₀₉	C₂²	1	2	yes	—
30	C₂×#120×C₁₀₉	C₂²	1	4	yes	—
31	C₂×C₄×D₄×C₁₀₉	C₂²	1	4	yes	—
32	C₂×C₄×D₄×C₁₀₉	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₁₀₉	C₂²	1	1	yes	characteristic
37	#400×C₁₀₉	C₂²	1	4	yes	complemented
38	#397×C₁₀₉	C₂²	1	4	yes	—
39	#397×C₁₀₉	C₂²	1	4	yes	complemented
40	#394×C₁₀₉	C₂²	1	4	yes	—
41	#394×C₁₀₉	C₂²	1	4	yes	—
42	#394×C₁₀₉	C₂²	1	4	yes	complemented
43	#393×C₁₀₉	C₂²	1	4	yes	complemented
44	#392×C₁₀₉	C₂²	1	4	yes	—
45	#391×C₁₀₉	C₂²	1	2	yes	complemented
46	#390×C₁₀₉	C₂²	1	2	yes	complemented
47	#390×C₁₀₉	C₂²	1	2	yes	complemented
48	#390×C₁₀₉	C₂²	1	2	yes	complemented
49	#390×C₁₀₉	C₂²	1	2	yes	complemented
50	#389×C₁₀₉	C₂²	1	2	yes	complemented
51	#389×C₁₀₉	C₂²	1	2	yes	complemented
52	#389×C₁₀₉	C₂²	1	2	yes	complemented
53	#388×C₁₀₉	C₂²	1	4	yes	complemented
54	#388×C₁₀₉	C₂²	1	4	yes	complemented
55	#387×C₁₀₉	C₂²	1	4	yes	complemented
56	#386×C₁₀₉	C₂²	1	4	yes	—
57	#386×C₁₀₉	C₂²	1	4	yes	—
58	#386×C₁₀₉	C₂²	1	4	yes	—
59	#386×C₁₀₉	C₂²	1	4	yes	—
60	#386×C₁₀₉	C₂²	1	4	yes	complemented
61	#385×C₁₀₉	C₂²	1	4	yes	complemented
62	#384×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
63	#384×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
64	#380×C₁₀₉	C₂²	1	2	yes	—
65	#380×C₁₀₉	C₂²	1	2	yes	—
66	#380×C₁₀₉	C₂²	1	2	yes	—
67	#380×C₁₀₉	C₂²	1	2	yes	—
68	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	2	yes	complemented
69	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
72	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	2	yes	—
73	C₄×C₂²⋊C₄×C₁₀₉	C₂²	1	4	yes	complemented
74	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic
75	C₂×#95×C₁₀₉	C₂²	1	1	yes	characteristic
76	C₂⁵×C₁₀₉	C₂³	1	1	yes	characteristic
77	C₂²×Q₈×C₁₀₉	C₂³	1	2	yes	—
78	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
79	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
80	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
81	C₂²×D₄×C₁₀₉	C₂³	1	4	yes	—
82	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₁₀₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₁₀₉	—	2	4	no	—
85	C₂³×C₄×C₁₀₉	—	4	2	no	—
86	C₂³×C₄×C₁₀₉	—	4	2	no	—
87	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₁₀₉	C₂³	1	4	yes	—
91	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₁₀₉	C₂³	1	2	yes	—
93	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
96	C₄⋊Q₈×C₁₀₉	—	4	2	no	—
97	#127×C₁₀₉	—	4	2	no	—
98	#126×C₁₀₉	—	2	16	no	—
99	#124×C₁₀₉	—	2	16	no	—
100	#123×C₁₀₉	—	2	16	no	—
101	C₂²⋊Q₈×C₁₀₉	—	2	8	no	—
102	#121×C₁₀₉	—	2	8	no	—
103	#121×C₁₀₉	—	2	8	no	—
104	#121×C₁₀₉	—	2	8	no	—
105	#121×C₁₀₉	—	2	16	no	—
106	#121×C₁₀₉	—	4	4	no	—
107	#121×C₁₀₉	—	4	4	no	—
108	#120×C₁₀₉	—	2	16	no	—
109	C₄×D₄×C₁₀₉	—	2	16	no	—
110	C₄×D₄×C₁₀₉	—	4	4	no	—
111	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
118	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
120	C₂×C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₁₀₉	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₁₀₉	D₄	1	8	yes	complemented
123	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
127	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
137	C₂×C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
138	C₂×C₄²×C₁₀₉	—	4	2	no	—
139	C₂×C₄²×C₁₀₉	—	4	2	no	—
140	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
142	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
143	C₂×C₄²×C₁₀₉	C₂³	1	4	yes	—
144	C₂×C₄²×C₁₀₉	C₂³	1	2	yes	—
145	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
146	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
147	#95×C₁₀₉	C₂³	1	2	yes	—
148	#95×C₁₀₉	C₂³	1	2	yes	—
149	#95×C₁₀₉	C₂³	1	2	yes	—
150	#95×C₁₀₉	C₂³	1	2	yes	—
151	#95×C₁₀₉	C₂³	1	4	yes	—
152	#95×C₁₀₉	C₂³	1	4	yes	—
153	#95×C₁₀₉	C₂³	1	4	yes	—
154	#95×C₁₀₉	C₂³	1	4	yes	—
155	#95×C₁₀₉	C₂³	1	4	yes	—
156	#95×C₁₀₉	C₂³	1	4	yes	—
157	C₂⁴×C₁₀₉	—	2	2	no	—
158	C₂⁴×C₁₀₉	—	2	2	no	—
159	C₂⁴×C₁₀₉	—	4	1	no	—
160	C₂⁴×C₁₀₉	—	4	1	no	—
161	C₂⁴×C₁₀₉	—	4	1	no	—
162	C₂⁴×C₁₀₉	—	4	1	no	—
163	C₂⁴×C₁₀₉	C₂×D₄	1	4	yes	—
164	C₂⁴×C₁₀₉	C₂⁴	1	4	yes	—
165	C₂⁴×C₁₀₉	C₂⁴	1	2	yes	—
166	C₂⁴×C₁₀₉	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₁₀₉	—	2	4	no	—
168	C₂×Q₈×C₁₀₉	—	4	2	no	—
169	C₂×Q₈×C₁₀₉	—	4	2	no	—
170	C₂×D₄×C₁₀₉	—	2	8	no	—
171	C₂×D₄×C₁₀₉	—	2	8	no	—
172	C₂×D₄×C₁₀₉	—	2	8	no	—
173	C₂×D₄×C₁₀₉	—	2	8	no	—
174	C₂×D₄×C₁₀₉	—	2	8	no	—
175	C₂×D₄×C₁₀₉	—	2	4	no	—
176	C₂×D₄×C₁₀₉	—	2	4	no	—
177	C₂×D₄×C₁₀₉	—	2	4	no	—
178	C₂×D₄×C₁₀₉	—	2	4	no	—
179	C₂×D₄×C₁₀₉	—	2	4	no	—
180	C₂×D₄×C₁₀₉	—	4	4	no	—
181	C₂×D₄×C₁₀₉	—	4	4	no	—
182	C₂×D₄×C₁₀₉	—	4	2	no	—
183	C₂×D₄×C₁₀₉	—	4	2	no	—
184	C₂×D₄×C₁₀₉	—	4	2	no	—
185	C₂×D₄×C₁₀₉	—	4	2	no	—
186	C₂×D₄×C₁₀₉	—	4	4	no	—
187	C₂×D₄×C₁₀₉	—	4	4	no	—
188	C₂²×C₄×C₁₀₉	—	2	2	no	—
189	C₂²×C₄×C₁₀₉	—	2	2	no	—
190	C₂²×C₄×C₁₀₉	—	2	2	no	—
191	C₂²×C₄×C₁₀₉	—	2	2	no	—
192	C₂²×C₄×C₁₀₉	—	2	4	no	—
193	C₂²×C₄×C₁₀₉	—	2	4	no	—
194	C₂²×C₄×C₁₀₉	—	2	4	no	—
195	C₂²×C₄×C₁₀₉	—	2	4	no	—
196	C₂²×C₄×C₁₀₉	—	2	8	no	—
197	C₂²×C₄×C₁₀₉	—	4	1	no	—
198	C₂²×C₄×C₁₀₉	—	4	1	no	—
199	C₂²×C₄×C₁₀₉	—	4	1	no	—
200	C₂²×C₄×C₁₀₉	—	4	1	no	—
201	C₂²×C₄×C₁₀₉	—	4	2	no	—
202	C₂²×C₄×C₁₀₉	—	4	2	no	—
203	C₂²×C₄×C₁₀₉	—	4	1	no	—
204	C₂²×C₄×C₁₀₉	—	4	1	no	—
205	C₂²×C₄×C₁₀₉	—	4	1	no	—
206	C₂²×C₄×C₁₀₉	—	4	1	no	—
207	C₂²×C₄×C₁₀₉	—	4	1	no	—
208	C₂²×C₄×C₁₀₉	—	4	1	no	—
209	C₂²×C₄×C₁₀₉	—	4	4	no	—
210	C₂²×C₄×C₁₀₉	—	4	4	no	—
211	C₂²×C₄×C₁₀₉	—	4	16	no	—
212	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
213	C₂²×C₄×C₁₀₉	C₂×D₄	1	4	yes	—
214	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
215	C₂²×C₄×C₁₀₉	#41	1	4	yes	—
216	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
217	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
218	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
219	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
220	C₂²×C₄×C₁₀₉	C₂⁴	1	4	yes	—
221	C₂²×C₄×C₁₀₉	C₂⁴	1	2	yes	—
222	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
223	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
225	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
226	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
228	C₄⋊C₄×C₁₀₉	—	2	8	no	—
229	C₄⋊C₄×C₁₀₉	—	2	8	no	—
230	C₄⋊C₄×C₁₀₉	—	2	4	no	—
231	C₄⋊C₄×C₁₀₉	—	2	4	no	—
232	C₄⋊C₄×C₁₀₉	—	2	4	no	—
233	C₄⋊C₄×C₁₀₉	—	2	4	no	—
234	C₄⋊C₄×C₁₀₉	—	2	4	no	—
235	C₄⋊C₄×C₁₀₉	—	2	4	no	—
236	C₄⋊C₄×C₁₀₉	—	4	2	no	—
237	C₄⋊C₄×C₁₀₉	—	4	2	no	—
238	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
239	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
240	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
241	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
242	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
243	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
244	C₂²⋊C₄×C₁₀₉	—	2	4	no	—
245	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
246	C₂²⋊C₄×C₁₀₉	—	2	8	no	—
247	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
248	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
249	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
250	C₂²⋊C₄×C₁₀₉	—	4	4	no	—
251	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
252	C₂²⋊C₄×C₁₀₉	C₂×D₄	1	8	yes	—
253	C₄²×C₁₀₉	—	2	8	no	—
254	C₄²×C₁₀₉	—	2	4	no	—
255	C₄²×C₁₀₉	—	2	2	no	—
256	C₄²×C₁₀₉	—	2	2	no	—
257	C₄²×C₁₀₉	—	4	1	no	—
258	C₄²×C₁₀₉	—	4	2	no	—
259	C₄²×C₁₀₉	—	4	1	no	—
260	C₂³×C₁₀₉	—	2	1	no	—
261	C₂³×C₁₀₉	—	2	1	no	—
262	C₂³×C₁₀₉	—	2	1	no	—
263	C₂³×C₁₀₉	—	2	1	no	—
264	C₂³×C₁₀₉	—	2	8	no	—
265	C₂³×C₁₀₉	—	2	2	no	—
266	C₂³×C₁₀₉	—	2	2	no	—
267	C₂³×C₁₀₉	—	2	2	no	—
268	C₂³×C₁₀₉	—	2	2	no	—
269	C₂³×C₁₀₉	—	2	2	no	—
270	C₂³×C₁₀₉	—	2	2	no	—
271	C₂³×C₁₀₉	—	2	4	no	—
272	C₂³×C₁₀₉	—	2	4	no	—
273	C₂³×C₁₀₉	—	2	4	no	—
274	C₂³×C₁₀₉	—	2	4	no	—
275	C₂³×C₁₀₉	—	2	4	no	—
276	C₂³×C₁₀₉	—	2	4	no	—
277	C₂³×C₁₀₉	—	2	4	no	—
278	C₂³×C₁₀₉	—	4	4	no	—
279	C₂³×C₁₀₉	—	4	4	no	—
280	C₂³×C₁₀₉	—	4	4	no	—
281	C₂³×C₁₀₉	—	4	4	no	—
282	C₂³×C₁₀₉	—	4	4	no	—
283	C₂³×C₁₀₉	—	4	4	no	—
284	C₂³×C₁₀₉	C₂²×D₄	1	4	yes	—
285	C₂³×C₁₀₉	C₂²×D₄	1	2	yes	—
286	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
287	C₂³×C₁₀₉	C₂×#41	1	2	yes	—
288	C₂³×C₁₀₉	C₂⁵	1	1	yes	characteristic
289	Q₈×C₁₀₉	—	8	4	no	—
290	D₄×C₁₀₉	—	4	16	no	—
291	D₄×C₁₀₉	—	4	8	no	—
292	D₄×C₁₀₉	—	8	4	no	—
293	D₄×C₁₀₉	—	8	4	no	—
294	D₄×C₁₀₉	—	8	8	no	—
295	D₄×C₁₀₉	—	8	8	no	—
296	C₂×C₄×C₁₀₉	—	2	1	no	—
297	C₂×C₄×C₁₀₉	—	2	2	no	—
298	C₂×C₄×C₁₀₉	—	2	1	no	—
299	C₂×C₄×C₁₀₉	—	2	1	no	—
300	C₂×C₄×C₁₀₉	—	2	1	no	—
301	C₂×C₄×C₁₀₉	—	2	1	no	—
302	C₂×C₄×C₁₀₉	—	2	1	no	—
303	C₂×C₄×C₁₀₉	—	2	1	no	—
304	C₂×C₄×C₁₀₉	—	2	2	no	—
305	C₂×C₄×C₁₀₉	—	2	1	no	—
306	C₂×C₄×C₁₀₉	—	2	1	no	—
307	C₂×C₄×C₁₀₉	—	2	1	no	—
308	C₂×C₄×C₁₀₉	—	2	8	no	—
309	C₂×C₄×C₁₀₉	—	2	4	no	—
310	C₂×C₄×C₁₀₉	—	2	4	no	—
311	C₂×C₄×C₁₀₉	—	2	4	no	—
312	C₂×C₄×C₁₀₉	—	2	2	no	—
313	C₂×C₄×C₁₀₉	—	2	4	no	—
314	C₂×C₄×C₁₀₉	—	2	4	no	—
315	C₂×C₄×C₁₀₉	—	2	2	no	—
316	C₂×C₄×C₁₀₉	—	2	2	no	—
317	C₂×C₄×C₁₀₉	—	2	4	no	—
318	C₂×C₄×C₁₀₉	—	2	2	no	—
319	C₂×C₄×C₁₀₉	—	2	2	no	—
320	C₂×C₄×C₁₀₉	—	2	4	no	—
321	C₂×C₄×C₁₀₉	—	2	2	no	—
322	C₂×C₄×C₁₀₉	—	2	4	no	—
323	C₂×C₄×C₁₀₉	—	2	4	no	—
324	C₂×C₄×C₁₀₉	—	4	4	no	—
325	C₂×C₄×C₁₀₉	—	4	4	no	—
326	C₂×C₄×C₁₀₉	—	4	4	no	—
327	C₂×C₄×C₁₀₉	—	4	8	no	—
328	C₂×C₄×C₁₀₉	—	4	4	no	—
329	C₂×C₄×C₁₀₉	—	4	4	no	—
330	C₂×C₄×C₁₀₉	—	4	8	no	—
331	C₂×C₄×C₁₀₉	—	8	8	no	—
332	C₂×C₄×C₁₀₉	C₂²×D₄	1	4	yes	—
333	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
334	C₂×C₄×C₁₀₉	C₂²×D₄	1	2	yes	—
335	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
336	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
337	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
338	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
339	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
340	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
341	C₂²×C₁₀₉	—	2	2	no	—
342	C₂²×C₁₀₉	—	2	2	no	—
343	C₂²×C₁₀₉	—	2	2	no	—
344	C₂²×C₁₀₉	—	2	2	no	—
345	C₂²×C₁₀₉	—	2	2	no	—
346	C₂²×C₁₀₉	—	2	2	no	—
347	C₂²×C₁₀₉	—	2	4	no	—
348	C₂²×C₁₀₉	—	2	4	no	—
349	C₂²×C₁₀₉	—	2	4	no	—
350	C₂²×C₁₀₉	—	4	16	no	—
351	C₂²×C₁₀₉	—	4	2	no	—
352	C₂²×C₁₀₉	—	4	2	no	—
353	C₂²×C₁₀₉	—	4	2	no	—
354	C₂²×C₁₀₉	—	4	2	no	—
355	C₂²×C₁₀₉	—	4	4	no	—
356	C₂²×C₁₀₉	—	4	4	no	—
357	C₂²×C₁₀₉	—	4	4	no	—
358	C₂²×C₁₀₉	—	4	4	no	—
359	C₂²×C₁₀₉	—	4	4	no	—
360	C₂²×C₁₀₉	—	4	4	no	—
361	C₂²×C₁₀₉	—	4	4	no	—
362	C₂²×C₁₀₉	#532	1	4	yes	—
363	C₂²×C₁₀₉	C₂³×D₄	1	1	yes	characteristic
364	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
365	C₂²×C₁₀₉	C₂²×#41	1	1	yes	characteristic
366	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
367	C₂²×C₁₀₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
368	C₂²×C₁₀₉	#585	1	1	yes	characteristic
369	C₂²×C₁₀₉	#585	1	1	yes	characteristic
370	C₄×C₁₀₉	—	2	2	no	—
371	C₄×C₁₀₉	—	2	4	no	—
372	C₄×C₁₀₉	—	2	2	no	—
373	C₄×C₁₀₉	—	2	2	no	—
374	C₄×C₁₀₉	—	2	2	no	—
375	C₄×C₁₀₉	—	2	2	no	—
376	C₄×C₁₀₉	—	4	4	no	—
377	C₄×C₁₀₉	—	4	2	no	—
378	C₄×C₁₀₉	—	4	4	no	—
379	C₄×C₁₀₉	—	4	4	no	—
380	C₄×C₁₀₉	—	4	2	no	—
381	C₄×C₁₀₉	#538	1	4	yes	complemented
382	#35005	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
383	C₂×C₁₀₉	—	2	4	no	—
384	C₂×C₁₀₉	—	4	4	no	—
385	C₂×C₁₀₉	—	8	4	no	—
386	C₂×C₁₀₉	C₂×#532	1	1	yes	characteristic
387	C₂×C₁₀₉	C₂×#538	1	1	yes	characteristic
388	C₂×C₁₀₉	#3455	1	1	yes	characteristic
389	C₂×C₁₀₉	#3496	1	1	yes	characteristic
390	C₂×C₁₀₉	#3496	1	1	yes	characteristic
391	C₂×C₁₀₉	#3505	1	1	yes	characteristic
392	C₂×C₁₀₉	#3506	1	1	yes	characteristic
393	C₂×#538	C₂×C₁₀₉	1	2	yes	complemented
394	#2857	C₂×C₁₀₉	1	1	yes	characteristic, complemented
395	#2856	C₂×C₁₀₉	1	1	yes	characteristic, complemented
396	#2847	C₂×C₁₀₉	1	2	yes	complemented
397	#2639	C₂×C₁₀₉	1	2	yes	complemented
398	#2617	C₂×C₁₀₉	1	2	yes	complemented
399	#2559	C₂×C₁₀₉	1	4	yes	complemented
400	#2557	C₂×C₁₀₉	1	4	yes	complemented
401	#2496	C₂×C₁₀₉	1	2	yes	complemented
402	#2491	C₂×C₁₀₉	1	2	yes	complemented
403	#2428	C₂×C₁₀₉	1	2	yes	complemented
404	#2422	C₂×C₁₀₉	1	2	yes	complemented
405	#2325	C₂×C₁₀₉	1	2	yes	complemented
406	C₄×#121	C₂×C₁₀₉	1	2	yes	complemented
407	C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	1	1	yes	characteristic, complemented
408	C₁₀₉	#35005	1	1	yes	characteristic, direct product factor, Sylow
409	C₂⁴×C₄	C₂²×C₁₀₉	1	1	yes	characteristic
410	#538	—	2	16	no	—
411	C₂×C₄⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
412	C₂×#127	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
413	C₂×#126	C₂²×C₁₀₉	1	4	yes	—
414	C₂×#124	C₂²×C₁₀₉	1	4	yes	—
415	C₂×#123	C₂²×C₁₀₉	1	4	yes	—
416	C₂×C₂²⋊Q₈	C₂²×C₁₀₉	1	2	yes	—
417	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
418	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
419	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
420	C₂×#121	C₂²×C₁₀₉	1	4	yes	—
421	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
422	C₂×#121	C₂²×C₁₀₉	1	2	yes	—
423	C₂×#120	C₂²×C₁₀₉	1	4	yes	—
424	C₂×C₄×D₄	C₂²×C₁₀₉	1	4	yes	—
425	C₂×C₄×D₄	C₂²×C₁₀₉	1	2	yes	complemented
426	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
427	C₂²×C₂²⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
428	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
429	C₂²×C₄²	C₂²×C₁₀₉	1	1	yes	characteristic
430	#400	C₂²×C₁₀₉	1	4	yes	complemented
431	#397	C₂²×C₁₀₉	1	4	yes	—
432	#397	C₂²×C₁₀₉	1	4	yes	complemented
433	#394	C₂²×C₁₀₉	1	4	yes	—
434	#394	C₂²×C₁₀₉	1	4	yes	—
435	#394	C₂²×C₁₀₉	1	4	yes	complemented
436	#393	C₂²×C₁₀₉	1	4	yes	complemented
437	#392	C₂²×C₁₀₉	1	4	yes	—
438	#391	C₂²×C₁₀₉	1	2	yes	complemented
439	#390	C₂²×C₁₀₉	1	2	yes	complemented
440	#390	C₂²×C₁₀₉	1	2	yes	complemented
441	#390	C₂²×C₁₀₉	1	2	yes	complemented
442	#390	C₂²×C₁₀₉	1	2	yes	complemented
443	#389	C₂²×C₁₀₉	1	2	yes	complemented
444	#389	C₂²×C₁₀₉	1	2	yes	complemented
445	#389	C₂²×C₁₀₉	1	2	yes	complemented
446	#388	C₂²×C₁₀₉	1	4	yes	complemented
447	#388	C₂²×C₁₀₉	1	4	yes	complemented
448	#387	C₂²×C₁₀₉	1	4	yes	complemented
449	#386	C₂²×C₁₀₉	1	4	yes	—
450	#386	C₂²×C₁₀₉	1	4	yes	—
451	#386	C₂²×C₁₀₉	1	4	yes	—
452	#386	C₂²×C₁₀₉	1	4	yes	—
453	#386	C₂²×C₁₀₉	1	4	yes	complemented
454	#385	C₂²×C₁₀₉	1	4	yes	complemented
455	#384	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
456	#384	C₂²×C₁₀₉	1	1	yes	characteristic, complemented
457	#380	C₂²×C₁₀₉	1	2	yes	—
458	#380	C₂²×C₁₀₉	1	2	yes	—
459	#380	C₂²×C₁₀₉	1	2	yes	—
460	#380	C₂²×C₁₀₉	1	2	yes	—
461	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	2	yes	complemented
462	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
463	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
464	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
465	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	2	yes	—
466	C₄×C₂²⋊C₄	C₂²×C₁₀₉	1	4	yes	complemented
467	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic
468	C₂×#95	C₂²×C₁₀₉	1	1	yes	characteristic
469	C₂⁵	C₂³×C₁₀₉	1	1	yes	characteristic
470	C₂²×Q₈	C₂³×C₁₀₉	1	2	yes	—
471	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
472	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
473	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
474	C₂²×D₄	C₂³×C₁₀₉	1	4	yes	—
475	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
476	C₂²×D₄	C₂³×C₁₀₉	1	2	yes	—
477	C₂³×C₄	—	2	4	no	—
478	C₂³×C₄	—	4	2	no	—
479	C₂³×C₄	—	4	2	no	—
480	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
481	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
482	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
483	C₂³×C₄	C₂³×C₁₀₉	1	4	yes	—
484	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
485	C₂³×C₄	C₂³×C₁₀₉	1	2	yes	—
486	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
487	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
488	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
489	C₄⋊Q₈	—	4	2	no	—
490	#127	—	4	2	no	—
491	#126	—	2	16	no	—
492	#124	—	2	16	no	—
493	#123	—	2	16	no	—
494	C₂²⋊Q₈	—	2	8	no	—
495	#121	—	2	8	no	—
496	#121	—	2	8	no	—
497	#121	—	2	8	no	—
498	#121	—	2	16	no	—
499	#121	—	4	4	no	—
500	#121	—	4	4	no	—
501	#120	—	2	16	no	—
502	C₄×D₄	—	2	16	no	—
503	C₄×D₄	—	4	4	no	—
504	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
505	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
506	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	4	yes	—
507	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
508	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
509	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
510	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
511	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
512	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
513	C₂×C₄⋊C₄	C₂³×C₁₀₉	1	2	yes	—
514	C₂×C₂²⋊C₄	—	2	4	no	—
515	C₂×C₂²⋊C₄	D₄×C₁₀₉	1	8	yes	complemented
516	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
517	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
518	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
519	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
520	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
521	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
522	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
523	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
524	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
525	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
526	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
527	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
528	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	4	yes	—
529	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
530	C₂×C₂²⋊C₄	C₂³×C₁₀₉	1	2	yes	—
531	C₂×C₄²	—	4	2	no	—
532	C₂×C₄²	—	4	2	no	—
533	C₂×C₄²	C₂³×C₁₀₉	1	4	yes	—
534	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
535	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
536	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
537	C₂×C₄²	C₂³×C₁₀₉	1	2	yes	—
538	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
539	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
540	#95	C₂³×C₁₀₉	1	2	yes	—
541	#95	C₂³×C₁₀₉	1	2	yes	—
542	#95	C₂³×C₁₀₉	1	2	yes	—
543	#95	C₂³×C₁₀₉	1	2	yes	—
544	#95	C₂³×C₁₀₉	1	4	yes	—
545	#95	C₂³×C₁₀₉	1	4	yes	—
546	#95	C₂³×C₁₀₉	1	4	yes	—
547	#95	C₂³×C₁₀₉	1	4	yes	—
548	#95	C₂³×C₁₀₉	1	4	yes	—
549	#95	C₂³×C₁₀₉	1	4	yes	—
550	C₂⁴	—	2	2	no	—
551	C₂⁴	—	2	2	no	—
552	C₂⁴	—	4	1	no	—
553	C₂⁴	—	4	1	no	—
554	C₂⁴	—	4	1	no	—
555	C₂⁴	—	4	1	no	—
556	C₂⁴	C₂×D₄×C₁₀₉	1	4	yes	—
557	C₂⁴	C₂⁴×C₁₀₉	1	4	yes	—
558	C₂⁴	C₂⁴×C₁₀₉	1	2	yes	—
559	C₂⁴	C₂⁴×C₁₀₉	1	1	yes	characteristic
560	C₂×Q₈	—	2	4	no	—
561	C₂×Q₈	—	4	2	no	—
562	C₂×Q₈	—	4	2	no	—
563	C₂×D₄	—	2	8	no	—
564	C₂×D₄	—	2	8	no	—
565	C₂×D₄	—	2	8	no	—
566	C₂×D₄	—	2	8	no	—
567	C₂×D₄	—	2	8	no	—
568	C₂×D₄	—	2	4	no	—
569	C₂×D₄	—	2	4	no	—
570	C₂×D₄	—	2	4	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	4	4	no	—
574	C₂×D₄	—	4	4	no	—
575	C₂×D₄	—	4	2	no	—
576	C₂×D₄	—	4	2	no	—
577	C₂×D₄	—	4	2	no	—
578	C₂×D₄	—	4	2	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂²×C₄	—	2	2	no	—
582	C₂²×C₄	—	2	2	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	4	no	—
587	C₂²×C₄	—	2	4	no	—
588	C₂²×C₄	—	2	4	no	—
589	C₂²×C₄	—	2	8	no	—
590	C₂²×C₄	—	4	1	no	—
591	C₂²×C₄	—	4	1	no	—
592	C₂²×C₄	—	4	1	no	—
593	C₂²×C₄	—	4	1	no	—
594	C₂²×C₄	—	4	2	no	—
595	C₂²×C₄	—	4	2	no	—
596	C₂²×C₄	—	4	1	no	—
597	C₂²×C₄	—	4	1	no	—
598	C₂²×C₄	—	4	1	no	—
599	C₂²×C₄	—	4	1	no	—
600	C₂²×C₄	—	4	1	no	—
601	C₂²×C₄	—	4	1	no	—
602	C₂²×C₄	—	4	4	no	—
603	C₂²×C₄	—	4	4	no	—
604	C₂²×C₄	—	4	16	no	—
605	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
606	C₂²×C₄	C₂×D₄×C₁₀₉	1	4	yes	—
607	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
608	C₂²×C₄	#41×C₁₀₉	1	4	yes	—
609	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
610	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
611	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
612	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
613	C₂²×C₄	C₂⁴×C₁₀₉	1	4	yes	—
614	C₂²×C₄	C₂⁴×C₁₀₉	1	2	yes	—
615	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
616	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
617	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
618	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
619	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
620	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
621	C₄⋊C₄	—	2	8	no	—
622	C₄⋊C₄	—	2	8	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	4	2	no	—
630	C₄⋊C₄	—	4	2	no	—
631	C₂²⋊C₄	—	2	8	no	—
632	C₂²⋊C₄	—	2	8	no	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	2	8	no	—
635	C₂²⋊C₄	—	2	8	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	—	2	4	no	—
638	C₂²⋊C₄	—	2	8	no	—
639	C₂²⋊C₄	—	2	8	no	—
640	C₂²⋊C₄	—	4	4	no	—
641	C₂²⋊C₄	—	4	4	no	—
642	C₂²⋊C₄	—	4	4	no	—
643	C₂²⋊C₄	—	4	4	no	—
644	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
645	C₂²⋊C₄	C₂×D₄×C₁₀₉	1	8	yes	—
646	C₄²	—	2	8	no	—
647	C₄²	—	2	4	no	—
648	C₄²	—	2	2	no	—
649	C₄²	—	2	2	no	—
650	C₄²	—	4	1	no	—
651	C₄²	—	4	2	no	—
652	C₄²	—	4	1	no	—
653	C₂³	—	2	1	no	—
654	C₂³	—	2	1	no	—
655	C₂³	—	2	1	no	—
656	C₂³	—	2	1	no	—
657	C₂³	—	2	8	no	—
658	C₂³	—	2	2	no	—
659	C₂³	—	2	2	no	—
660	C₂³	—	2	2	no	—
661	C₂³	—	2	2	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	4	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	4	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	4	4	no	—
673	C₂³	—	4	4	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	4	no	—
676	C₂³	—	4	4	no	—
677	C₂³	C₂²×D₄×C₁₀₉	1	4	yes	—
678	C₂³	C₂²×D₄×C₁₀₉	1	2	yes	—
679	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
680	C₂³	C₂×#41×C₁₀₉	1	2	yes	—
681	C₂³	C₂⁵×C₁₀₉	1	1	yes	characteristic
682	Q₈	—	8	4	no	—
683	D₄	—	4	16	no	—
684	D₄	—	4	8	no	—
685	D₄	—	8	4	no	—
686	D₄	—	8	4	no	—
687	D₄	—	8	8	no	—
688	D₄	—	8	8	no	—
689	C₂×C₄	—	2	1	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	1	no	—
692	C₂×C₄	—	2	1	no	—
693	C₂×C₄	—	2	1	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	1	no	—
697	C₂×C₄	—	2	2	no	—
698	C₂×C₄	—	2	1	no	—
699	C₂×C₄	—	2	1	no	—
700	C₂×C₄	—	2	1	no	—
701	C₂×C₄	—	2	8	no	—
702	C₂×C₄	—	2	4	no	—
703	C₂×C₄	—	2	4	no	—
704	C₂×C₄	—	2	4	no	—
705	C₂×C₄	—	2	2	no	—
706	C₂×C₄	—	2	4	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	2	2	no	—
709	C₂×C₄	—	2	2	no	—
710	C₂×C₄	—	2	4	no	—
711	C₂×C₄	—	2	2	no	—
712	C₂×C₄	—	2	2	no	—
713	C₂×C₄	—	2	4	no	—
714	C₂×C₄	—	2	2	no	—
715	C₂×C₄	—	2	4	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	4	4	no	—
718	C₂×C₄	—	4	4	no	—
719	C₂×C₄	—	4	4	no	—
720	C₂×C₄	—	4	8	no	—
721	C₂×C₄	—	4	4	no	—
722	C₂×C₄	—	4	4	no	—
723	C₂×C₄	—	4	8	no	—
724	C₂×C₄	—	8	8	no	—
725	C₂×C₄	C₂²×D₄×C₁₀₉	1	4	yes	—
726	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
727	C₂×C₄	C₂²×D₄×C₁₀₉	1	2	yes	—
728	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
729	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
730	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
731	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
732	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
733	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
734	C₂²	—	2	2	no	—
735	C₂²	—	2	2	no	—
736	C₂²	—	2	2	no	—
737	C₂²	—	2	2	no	—
738	C₂²	—	2	2	no	—
739	C₂²	—	2	2	no	—
740	C₂²	—	2	4	no	—
741	C₂²	—	2	4	no	—
742	C₂²	—	2	4	no	—
743	C₂²	—	4	16	no	—
744	C₂²	—	4	2	no	—
745	C₂²	—	4	2	no	—
746	C₂²	—	4	2	no	—
747	C₂²	—	4	2	no	—
748	C₂²	—	4	4	no	—
749	C₂²	—	4	4	no	—
750	C₂²	—	4	4	no	—
751	C₂²	—	4	4	no	—
752	C₂²	—	4	4	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	4	no	—
755	C₂²	#532×C₁₀₉	1	4	yes	—
756	C₂²	C₂³×D₄×C₁₀₉	1	1	yes	characteristic
757	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
758	C₂²	C₂²×#41×C₁₀₉	1	1	yes	characteristic
759	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
760	C₂²	C₂×H(5,𝔽₂)×C₁₀₉	1	1	yes	characteristic
761	C₂²	#585×C₁₀₉	1	1	yes	characteristic
762	C₂²	#585×C₁₀₉	1	1	yes	characteristic
763	C₄	—	2	2	no	—
764	C₄	—	2	4	no	—
765	C₄	—	2	2	no	—
766	C₄	—	2	2	no	—
767	C₄	—	2	2	no	—
768	C₄	—	2	2	no	—
769	C₄	—	4	2	no	—
770	C₄	—	4	4	no	—
771	C₄	—	4	4	no	—
772	C₄	—	4	2	no	—
773	C₄	—	4	4	no	—
774	C₄	#538×C₁₀₉	1	4	yes	complemented
775	C₂	—	2	4	no	—
776	C₂	—	4	4	no	—
777	C₂	—	8	4	no	—
778	C₂	C₂×#532×C₁₀₉	1	1	yes	characteristic
779	C₂	C₂×#538×C₁₀₉	1	1	yes	characteristic
780	C₂	C₁₀₉×#3455	1	1	yes	characteristic
781	C₂	C₁₀₉×#3496	1	1	yes	characteristic
782	C₂	C₁₀₉×#3496	1	1	yes	characteristic
783	C₂	C₁₀₉×#3505	1	1	yes	characteristic
784	C₂	C₁₀₉×#3506	1	1	yes	characteristic

	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×#538×C₁₀₉	C₂	semidirect
2. C₁₀₉×#2857	C₂	semidirect
3. C₁₀₉×#2856	C₂	semidirect
4. C₁₀₉×#2847	C₂	semidirect
5. C₁₀₉×#2639	C₂	semidirect
6. C₁₀₉×#2617	C₂	semidirect
7. C₁₀₉×#2559	C₂	semidirect
8. C₁₀₉×#2557	C₂	semidirect
9. C₁₀₉×#2496	C₂	semidirect
10. C₁₀₉×#2491	C₂	semidirect
11. C₁₀₉×#2428	C₂	semidirect
12. C₁₀₉×#2422	C₂	semidirect
13. C₁₀₉×#2325	C₂	semidirect
14. C₄×#121×C₁₀₉	C₂	semidirect
15. C₂×C₄×C₂²⋊C₄×C₁₀₉	C₂	semidirect
18. C₂×C₄⋊Q₈×C₁₀₉	C₂²	semidirect
19. C₂×#127×C₁₀₉	C₂²	semidirect
32. C₂×C₄×D₄×C₁₀₉	C₂²	semidirect
37. #400×C₁₀₉	C₂²	semidirect
39. #397×C₁₀₉	C₂²	semidirect
42. #394×C₁₀₉	C₂²	semidirect
43. #393×C₁₀₉	C₂²	semidirect
45. #391×C₁₀₉	C₂²	semidirect
46. #390×C₁₀₉	C₂²	semidirect
47. #390×C₁₀₉	C₂²	semidirect
48. #390×C₁₀₉	C₂²	semidirect
49. #390×C₁₀₉	C₂²	semidirect
50. #389×C₁₀₉	C₂²	semidirect
51. #389×C₁₀₉	C₂²	semidirect
52. #389×C₁₀₉	C₂²	semidirect
53. #388×C₁₀₉	C₂²	semidirect
54. #388×C₁₀₉	C₂²	semidirect
55. #387×C₁₀₉	C₂²	semidirect
60. #386×C₁₀₉	C₂²	semidirect
61. #385×C₁₀₉	C₂²	semidirect
62. #384×C₁₀₉	C₂²	semidirect
63. #384×C₁₀₉	C₂²	semidirect
68. C₄×C₄⋊C₄×C₁₀₉	C₂²	semidirect
73. C₄×C₂²⋊C₄×C₁₀₉	C₂²	semidirect
122. C₂×C₂²⋊C₄×C₁₀₉	D₄	semidirect
381. C₄×C₁₀₉	#538	semidirect
382. #35005	C₁₀₉	direct (N × H)
393. C₂×#538	C₂×C₁₀₉	semidirect
394. #2857	C₂×C₁₀₉	semidirect
395. #2856	C₂×C₁₀₉	semidirect
396. #2847	C₂×C₁₀₉	semidirect
397. #2639	C₂×C₁₀₉	semidirect
398. #2617	C₂×C₁₀₉	semidirect
399. #2559	C₂×C₁₀₉	semidirect
400. #2557	C₂×C₁₀₉	semidirect
401. #2496	C₂×C₁₀₉	semidirect
402. #2491	C₂×C₁₀₉	semidirect
403. #2428	C₂×C₁₀₉	semidirect
404. #2422	C₂×C₁₀₉	semidirect
405. #2325	C₂×C₁₀₉	semidirect
406. C₄×#121	C₂×C₁₀₉	semidirect
407. C₂×C₄×C₂²⋊C₄	C₂×C₁₀₉	semidirect
408. C₁₀₉	#35005	direct (N × H)
411. C₂×C₄⋊Q₈	C₂²×C₁₀₉	semidirect
412. C₂×#127	C₂²×C₁₀₉	semidirect
425. C₂×C₄×D₄	C₂²×C₁₀₉	semidirect
430. #400	C₂²×C₁₀₉	semidirect
432. #397	C₂²×C₁₀₉	semidirect
435. #394	C₂²×C₁₀₉	semidirect
436. #393	C₂²×C₁₀₉	semidirect
438. #391	C₂²×C₁₀₉	semidirect
439. #390	C₂²×C₁₀₉	semidirect
440. #390	C₂²×C₁₀₉	semidirect
441. #390	C₂²×C₁₀₉	semidirect
442. #390	C₂²×C₁₀₉	semidirect
443. #389	C₂²×C₁₀₉	semidirect
444. #389	C₂²×C₁₀₉	semidirect
445. #389	C₂²×C₁₀₉	semidirect
446. #388	C₂²×C₁₀₉	semidirect
447. #388	C₂²×C₁₀₉	semidirect
448. #387	C₂²×C₁₀₉	semidirect
453. #386	C₂²×C₁₀₉	semidirect
454. #385	C₂²×C₁₀₉	semidirect
455. #384	C₂²×C₁₀₉	semidirect
456. #384	C₂²×C₁₀₉	semidirect
461. C₄×C₄⋊C₄	C₂²×C₁₀₉	semidirect
466. C₄×C₂²⋊C₄	C₂²×C₁₀₉	semidirect
515. C₂×C₂²⋊C₄	D₄×C₁₀₉	semidirect
774. C₄	#538×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#538×C₁₀₉	2
C₁₀₉×#2857	2
C₁₀₉×#2856	2
C₁₀₉×#2847	2
C₁₀₉×#2639	2
C₁₀₉×#2617	2
C₁₀₉×#2559	2
C₁₀₉×#2557	2
C₁₀₉×#2496	2
C₁₀₉×#2491	2
C₁₀₉×#2428	2
C₁₀₉×#2422	2
C₁₀₉×#2325	2
C₄×#121×C₁₀₉	2
C₂×C₄×C₂²⋊C₄×C₁₀₉	2
#35005	109

Subgroups — C109×#35005 #42152999

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#35005 #42152999