Subgroups — C₂×C₆₇×#2602 #30714155

Order 17152.

3330 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	C₂²×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#2602	C₂	1	16	yes	maximal, direct product factor
4	C₂×#397×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#394×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#394×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#392×C₆₇	C₂	1	1	yes	maximal, characteristic
8	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#389×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#388×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#387×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#386×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#385×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
18	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
19	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
20	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂×#123×C₆₇	—	2	8	no	—
23	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
24	C₂×C₄×D₄×C₆₇	—	2	8	no	—
25	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
26	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
44	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
45	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
48	#397×C₆₇	C₂²	1	8	yes	complemented
49	#394×C₆₇	C₂²	1	8	yes	complemented
50	#394×C₆₇	C₂²	1	8	yes	complemented
51	#392×C₆₇	C₂²	1	8	yes	—
52	#390×C₆₇	C₂²	1	8	yes	complemented
53	#389×C₆₇	C₂²	1	8	yes	complemented
54	#388×C₆₇	C₂²	1	8	yes	complemented
55	#388×C₆₇	C₂²	1	8	yes	complemented
56	#388×C₆₇	C₂²	1	8	yes	complemented
57	#387×C₆₇	C₂²	1	8	yes	complemented
58	#386×C₆₇	C₂²	1	8	yes	complemented
59	#385×C₆₇	C₂²	1	8	yes	complemented
60	C₄×C₂²⋊C₄×C₆₇	C₂²	1	8	yes	complemented
61	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
62	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
63	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
64	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
65	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
66	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
67	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
68	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
69	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
70	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
71	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₆₇	—	2	4	no	—
73	C₂²×D₄×C₆₇	—	2	4	no	—
74	C₂²×D₄×C₆₇	—	2	4	no	—
75	C₂²×D₄×C₆₇	—	2	4	no	—
76	C₂²×D₄×C₆₇	—	2	4	no	—
77	C₂²×D₄×C₆₇	—	2	4	no	—
78	C₂²×D₄×C₆₇	—	4	2	no	—
79	C₂²×D₄×C₆₇	—	4	2	no	—
80	C₂²×D₄×C₆₇	—	4	2	no	—
81	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
82	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
83	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
84	C₂³×C₄×C₆₇	—	2	4	no	—
85	C₂³×C₄×C₆₇	—	4	2	no	—
86	C₂³×C₄×C₆₇	—	4	2	no	—
87	C₂³×C₄×C₆₇	—	4	2	no	—
88	C₂³×C₄×C₆₇	—	4	2	no	—
89	C₂³×C₄×C₆₇	D₄	1	8	yes	complemented
90	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
93	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
94	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
95	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
96	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
97	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
98	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
99	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
101	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
102	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
103	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
104	#123×C₆₇	—	2	32	no	—
105	C₄×D₄×C₆₇	—	2	32	no	—
106	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
107	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
108	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
109	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
110	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
111	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
112	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
113	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
115	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
119	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
120	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
124	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
125	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
126	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
127	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
128	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
130	C₂×C₂²⋊C₄×C₆₇	—	4	2	no	—
131	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
132	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
133	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
134	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
138	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
139	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
140	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
141	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
142	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
144	C₂×C₄²×C₆₇	—	2	4	no	—
145	C₂×C₄²×C₆₇	—	4	2	no	—
146	C₂×C₄²×C₆₇	—	4	2	no	—
147	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
148	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
149	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
150	#95×C₆₇	C₂³	1	4	yes	—
151	#95×C₆₇	C₂³	1	4	yes	—
152	#95×C₆₇	C₂³	1	4	yes	—
153	#95×C₆₇	C₂³	1	4	yes	—
154	#95×C₆₇	C₂³	1	4	yes	—
155	#95×C₆₇	C₂³	1	4	yes	—
156	#95×C₆₇	C₂³	1	4	yes	—
157	#95×C₆₇	C₂³	1	4	yes	—
158	C₂⁴×C₆₇	—	2	2	no	—
159	C₂⁴×C₆₇	—	2	2	no	—
160	C₂⁴×C₆₇	—	2	2	no	—
161	C₂⁴×C₆₇	—	2	2	no	—
162	C₂⁴×C₆₇	—	2	2	no	—
163	C₂⁴×C₆₇	—	2	2	no	—
164	C₂⁴×C₆₇	—	2	2	no	—
165	C₂⁴×C₆₇	—	2	2	no	—
166	C₂⁴×C₆₇	—	2	2	no	—
167	C₂⁴×C₆₇	—	2	2	no	—
168	C₂⁴×C₆₇	—	2	2	no	—
169	C₂⁴×C₆₇	—	2	2	no	—
170	C₂⁴×C₆₇	—	2	2	no	—
171	C₂⁴×C₆₇	—	2	2	no	—
172	C₂⁴×C₆₇	—	2	2	no	—
173	C₂⁴×C₆₇	—	2	2	no	—
174	C₂⁴×C₆₇	—	2	2	no	—
175	C₂⁴×C₆₇	—	2	2	no	—
176	C₂⁴×C₆₇	—	2	2	no	—
177	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
178	C₂⁴×C₆₇	#41	1	4	yes	—
179	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
180	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
181	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
182	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
183	C₂×D₄×C₆₇	—	2	32	no	—
184	C₂×D₄×C₆₇	—	2	8	no	—
185	C₂×D₄×C₆₇	—	2	8	no	—
186	C₂×D₄×C₆₇	—	2	8	no	—
187	C₂×D₄×C₆₇	—	2	8	no	—
188	C₂×D₄×C₆₇	—	2	8	no	—
189	C₂×D₄×C₆₇	—	2	8	no	—
190	C₂×D₄×C₆₇	—	4	4	no	—
191	C₂×D₄×C₆₇	—	4	4	no	—
192	C₂×D₄×C₆₇	—	4	4	no	—
193	C₂×D₄×C₆₇	—	4	16	no	—
194	C₂×D₄×C₆₇	—	4	16	no	—
195	C₂²×C₄×C₆₇	—	2	2	no	—
196	C₂²×C₄×C₆₇	—	2	2	no	—
197	C₂²×C₄×C₆₇	—	2	2	no	—
198	C₂²×C₄×C₆₇	—	2	2	no	—
199	C₂²×C₄×C₆₇	—	2	2	no	—
200	C₂²×C₄×C₆₇	—	2	2	no	—
201	C₂²×C₄×C₆₇	—	2	2	no	—
202	C₂²×C₄×C₆₇	—	2	2	no	—
203	C₂²×C₄×C₆₇	—	2	2	no	—
204	C₂²×C₄×C₆₇	—	2	2	no	—
205	C₂²×C₄×C₆₇	—	2	2	no	—
206	C₂²×C₄×C₆₇	—	2	2	no	—
207	C₂²×C₄×C₆₇	—	2	2	no	—
208	C₂²×C₄×C₆₇	—	2	2	no	—
209	C₂²×C₄×C₆₇	—	2	2	no	—
210	C₂²×C₄×C₆₇	—	2	2	no	—
211	C₂²×C₄×C₆₇	—	2	2	no	—
212	C₂²×C₄×C₆₇	—	2	2	no	—
213	C₂²×C₄×C₆₇	—	2	2	no	—
214	C₂²×C₄×C₆₇	—	2	2	no	—
215	C₂²×C₄×C₆₇	—	2	2	no	—
216	C₂²×C₄×C₆₇	—	2	2	no	—
217	C₂²×C₄×C₆₇	—	2	2	no	—
218	C₂²×C₄×C₆₇	—	2	2	no	—
219	C₂²×C₄×C₆₇	—	2	2	no	—
220	C₂²×C₄×C₆₇	—	2	2	no	—
221	C₂²×C₄×C₆₇	—	2	2	no	—
222	C₂²×C₄×C₆₇	—	2	2	no	—
223	C₂²×C₄×C₆₇	—	2	2	no	—
224	C₂²×C₄×C₆₇	—	2	2	no	—
225	C₂²×C₄×C₆₇	—	2	2	no	—
226	C₂²×C₄×C₆₇	—	2	8	no	—
227	C₂²×C₄×C₆₇	—	4	16	no	—
228	C₂²×C₄×C₆₇	—	4	4	no	—
229	C₂²×C₄×C₆₇	—	4	4	no	—
230	C₂²×C₄×C₆₇	—	4	4	no	—
231	C₂²×C₄×C₆₇	—	4	4	no	—
232	C₂²×C₄×C₆₇	—	4	16	no	—
233	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
234	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
235	C₂²×C₄×C₆₇	C₂×D₄	1	16	yes	complemented
236	C₂²×C₄×C₆₇	#41	1	4	yes	—
237	C₂²×C₄×C₆₇	#41	1	4	yes	—
238	C₂²×C₄×C₆₇	#41	1	4	yes	—
239	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
240	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
241	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
244	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
245	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
249	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
250	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
251	C₄⋊C₄×C₆₇	—	2	8	no	—
252	C₄⋊C₄×C₆₇	—	2	8	no	—
253	C₄⋊C₄×C₆₇	—	2	8	no	—
254	C₄⋊C₄×C₆₇	—	2	8	no	—
255	C₄⋊C₄×C₆₇	—	2	8	no	—
256	C₄⋊C₄×C₆₇	—	4	4	no	—
257	C₂²⋊C₄×C₆₇	—	2	8	no	—
258	C₂²⋊C₄×C₆₇	—	2	8	no	—
259	C₂²⋊C₄×C₆₇	—	2	8	no	—
260	C₂²⋊C₄×C₆₇	—	2	8	no	—
261	C₂²⋊C₄×C₆₇	—	2	8	no	—
262	C₂²⋊C₄×C₆₇	—	2	8	no	—
263	C₂²⋊C₄×C₆₇	—	2	8	no	—
264	C₂²⋊C₄×C₆₇	—	2	8	no	—
265	C₂²⋊C₄×C₆₇	—	2	8	no	—
266	C₂²⋊C₄×C₆₇	—	2	8	no	—
267	C₂²⋊C₄×C₆₇	—	2	8	no	—
268	C₂²⋊C₄×C₆₇	—	4	4	no	—
269	C₂²⋊C₄×C₆₇	—	4	4	no	—
270	C₄²×C₆₇	—	2	8	no	—
271	C₄²×C₆₇	—	4	4	no	—
272	C₄²×C₆₇	—	4	4	no	—
273	C₂³×C₆₇	—	2	8	no	—
274	C₂³×C₆₇	—	2	8	no	—
275	C₂³×C₆₇	—	2	8	no	—
276	C₂³×C₆₇	—	2	8	no	—
277	C₂³×C₆₇	—	2	8	no	—
278	C₂³×C₆₇	—	2	8	no	—
279	C₂³×C₆₇	—	2	2	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	2	2	no	—
282	C₂³×C₆₇	—	2	2	no	—
283	C₂³×C₆₇	—	2	2	no	—
284	C₂³×C₆₇	—	2	2	no	—
285	C₂³×C₆₇	—	2	2	no	—
286	C₂³×C₆₇	—	2	2	no	—
287	C₂³×C₆₇	—	2	2	no	—
288	C₂³×C₆₇	—	2	2	no	—
289	C₂³×C₆₇	—	2	2	no	—
290	C₂³×C₆₇	—	2	2	no	—
291	C₂³×C₆₇	—	2	2	no	—
292	C₂³×C₆₇	—	2	2	no	—
293	C₂³×C₆₇	—	2	2	no	—
294	C₂³×C₆₇	—	2	2	no	—
295	C₂³×C₆₇	—	2	2	no	—
296	C₂³×C₆₇	—	2	2	no	—
297	C₂³×C₆₇	—	2	2	no	—
298	C₂³×C₆₇	—	4	4	no	—
299	C₂³×C₆₇	—	4	4	no	—
300	C₂³×C₆₇	—	4	4	no	—
301	C₂³×C₆₇	—	4	4	no	—
302	C₂³×C₆₇	—	4	4	no	—
303	C₂³×C₆₇	—	4	4	no	—
304	C₂³×C₆₇	—	4	4	no	—
305	C₂³×C₆₇	—	4	4	no	—
306	C₂³×C₆₇	—	4	4	no	—
307	C₂³×C₆₇	—	4	4	no	—
308	C₂³×C₆₇	—	4	4	no	—
309	C₂³×C₆₇	—	4	4	no	—
310	C₂³×C₆₇	—	4	4	no	—
311	C₂³×C₆₇	—	4	4	no	—
312	C₂³×C₆₇	—	4	4	no	—
313	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
314	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
315	C₂³×C₆₇	C₂×#41	1	4	yes	—
316	C₂³×C₆₇	C₂×#41	1	2	yes	—
317	C₂³×C₆₇	C₂×#41	1	2	yes	—
318	C₂³×C₆₇	C₂×#41	1	2	yes	—
319	C₂³×C₆₇	C₂×#41	1	2	yes	—
320	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
321	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
322	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
323	D₄×C₆₇	—	2	32	no	—
324	D₄×C₆₇	—	4	16	no	—
325	D₄×C₆₇	—	4	16	no	—
326	C₂×C₄×C₆₇	—	2	8	no	—
327	C₂×C₄×C₆₇	—	2	8	no	—
328	C₂×C₄×C₆₇	—	2	8	no	—
329	C₂×C₄×C₆₇	—	2	8	no	—
330	C₂×C₄×C₆₇	—	2	8	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	2	2	no	—
333	C₂×C₄×C₆₇	—	2	2	no	—
334	C₂×C₄×C₆₇	—	2	2	no	—
335	C₂×C₄×C₆₇	—	2	2	no	—
336	C₂×C₄×C₆₇	—	2	2	no	—
337	C₂×C₄×C₆₇	—	2	2	no	—
338	C₂×C₄×C₆₇	—	2	2	no	—
339	C₂×C₄×C₆₇	—	2	2	no	—
340	C₂×C₄×C₆₇	—	2	2	no	—
341	C₂×C₄×C₆₇	—	2	2	no	—
342	C₂×C₄×C₆₇	—	2	2	no	—
343	C₂×C₄×C₆₇	—	2	2	no	—
344	C₂×C₄×C₆₇	—	2	2	no	—
345	C₂×C₄×C₆₇	—	2	2	no	—
346	C₂×C₄×C₆₇	—	2	2	no	—
347	C₂×C₄×C₆₇	—	2	2	no	—
348	C₂×C₄×C₆₇	—	2	2	no	—
349	C₂×C₄×C₆₇	—	2	2	no	—
350	C₂×C₄×C₆₇	—	2	2	no	—
351	C₂×C₄×C₆₇	—	2	2	no	—
352	C₂×C₄×C₆₇	—	2	2	no	—
353	C₂×C₄×C₆₇	—	2	2	no	—
354	C₂×C₄×C₆₇	—	2	2	no	—
355	C₂×C₄×C₆₇	—	2	2	no	—
356	C₂×C₄×C₆₇	—	2	2	no	—
357	C₂×C₄×C₆₇	—	2	2	no	—
358	C₂×C₄×C₆₇	—	2	2	no	—
359	C₂×C₄×C₆₇	—	2	2	no	—
360	C₂×C₄×C₆₇	—	2	2	no	—
361	C₂×C₄×C₆₇	—	2	2	no	—
362	C₂×C₄×C₆₇	—	4	16	no	—
363	C₂×C₄×C₆₇	—	4	16	no	—
364	C₂×C₄×C₆₇	—	4	4	no	—
365	C₂×C₄×C₆₇	—	4	4	no	—
366	C₂×C₄×C₆₇	—	4	4	no	—
367	C₂×C₄×C₆₇	—	4	4	no	—
368	C₂×C₄×C₆₇	—	4	4	no	—
369	C₂×C₄×C₆₇	—	4	4	no	—
370	C₂×C₄×C₆₇	—	4	4	no	—
371	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
372	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
373	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
374	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
375	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
376	C₂²×C₆₇	—	2	4	no	—
377	C₂²×C₆₇	—	2	4	no	—
378	C₂²×C₆₇	—	2	4	no	—
379	C₂²×C₆₇	—	2	4	no	—
380	C₂²×C₆₇	—	2	4	no	—
381	C₂²×C₆₇	—	2	4	no	—
382	C₂²×C₆₇	—	4	16	no	—
383	C₂²×C₆₇	—	4	16	no	—
384	C₂²×C₆₇	—	4	2	no	—
385	C₂²×C₆₇	—	4	2	no	—
386	C₂²×C₆₇	—	4	2	no	—
387	C₂²×C₆₇	—	4	2	no	—
388	C₂²×C₆₇	—	4	2	no	—
389	C₂²×C₆₇	—	4	2	no	—
390	C₂²×C₆₇	—	4	2	no	—
391	C₂²×C₆₇	—	4	2	no	—
392	C₂²×C₆₇	—	4	2	no	—
393	C₂²×C₆₇	—	4	2	no	—
394	C₂²×C₆₇	—	4	2	no	—
395	C₂²×C₆₇	—	4	2	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	2	no	—
399	C₂²×C₆₇	—	8	8	no	—
400	C₂²×C₆₇	#525	1	4	yes	—
401	C₂²×C₆₇	#532	1	4	yes	—
402	C₂²×C₆₇	#534	1	4	yes	—
403	C₂²×C₆₇	#551	1	4	yes	—
404	C₂²×C₆₇	#553	1	4	yes	—
405	C₂²×C₆₇	#553	1	4	yes	—
406	C₂²×C₆₇	#559	1	4	yes	—
407	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
408	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
409	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
410	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
411	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
412	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
413	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
414	C₄×C₆₇	—	2	4	no	—
415	C₄×C₆₇	—	2	4	no	—
416	C₄×C₆₇	—	2	4	no	—
417	C₄×C₆₇	—	2	4	no	—
418	C₄×C₆₇	—	2	4	no	—
419	C₄×C₆₇	—	4	2	no	—
420	C₄×C₆₇	—	4	2	no	—
421	C₄×C₆₇	—	4	2	no	—
422	C₄×C₆₇	—	4	2	no	—
423	C₄×C₆₇	—	4	2	no	—
424	C₄×C₆₇	—	4	2	no	—
425	C₄×C₆₇	—	4	2	no	—
426	C₂×#2602	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
427	C₂×C₆₇	—	4	4	no	—
428	C₂×C₆₇	—	4	4	no	—
429	C₂×C₆₇	—	8	2	no	—
430	C₂×C₆₇	#2602	1	8	yes	direct product factor
431	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
432	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
433	C₂×C₆₇	C₂×#534	1	1	yes	characteristic
434	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
435	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
436	C₂×C₆₇	C₂×#553	1	1	yes	characteristic
437	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
438	C₂²×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
439	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
440	#2602	C₂×C₆₇	1	16	yes	direct product factor
441	C₂×#397	C₂×C₆₇	1	1	yes	characteristic, complemented
442	C₂×#394	C₂×C₆₇	1	1	yes	characteristic, complemented
443	C₂×#394	C₂×C₆₇	1	1	yes	characteristic, complemented
444	C₂×#392	C₂×C₆₇	1	1	yes	characteristic
445	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
446	C₂×#389	C₂×C₆₇	1	1	yes	characteristic, complemented
447	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
448	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
449	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
450	C₂×#387	C₂×C₆₇	1	1	yes	characteristic, complemented
451	C₂×#386	C₂×C₆₇	1	1	yes	characteristic, complemented
452	C₂×#385	C₂×C₆₇	1	1	yes	characteristic, complemented
453	C₂×C₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
454	C₆₇	C₂×#2602	1	1	yes	characteristic, direct product factor, Sylow
455	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
456	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
457	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
458	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
459	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
460	C₂×#123	—	2	8	no	—
461	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
462	C₂×C₄×D₄	—	2	8	no	—
463	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
464	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
465	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
466	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
467	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
468	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
469	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
470	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
471	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
472	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
473	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
474	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
475	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
476	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
477	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
478	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
479	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
480	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
481	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
482	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
483	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
484	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
485	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
486	#397	C₂²×C₆₇	1	8	yes	complemented
487	#394	C₂²×C₆₇	1	8	yes	complemented
488	#394	C₂²×C₆₇	1	8	yes	complemented
489	#392	C₂²×C₆₇	1	8	yes	—
490	#390	C₂²×C₆₇	1	8	yes	complemented
491	#389	C₂²×C₆₇	1	8	yes	complemented
492	#388	C₂²×C₆₇	1	8	yes	complemented
493	#388	C₂²×C₆₇	1	8	yes	complemented
494	#388	C₂²×C₆₇	1	8	yes	complemented
495	#387	C₂²×C₆₇	1	8	yes	complemented
496	#386	C₂²×C₆₇	1	8	yes	complemented
497	#385	C₂²×C₆₇	1	8	yes	complemented
498	C₄×C₂²⋊C₄	C₂²×C₆₇	1	8	yes	complemented
499	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
500	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
501	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
502	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
503	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
504	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
505	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
506	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
507	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
508	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
509	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
510	C₂²×D₄	—	2	4	no	—
511	C₂²×D₄	—	2	4	no	—
512	C₂²×D₄	—	2	4	no	—
513	C₂²×D₄	—	2	4	no	—
514	C₂²×D₄	—	2	4	no	—
515	C₂²×D₄	—	2	4	no	—
516	C₂²×D₄	—	4	2	no	—
517	C₂²×D₄	—	4	2	no	—
518	C₂²×D₄	—	4	2	no	—
519	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
520	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
521	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
522	C₂³×C₄	—	2	4	no	—
523	C₂³×C₄	—	4	2	no	—
524	C₂³×C₄	—	4	2	no	—
525	C₂³×C₄	—	4	2	no	—
526	C₂³×C₄	—	4	2	no	—
527	C₂³×C₄	D₄×C₆₇	1	8	yes	complemented
528	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
529	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
530	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
531	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
532	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
533	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
534	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
535	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
536	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
537	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
538	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
539	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
540	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
541	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
542	#123	—	2	32	no	—
543	C₄×D₄	—	2	32	no	—
544	C₂×C₄⋊C₄	—	2	4	no	—
545	C₂×C₄⋊C₄	—	2	4	no	—
546	C₂×C₄⋊C₄	—	2	4	no	—
547	C₂×C₄⋊C₄	—	2	4	no	—
548	C₂×C₄⋊C₄	—	2	4	no	—
549	C₂×C₄⋊C₄	—	4	2	no	—
550	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
551	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
552	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
553	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
554	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
555	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
556	C₂×C₂²⋊C₄	—	2	4	no	—
557	C₂×C₂²⋊C₄	—	2	4	no	—
558	C₂×C₂²⋊C₄	—	2	4	no	—
559	C₂×C₂²⋊C₄	—	2	4	no	—
560	C₂×C₂²⋊C₄	—	2	4	no	—
561	C₂×C₂²⋊C₄	—	2	4	no	—
562	C₂×C₂²⋊C₄	—	2	4	no	—
563	C₂×C₂²⋊C₄	—	2	4	no	—
564	C₂×C₂²⋊C₄	—	2	4	no	—
565	C₂×C₂²⋊C₄	—	2	4	no	—
566	C₂×C₂²⋊C₄	—	2	4	no	—
567	C₂×C₂²⋊C₄	—	4	2	no	—
568	C₂×C₂²⋊C₄	—	4	2	no	—
569	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
570	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
571	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
572	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
573	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
575	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
576	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
577	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
578	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
579	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
580	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
581	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
582	C₂×C₄²	—	2	4	no	—
583	C₂×C₄²	—	4	2	no	—
584	C₂×C₄²	—	4	2	no	—
585	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
586	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
587	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
588	#95	C₂³×C₆₇	1	4	yes	—
589	#95	C₂³×C₆₇	1	4	yes	—
590	#95	C₂³×C₆₇	1	4	yes	—
591	#95	C₂³×C₆₇	1	4	yes	—
592	#95	C₂³×C₆₇	1	4	yes	—
593	#95	C₂³×C₆₇	1	4	yes	—
594	#95	C₂³×C₆₇	1	4	yes	—
595	#95	C₂³×C₆₇	1	4	yes	—
596	C₂⁴	—	2	2	no	—
597	C₂⁴	—	2	2	no	—
598	C₂⁴	—	2	2	no	—
599	C₂⁴	—	2	2	no	—
600	C₂⁴	—	2	2	no	—
601	C₂⁴	—	2	2	no	—
602	C₂⁴	—	2	2	no	—
603	C₂⁴	—	2	2	no	—
604	C₂⁴	—	2	2	no	—
605	C₂⁴	—	2	2	no	—
606	C₂⁴	—	2	2	no	—
607	C₂⁴	—	2	2	no	—
608	C₂⁴	—	2	2	no	—
609	C₂⁴	—	2	2	no	—
610	C₂⁴	—	2	2	no	—
611	C₂⁴	—	2	2	no	—
612	C₂⁴	—	2	2	no	—
613	C₂⁴	—	2	2	no	—
614	C₂⁴	—	2	2	no	—
615	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
616	C₂⁴	#41×C₆₇	1	4	yes	—
617	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
618	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
619	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
620	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
621	C₂×D₄	—	2	32	no	—
622	C₂×D₄	—	2	8	no	—
623	C₂×D₄	—	2	8	no	—
624	C₂×D₄	—	2	8	no	—
625	C₂×D₄	—	2	8	no	—
626	C₂×D₄	—	2	8	no	—
627	C₂×D₄	—	2	8	no	—
628	C₂×D₄	—	4	4	no	—
629	C₂×D₄	—	4	4	no	—
630	C₂×D₄	—	4	4	no	—
631	C₂×D₄	—	4	16	no	—
632	C₂×D₄	—	4	16	no	—
633	C₂²×C₄	—	2	2	no	—
634	C₂²×C₄	—	2	2	no	—
635	C₂²×C₄	—	2	2	no	—
636	C₂²×C₄	—	2	2	no	—
637	C₂²×C₄	—	2	2	no	—
638	C₂²×C₄	—	2	2	no	—
639	C₂²×C₄	—	2	2	no	—
640	C₂²×C₄	—	2	2	no	—
641	C₂²×C₄	—	2	2	no	—
642	C₂²×C₄	—	2	2	no	—
643	C₂²×C₄	—	2	2	no	—
644	C₂²×C₄	—	2	2	no	—
645	C₂²×C₄	—	2	2	no	—
646	C₂²×C₄	—	2	2	no	—
647	C₂²×C₄	—	2	2	no	—
648	C₂²×C₄	—	2	2	no	—
649	C₂²×C₄	—	2	2	no	—
650	C₂²×C₄	—	2	2	no	—
651	C₂²×C₄	—	2	2	no	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	2	no	—
654	C₂²×C₄	—	2	2	no	—
655	C₂²×C₄	—	2	2	no	—
656	C₂²×C₄	—	2	2	no	—
657	C₂²×C₄	—	2	2	no	—
658	C₂²×C₄	—	2	2	no	—
659	C₂²×C₄	—	2	2	no	—
660	C₂²×C₄	—	2	2	no	—
661	C₂²×C₄	—	2	2	no	—
662	C₂²×C₄	—	2	2	no	—
663	C₂²×C₄	—	2	2	no	—
664	C₂²×C₄	—	2	8	no	—
665	C₂²×C₄	—	4	16	no	—
666	C₂²×C₄	—	4	4	no	—
667	C₂²×C₄	—	4	4	no	—
668	C₂²×C₄	—	4	4	no	—
669	C₂²×C₄	—	4	4	no	—
670	C₂²×C₄	—	4	16	no	—
671	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
672	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
673	C₂²×C₄	C₂×D₄×C₆₇	1	16	yes	complemented
674	C₂²×C₄	#41×C₆₇	1	4	yes	—
675	C₂²×C₄	#41×C₆₇	1	4	yes	—
676	C₂²×C₄	#41×C₆₇	1	4	yes	—
677	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
678	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
679	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
680	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
681	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
682	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
683	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
684	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
685	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
686	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
687	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
688	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
689	C₄⋊C₄	—	2	8	no	—
690	C₄⋊C₄	—	2	8	no	—
691	C₄⋊C₄	—	2	8	no	—
692	C₄⋊C₄	—	2	8	no	—
693	C₄⋊C₄	—	2	8	no	—
694	C₄⋊C₄	—	4	4	no	—
695	C₂²⋊C₄	—	2	8	no	—
696	C₂²⋊C₄	—	2	8	no	—
697	C₂²⋊C₄	—	2	8	no	—
698	C₂²⋊C₄	—	2	8	no	—
699	C₂²⋊C₄	—	2	8	no	—
700	C₂²⋊C₄	—	2	8	no	—
701	C₂²⋊C₄	—	2	8	no	—
702	C₂²⋊C₄	—	2	8	no	—
703	C₂²⋊C₄	—	2	8	no	—
704	C₂²⋊C₄	—	2	8	no	—
705	C₂²⋊C₄	—	2	8	no	—
706	C₂²⋊C₄	—	4	4	no	—
707	C₂²⋊C₄	—	4	4	no	—
708	C₄²	—	2	8	no	—
709	C₄²	—	4	4	no	—
710	C₄²	—	4	4	no	—
711	C₂³	—	2	8	no	—
712	C₂³	—	2	8	no	—
713	C₂³	—	2	8	no	—
714	C₂³	—	2	8	no	—
715	C₂³	—	2	8	no	—
716	C₂³	—	2	8	no	—
717	C₂³	—	2	2	no	—
718	C₂³	—	2	2	no	—
719	C₂³	—	2	2	no	—
720	C₂³	—	2	2	no	—
721	C₂³	—	2	2	no	—
722	C₂³	—	2	2	no	—
723	C₂³	—	2	2	no	—
724	C₂³	—	2	2	no	—
725	C₂³	—	2	2	no	—
726	C₂³	—	2	2	no	—
727	C₂³	—	2	2	no	—
728	C₂³	—	2	2	no	—
729	C₂³	—	2	2	no	—
730	C₂³	—	2	2	no	—
731	C₂³	—	2	2	no	—
732	C₂³	—	2	2	no	—
733	C₂³	—	2	2	no	—
734	C₂³	—	2	2	no	—
735	C₂³	—	2	2	no	—
736	C₂³	—	4	4	no	—
737	C₂³	—	4	4	no	—
738	C₂³	—	4	4	no	—
739	C₂³	—	4	4	no	—
740	C₂³	—	4	4	no	—
741	C₂³	—	4	4	no	—
742	C₂³	—	4	4	no	—
743	C₂³	—	4	4	no	—
744	C₂³	—	4	4	no	—
745	C₂³	—	4	4	no	—
746	C₂³	—	4	4	no	—
747	C₂³	—	4	4	no	—
748	C₂³	—	4	4	no	—
749	C₂³	—	4	4	no	—
750	C₂³	—	4	4	no	—
751	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
752	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
753	C₂³	C₂×#41×C₆₇	1	4	yes	—
754	C₂³	C₂×#41×C₆₇	1	2	yes	—
755	C₂³	C₂×#41×C₆₇	1	2	yes	—
756	C₂³	C₂×#41×C₆₇	1	2	yes	—
757	C₂³	C₂×#41×C₆₇	1	2	yes	—
758	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
759	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
760	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
761	D₄	—	2	32	no	—
762	D₄	—	4	16	no	—
763	D₄	—	4	16	no	—
764	C₂×C₄	—	2	8	no	—
765	C₂×C₄	—	2	8	no	—
766	C₂×C₄	—	2	8	no	—
767	C₂×C₄	—	2	8	no	—
768	C₂×C₄	—	2	8	no	—
769	C₂×C₄	—	2	2	no	—
770	C₂×C₄	—	2	2	no	—
771	C₂×C₄	—	2	2	no	—
772	C₂×C₄	—	2	2	no	—
773	C₂×C₄	—	2	2	no	—
774	C₂×C₄	—	2	2	no	—
775	C₂×C₄	—	2	2	no	—
776	C₂×C₄	—	2	2	no	—
777	C₂×C₄	—	2	2	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	2	no	—
784	C₂×C₄	—	2	2	no	—
785	C₂×C₄	—	2	2	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	2	no	—
792	C₂×C₄	—	2	2	no	—
793	C₂×C₄	—	2	2	no	—
794	C₂×C₄	—	2	2	no	—
795	C₂×C₄	—	2	2	no	—
796	C₂×C₄	—	2	2	no	—
797	C₂×C₄	—	2	2	no	—
798	C₂×C₄	—	2	2	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	4	16	no	—
801	C₂×C₄	—	4	16	no	—
802	C₂×C₄	—	4	4	no	—
803	C₂×C₄	—	4	4	no	—
804	C₂×C₄	—	4	4	no	—
805	C₂×C₄	—	4	4	no	—
806	C₂×C₄	—	4	4	no	—
807	C₂×C₄	—	4	4	no	—
808	C₂×C₄	—	4	4	no	—
809	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
810	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
811	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
812	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
813	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
814	C₂²	—	2	4	no	—
815	C₂²	—	2	4	no	—
816	C₂²	—	2	4	no	—
817	C₂²	—	2	4	no	—
818	C₂²	—	2	4	no	—
819	C₂²	—	2	4	no	—
820	C₂²	—	4	16	no	—
821	C₂²	—	4	16	no	—
822	C₂²	—	4	2	no	—
823	C₂²	—	4	2	no	—
824	C₂²	—	4	2	no	—
825	C₂²	—	4	2	no	—
826	C₂²	—	4	2	no	—
827	C₂²	—	4	2	no	—
828	C₂²	—	4	2	no	—
829	C₂²	—	4	2	no	—
830	C₂²	—	4	2	no	—
831	C₂²	—	4	2	no	—
832	C₂²	—	4	2	no	—
833	C₂²	—	4	2	no	—
834	C₂²	—	4	2	no	—
835	C₂²	—	4	2	no	—
836	C₂²	—	4	2	no	—
837	C₂²	—	8	8	no	—
838	C₂²	#525×C₆₇	1	4	yes	—
839	C₂²	#532×C₆₇	1	4	yes	—
840	C₂²	#534×C₆₇	1	4	yes	—
841	C₂²	#551×C₆₇	1	4	yes	—
842	C₂²	#553×C₆₇	1	4	yes	—
843	C₂²	#553×C₆₇	1	4	yes	—
844	C₂²	#559×C₆₇	1	4	yes	—
845	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
846	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
847	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
848	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
849	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
850	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
851	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
852	C₄	—	2	4	no	—
853	C₄	—	2	4	no	—
854	C₄	—	2	4	no	—
855	C₄	—	2	4	no	—
856	C₄	—	2	4	no	—
857	C₄	—	4	2	no	—
858	C₄	—	4	2	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	C₂	—	4	4	no	—
865	C₂	—	4	4	no	—
866	C₂	—	8	2	no	—
867	C₂	C₆₇×#2602	1	8	yes	direct product factor
868	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
869	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
870	C₂	C₂×#534×C₆₇	1	1	yes	characteristic
871	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
872	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
873	C₂	C₂×#553×C₆₇	1	1	yes	characteristic
874	C₂	C₂×#559×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₆₇	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₂×#392×C₆₇	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#123×C₆₇	C₂	semidirect
2. C₂²×C₄×D₄×C₆₇	C₂	semidirect
3. C₆₇×#2602	C₂	direct (N × H)
4. C₂×#397×C₆₇	C₂	semidirect
5. C₂×#394×C₆₇	C₂	semidirect
6. C₂×#394×C₆₇	C₂	semidirect
8. C₂×#390×C₆₇	C₂	semidirect
9. C₂×#389×C₆₇	C₂	semidirect
10. C₂×#388×C₆₇	C₂	semidirect
11. C₂×#388×C₆₇	C₂	semidirect
12. C₂×#388×C₆₇	C₂	semidirect
13. C₂×#387×C₆₇	C₂	semidirect
14. C₂×#386×C₆₇	C₂	semidirect
15. C₂×#385×C₆₇	C₂	semidirect
16. C₂×C₄×C₂²⋊C₄×C₆₇	C₂	semidirect
23. C₂×#123×C₆₇	C₂²	semidirect
25. C₂×C₄×D₄×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #394×C₆₇	C₂²	semidirect
50. #394×C₆₇	C₂²	semidirect
52. #390×C₆₇	C₂²	semidirect
53. #389×C₆₇	C₂²	semidirect
54. #388×C₆₇	C₂²	semidirect
55. #388×C₆₇	C₂²	semidirect
56. #388×C₆₇	C₂²	semidirect
57. #387×C₆₇	C₂²	semidirect
58. #386×C₆₇	C₂²	semidirect
59. #385×C₆₇	C₂²	semidirect
60. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
89. C₂³×C₄×C₆₇	D₄	semidirect
235. C₂²×C₄×C₆₇	C₂×D₄	semidirect
426. C₂×#2602	C₆₇	direct (N × H)
430. C₂×C₆₇	#2602	direct (N × H)
438. C₂²×#123	C₂×C₆₇	semidirect
439. C₂²×C₄×D₄	C₂×C₆₇	semidirect
440. #2602	C₂×C₆₇	direct (N × H)
441. C₂×#397	C₂×C₆₇	semidirect
442. C₂×#394	C₂×C₆₇	semidirect
443. C₂×#394	C₂×C₆₇	semidirect
445. C₂×#390	C₂×C₆₇	semidirect
446. C₂×#389	C₂×C₆₇	semidirect
447. C₂×#388	C₂×C₆₇	semidirect
448. C₂×#388	C₂×C₆₇	semidirect
449. C₂×#388	C₂×C₆₇	semidirect
450. C₂×#387	C₂×C₆₇	semidirect
451. C₂×#386	C₂×C₆₇	semidirect
452. C₂×#385	C₂×C₆₇	semidirect
453. C₂×C₄×C₂²⋊C₄	C₂×C₆₇	semidirect
454. C₆₇	C₂×#2602	direct (N × H)
461. C₂×#123	C₂²×C₆₇	semidirect
463. C₂×C₄×D₄	C₂²×C₆₇	semidirect
486. #397	C₂²×C₆₇	semidirect
487. #394	C₂²×C₆₇	semidirect
488. #394	C₂²×C₆₇	semidirect
490. #390	C₂²×C₆₇	semidirect
491. #389	C₂²×C₆₇	semidirect
492. #388	C₂²×C₆₇	semidirect
493. #388	C₂²×C₆₇	semidirect
494. #388	C₂²×C₆₇	semidirect
495. #387	C₂²×C₆₇	semidirect
496. #386	C₂²×C₆₇	semidirect
497. #385	C₂²×C₆₇	semidirect
498. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
527. C₂³×C₄	D₄×C₆₇	semidirect
673. C₂²×C₄	C₂×D₄×C₆₇	semidirect
867. C₂	C₆₇×#2602	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#123×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2602	2
C₂×#397×C₆₇	2
C₂×#394×C₆₇	2
C₂×#392×C₆₇	2
C₂×#390×C₆₇	2
C₂×#389×C₆₇	2
C₂×#388×C₆₇	2
C₂×#387×C₆₇	2
C₂×#386×C₆₇	2
C₂×#385×C₆₇	2
C₂×C₄×C₂²⋊C₄×C₆₇	2
C₂×#2602	67

Subgroups — C2×C67×#2602 #30714155

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2602 #30714155