Subgroups — C₂×C₆₇×#2461 #30713927

Order 17152.

3786 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₄×D₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2461	C₂	1	16	yes	maximal, direct product factor
6	C₂×#396×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#395×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#394×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#392×C₆₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#390×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×#388×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×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂³×Q₈×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	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#124×C₆₇	—	2	8	no	—
24	C₂×#124×C₆₇	C₂²	1	8	yes	complemented
25	C₂×#123×C₆₇	—	2	8	no	—
26	C₂×#123×C₆₇	C₂²	1	8	yes	complemented
27	C₂×C₂²⋊Q₈×C₆₇	—	2	8	no	—
28	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	8	yes	complemented
29	C₂×C₄×D₄×C₆₇	—	2	8	no	—
30	C₂×C₄×D₄×C₆₇	C₂²	1	8	yes	complemented
31	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊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×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
46	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
47	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
48	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
49	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
50	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
51	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
52	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
53	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
54	#396×C₆₇	C₂²	1	8	yes	complemented
55	#395×C₆₇	C₂²	1	8	yes	complemented
56	#394×C₆₇	C₂²	1	8	yes	complemented
57	#392×C₆₇	C₂²	1	8	yes	—
58	#390×C₆₇	C₂²	1	8	yes	complemented
59	#388×C₆₇	C₂²	1	8	yes	complemented
60	#388×C₆₇	C₂²	1	8	yes	complemented
61	#388×C₆₇	C₂²	1	8	yes	complemented
62	#386×C₆₇	C₂²	1	8	yes	complemented
63	#385×C₆₇	C₂²	1	8	yes	complemented
64	C₄×C₄⋊C₄×C₆₇	C₂²	1	8	yes	complemented
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	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
70	C₂×#95×C₆₇	C₂²	1	1	yes	characteristic
71	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
72	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
73	C₂⁵×C₆₇	C₂³	1	1	yes	characteristic
74	C₂²×Q₈×C₆₇	—	2	4	no	—
75	C₂²×Q₈×C₆₇	—	2	4	no	—
76	C₂²×Q₈×C₆₇	—	4	2	no	—
77	C₂²×Q₈×C₆₇	C₂³	1	4	yes	—
78	C₂²×D₄×C₆₇	—	2	4	no	—
79	C₂²×D₄×C₆₇	—	2	4	no	—
80	C₂²×D₄×C₆₇	—	2	4	no	—
81	C₂²×D₄×C₆₇	—	2	4	no	—
82	C₂²×D₄×C₆₇	—	2	4	no	—
83	C₂²×D₄×C₆₇	—	2	4	no	—
84	C₂²×D₄×C₆₇	—	2	4	no	—
85	C₂²×D₄×C₆₇	—	4	2	no	—
86	C₂²×D₄×C₆₇	—	4	2	no	—
87	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
88	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
89	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
90	C₂³×C₄×C₆₇	—	2	4	no	—
91	C₂³×C₄×C₆₇	—	2	4	no	—
92	C₂³×C₄×C₆₇	—	2	4	no	—
93	C₂³×C₄×C₆₇	—	2	4	no	—
94	C₂³×C₄×C₆₇	—	4	2	no	—
95	C₂³×C₄×C₆₇	—	4	2	no	—
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	4	yes	—
102	C₂³×C₄×C₆₇	C₂³	1	4	yes	—
103	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
104	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
108	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
109	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
110	#124×C₆₇	—	2	32	no	—
111	#123×C₆₇	—	2	32	no	—
112	C₂²⋊Q₈×C₆₇	—	2	32	no	—
113	C₄×D₄×C₆₇	—	2	32	no	—
114	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
115	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
116	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
117	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
118	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
119	C₂×C₄⋊C₄×C₆₇	—	4	2	no	—
120	C₂×C₄⋊C₄×C₆₇	D₄	1	8	yes	complemented
121	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
122	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
123	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
124	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
125	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
126	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
127	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
128	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
129	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
130	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
131	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
132	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
133	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
134	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
135	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
136	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
137	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
138	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
139	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
140	C₂×C₂²⋊C₄×C₆₇	D₄	1	8	yes	complemented
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×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
145	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
146	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
147	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
148	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
149	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
150	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
151	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
152	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
153	C₂×C₂²⋊C₄×C₆₇	C₂³	1	4	yes	—
154	C₂×C₄²×C₆₇	—	2	4	no	—
155	C₂×C₄²×C₆₇	—	2	4	no	—
156	C₂×C₄²×C₆₇	—	2	4	no	—
157	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
158	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
159	C₂×C₄²×C₆₇	C₂³	1	4	yes	—
160	#95×C₆₇	C₂³	1	4	yes	—
161	#95×C₆₇	C₂³	1	4	yes	—
162	#95×C₆₇	C₂³	1	4	yes	—
163	#95×C₆₇	C₂³	1	4	yes	—
164	#95×C₆₇	C₂³	1	4	yes	—
165	#95×C₆₇	C₂³	1	4	yes	—
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	—	2	2	no	—
178	C₂⁴×C₆₇	—	2	2	no	—
179	C₂⁴×C₆₇	—	2	2	no	—
180	C₂⁴×C₆₇	—	2	2	no	—
181	C₂⁴×C₆₇	—	2	2	no	—
182	C₂⁴×C₆₇	—	2	2	no	—
183	C₂⁴×C₆₇	—	2	2	no	—
184	C₂⁴×C₆₇	—	2	2	no	—
185	C₂⁴×C₆₇	C₂×D₄	1	4	yes	—
186	C₂⁴×C₆₇	#41	1	4	yes	—
187	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
188	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
189	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
190	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
191	C₂×Q₈×C₆₇	—	2	8	no	—
192	C₂×Q₈×C₆₇	—	2	8	no	—
193	C₂×Q₈×C₆₇	—	4	4	no	—
194	C₂×Q₈×C₆₇	—	4	16	no	—
195	C₂×D₄×C₆₇	—	2	32	no	—
196	C₂×D₄×C₆₇	—	2	8	no	—
197	C₂×D₄×C₆₇	—	2	8	no	—
198	C₂×D₄×C₆₇	—	2	8	no	—
199	C₂×D₄×C₆₇	—	2	8	no	—
200	C₂×D₄×C₆₇	—	2	8	no	—
201	C₂×D₄×C₆₇	—	2	8	no	—
202	C₂×D₄×C₆₇	—	2	8	no	—
203	C₂×D₄×C₆₇	—	4	4	no	—
204	C₂×D₄×C₆₇	—	4	4	no	—
205	C₂×D₄×C₆₇	—	4	16	no	—
206	C₂×D₄×C₆₇	—	4	16	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	2	no	—
227	C₂²×C₄×C₆₇	—	2	2	no	—
228	C₂²×C₄×C₆₇	—	2	8	no	—
229	C₂²×C₄×C₆₇	—	2	2	no	—
230	C₂²×C₄×C₆₇	—	2	2	no	—
231	C₂²×C₄×C₆₇	—	2	2	no	—
232	C₂²×C₄×C₆₇	—	2	2	no	—
233	C₂²×C₄×C₆₇	—	2	2	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	2	no	—
236	C₂²×C₄×C₆₇	—	2	2	no	—
237	C₂²×C₄×C₆₇	—	2	8	no	—
238	C₂²×C₄×C₆₇	—	2	8	no	—
239	C₂²×C₄×C₆₇	—	2	8	no	—
240	C₂²×C₄×C₆₇	—	4	4	no	—
241	C₂²×C₄×C₆₇	—	4	4	no	—
242	C₂²×C₄×C₆₇	—	4	16	no	—
243	C₂²×C₄×C₆₇	—	4	16	no	—
244	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
247	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
248	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
249	C₂²×C₄×C₆₇	#41	1	4	yes	—
250	C₂²×C₄×C₆₇	#41	1	4	yes	—
251	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
252	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
253	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
254	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
255	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
256	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
257	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
258	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
259	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
260	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
261	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
262	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
263	C₄⋊C₄×C₆₇	—	2	8	no	—
264	C₄⋊C₄×C₆₇	—	2	8	no	—
265	C₄⋊C₄×C₆₇	—	2	8	no	—
266	C₄⋊C₄×C₆₇	—	2	8	no	—
267	C₄⋊C₄×C₆₇	—	2	8	no	—
268	C₄⋊C₄×C₆₇	—	4	4	no	—
269	C₄⋊C₄×C₆₇	C₂×D₄	1	16	yes	complemented
270	C₂²⋊C₄×C₆₇	—	2	8	no	—
271	C₂²⋊C₄×C₆₇	—	2	8	no	—
272	C₂²⋊C₄×C₆₇	—	2	8	no	—
273	C₂²⋊C₄×C₆₇	—	2	8	no	—
274	C₂²⋊C₄×C₆₇	—	2	8	no	—
275	C₂²⋊C₄×C₆₇	—	2	8	no	—
276	C₂²⋊C₄×C₆₇	—	2	8	no	—
277	C₂²⋊C₄×C₆₇	—	2	8	no	—
278	C₂²⋊C₄×C₆₇	—	2	8	no	—
279	C₂²⋊C₄×C₆₇	—	2	8	no	—
280	C₂²⋊C₄×C₆₇	—	2	8	no	—
281	C₂²⋊C₄×C₆₇	—	2	8	no	—
282	C₂²⋊C₄×C₆₇	C₂×D₄	1	16	yes	complemented
283	C₄²×C₆₇	—	2	8	no	—
284	C₄²×C₆₇	—	2	8	no	—
285	C₄²×C₆₇	—	2	8	no	—
286	C₂³×C₆₇	—	2	8	no	—
287	C₂³×C₆₇	—	2	8	no	—
288	C₂³×C₆₇	—	2	8	no	—
289	C₂³×C₆₇	—	2	8	no	—
290	C₂³×C₆₇	—	2	8	no	—
291	C₂³×C₆₇	—	2	8	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	—	2	2	no	—
299	C₂³×C₆₇	—	2	2	no	—
300	C₂³×C₆₇	—	2	2	no	—
301	C₂³×C₆₇	—	2	2	no	—
302	C₂³×C₆₇	—	2	2	no	—
303	C₂³×C₆₇	—	2	2	no	—
304	C₂³×C₆₇	—	2	2	no	—
305	C₂³×C₆₇	—	2	2	no	—
306	C₂³×C₆₇	—	2	2	no	—
307	C₂³×C₆₇	—	2	2	no	—
308	C₂³×C₆₇	—	2	2	no	—
309	C₂³×C₆₇	—	2	2	no	—
310	C₂³×C₆₇	—	2	2	no	—
311	C₂³×C₆₇	—	4	4	no	—
312	C₂³×C₆₇	—	4	4	no	—
313	C₂³×C₆₇	—	4	4	no	—
314	C₂³×C₆₇	—	4	4	no	—
315	C₂³×C₆₇	—	4	4	no	—
316	C₂³×C₆₇	—	4	4	no	—
317	C₂³×C₆₇	—	4	4	no	—
318	C₂³×C₆₇	—	4	4	no	—
319	C₂³×C₆₇	—	4	4	no	—
320	C₂³×C₆₇	—	4	4	no	—
321	C₂³×C₆₇	—	4	4	no	—
322	C₂³×C₆₇	—	4	4	no	—
323	C₂³×C₆₇	—	4	4	no	—
324	C₂³×C₆₇	—	4	4	no	—
325	C₂³×C₆₇	—	4	4	no	—
326	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
327	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
328	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
329	C₂³×C₆₇	C₂×#41	1	4	yes	—
330	C₂³×C₆₇	C₂×#41	1	2	yes	—
331	C₂³×C₆₇	C₂×#41	1	2	yes	—
332	C₂³×C₆₇	C₂×#41	1	2	yes	—
333	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
334	C₂³×C₆₇	2₋¹⁺⁴	1	2	yes	—
335	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
336	Q₈×C₆₇	—	4	16	no	—
337	D₄×C₆₇	—	2	32	no	—
338	D₄×C₆₇	—	4	16	no	—
339	D₄×C₆₇	—	4	16	no	—
340	C₂×C₄×C₆₇	—	2	8	no	—
341	C₂×C₄×C₆₇	—	2	8	no	—
342	C₂×C₄×C₆₇	—	2	8	no	—
343	C₂×C₄×C₆₇	—	2	8	no	—
344	C₂×C₄×C₆₇	—	2	8	no	—
345	C₂×C₄×C₆₇	—	2	8	no	—
346	C₂×C₄×C₆₇	—	2	8	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	—	2	2	no	—
363	C₂×C₄×C₆₇	—	2	2	no	—
364	C₂×C₄×C₆₇	—	2	2	no	—
365	C₂×C₄×C₆₇	—	2	2	no	—
366	C₂×C₄×C₆₇	—	2	2	no	—
367	C₂×C₄×C₆₇	—	2	2	no	—
368	C₂×C₄×C₆₇	—	2	2	no	—
369	C₂×C₄×C₆₇	—	2	2	no	—
370	C₂×C₄×C₆₇	—	2	2	no	—
371	C₂×C₄×C₆₇	—	2	2	no	—
372	C₂×C₄×C₆₇	—	2	2	no	—
373	C₂×C₄×C₆₇	—	2	2	no	—
374	C₂×C₄×C₆₇	—	2	2	no	—
375	C₂×C₄×C₆₇	—	2	2	no	—
376	C₂×C₄×C₆₇	—	4	16	no	—
377	C₂×C₄×C₆₇	—	4	16	no	—
378	C₂×C₄×C₆₇	—	4	4	no	—
379	C₂×C₄×C₆₇	—	4	4	no	—
380	C₂×C₄×C₆₇	—	4	4	no	—
381	C₂×C₄×C₆₇	—	4	4	no	—
382	C₂×C₄×C₆₇	—	4	4	no	—
383	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
384	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
385	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
386	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
387	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
388	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
389	C₂×C₄×C₆₇	C₂×#41	1	4	yes	—
390	C₂²×C₆₇	—	2	4	no	—
391	C₂²×C₆₇	—	2	4	no	—
392	C₂²×C₆₇	—	2	4	no	—
393	C₂²×C₆₇	—	2	4	no	—
394	C₂²×C₆₇	—	2	4	no	—
395	C₂²×C₆₇	—	2	4	no	—
396	C₂²×C₆₇	—	4	2	no	—
397	C₂²×C₆₇	—	4	2	no	—
398	C₂²×C₆₇	—	4	2	no	—
399	C₂²×C₆₇	—	4	2	no	—
400	C₂²×C₆₇	—	4	2	no	—
401	C₂²×C₆₇	—	4	2	no	—
402	C₂²×C₆₇	—	4	2	no	—
403	C₂²×C₆₇	—	4	2	no	—
404	C₂²×C₆₇	—	4	16	no	—
405	C₂²×C₆₇	—	4	16	no	—
406	C₂²×C₆₇	—	4	2	no	—
407	C₂²×C₆₇	—	4	2	no	—
408	C₂²×C₆₇	—	4	2	no	—
409	C₂²×C₆₇	—	4	2	no	—
410	C₂²×C₆₇	—	4	2	no	—
411	C₂²×C₆₇	—	4	2	no	—
412	C₂²×C₆₇	—	4	2	no	—
413	C₂²×C₆₇	—	8	8	no	—
414	C₂²×C₆₇	#525	1	4	yes	—
415	C₂²×C₆₇	#532	1	4	yes	—
416	C₂²×C₆₇	#542	1	4	yes	—
417	C₂²×C₆₇	D₄²	1	4	yes	—
418	C₂²×C₆₇	#547	1	4	yes	—
419	C₂²×C₆₇	#548	1	4	yes	—
420	C₂²×C₆₇	#551	1	4	yes	—
421	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
422	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
423	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
424	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
425	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
426	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
427	C₂²×C₆₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
428	C₄×C₆₇	—	2	4	no	—
429	C₄×C₆₇	—	2	4	no	—
430	C₄×C₆₇	—	2	4	no	—
431	C₄×C₆₇	—	2	4	no	—
432	C₄×C₆₇	—	2	4	no	—
433	C₄×C₆₇	—	2	4	no	—
434	C₄×C₆₇	—	2	4	no	—
435	C₄×C₆₇	—	4	2	no	—
436	C₄×C₆₇	—	4	2	no	—
437	C₄×C₆₇	—	4	2	no	—
438	C₄×C₆₇	—	4	2	no	—
439	C₄×C₆₇	—	4	2	no	—
440	C₂×#2461	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
441	C₂×C₆₇	—	4	4	no	—
442	C₂×C₆₇	—	4	4	no	—
443	C₂×C₆₇	—	8	2	no	—
444	C₂×C₆₇	#2461	1	8	yes	direct product factor
445	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
446	C₂×C₆₇	C₂×#532	1	1	yes	characteristic
447	C₂×C₆₇	C₂×#542	1	1	yes	characteristic
448	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
449	C₂×C₆₇	C₂×#547	1	1	yes	characteristic
450	C₂×C₆₇	C₂×#548	1	1	yes	characteristic
451	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
452	C₂²×#124	C₂×C₆₇	1	1	yes	characteristic, complemented
453	C₂²×#123	C₂×C₆₇	1	1	yes	characteristic, complemented
454	C₂²×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
455	C₂²×C₄×D₄	C₂×C₆₇	1	1	yes	characteristic, complemented
456	#2461	C₂×C₆₇	1	16	yes	direct product factor
457	C₂×#396	C₂×C₆₇	1	1	yes	characteristic, complemented
458	C₂×#395	C₂×C₆₇	1	1	yes	characteristic, complemented
459	C₂×#394	C₂×C₆₇	1	1	yes	characteristic, complemented
460	C₂×#392	C₂×C₆₇	1	1	yes	characteristic
461	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
462	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
463	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
464	C₂×#388	C₂×C₆₇	1	1	yes	characteristic, complemented
465	C₂×#386	C₂×C₆₇	1	1	yes	characteristic, complemented
466	C₂×#385	C₂×C₆₇	1	1	yes	characteristic, complemented
467	C₂×C₄×C₄⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
468	C₆₇	C₂×#2461	1	1	yes	characteristic, direct product factor, Sylow
469	C₂³×Q₈	C₂²×C₆₇	1	1	yes	characteristic
470	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
471	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
472	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
473	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
474	C₂⁴×C₄	C₂²×C₆₇	1	1	yes	characteristic
475	C₂×#124	—	2	8	no	—
476	C₂×#124	C₂²×C₆₇	1	8	yes	complemented
477	C₂×#123	—	2	8	no	—
478	C₂×#123	C₂²×C₆₇	1	8	yes	complemented
479	C₂×C₂²⋊Q₈	—	2	8	no	—
480	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	8	yes	complemented
481	C₂×C₄×D₄	—	2	8	no	—
482	C₂×C₄×D₄	C₂²×C₆₇	1	8	yes	complemented
483	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
484	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
485	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
486	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
487	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
488	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
489	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
490	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
491	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
492	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
493	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
494	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
495	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
496	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
497	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
498	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
499	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
500	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
501	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
502	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
503	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
504	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
505	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
506	#396	C₂²×C₆₇	1	8	yes	complemented
507	#395	C₂²×C₆₇	1	8	yes	complemented
508	#394	C₂²×C₆₇	1	8	yes	complemented
509	#392	C₂²×C₆₇	1	8	yes	—
510	#390	C₂²×C₆₇	1	8	yes	complemented
511	#388	C₂²×C₆₇	1	8	yes	complemented
512	#388	C₂²×C₆₇	1	8	yes	complemented
513	#388	C₂²×C₆₇	1	8	yes	complemented
514	#386	C₂²×C₆₇	1	8	yes	complemented
515	#385	C₂²×C₆₇	1	8	yes	complemented
516	C₄×C₄⋊C₄	C₂²×C₆₇	1	8	yes	complemented
517	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
518	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
519	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
520	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
521	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
522	C₂×#95	C₂²×C₆₇	1	1	yes	characteristic
523	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
524	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
525	C₂⁵	C₂³×C₆₇	1	1	yes	characteristic
526	C₂²×Q₈	—	2	4	no	—
527	C₂²×Q₈	—	2	4	no	—
528	C₂²×Q₈	—	4	2	no	—
529	C₂²×Q₈	C₂³×C₆₇	1	4	yes	—
530	C₂²×D₄	—	2	4	no	—
531	C₂²×D₄	—	2	4	no	—
532	C₂²×D₄	—	2	4	no	—
533	C₂²×D₄	—	2	4	no	—
534	C₂²×D₄	—	2	4	no	—
535	C₂²×D₄	—	2	4	no	—
536	C₂²×D₄	—	2	4	no	—
537	C₂²×D₄	—	4	2	no	—
538	C₂²×D₄	—	4	2	no	—
539	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
540	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
541	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
542	C₂³×C₄	—	2	4	no	—
543	C₂³×C₄	—	2	4	no	—
544	C₂³×C₄	—	2	4	no	—
545	C₂³×C₄	—	2	4	no	—
546	C₂³×C₄	—	4	2	no	—
547	C₂³×C₄	—	4	2	no	—
548	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
549	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
550	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
551	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
552	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
553	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
554	C₂³×C₄	C₂³×C₆₇	1	4	yes	—
555	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
556	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
557	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
558	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
559	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
560	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
561	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
562	#124	—	2	32	no	—
563	#123	—	2	32	no	—
564	C₂²⋊Q₈	—	2	32	no	—
565	C₄×D₄	—	2	32	no	—
566	C₂×C₄⋊C₄	—	2	4	no	—
567	C₂×C₄⋊C₄	—	2	4	no	—
568	C₂×C₄⋊C₄	—	2	4	no	—
569	C₂×C₄⋊C₄	—	2	4	no	—
570	C₂×C₄⋊C₄	—	2	4	no	—
571	C₂×C₄⋊C₄	—	4	2	no	—
572	C₂×C₄⋊C₄	D₄×C₆₇	1	8	yes	complemented
573	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
574	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
575	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
576	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
577	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
578	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
579	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
580	C₂×C₂²⋊C₄	—	2	4	no	—
581	C₂×C₂²⋊C₄	—	2	4	no	—
582	C₂×C₂²⋊C₄	—	2	4	no	—
583	C₂×C₂²⋊C₄	—	2	4	no	—
584	C₂×C₂²⋊C₄	—	2	4	no	—
585	C₂×C₂²⋊C₄	—	2	4	no	—
586	C₂×C₂²⋊C₄	—	2	4	no	—
587	C₂×C₂²⋊C₄	—	2	4	no	—
588	C₂×C₂²⋊C₄	—	2	4	no	—
589	C₂×C₂²⋊C₄	—	2	4	no	—
590	C₂×C₂²⋊C₄	—	2	4	no	—
591	C₂×C₂²⋊C₄	—	2	4	no	—
592	C₂×C₂²⋊C₄	D₄×C₆₇	1	8	yes	complemented
593	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
594	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
595	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
596	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
597	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
598	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
599	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
600	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
601	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
602	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
603	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
604	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
605	C₂×C₂²⋊C₄	C₂³×C₆₇	1	4	yes	—
606	C₂×C₄²	—	2	4	no	—
607	C₂×C₄²	—	2	4	no	—
608	C₂×C₄²	—	2	4	no	—
609	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
610	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
611	C₂×C₄²	C₂³×C₆₇	1	4	yes	—
612	#95	C₂³×C₆₇	1	4	yes	—
613	#95	C₂³×C₆₇	1	4	yes	—
614	#95	C₂³×C₆₇	1	4	yes	—
615	#95	C₂³×C₆₇	1	4	yes	—
616	#95	C₂³×C₆₇	1	4	yes	—
617	#95	C₂³×C₆₇	1	4	yes	—
618	C₂⁴	—	2	2	no	—
619	C₂⁴	—	2	2	no	—
620	C₂⁴	—	2	2	no	—
621	C₂⁴	—	2	2	no	—
622	C₂⁴	—	2	2	no	—
623	C₂⁴	—	2	2	no	—
624	C₂⁴	—	2	2	no	—
625	C₂⁴	—	2	2	no	—
626	C₂⁴	—	2	2	no	—
627	C₂⁴	—	2	2	no	—
628	C₂⁴	—	2	2	no	—
629	C₂⁴	—	2	2	no	—
630	C₂⁴	—	2	2	no	—
631	C₂⁴	—	2	2	no	—
632	C₂⁴	—	2	2	no	—
633	C₂⁴	—	2	2	no	—
634	C₂⁴	—	2	2	no	—
635	C₂⁴	—	2	2	no	—
636	C₂⁴	—	2	2	no	—
637	C₂⁴	C₂×D₄×C₆₇	1	4	yes	—
638	C₂⁴	#41×C₆₇	1	4	yes	—
639	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
640	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
641	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
642	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
643	C₂×Q₈	—	2	8	no	—
644	C₂×Q₈	—	2	8	no	—
645	C₂×Q₈	—	4	4	no	—
646	C₂×Q₈	—	4	16	no	—
647	C₂×D₄	—	2	32	no	—
648	C₂×D₄	—	2	8	no	—
649	C₂×D₄	—	2	8	no	—
650	C₂×D₄	—	2	8	no	—
651	C₂×D₄	—	2	8	no	—
652	C₂×D₄	—	2	8	no	—
653	C₂×D₄	—	2	8	no	—
654	C₂×D₄	—	2	8	no	—
655	C₂×D₄	—	4	4	no	—
656	C₂×D₄	—	4	4	no	—
657	C₂×D₄	—	4	16	no	—
658	C₂×D₄	—	4	16	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	2	no	—
665	C₂²×C₄	—	2	2	no	—
666	C₂²×C₄	—	2	2	no	—
667	C₂²×C₄	—	2	2	no	—
668	C₂²×C₄	—	2	2	no	—
669	C₂²×C₄	—	2	2	no	—
670	C₂²×C₄	—	2	2	no	—
671	C₂²×C₄	—	2	2	no	—
672	C₂²×C₄	—	2	2	no	—
673	C₂²×C₄	—	2	2	no	—
674	C₂²×C₄	—	2	2	no	—
675	C₂²×C₄	—	2	2	no	—
676	C₂²×C₄	—	2	2	no	—
677	C₂²×C₄	—	2	2	no	—
678	C₂²×C₄	—	2	2	no	—
679	C₂²×C₄	—	2	2	no	—
680	C₂²×C₄	—	2	8	no	—
681	C₂²×C₄	—	2	2	no	—
682	C₂²×C₄	—	2	2	no	—
683	C₂²×C₄	—	2	2	no	—
684	C₂²×C₄	—	2	2	no	—
685	C₂²×C₄	—	2	2	no	—
686	C₂²×C₄	—	2	2	no	—
687	C₂²×C₄	—	2	2	no	—
688	C₂²×C₄	—	2	2	no	—
689	C₂²×C₄	—	2	8	no	—
690	C₂²×C₄	—	2	8	no	—
691	C₂²×C₄	—	2	8	no	—
692	C₂²×C₄	—	4	4	no	—
693	C₂²×C₄	—	4	4	no	—
694	C₂²×C₄	—	4	16	no	—
695	C₂²×C₄	—	4	16	no	—
696	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
697	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
698	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
699	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
700	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
701	C₂²×C₄	#41×C₆₇	1	4	yes	—
702	C₂²×C₄	#41×C₆₇	1	4	yes	—
703	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
704	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
705	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
706	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
707	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
708	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
709	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
710	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
711	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
712	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
713	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
714	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
715	C₄⋊C₄	—	2	8	no	—
716	C₄⋊C₄	—	2	8	no	—
717	C₄⋊C₄	—	2	8	no	—
718	C₄⋊C₄	—	2	8	no	—
719	C₄⋊C₄	—	2	8	no	—
720	C₄⋊C₄	—	4	4	no	—
721	C₄⋊C₄	C₂×D₄×C₆₇	1	16	yes	complemented
722	C₂²⋊C₄	—	2	8	no	—
723	C₂²⋊C₄	—	2	8	no	—
724	C₂²⋊C₄	—	2	8	no	—
725	C₂²⋊C₄	—	2	8	no	—
726	C₂²⋊C₄	—	2	8	no	—
727	C₂²⋊C₄	—	2	8	no	—
728	C₂²⋊C₄	—	2	8	no	—
729	C₂²⋊C₄	—	2	8	no	—
730	C₂²⋊C₄	—	2	8	no	—
731	C₂²⋊C₄	—	2	8	no	—
732	C₂²⋊C₄	—	2	8	no	—
733	C₂²⋊C₄	—	2	8	no	—
734	C₂²⋊C₄	C₂×D₄×C₆₇	1	16	yes	complemented
735	C₄²	—	2	8	no	—
736	C₄²	—	2	8	no	—
737	C₄²	—	2	8	no	—
738	C₂³	—	2	8	no	—
739	C₂³	—	2	8	no	—
740	C₂³	—	2	8	no	—
741	C₂³	—	2	8	no	—
742	C₂³	—	2	8	no	—
743	C₂³	—	2	8	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	2	no	—
753	C₂³	—	2	2	no	—
754	C₂³	—	2	2	no	—
755	C₂³	—	2	2	no	—
756	C₂³	—	2	2	no	—
757	C₂³	—	2	2	no	—
758	C₂³	—	2	2	no	—
759	C₂³	—	2	2	no	—
760	C₂³	—	2	2	no	—
761	C₂³	—	2	2	no	—
762	C₂³	—	2	2	no	—
763	C₂³	—	4	4	no	—
764	C₂³	—	4	4	no	—
765	C₂³	—	4	4	no	—
766	C₂³	—	4	4	no	—
767	C₂³	—	4	4	no	—
768	C₂³	—	4	4	no	—
769	C₂³	—	4	4	no	—
770	C₂³	—	4	4	no	—
771	C₂³	—	4	4	no	—
772	C₂³	—	4	4	no	—
773	C₂³	—	4	4	no	—
774	C₂³	—	4	4	no	—
775	C₂³	—	4	4	no	—
776	C₂³	—	4	4	no	—
777	C₂³	—	4	4	no	—
778	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
779	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
780	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
781	C₂³	C₂×#41×C₆₇	1	4	yes	—
782	C₂³	C₂×#41×C₆₇	1	2	yes	—
783	C₂³	C₂×#41×C₆₇	1	2	yes	—
784	C₂³	C₂×#41×C₆₇	1	2	yes	—
785	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
786	C₂³	2₋¹⁺⁴×C₆₇	1	2	yes	—
787	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
788	Q₈	—	4	16	no	—
789	D₄	—	2	32	no	—
790	D₄	—	4	16	no	—
791	D₄	—	4	16	no	—
792	C₂×C₄	—	2	8	no	—
793	C₂×C₄	—	2	8	no	—
794	C₂×C₄	—	2	8	no	—
795	C₂×C₄	—	2	8	no	—
796	C₂×C₄	—	2	8	no	—
797	C₂×C₄	—	2	8	no	—
798	C₂×C₄	—	2	8	no	—
799	C₂×C₄	—	2	2	no	—
800	C₂×C₄	—	2	2	no	—
801	C₂×C₄	—	2	2	no	—
802	C₂×C₄	—	2	2	no	—
803	C₂×C₄	—	2	2	no	—
804	C₂×C₄	—	2	2	no	—
805	C₂×C₄	—	2	2	no	—
806	C₂×C₄	—	2	2	no	—
807	C₂×C₄	—	2	2	no	—
808	C₂×C₄	—	2	2	no	—
809	C₂×C₄	—	2	2	no	—
810	C₂×C₄	—	2	2	no	—
811	C₂×C₄	—	2	2	no	—
812	C₂×C₄	—	2	2	no	—
813	C₂×C₄	—	2	2	no	—
814	C₂×C₄	—	2	2	no	—
815	C₂×C₄	—	2	2	no	—
816	C₂×C₄	—	2	2	no	—
817	C₂×C₄	—	2	2	no	—
818	C₂×C₄	—	2	2	no	—
819	C₂×C₄	—	2	2	no	—
820	C₂×C₄	—	2	2	no	—
821	C₂×C₄	—	2	2	no	—
822	C₂×C₄	—	2	2	no	—
823	C₂×C₄	—	2	2	no	—
824	C₂×C₄	—	2	2	no	—
825	C₂×C₄	—	2	2	no	—
826	C₂×C₄	—	2	2	no	—
827	C₂×C₄	—	2	2	no	—
828	C₂×C₄	—	4	16	no	—
829	C₂×C₄	—	4	16	no	—
830	C₂×C₄	—	4	4	no	—
831	C₂×C₄	—	4	4	no	—
832	C₂×C₄	—	4	4	no	—
833	C₂×C₄	—	4	4	no	—
834	C₂×C₄	—	4	4	no	—
835	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
836	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
837	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
838	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
839	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
840	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
841	C₂×C₄	C₂×#41×C₆₇	1	4	yes	—
842	C₂²	—	2	4	no	—
843	C₂²	—	2	4	no	—
844	C₂²	—	2	4	no	—
845	C₂²	—	2	4	no	—
846	C₂²	—	2	4	no	—
847	C₂²	—	2	4	no	—
848	C₂²	—	4	2	no	—
849	C₂²	—	4	2	no	—
850	C₂²	—	4	2	no	—
851	C₂²	—	4	2	no	—
852	C₂²	—	4	2	no	—
853	C₂²	—	4	2	no	—
854	C₂²	—	4	2	no	—
855	C₂²	—	4	2	no	—
856	C₂²	—	4	16	no	—
857	C₂²	—	4	16	no	—
858	C₂²	—	4	2	no	—
859	C₂²	—	4	2	no	—
860	C₂²	—	4	2	no	—
861	C₂²	—	4	2	no	—
862	C₂²	—	4	2	no	—
863	C₂²	—	4	2	no	—
864	C₂²	—	4	2	no	—
865	C₂²	—	8	8	no	—
866	C₂²	#525×C₆₇	1	4	yes	—
867	C₂²	#532×C₆₇	1	4	yes	—
868	C₂²	#542×C₆₇	1	4	yes	—
869	C₂²	D₄²×C₆₇	1	4	yes	—
870	C₂²	#547×C₆₇	1	4	yes	—
871	C₂²	#548×C₆₇	1	4	yes	—
872	C₂²	#551×C₆₇	1	4	yes	—
873	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
874	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
875	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
876	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
877	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
878	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
879	C₂²	C₂×2₋¹⁺⁴×C₆₇	1	1	yes	characteristic
880	C₄	—	2	4	no	—
881	C₄	—	2	4	no	—
882	C₄	—	2	4	no	—
883	C₄	—	2	4	no	—
884	C₄	—	2	4	no	—
885	C₄	—	2	4	no	—
886	C₄	—	2	4	no	—
887	C₄	—	4	2	no	—
888	C₄	—	4	2	no	—
889	C₄	—	4	2	no	—
890	C₄	—	4	2	no	—
891	C₄	—	4	2	no	—
892	C₂	—	4	4	no	—
893	C₂	—	4	4	no	—
894	C₂	—	8	2	no	—
895	C₂	C₆₇×#2461	1	8	yes	direct product factor
896	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
897	C₂	C₂×#532×C₆₇	1	1	yes	characteristic
898	C₂	C₂×#542×C₆₇	1	1	yes	characteristic
899	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
900	C₂	C₂×#547×C₆₇	1	1	yes	characteristic
901	C₂	C₂×#548×C₆₇	1	1	yes	characteristic
902	C₂	C₂×#551×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×#124×C₆₇	C₂	semidirect
2. C₂²×#123×C₆₇	C₂	semidirect
3. C₂²×C₂²⋊Q₈×C₆₇	C₂	semidirect
4. C₂²×C₄×D₄×C₆₇	C₂	semidirect
5. C₆₇×#2461	C₂	direct (N × H)
6. C₂×#396×C₆₇	C₂	semidirect
7. C₂×#395×C₆₇	C₂	semidirect
8. C₂×#394×C₆₇	C₂	semidirect
10. C₂×#390×C₆₇	C₂	semidirect
11. C₂×#388×C₆₇	C₂	semidirect
12. C₂×#388×C₆₇	C₂	semidirect
13. C₂×#388×C₆₇	C₂	semidirect
14. C₂×#386×C₆₇	C₂	semidirect
15. C₂×#385×C₆₇	C₂	semidirect
16. C₂×C₄×C₄⋊C₄×C₆₇	C₂	semidirect
24. C₂×#124×C₆₇	C₂²	semidirect
26. C₂×#123×C₆₇	C₂²	semidirect
28. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
30. C₂×C₄×D₄×C₆₇	C₂²	semidirect
54. #396×C₆₇	C₂²	semidirect
55. #395×C₆₇	C₂²	semidirect
56. #394×C₆₇	C₂²	semidirect
58. #390×C₆₇	C₂²	semidirect
59. #388×C₆₇	C₂²	semidirect
60. #388×C₆₇	C₂²	semidirect
61. #388×C₆₇	C₂²	semidirect
62. #386×C₆₇	C₂²	semidirect
63. #385×C₆₇	C₂²	semidirect
64. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
120. C₂×C₄⋊C₄×C₆₇	D₄	semidirect
140. C₂×C₂²⋊C₄×C₆₇	D₄	semidirect
269. C₄⋊C₄×C₆₇	C₂×D₄	semidirect
282. C₂²⋊C₄×C₆₇	C₂×D₄	semidirect
440. C₂×#2461	C₆₇	direct (N × H)
444. C₂×C₆₇	#2461	direct (N × H)
452. C₂²×#124	C₂×C₆₇	semidirect
453. C₂²×#123	C₂×C₆₇	semidirect
454. C₂²×C₂²⋊Q₈	C₂×C₆₇	semidirect
455. C₂²×C₄×D₄	C₂×C₆₇	semidirect
456. #2461	C₂×C₆₇	direct (N × H)
457. C₂×#396	C₂×C₆₇	semidirect
458. C₂×#395	C₂×C₆₇	semidirect
459. C₂×#394	C₂×C₆₇	semidirect
461. C₂×#390	C₂×C₆₇	semidirect
462. C₂×#388	C₂×C₆₇	semidirect
463. C₂×#388	C₂×C₆₇	semidirect
464. C₂×#388	C₂×C₆₇	semidirect
465. C₂×#386	C₂×C₆₇	semidirect
466. C₂×#385	C₂×C₆₇	semidirect
467. C₂×C₄×C₄⋊C₄	C₂×C₆₇	semidirect
468. C₆₇	C₂×#2461	direct (N × H)
476. C₂×#124	C₂²×C₆₇	semidirect
478. C₂×#123	C₂²×C₆₇	semidirect
480. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
482. C₂×C₄×D₄	C₂²×C₆₇	semidirect
506. #396	C₂²×C₆₇	semidirect
507. #395	C₂²×C₆₇	semidirect
508. #394	C₂²×C₆₇	semidirect
510. #390	C₂²×C₆₇	semidirect
511. #388	C₂²×C₆₇	semidirect
512. #388	C₂²×C₆₇	semidirect
513. #388	C₂²×C₆₇	semidirect
514. #386	C₂²×C₆₇	semidirect
515. #385	C₂²×C₆₇	semidirect
516. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
572. C₂×C₄⋊C₄	D₄×C₆₇	semidirect
592. C₂×C₂²⋊C₄	D₄×C₆₇	semidirect
721. C₄⋊C₄	C₂×D₄×C₆₇	semidirect
734. C₂²⋊C₄	C₂×D₄×C₆₇	semidirect
895. C₂	C₆₇×#2461	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×#124×C₆₇	2
C₂²×#123×C₆₇	2
C₂²×C₂²⋊Q₈×C₆₇	2
C₂²×C₄×D₄×C₆₇	2
C₆₇×#2461	2
C₂×#396×C₆₇	2
C₂×#395×C₆₇	2
C₂×#394×C₆₇	2
C₂×#392×C₆₇	2
C₂×#390×C₆₇	2
C₂×#388×C₆₇	2
C₂×#386×C₆₇	2
C₂×#385×C₆₇	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₂×#2461	67

Subgroups — C2×C67×#2461 #30713927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#2461 #30713927