Subgroups — C₆₇×#59637 #30738888

Order 17152.

2334 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#2797	C₂	1	2	yes	maximal, complemented
2	C₆₇×#2752	C₂	1	2	yes	maximal, complemented
3	C₆₇×#2602	C₂	1	2	yes	maximal, complemented
4	C₆₇×#2580	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#2557	C₂	1	2	yes	maximal, complemented
6	C₆₇×#2548	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#2513	C₂	1	1	yes	maximal, characteristic, complemented
9	C₆₇×#2504	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#2472	C₂	1	2	yes	maximal, complemented
11	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#2445	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#2433	C₂	1	1	yes	maximal, characteristic
14	C₆₇×#2418	C₂	1	2	yes	maximal, complemented
15	C₆₇×#2412	C₂	1	2	yes	maximal, complemented
16	C₆₇×#2366	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#2358	C₂	1	2	yes	maximal, complemented
18	C₆₇×#2357	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2345	C₂	1	1	yes	maximal, characteristic, complemented
20	D₄×C₂²⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×C₂²⋊Q₈×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#121×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#390×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#124×C₆₇	C₂²	1	2	yes	complemented
28	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
29	C₂×#123×C₆₇	C₂²	1	2	yes	complemented
30	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×#121×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#120×C₆₇	C₂²	1	2	yes	—
33	C₂×#120×C₆₇	C₂²	1	2	yes	—
34	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	complemented
40	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
41	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
42	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
43	C₂²×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
44	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
45	#399×C₆₇	C₂²	1	2	yes	complemented
46	#397×C₆₇	C₂²	1	2	yes	complemented
47	#397×C₆₇	C₂²	1	2	yes	complemented
48	#397×C₆₇	C₂²	1	2	yes	complemented
49	#397×C₆₇	C₂²	1	2	yes	complemented
50	#397×C₆₇	C₂²	1	2	yes	complemented
51	#397×C₆₇	C₂²	1	2	yes	complemented
52	#394×C₆₇	C₂²	1	2	yes	complemented
53	#394×C₆₇	C₂²	1	2	yes	complemented
54	#394×C₆₇	C₂²	1	2	yes	complemented
55	#394×C₆₇	C₂²	1	2	yes	complemented
56	#394×C₆₇	C₂²	1	2	yes	complemented
57	#394×C₆₇	C₂²	1	2	yes	complemented
58	#393×C₆₇	C₂²	1	2	yes	complemented
59	#392×C₆₇	C₂²	1	2	yes	—
60	#392×C₆₇	C₂²	1	2	yes	—
61	#391×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#390×C₆₇	C₂²	1	1	yes	characteristic
63	#390×C₆₇	C₂²	1	1	yes	characteristic
64	#390×C₆₇	C₂²	1	1	yes	characteristic
65	#390×C₆₇	C₂²	1	1	yes	characteristic
66	#390×C₆₇	C₂²	1	1	yes	characteristic
67	#390×C₆₇	C₂²	1	2	yes	—
68	#390×C₆₇	C₂²	1	2	yes	—
69	#390×C₆₇	C₂²	1	1	yes	characteristic
70	#390×C₆₇	C₂²	1	1	yes	characteristic
71	#390×C₆₇	C₂²	1	1	yes	characteristic
72	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
73	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
74	#390×C₆₇	C₂²	1	2	yes	complemented
75	#390×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	#390×C₆₇	C₂²	1	2	yes	complemented
77	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	#389×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	#388×C₆₇	C₂²	1	2	yes	complemented
82	#388×C₆₇	C₂²	1	2	yes	complemented
83	#388×C₆₇	C₂²	1	2	yes	complemented
84	#388×C₆₇	C₂²	1	2	yes	complemented
85	#388×C₆₇	C₂²	1	2	yes	complemented
86	#388×C₆₇	C₂²	1	2	yes	complemented
87	#388×C₆₇	C₂²	1	2	yes	complemented
88	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#387×C₆₇	C₂²	1	2	yes	complemented
90	#387×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#387×C₆₇	C₂²	1	2	yes	complemented
92	#386×C₆₇	C₂²	1	2	yes	—
93	#386×C₆₇	C₂²	1	2	yes	—
94	#386×C₆₇	C₂²	1	2	yes	—
95	#386×C₆₇	C₂²	1	2	yes	—
96	#386×C₆₇	C₂²	1	2	yes	—
97	#386×C₆₇	C₂²	1	2	yes	complemented
98	#386×C₆₇	C₂²	1	2	yes	complemented
99	#386×C₆₇	C₂²	1	2	yes	complemented
100	#386×C₆₇	C₂²	1	2	yes	complemented
101	#385×C₆₇	C₂²	1	1	yes	characteristic
102	#385×C₆₇	C₂²	1	1	yes	characteristic
103	#385×C₆₇	C₂²	1	2	yes	complemented
104	#385×C₆₇	C₂²	1	2	yes	complemented
105	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#382×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#381×C₆₇	C₂²	1	2	yes	complemented
108	#380×C₆₇	C₂²	1	1	yes	characteristic
109	#380×C₆₇	C₂²	1	1	yes	characteristic
110	#380×C₆₇	C₂²	1	2	yes	—
111	#379×C₆₇	C₂²	1	2	yes	—
112	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
116	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
117	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
119	C₄×C₂²⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
120	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
121	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
122	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	complemented
123	C₂⁵×C₆₇	C₂³	1	2	yes	—
124	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂²×D₄×C₆₇	—	2	4	no	—
126	C₂²×D₄×C₆₇	—	2	4	no	—
127	C₂²×D₄×C₆₇	—	4	2	no	—
128	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
135	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
136	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
137	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
140	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
141	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
142	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
143	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
144	#127×C₆₇	—	2	4	no	—
145	#127×C₆₇	—	4	2	no	—
146	#124×C₆₇	—	4	4	no	—
147	#123×C₆₇	—	4	4	no	—
148	#123×C₆₇	—	4	4	no	—
149	C₂²⋊Q₈×C₆₇	—	2	4	no	—
150	#121×C₆₇	—	2	4	no	—
151	#120×C₆₇	—	2	8	no	—
152	#120×C₆₇	—	4	4	no	—
153	C₄×Q₈×C₆₇	—	4	2	no	—
154	C₄×D₄×C₆₇	—	2	4	no	—
155	C₄×D₄×C₆₇	—	4	2	no	—
156	C₄×D₄×C₆₇	—	4	2	no	—
157	C₄×D₄×C₆₇	—	4	4	no	—
158	C₄×D₄×C₆₇	—	4	4	no	—
159	C₂×C₄⋊C₄×C₆₇	—	2	4	no	—
160	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
163	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
166	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
167	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
168	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
171	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
172	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
173	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
176	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
177	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
178	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
179	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
180	C₂×C₂²⋊C₄×C₆₇	—	4	4	no	—
181	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
182	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
183	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
184	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
185	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
186	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
187	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
188	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
190	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
191	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
192	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
193	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
194	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
195	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
196	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
197	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
198	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
200	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
202	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
203	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
204	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
205	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
206	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄×C₆₇	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
212	C₂×C₄²×C₆₇	—	4	2	no	—
213	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
214	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
215	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
216	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
217	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
218	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
219	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
220	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
221	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
222	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
223	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
224	#95×C₆₇	C₂³	1	2	yes	—
225	#95×C₆₇	C₂³	1	1	yes	characteristic
226	#95×C₆₇	C₂³	1	1	yes	characteristic
227	#95×C₆₇	C₂³	1	2	yes	—
228	#95×C₆₇	C₂³	1	1	yes	characteristic
229	#95×C₆₇	C₂³	1	1	yes	characteristic
230	#95×C₆₇	C₂³	1	1	yes	characteristic
231	#95×C₆₇	C₂³	1	2	yes	—
232	#95×C₆₇	C₂³	1	2	yes	—
233	#95×C₆₇	C₂³	1	2	yes	—
234	#95×C₆₇	C₂³	1	1	yes	characteristic
235	#95×C₆₇	C₂³	1	2	yes	—
236	#95×C₆₇	C₂³	1	1	yes	characteristic
237	#95×C₆₇	C₂³	1	2	yes	—
238	#95×C₆₇	C₂³	1	2	yes	—
239	#95×C₆₇	C₂³	1	1	yes	characteristic
240	#95×C₆₇	C₂³	1	1	yes	characteristic
241	#95×C₆₇	C₂³	1	1	yes	characteristic
242	#95×C₆₇	C₂³	1	2	yes	—
243	#95×C₆₇	C₂³	1	2	yes	—
244	#95×C₆₇	C₂³	1	2	yes	—
245	C₂⁴×C₆₇	—	2	4	no	—
246	C₂⁴×C₆₇	—	2	4	no	—
247	C₂⁴×C₆₇	—	2	4	no	—
248	C₂⁴×C₆₇	—	2	4	no	—
249	C₂⁴×C₆₇	—	4	2	no	—
250	C₂⁴×C₆₇	—	4	2	no	—
251	C₂⁴×C₆₇	—	4	2	no	—
252	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
253	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
254	C₂⁴×C₆₇	C₂⁴	1	2	yes	—
255	C₂⁴×C₆₇	C₂⁴	1	1	yes	characteristic
256	C₂×Q₈×C₆₇	—	2	2	no	—
257	C₂×Q₈×C₆₇	—	2	2	no	—
258	C₂×Q₈×C₆₇	—	4	1	no	—
259	C₂×D₄×C₆₇	—	2	4	no	—
260	C₂×D₄×C₆₇	—	2	4	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	4	no	—
263	C₂×D₄×C₆₇	—	2	4	no	—
264	C₂×D₄×C₆₇	—	2	4	no	—
265	C₂×D₄×C₆₇	—	2	2	no	—
266	C₂×D₄×C₆₇	—	2	4	no	—
267	C₂×D₄×C₆₇	—	2	2	no	—
268	C₂×D₄×C₆₇	—	2	2	no	—
269	C₂×D₄×C₆₇	—	2	4	no	—
270	C₂×D₄×C₆₇	—	2	2	no	—
271	C₂×D₄×C₆₇	—	2	2	no	—
272	C₂×D₄×C₆₇	—	2	4	no	—
273	C₂×D₄×C₆₇	—	2	2	no	—
274	C₂×D₄×C₆₇	—	2	2	no	—
275	C₂×D₄×C₆₇	—	2	2	no	—
276	C₂×D₄×C₆₇	—	4	16	no	—
277	C₂×D₄×C₆₇	—	4	2	no	—
278	C₂×D₄×C₆₇	—	4	2	no	—
279	C₂×D₄×C₆₇	—	4	2	no	—
280	C₂×D₄×C₆₇	—	4	2	no	—
281	C₂×D₄×C₆₇	—	4	2	no	—
282	C₂×D₄×C₆₇	—	4	2	no	—
283	C₂×D₄×C₆₇	—	4	2	no	—
284	C₂×D₄×C₆₇	—	4	2	no	—
285	C₂×D₄×C₆₇	—	4	2	no	—
286	C₂×D₄×C₆₇	#41	1	4	yes	—
287	C₂²×C₄×C₆₇	—	2	2	no	—
288	C₂²×C₄×C₆₇	—	2	2	no	—
289	C₂²×C₄×C₆₇	—	2	2	no	—
290	C₂²×C₄×C₆₇	—	2	2	no	—
291	C₂²×C₄×C₆₇	—	2	4	no	—
292	C₂²×C₄×C₆₇	—	2	4	no	—
293	C₂²×C₄×C₆₇	—	2	2	no	—
294	C₂²×C₄×C₆₇	—	2	2	no	—
295	C₂²×C₄×C₆₇	—	2	4	no	—
296	C₂²×C₄×C₆₇	—	4	1	no	—
297	C₂²×C₄×C₆₇	—	4	1	no	—
298	C₂²×C₄×C₆₇	—	4	2	no	—
299	C₂²×C₄×C₆₇	—	4	2	no	—
300	C₂²×C₄×C₆₇	—	4	2	no	—
301	C₂²×C₄×C₆₇	—	4	2	no	—
302	C₂²×C₄×C₆₇	—	4	2	no	—
303	C₂²×C₄×C₆₇	—	4	2	no	—
304	C₂²×C₄×C₆₇	—	4	2	no	—
305	C₂²×C₄×C₆₇	—	4	2	no	—
306	C₂²×C₄×C₆₇	—	4	2	no	—
307	C₂²×C₄×C₆₇	#41	1	4	yes	—
308	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
310	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
311	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
312	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
313	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
314	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
315	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
316	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
317	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
318	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
319	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
321	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
323	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
327	C₄⋊C₄×C₆₇	—	2	4	no	—
328	C₄⋊C₄×C₆₇	—	2	2	no	—
329	C₄⋊C₄×C₆₇	—	2	2	no	—
330	C₄⋊C₄×C₆₇	—	2	2	no	—
331	C₄⋊C₄×C₆₇	—	2	2	no	—
332	C₄⋊C₄×C₆₇	—	2	2	no	—
333	C₄⋊C₄×C₆₇	—	2	2	no	—
334	C₄⋊C₄×C₆₇	—	2	2	no	—
335	C₄⋊C₄×C₆₇	—	2	2	no	—
336	C₄⋊C₄×C₆₇	—	2	2	no	—
337	C₄⋊C₄×C₆₇	—	2	2	no	—
338	C₄⋊C₄×C₆₇	—	2	2	no	—
339	C₄⋊C₄×C₆₇	—	4	2	no	—
340	C₄⋊C₄×C₆₇	—	4	1	no	—
341	C₄⋊C₄×C₆₇	—	4	1	no	—
342	C₄⋊C₄×C₆₇	—	4	1	no	—
343	C₄⋊C₄×C₆₇	—	4	2	no	—
344	C₄⋊C₄×C₆₇	—	4	2	no	—
345	C₂²⋊C₄×C₆₇	—	2	4	no	—
346	C₂²⋊C₄×C₆₇	—	2	2	no	—
347	C₂²⋊C₄×C₆₇	—	2	2	no	—
348	C₂²⋊C₄×C₆₇	—	2	4	no	—
349	C₂²⋊C₄×C₆₇	—	2	2	no	—
350	C₂²⋊C₄×C₆₇	—	2	4	no	—
351	C₂²⋊C₄×C₆₇	—	2	4	no	—
352	C₂²⋊C₄×C₆₇	—	2	4	no	—
353	C₂²⋊C₄×C₆₇	—	2	4	no	—
354	C₂²⋊C₄×C₆₇	—	2	4	no	—
355	C₂²⋊C₄×C₆₇	—	2	4	no	—
356	C₂²⋊C₄×C₆₇	—	2	4	no	—
357	C₂²⋊C₄×C₆₇	—	2	4	no	—
358	C₂²⋊C₄×C₆₇	—	4	2	no	—
359	C₂²⋊C₄×C₆₇	—	4	2	no	—
360	C₂²⋊C₄×C₆₇	—	4	2	no	—
361	C₂²⋊C₄×C₆₇	—	4	2	no	—
362	C₂²⋊C₄×C₆₇	—	4	2	no	—
363	C₂²⋊C₄×C₆₇	—	4	2	no	—
364	C₂²⋊C₄×C₆₇	—	4	2	no	—
365	C₂²⋊C₄×C₆₇	—	4	2	no	—
366	C₂²⋊C₄×C₆₇	—	4	2	no	—
367	C₂²⋊C₄×C₆₇	—	4	2	no	—
368	C₂²⋊C₄×C₆₇	—	4	2	no	—
369	C₂²⋊C₄×C₆₇	—	4	2	no	—
370	C₂²⋊C₄×C₆₇	—	4	2	no	—
371	C₂²⋊C₄×C₆₇	—	4	2	no	—
372	C₂²⋊C₄×C₆₇	—	4	2	no	—
373	C₂²⋊C₄×C₆₇	—	4	2	no	—
374	C₂²⋊C₄×C₆₇	—	4	2	no	—
375	C₂²⋊C₄×C₆₇	#41	1	4	yes	—
376	C₄²×C₆₇	—	2	2	no	—
377	C₄²×C₆₇	—	2	2	no	—
378	C₄²×C₆₇	—	2	2	no	—
379	C₄²×C₆₇	—	2	2	no	—
380	C₄²×C₆₇	—	2	2	no	—
381	C₄²×C₆₇	—	2	2	no	—
382	C₄²×C₆₇	—	4	1	no	—
383	C₄²×C₆₇	—	4	1	no	—
384	C₄²×C₆₇	—	4	2	no	—
385	C₄²×C₆₇	—	4	2	no	—
386	C₄²×C₆₇	—	4	2	no	—
387	C₂³×C₆₇	—	2	1	no	—
388	C₂³×C₆₇	—	2	1	no	—
389	C₂³×C₆₇	—	2	1	no	—
390	C₂³×C₆₇	—	2	1	no	—
391	C₂³×C₆₇	—	2	2	no	—
392	C₂³×C₆₇	—	2	2	no	—
393	C₂³×C₆₇	—	2	2	no	—
394	C₂³×C₆₇	—	2	2	no	—
395	C₂³×C₆₇	—	2	2	no	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	2	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	2	no	—
402	C₂³×C₆₇	—	2	2	no	—
403	C₂³×C₆₇	—	2	2	no	—
404	C₂³×C₆₇	—	2	2	no	—
405	C₂³×C₆₇	—	2	2	no	—
406	C₂³×C₆₇	—	2	2	no	—
407	C₂³×C₆₇	—	2	2	no	—
408	C₂³×C₆₇	—	2	2	no	—
409	C₂³×C₆₇	—	2	2	no	—
410	C₂³×C₆₇	—	2	2	no	—
411	C₂³×C₆₇	—	4	8	no	—
412	C₂³×C₆₇	—	4	8	no	—
413	C₂³×C₆₇	—	4	8	no	—
414	C₂³×C₆₇	—	4	8	no	—
415	C₂³×C₆₇	—	8	4	no	—
416	C₂³×C₆₇	—	8	4	no	—
417	C₂³×C₆₇	—	8	4	no	—
418	C₂³×C₆₇	C₂×#41	1	4	yes	—
419	C₂³×C₆₇	C₂×#41	1	2	yes	—
420	C₂³×C₆₇	C₂×#41	1	2	yes	—
421	C₂³×C₆₇	H(5,𝔽₂)	1	2	yes	—
422	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
423	Q₈×C₆₇	—	4	4	no	—
424	D₄×C₆₇	—	2	8	no	—
425	D₄×C₆₇	—	4	8	no	—
426	D₄×C₆₇	—	4	8	no	—
427	D₄×C₆₇	—	4	8	no	—
428	D₄×C₆₇	—	4	4	no	—
429	D₄×C₆₇	—	4	4	no	—
430	D₄×C₆₇	—	8	4	no	—
431	D₄×C₆₇	—	8	4	no	—
432	D₄×C₆₇	—	8	4	no	—
433	C₂×C₄×C₆₇	—	2	1	no	—
434	C₂×C₄×C₆₇	—	2	1	no	—
435	C₂×C₄×C₆₇	—	2	1	no	—
436	C₂×C₄×C₆₇	—	2	1	no	—
437	C₂×C₄×C₆₇	—	2	1	no	—
438	C₂×C₄×C₆₇	—	2	1	no	—
439	C₂×C₄×C₆₇	—	2	1	no	—
440	C₂×C₄×C₆₇	—	2	1	no	—
441	C₂×C₄×C₆₇	—	2	1	no	—
442	C₂×C₄×C₆₇	—	2	1	no	—
443	C₂×C₄×C₆₇	—	2	8	no	—
444	C₂×C₄×C₆₇	—	2	1	no	—
445	C₂×C₄×C₆₇	—	2	1	no	—
446	C₂×C₄×C₆₇	—	2	1	no	—
447	C₂×C₄×C₆₇	—	2	2	no	—
448	C₂×C₄×C₆₇	—	2	1	no	—
449	C₂×C₄×C₆₇	—	2	2	no	—
450	C₂×C₄×C₆₇	—	2	2	no	—
451	C₂×C₄×C₆₇	—	2	1	no	—
452	C₂×C₄×C₆₇	—	2	2	no	—
453	C₂×C₄×C₆₇	—	2	2	no	—
454	C₂×C₄×C₆₇	—	2	1	no	—
455	C₂×C₄×C₆₇	—	2	1	no	—
456	C₂×C₄×C₆₇	—	2	1	no	—
457	C₂×C₄×C₆₇	—	2	1	no	—
458	C₂×C₄×C₆₇	—	2	1	no	—
459	C₂×C₄×C₆₇	—	2	1	no	—
460	C₂×C₄×C₆₇	—	2	2	no	—
461	C₂×C₄×C₆₇	—	2	2	no	—
462	C₂×C₄×C₆₇	—	2	2	no	—
463	C₂×C₄×C₆₇	—	2	2	no	—
464	C₂×C₄×C₆₇	—	2	2	no	—
465	C₂×C₄×C₆₇	—	2	2	no	—
466	C₂×C₄×C₆₇	—	2	2	no	—
467	C₂×C₄×C₆₇	—	2	2	no	—
468	C₂×C₄×C₆₇	—	2	1	no	—
469	C₂×C₄×C₆₇	—	2	1	no	—
470	C₂×C₄×C₆₇	—	2	1	no	—
471	C₂×C₄×C₆₇	—	2	1	no	—
472	C₂×C₄×C₆₇	—	2	2	no	—
473	C₂×C₄×C₆₇	—	2	1	no	—
474	C₂×C₄×C₆₇	—	2	1	no	—
475	C₂×C₄×C₆₇	—	2	1	no	—
476	C₂×C₄×C₆₇	—	2	1	no	—
477	C₂×C₄×C₆₇	—	2	1	no	—
478	C₂×C₄×C₆₇	—	2	2	no	—
479	C₂×C₄×C₆₇	—	2	1	no	—
480	C₂×C₄×C₆₇	—	2	1	no	—
481	C₂×C₄×C₆₇	—	2	1	no	—
482	C₂×C₄×C₆₇	—	2	1	no	—
483	C₂×C₄×C₆₇	—	4	4	no	—
484	C₂×C₄×C₆₇	—	4	4	no	—
485	C₂×C₄×C₆₇	—	8	4	no	—
486	C₂×C₄×C₆₇	—	8	4	no	—
487	C₂×C₄×C₆₇	—	8	4	no	—
488	C₂×C₄×C₆₇	—	8	4	no	—
489	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
490	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
491	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
493	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
494	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
496	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
497	C₂²×C₆₇	—	2	2	no	—
498	C₂²×C₆₇	—	2	2	no	—
499	C₂²×C₆₇	—	2	2	no	—
500	C₂²×C₆₇	—	2	2	no	—
501	C₂²×C₆₇	—	2	2	no	—
502	C₂²×C₆₇	—	2	2	no	—
503	C₂²×C₆₇	—	2	4	no	—
504	C₂²×C₆₇	—	2	4	no	—
505	C₂²×C₆₇	—	2	4	no	—
506	C₂²×C₆₇	—	4	2	no	—
507	C₂²×C₆₇	—	4	2	no	—
508	C₂²×C₆₇	—	4	2	no	—
509	C₂²×C₆₇	—	4	2	no	—
510	C₂²×C₆₇	—	4	2	no	—
511	C₂²×C₆₇	—	4	2	no	—
512	C₂²×C₆₇	—	4	2	no	—
513	C₂²×C₆₇	—	4	2	no	—
514	C₂²×C₆₇	—	4	2	no	—
515	C₂²×C₆₇	—	4	2	no	—
516	C₂²×C₆₇	—	4	2	no	—
517	C₂²×C₆₇	—	4	2	no	—
518	C₂²×C₆₇	—	4	2	no	—
519	C₂²×C₆₇	—	4	2	no	—
520	C₂²×C₆₇	—	4	2	no	—
521	C₂²×C₆₇	—	4	2	no	—
522	C₂²×C₆₇	—	4	2	no	—
523	C₂²×C₆₇	—	4	2	no	—
524	C₂²×C₆₇	—	8	16	no	—
525	C₂²×C₆₇	#559	1	4	yes	—
526	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
527	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
528	C₂²×C₆₇	C₂²×#41	1	1	yes	characteristic
529	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
530	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
531	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂²×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
533	C₄×C₆₇	—	2	2	no	—
534	C₄×C₆₇	—	2	2	no	—
535	C₄×C₆₇	—	2	2	no	—
536	C₄×C₆₇	—	2	2	no	—
537	C₄×C₆₇	—	2	2	no	—
538	C₄×C₆₇	—	4	2	no	—
539	C₄×C₆₇	—	4	1	no	—
540	C₄×C₆₇	—	4	2	no	—
541	C₄×C₆₇	—	4	2	no	—
542	C₄×C₆₇	—	4	1	no	—
543	C₄×C₆₇	—	4	2	no	—
544	C₄×C₆₇	—	4	1	no	—
545	C₄×C₆₇	—	4	1	no	—
546	C₄×C₆₇	—	4	1	no	—
547	C₄×C₆₇	—	4	1	no	—
548	C₄×C₆₇	—	4	1	no	—
549	C₄×C₆₇	—	4	2	no	—
550	C₄×C₆₇	—	4	1	no	—
551	C₄×C₆₇	#551	1	4	yes	—
552	#59637	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
553	C₂×C₆₇	—	2	4	no	—
554	C₂×C₆₇	—	4	4	no	—
555	C₂×C₆₇	—	8	2	no	—
556	C₂×C₆₇	—	8	2	no	—
557	C₂×C₆₇	C₂×#551	1	1	yes	characteristic
558	C₂×C₆₇	C₂×#559	1	1	yes	characteristic
559	C₂×C₆₇	#3481	1	1	yes	characteristic
560	C₂×C₆₇	#3508	1	1	yes	characteristic
561	C₂×C₆₇	#3519	1	1	yes	characteristic
562	C₂×C₆₇	#3519	1	1	yes	characteristic
563	C₂×C₆₇	#3537	1	1	yes	characteristic
564	#2797	C₂×C₆₇	1	2	yes	complemented
565	#2752	C₂×C₆₇	1	2	yes	complemented
566	#2602	C₂×C₆₇	1	2	yes	complemented
567	#2580	C₂×C₆₇	1	1	yes	characteristic, complemented
568	#2557	C₂×C₆₇	1	2	yes	complemented
569	#2548	C₂×C₆₇	1	1	yes	characteristic, complemented
570	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
571	#2513	C₂×C₆₇	1	1	yes	characteristic, complemented
572	#2504	C₂×C₆₇	1	1	yes	characteristic, complemented
573	#2472	C₂×C₆₇	1	2	yes	complemented
574	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
575	#2445	C₂×C₆₇	1	1	yes	characteristic, complemented
576	#2433	C₂×C₆₇	1	1	yes	characteristic
577	#2418	C₂×C₆₇	1	2	yes	complemented
578	#2412	C₂×C₆₇	1	2	yes	complemented
579	#2366	C₂×C₆₇	1	1	yes	characteristic, complemented
580	#2358	C₂×C₆₇	1	2	yes	complemented
581	#2357	C₂×C₆₇	1	1	yes	characteristic, complemented
582	#2345	C₂×C₆₇	1	1	yes	characteristic, complemented
583	D₄×C₂²⋊C₄	C₂×C₆₇	1	1	yes	characteristic, complemented
584	C₄×C₂²⋊Q₈	C₂×C₆₇	1	1	yes	characteristic, complemented
585	C₄×#121	C₂×C₆₇	1	1	yes	characteristic, complemented
586	C₂×#390	C₂×C₆₇	1	1	yes	characteristic, complemented
587	C₆₇	#59637	1	1	yes	characteristic, direct product factor, Sylow
588	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
589	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
590	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
591	C₂×#124	C₂²×C₆₇	1	2	yes	complemented
592	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
593	C₂×#123	C₂²×C₆₇	1	2	yes	complemented
594	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic
595	C₂×#121	C₂²×C₆₇	1	1	yes	characteristic
596	C₂×#120	C₂²×C₆₇	1	2	yes	—
597	C₂×#120	C₂²×C₆₇	1	2	yes	—
598	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
599	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
600	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
601	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
602	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	complemented
603	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
604	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
605	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
606	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
607	C₂²×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
608	C₂²×C₄²	C₂²×C₆₇	1	1	yes	characteristic
609	#399	C₂²×C₆₇	1	2	yes	complemented
610	#397	C₂²×C₆₇	1	2	yes	complemented
611	#397	C₂²×C₆₇	1	2	yes	complemented
612	#397	C₂²×C₆₇	1	2	yes	complemented
613	#397	C₂²×C₆₇	1	2	yes	complemented
614	#397	C₂²×C₆₇	1	2	yes	complemented
615	#397	C₂²×C₆₇	1	2	yes	complemented
616	#394	C₂²×C₆₇	1	2	yes	complemented
617	#394	C₂²×C₆₇	1	2	yes	complemented
618	#394	C₂²×C₆₇	1	2	yes	complemented
619	#394	C₂²×C₆₇	1	2	yes	complemented
620	#394	C₂²×C₆₇	1	2	yes	complemented
621	#394	C₂²×C₆₇	1	2	yes	complemented
622	#393	C₂²×C₆₇	1	2	yes	complemented
623	#392	C₂²×C₆₇	1	2	yes	—
624	#392	C₂²×C₆₇	1	2	yes	—
625	#391	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#390	C₂²×C₆₇	1	1	yes	characteristic
627	#390	C₂²×C₆₇	1	1	yes	characteristic
628	#390	C₂²×C₆₇	1	1	yes	characteristic
629	#390	C₂²×C₆₇	1	1	yes	characteristic
630	#390	C₂²×C₆₇	1	2	yes	—
631	#390	C₂²×C₆₇	1	1	yes	characteristic
632	#390	C₂²×C₆₇	1	1	yes	characteristic
633	#390	C₂²×C₆₇	1	1	yes	characteristic
634	#390	C₂²×C₆₇	1	2	yes	—
635	#390	C₂²×C₆₇	1	1	yes	characteristic
636	#390	C₂²×C₆₇	1	2	yes	complemented
637	#390	C₂²×C₆₇	1	2	yes	complemented
638	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
639	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
640	#390	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
642	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
643	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
644	#389	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	#388	C₂²×C₆₇	1	2	yes	complemented
646	#388	C₂²×C₆₇	1	2	yes	complemented
647	#388	C₂²×C₆₇	1	2	yes	complemented
648	#388	C₂²×C₆₇	1	2	yes	complemented
649	#388	C₂²×C₆₇	1	2	yes	complemented
650	#388	C₂²×C₆₇	1	2	yes	complemented
651	#388	C₂²×C₆₇	1	2	yes	complemented
652	#387	C₂²×C₆₇	1	2	yes	complemented
653	#387	C₂²×C₆₇	1	2	yes	complemented
654	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
655	#387	C₂²×C₆₇	1	1	yes	characteristic, complemented
656	#386	C₂²×C₆₇	1	2	yes	—
657	#386	C₂²×C₆₇	1	2	yes	—
658	#386	C₂²×C₆₇	1	2	yes	—
659	#386	C₂²×C₆₇	1	2	yes	—
660	#386	C₂²×C₆₇	1	2	yes	—
661	#386	C₂²×C₆₇	1	2	yes	complemented
662	#386	C₂²×C₆₇	1	2	yes	complemented
663	#386	C₂²×C₆₇	1	2	yes	complemented
664	#386	C₂²×C₆₇	1	2	yes	complemented
665	#385	C₂²×C₆₇	1	1	yes	characteristic
666	#385	C₂²×C₆₇	1	1	yes	characteristic
667	#385	C₂²×C₆₇	1	2	yes	complemented
668	#385	C₂²×C₆₇	1	2	yes	complemented
669	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	#382	C₂²×C₆₇	1	1	yes	characteristic, complemented
671	#381	C₂²×C₆₇	1	2	yes	complemented
672	#380	C₂²×C₆₇	1	1	yes	characteristic
673	#380	C₂²×C₆₇	1	2	yes	—
674	#380	C₂²×C₆₇	1	1	yes	characteristic
675	#379	C₂²×C₆₇	1	2	yes	—
676	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
677	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
678	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
679	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
680	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
681	C₄×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
682	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
683	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	—
684	C₄×C₂²⋊C₄	C₂²×C₆₇	1	1	yes	characteristic
685	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
686	C₄×C₂²⋊C₄	C₂²×C₆₇	1	2	yes	complemented
687	C₂⁵	C₂³×C₆₇	1	2	yes	—
688	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
689	C₂²×D₄	—	2	4	no	—
690	C₂²×D₄	—	2	4	no	—
691	C₂²×D₄	—	4	2	no	—
692	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
693	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
694	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
695	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
696	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
697	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
698	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
699	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
700	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
701	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
702	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
703	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
704	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
705	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
706	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
707	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
708	#127	—	2	4	no	—
709	#127	—	4	2	no	—
710	#124	—	4	4	no	—
711	#123	—	4	4	no	—
712	#123	—	4	4	no	—
713	C₂²⋊Q₈	—	2	4	no	—
714	#121	—	2	4	no	—
715	#120	—	2	8	no	—
716	#120	—	4	4	no	—
717	C₄×Q₈	—	4	2	no	—
718	C₄×D₄	—	2	4	no	—
719	C₄×D₄	—	4	2	no	—
720	C₄×D₄	—	4	2	no	—
721	C₄×D₄	—	4	4	no	—
722	C₄×D₄	—	4	4	no	—
723	C₂×C₄⋊C₄	—	2	4	no	—
724	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
725	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
726	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
727	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
728	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
729	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
730	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
731	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
734	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
735	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
737	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
740	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
741	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
742	C₂×C₂²⋊C₄	—	4	4	no	—
743	C₂×C₂²⋊C₄	—	4	4	no	—
744	C₂×C₂²⋊C₄	—	4	4	no	—
745	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
746	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
747	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
753	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
758	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
759	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
760	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
761	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
762	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
763	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
764	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
765	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
766	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
767	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
768	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
769	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
770	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
771	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
772	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
773	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
774	C₂×C₂²⋊C₄	C₂³×C₆₇	1	2	yes	—
775	C₂×C₂²⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×C₄²	—	4	2	no	—
777	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
778	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
780	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
781	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
782	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
784	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
785	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
786	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
787	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
788	#95	C₂³×C₆₇	1	2	yes	—
789	#95	C₂³×C₆₇	1	1	yes	characteristic
790	#95	C₂³×C₆₇	1	1	yes	characteristic
791	#95	C₂³×C₆₇	1	2	yes	—
792	#95	C₂³×C₆₇	1	1	yes	characteristic
793	#95	C₂³×C₆₇	1	1	yes	characteristic
794	#95	C₂³×C₆₇	1	1	yes	characteristic
795	#95	C₂³×C₆₇	1	2	yes	—
796	#95	C₂³×C₆₇	1	2	yes	—
797	#95	C₂³×C₆₇	1	2	yes	—
798	#95	C₂³×C₆₇	1	1	yes	characteristic
799	#95	C₂³×C₆₇	1	2	yes	—
800	#95	C₂³×C₆₇	1	2	yes	—
801	#95	C₂³×C₆₇	1	1	yes	characteristic
802	#95	C₂³×C₆₇	1	2	yes	—
803	#95	C₂³×C₆₇	1	1	yes	characteristic
804	#95	C₂³×C₆₇	1	1	yes	characteristic
805	#95	C₂³×C₆₇	1	1	yes	characteristic
806	#95	C₂³×C₆₇	1	2	yes	—
807	#95	C₂³×C₆₇	1	2	yes	—
808	#95	C₂³×C₆₇	1	2	yes	—
809	C₂⁴	—	2	4	no	—
810	C₂⁴	—	2	4	no	—
811	C₂⁴	—	2	4	no	—
812	C₂⁴	—	2	4	no	—
813	C₂⁴	—	4	2	no	—
814	C₂⁴	—	4	2	no	—
815	C₂⁴	—	4	2	no	—
816	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
817	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
818	C₂⁴	C₂⁴×C₆₇	1	2	yes	—
819	C₂⁴	C₂⁴×C₆₇	1	1	yes	characteristic
820	C₂×Q₈	—	2	2	no	—
821	C₂×Q₈	—	2	2	no	—
822	C₂×Q₈	—	4	1	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	4	no	—
825	C₂×D₄	—	2	4	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	4	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	4	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	2	no	—
833	C₂×D₄	—	2	4	no	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	2	2	no	—
836	C₂×D₄	—	2	4	no	—
837	C₂×D₄	—	2	2	no	—
838	C₂×D₄	—	2	2	no	—
839	C₂×D₄	—	2	2	no	—
840	C₂×D₄	—	4	16	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	2	no	—
843	C₂×D₄	—	4	2	no	—
844	C₂×D₄	—	4	2	no	—
845	C₂×D₄	—	4	2	no	—
846	C₂×D₄	—	4	2	no	—
847	C₂×D₄	—	4	2	no	—
848	C₂×D₄	—	4	2	no	—
849	C₂×D₄	—	4	2	no	—
850	C₂×D₄	#41×C₆₇	1	4	yes	—
851	C₂²×C₄	—	2	2	no	—
852	C₂²×C₄	—	2	2	no	—
853	C₂²×C₄	—	2	2	no	—
854	C₂²×C₄	—	2	2	no	—
855	C₂²×C₄	—	2	4	no	—
856	C₂²×C₄	—	2	4	no	—
857	C₂²×C₄	—	2	2	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	4	no	—
860	C₂²×C₄	—	4	1	no	—
861	C₂²×C₄	—	4	1	no	—
862	C₂²×C₄	—	4	2	no	—
863	C₂²×C₄	—	4	2	no	—
864	C₂²×C₄	—	4	2	no	—
865	C₂²×C₄	—	4	2	no	—
866	C₂²×C₄	—	4	2	no	—
867	C₂²×C₄	—	4	2	no	—
868	C₂²×C₄	—	4	2	no	—
869	C₂²×C₄	—	4	2	no	—
870	C₂²×C₄	—	4	2	no	—
871	C₂²×C₄	#41×C₆₇	1	4	yes	—
872	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
873	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
874	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
875	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
876	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
877	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
878	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
879	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
880	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
881	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
882	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
883	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
884	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
885	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
886	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
888	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
889	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
890	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
891	C₄⋊C₄	—	2	4	no	—
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	2	2	no	—
901	C₄⋊C₄	—	2	2	no	—
902	C₄⋊C₄	—	2	2	no	—
903	C₄⋊C₄	—	4	2	no	—
904	C₄⋊C₄	—	4	1	no	—
905	C₄⋊C₄	—	4	1	no	—
906	C₄⋊C₄	—	4	1	no	—
907	C₄⋊C₄	—	4	2	no	—
908	C₄⋊C₄	—	4	2	no	—
909	C₂²⋊C₄	—	2	4	no	—
910	C₂²⋊C₄	—	2	2	no	—
911	C₂²⋊C₄	—	2	2	no	—
912	C₂²⋊C₄	—	2	4	no	—
913	C₂²⋊C₄	—	2	2	no	—
914	C₂²⋊C₄	—	2	4	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	4	no	—
919	C₂²⋊C₄	—	2	4	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	—	4	2	no	—
923	C₂²⋊C₄	—	4	2	no	—
924	C₂²⋊C₄	—	4	2	no	—
925	C₂²⋊C₄	—	4	2	no	—
926	C₂²⋊C₄	—	4	2	no	—
927	C₂²⋊C₄	—	4	2	no	—
928	C₂²⋊C₄	—	4	2	no	—
929	C₂²⋊C₄	—	4	2	no	—
930	C₂²⋊C₄	—	4	2	no	—
931	C₂²⋊C₄	—	4	2	no	—
932	C₂²⋊C₄	—	4	2	no	—
933	C₂²⋊C₄	—	4	2	no	—
934	C₂²⋊C₄	—	4	2	no	—
935	C₂²⋊C₄	—	4	2	no	—
936	C₂²⋊C₄	—	4	2	no	—
937	C₂²⋊C₄	—	4	2	no	—
938	C₂²⋊C₄	—	4	2	no	—
939	C₂²⋊C₄	#41×C₆₇	1	4	yes	—
940	C₄²	—	2	2	no	—
941	C₄²	—	2	2	no	—
942	C₄²	—	2	2	no	—
943	C₄²	—	2	2	no	—
944	C₄²	—	2	2	no	—
945	C₄²	—	2	2	no	—
946	C₄²	—	4	1	no	—
947	C₄²	—	4	1	no	—
948	C₄²	—	4	2	no	—
949	C₄²	—	4	2	no	—
950	C₄²	—	4	2	no	—
951	C₂³	—	2	1	no	—
952	C₂³	—	2	1	no	—
953	C₂³	—	2	1	no	—
954	C₂³	—	2	1	no	—
955	C₂³	—	2	2	no	—
956	C₂³	—	2	2	no	—
957	C₂³	—	2	2	no	—
958	C₂³	—	2	2	no	—
959	C₂³	—	2	2	no	—
960	C₂³	—	2	2	no	—
961	C₂³	—	2	2	no	—
962	C₂³	—	2	2	no	—
963	C₂³	—	2	2	no	—
964	C₂³	—	2	2	no	—
965	C₂³	—	2	2	no	—
966	C₂³	—	2	2	no	—
967	C₂³	—	2	2	no	—
968	C₂³	—	2	2	no	—
969	C₂³	—	2	2	no	—
970	C₂³	—	2	2	no	—
971	C₂³	—	2	2	no	—
972	C₂³	—	2	2	no	—
973	C₂³	—	2	2	no	—
974	C₂³	—	2	2	no	—
975	C₂³	—	4	8	no	—
976	C₂³	—	4	8	no	—
977	C₂³	—	4	8	no	—
978	C₂³	—	4	8	no	—
979	C₂³	—	8	4	no	—
980	C₂³	—	8	4	no	—
981	C₂³	—	8	4	no	—
982	C₂³	C₂×#41×C₆₇	1	4	yes	—
983	C₂³	C₂×#41×C₆₇	1	2	yes	—
984	C₂³	C₂×#41×C₆₇	1	2	yes	—
985	C₂³	H(5,𝔽₂)×C₆₇	1	2	yes	—
986	C₂³	C₂⁵×C₆₇	1	1	yes	characteristic
987	Q₈	—	4	4	no	—
988	D₄	—	2	8	no	—
989	D₄	—	4	8	no	—
990	D₄	—	4	8	no	—
991	D₄	—	4	8	no	—
992	D₄	—	4	4	no	—
993	D₄	—	4	4	no	—
994	D₄	—	8	4	no	—
995	D₄	—	8	4	no	—
996	D₄	—	8	4	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	2	1	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	1	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	8	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	2	2	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	2	2	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	1	no	—
1033	C₂×C₄	—	2	1	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	4	no	—
1048	C₂×C₄	—	4	4	no	—
1049	C₂×C₄	—	8	4	no	—
1050	C₂×C₄	—	8	4	no	—
1051	C₂×C₄	—	8	4	no	—
1052	C₂×C₄	—	8	4	no	—
1053	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1054	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1055	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1056	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1057	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1058	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1059	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1060	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1061	C₂²	—	2	2	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	2	2	no	—
1064	C₂²	—	2	2	no	—
1065	C₂²	—	2	2	no	—
1066	C₂²	—	2	2	no	—
1067	C₂²	—	2	4	no	—
1068	C₂²	—	2	4	no	—
1069	C₂²	—	2	4	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	4	2	no	—
1073	C₂²	—	4	2	no	—
1074	C₂²	—	4	2	no	—
1075	C₂²	—	4	2	no	—
1076	C₂²	—	4	2	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	4	2	no	—
1081	C₂²	—	4	2	no	—
1082	C₂²	—	4	2	no	—
1083	C₂²	—	4	2	no	—
1084	C₂²	—	4	2	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	8	16	no	—
1089	C₂²	#559×C₆₇	1	4	yes	—
1090	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1091	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1092	C₂²	C₂²×#41×C₆₇	1	1	yes	characteristic
1093	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1094	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1095	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1096	C₂²	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1097	C₄	—	2	2	no	—
1098	C₄	—	2	2	no	—
1099	C₄	—	2	2	no	—
1100	C₄	—	2	2	no	—
1101	C₄	—	2	2	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	2	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	4	2	no	—
1109	C₄	—	4	2	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	#551×C₆₇	1	4	yes	—
1116	C₂	—	2	4	no	—
1117	C₂	—	4	4	no	—
1118	C₂	—	8	2	no	—
1119	C₂	—	8	2	no	—
1120	C₂	C₂×#551×C₆₇	1	1	yes	characteristic
1121	C₂	C₂×#559×C₆₇	1	1	yes	characteristic
1122	C₂	C₆₇×#3481	1	1	yes	characteristic
1123	C₂	C₆₇×#3508	1	1	yes	characteristic
1124	C₂	C₆₇×#3519	1	1	yes	characteristic
1125	C₂	C₆₇×#3519	1	1	yes	characteristic
1126	C₂	C₆₇×#3537	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₆₇
prime radical	C₆₇×#2433	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#2797	C₂	semidirect
2. C₆₇×#2752	C₂	semidirect
3. C₆₇×#2602	C₂	semidirect
4. C₆₇×#2580	C₂	semidirect
5. C₆₇×#2557	C₂	semidirect
6. C₆₇×#2548	C₂	semidirect
7. C₆₇×#2513	C₂	semidirect
8. C₆₇×#2513	C₂	semidirect
9. C₆₇×#2504	C₂	semidirect
10. C₆₇×#2472	C₂	semidirect
11. C₆₇×#2445	C₂	semidirect
12. C₆₇×#2445	C₂	semidirect
14. C₆₇×#2418	C₂	semidirect
15. C₆₇×#2412	C₂	semidirect
16. C₆₇×#2366	C₂	semidirect
17. C₆₇×#2358	C₂	semidirect
18. C₆₇×#2357	C₂	semidirect
19. C₆₇×#2345	C₂	semidirect
20. D₄×C₂²⋊C₄×C₆₇	C₂	semidirect
21. C₄×C₂²⋊Q₈×C₆₇	C₂	semidirect
22. C₄×#121×C₆₇	C₂	semidirect
23. C₂×#390×C₆₇	C₂	semidirect
27. C₂×#124×C₆₇	C₂²	semidirect
28. C₂×#123×C₆₇	C₂²	semidirect
29. C₂×#123×C₆₇	C₂²	semidirect
34. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
38. C₂×C₄×D₄×C₆₇	C₂²	semidirect
39. C₂×C₄×D₄×C₆₇	C₂²	semidirect
45. #399×C₆₇	C₂²	semidirect
46. #397×C₆₇	C₂²	semidirect
47. #397×C₆₇	C₂²	semidirect
48. #397×C₆₇	C₂²	semidirect
49. #397×C₆₇	C₂²	semidirect
50. #397×C₆₇	C₂²	semidirect
51. #397×C₆₇	C₂²	semidirect
52. #394×C₆₇	C₂²	semidirect
53. #394×C₆₇	C₂²	semidirect
54. #394×C₆₇	C₂²	semidirect
55. #394×C₆₇	C₂²	semidirect
56. #394×C₆₇	C₂²	semidirect
57. #394×C₆₇	C₂²	semidirect
58. #393×C₆₇	C₂²	semidirect
61. #391×C₆₇	C₂²	semidirect
72. #390×C₆₇	C₂²	semidirect
73. #390×C₆₇	C₂²	semidirect
74. #390×C₆₇	C₂²	semidirect
75. #390×C₆₇	C₂²	semidirect
76. #390×C₆₇	C₂²	semidirect
77. #389×C₆₇	C₂²	semidirect
78. #389×C₆₇	C₂²	semidirect
79. #389×C₆₇	C₂²	semidirect
80. #389×C₆₇	C₂²	semidirect
81. #388×C₆₇	C₂²	semidirect
82. #388×C₆₇	C₂²	semidirect
83. #388×C₆₇	C₂²	semidirect
84. #388×C₆₇	C₂²	semidirect
85. #388×C₆₇	C₂²	semidirect
86. #388×C₆₇	C₂²	semidirect
87. #388×C₆₇	C₂²	semidirect
88. #387×C₆₇	C₂²	semidirect
89. #387×C₆₇	C₂²	semidirect
90. #387×C₆₇	C₂²	semidirect
91. #387×C₆₇	C₂²	semidirect
97. #386×C₆₇	C₂²	semidirect
98. #386×C₆₇	C₂²	semidirect
99. #386×C₆₇	C₂²	semidirect
100. #386×C₆₇	C₂²	semidirect
103. #385×C₆₇	C₂²	semidirect
104. #385×C₆₇	C₂²	semidirect
105. #382×C₆₇	C₂²	semidirect
106. #382×C₆₇	C₂²	semidirect
107. #381×C₆₇	C₂²	semidirect
112. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
113. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
114. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
115. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
116. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
117. C₄×C₄⋊C₄×C₆₇	C₂²	semidirect
121. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
122. C₄×C₂²⋊C₄×C₆₇	C₂²	semidirect
552. #59637	C₆₇	direct (N × H)
564. #2797	C₂×C₆₇	semidirect
565. #2752	C₂×C₆₇	semidirect
566. #2602	C₂×C₆₇	semidirect
567. #2580	C₂×C₆₇	semidirect
568. #2557	C₂×C₆₇	semidirect
569. #2548	C₂×C₆₇	semidirect
570. #2513	C₂×C₆₇	semidirect
571. #2513	C₂×C₆₇	semidirect
572. #2504	C₂×C₆₇	semidirect
573. #2472	C₂×C₆₇	semidirect
574. #2445	C₂×C₆₇	semidirect
575. #2445	C₂×C₆₇	semidirect
577. #2418	C₂×C₆₇	semidirect
578. #2412	C₂×C₆₇	semidirect
579. #2366	C₂×C₆₇	semidirect
580. #2358	C₂×C₆₇	semidirect
581. #2357	C₂×C₆₇	semidirect
582. #2345	C₂×C₆₇	semidirect
583. D₄×C₂²⋊C₄	C₂×C₆₇	semidirect
584. C₄×C₂²⋊Q₈	C₂×C₆₇	semidirect
585. C₄×#121	C₂×C₆₇	semidirect
586. C₂×#390	C₂×C₆₇	semidirect
587. C₆₇	#59637	direct (N × H)
591. C₂×#124	C₂²×C₆₇	semidirect
592. C₂×#123	C₂²×C₆₇	semidirect
593. C₂×#123	C₂²×C₆₇	semidirect
598. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
602. C₂×C₄×D₄	C₂²×C₆₇	semidirect
603. C₂×C₄×D₄	C₂²×C₆₇	semidirect
609. #399	C₂²×C₆₇	semidirect
610. #397	C₂²×C₆₇	semidirect
611. #397	C₂²×C₆₇	semidirect
612. #397	C₂²×C₆₇	semidirect
613. #397	C₂²×C₆₇	semidirect
614. #397	C₂²×C₆₇	semidirect
615. #397	C₂²×C₆₇	semidirect
616. #394	C₂²×C₆₇	semidirect
617. #394	C₂²×C₆₇	semidirect
618. #394	C₂²×C₆₇	semidirect
619. #394	C₂²×C₆₇	semidirect
620. #394	C₂²×C₆₇	semidirect
621. #394	C₂²×C₆₇	semidirect
622. #393	C₂²×C₆₇	semidirect
625. #391	C₂²×C₆₇	semidirect
636. #390	C₂²×C₆₇	semidirect
637. #390	C₂²×C₆₇	semidirect
638. #390	C₂²×C₆₇	semidirect
639. #390	C₂²×C₆₇	semidirect
640. #390	C₂²×C₆₇	semidirect
641. #389	C₂²×C₆₇	semidirect
642. #389	C₂²×C₆₇	semidirect
643. #389	C₂²×C₆₇	semidirect
644. #389	C₂²×C₆₇	semidirect
645. #388	C₂²×C₆₇	semidirect
646. #388	C₂²×C₆₇	semidirect
647. #388	C₂²×C₆₇	semidirect
648. #388	C₂²×C₆₇	semidirect
649. #388	C₂²×C₆₇	semidirect
650. #388	C₂²×C₆₇	semidirect
651. #388	C₂²×C₆₇	semidirect
652. #387	C₂²×C₆₇	semidirect
653. #387	C₂²×C₆₇	semidirect
654. #387	C₂²×C₆₇	semidirect
655. #387	C₂²×C₆₇	semidirect
661. #386	C₂²×C₆₇	semidirect
662. #386	C₂²×C₆₇	semidirect
663. #386	C₂²×C₆₇	semidirect
664. #386	C₂²×C₆₇	semidirect
667. #385	C₂²×C₆₇	semidirect
668. #385	C₂²×C₆₇	semidirect
669. #382	C₂²×C₆₇	semidirect
670. #382	C₂²×C₆₇	semidirect
671. #381	C₂²×C₆₇	semidirect
676. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
677. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
678. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
679. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
680. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
681. C₄×C₄⋊C₄	C₂²×C₆₇	semidirect
685. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect
686. C₄×C₂²⋊C₄	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#2797	2
C₆₇×#2752	2
C₆₇×#2602	2
C₆₇×#2580	2
C₆₇×#2557	2
C₆₇×#2548	2
C₆₇×#2513	2
C₆₇×#2504	2
C₆₇×#2472	2
C₆₇×#2445	2
C₆₇×#2433	2
C₆₇×#2418	2
C₆₇×#2412	2
C₆₇×#2366	2
C₆₇×#2358	2
C₆₇×#2357	2
C₆₇×#2345	2
D₄×C₂²⋊C₄×C₆₇	2
C₄×C₂²⋊Q₈×C₆₇	2
C₄×#121×C₆₇	2
C₂×#390×C₆₇	2
#59637	67

Subgroups — C67×#59637 #30738888

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#59637 #30738888