Subgroups — C₆₇×#60575 #30739826

Order 17152.

2080 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3461	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3124	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3123	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3120	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3118	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3116	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3114	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3111	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3110	C₂	1	2	yes	maximal, complemented
11	C₆₇×#3098	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3083	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3081	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3046	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3042	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic
18	C₆₇×#3009	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#137×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2943	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#440×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2923	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
29	#544×C₆₇	C₂²	1	1	yes	characteristic, complemented
30	#542×C₆₇	—	2	1	no	—
31	#542×C₆₇	C₂²	1	2	yes	complemented
32	#541×C₆₇	—	2	1	no	—
33	#541×C₆₇	C₂²	1	2	yes	complemented
34	#539×C₆₇	—	2	2	no	—
35	#537×C₆₇	C₂²	1	1	yes	characteristic
36	#536×C₆₇	C₂²	1	1	yes	characteristic
37	#536×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#533×C₆₇	—	2	1	no	—
39	#533×C₆₇	C₂²	1	2	yes	complemented
40	#529×C₆₇	—	2	2	no	—
41	#529×C₆₇	—	2	1	no	—
42	#529×C₆₇	C₂²	1	2	yes	complemented
43	#520×C₆₇	—	2	1	no	—
44	#520×C₆₇	C₂²	1	1	yes	characteristic
45	#520×C₆₇	C₂²	1	2	yes	—
46	#520×C₆₇	C₂²	1	1	yes	characteristic
47	#518×C₆₇	—	2	2	no	—
48	#518×C₆₇	—	2	1	no	—
49	#518×C₆₇	C₂²	1	1	yes	characteristic
50	#518×C₆₇	C₂²	1	2	yes	—
51	C₄×#41×C₆₇	—	2	1	no	—
52	C₄×#41×C₆₇	C₂²	1	2	yes	—
53	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
54	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
55	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
57	C₂×C₄×D₄×C₆₇	—	2	2	no	—
58	C₂×C₄×D₄×C₆₇	—	2	1	no	—
59	C₂×C₄×D₄×C₆₇	C₂²	1	2	yes	—
60	C₂×C₄×D₄×C₆₇	C₂²	1	1	yes	characteristic
61	#485×C₆₇	C₂²	1	2	yes	complemented
62	#485×C₆₇	C₂²	1	2	yes	complemented
63	#485×C₆₇	C₂²	1	2	yes	complemented
64	#484×C₆₇	C₂²	1	2	yes	complemented
65	#484×C₆₇	C₂²	1	2	yes	complemented
66	#483×C₆₇	C₂²	1	2	yes	complemented
67	#482×C₆₇	C₂²	1	2	yes	complemented
68	#480×C₆₇	C₂²	1	2	yes	complemented
69	#479×C₆₇	C₂²	1	2	yes	complemented
70	#478×C₆₇	C₂²	1	2	yes	complemented
71	#478×C₆₇	C₂²	1	2	yes	complemented
72	#478×C₆₇	C₂²	1	2	yes	complemented
73	#477×C₆₇	C₂²	1	2	yes	complemented
74	#476×C₆₇	C₂²	1	2	yes	complemented
75	#474×C₆₇	C₂²	1	2	yes	complemented
76	#474×C₆₇	C₂²	1	2	yes	complemented
77	#464×C₆₇	C₂²	1	2	yes	complemented
78	#463×C₆₇	C₂²	1	2	yes	complemented
79	#463×C₆₇	C₂²	1	2	yes	complemented
80	#463×C₆₇	C₂²	1	2	yes	complemented
81	#462×C₆₇	C₂²	1	2	yes	complemented
82	#461×C₆₇	C₂²	1	2	yes	complemented
83	#461×C₆₇	C₂²	1	2	yes	complemented
84	#461×C₆₇	C₂²	1	2	yes	complemented
85	#452×C₆₇	C₂²	1	2	yes	—
86	#452×C₆₇	C₂²	1	2	yes	—
87	#452×C₆₇	C₂²	1	2	yes	—
88	#450×C₆₇	C₂²	1	2	yes	—
89	#450×C₆₇	C₂²	1	2	yes	—
90	#450×C₆₇	C₂²	1	2	yes	—
91	#449×C₆₇	C₂²	1	2	yes	—
92	#447×C₆₇	C₂²	1	2	yes	—
93	#442×C₆₇	C₂²	1	2	yes	complemented
94	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#442×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#441×C₆₇	C₂²	1	2	yes	complemented
97	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#441×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#440×C₆₇	C₂²	1	2	yes	complemented
101	#440×C₆₇	C₂²	1	2	yes	complemented
102	#440×C₆₇	C₂²	1	2	yes	complemented
103	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	#440×C₆₇	C₂²	1	2	yes	complemented
105	#440×C₆₇	C₂²	1	2	yes	complemented
106	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
107	#440×C₆₇	C₂²	1	2	yes	complemented
108	#440×C₆₇	C₂²	1	1	yes	characteristic, complemented
109	C₄×Q₁₆×C₆₇	C₂²	1	2	yes	complemented
110	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
111	C₄×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
112	C₄×D₈×C₆₇	C₂²	1	2	yes	complemented
113	#433×C₆₇	C₂²	1	2	yes	complemented
114	#433×C₆₇	C₂²	1	2	yes	complemented
115	#432×C₆₇	C₂²	1	2	yes	complemented
116	#432×C₆₇	C₂²	1	2	yes	complemented
117	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
118	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
119	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
120	C₂×#107×C₆₇	C₂²	1	1	yes	characteristic, complemented
121	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
122	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
123	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
124	#418×C₆₇	C₂²	1	1	yes	characteristic
125	#417×C₆₇	C₂²	1	1	yes	characteristic
126	#417×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	#416×C₆₇	C₂²	1	1	yes	characteristic
128	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
130	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
131	#408×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	C₄×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	H(5,𝔽₂)×C₆₇	—	2	4	no	—
136	H(5,𝔽₂)×C₆₇	—	2	4	no	—
137	C₂×#41×C₆₇	—	2	1	no	—
138	C₂×#41×C₆₇	C₂³	1	2	yes	—
139	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
140	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
141	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
142	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
143	C₂²×D₄×C₆₇	—	2	2	no	—
144	C₂²×D₄×C₆₇	—	2	1	no	—
145	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
146	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
147	C₂³×C₄×C₆₇	—	2	1	no	—
148	C₂³×C₄×C₆₇	—	2	2	no	—
149	#137×C₆₇	—	2	4	no	—
150	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
151	#135×C₆₇	—	2	4	no	—
152	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
153	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	—	2	4	no	—
155	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
156	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
157	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
158	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
161	C₂×D₈×C₆₇	C₂³	1	2	yes	—
162	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
163	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
164	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
165	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₆₇	—	2	1	no	—
168	C₄⋊Q₈×C₆₇	—	2	1	no	—
169	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
170	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
171	#126×C₆₇	—	2	2	no	—
172	#126×C₆₇	—	2	2	no	—
173	#126×C₆₇	—	2	2	no	—
174	#126×C₆₇	—	2	2	no	—
175	#125×C₆₇	—	2	2	no	—
176	#125×C₆₇	—	2	1	no	—
177	#125×C₆₇	—	2	2	no	—
178	#125×C₆₇	—	2	2	no	—
179	#125×C₆₇	C₂³	1	2	yes	—
180	#124×C₆₇	—	2	1	no	—
181	#124×C₆₇	—	2	2	no	—
182	#124×C₆₇	C₂³	1	2	yes	—
183	#123×C₆₇	—	2	2	no	—
184	#123×C₆₇	—	2	2	no	—
185	#123×C₆₇	—	2	2	no	—
186	#123×C₆₇	—	2	2	no	—
187	C₂²⋊Q₈×C₆₇	—	2	1	no	—
188	C₂²⋊Q₈×C₆₇	—	2	2	no	—
189	C₂²⋊Q₈×C₆₇	—	2	1	no	—
190	C₂²⋊Q₈×C₆₇	—	2	1	no	—
191	C₂²⋊Q₈×C₆₇	—	2	2	no	—
192	C₂²⋊Q₈×C₆₇	—	2	2	no	—
193	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
194	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	#121×C₆₇	—	2	2	no	—
197	#121×C₆₇	—	2	1	no	—
198	#121×C₆₇	C₂³	1	2	yes	—
199	C₄×Q₈×C₆₇	—	2	1	no	—
200	C₄×Q₈×C₆₇	—	2	1	no	—
201	C₄×Q₈×C₆₇	—	2	1	no	—
202	C₄×Q₈×C₆₇	—	2	2	no	—
203	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
204	C₄×Q₈×C₆₇	D₄	1	1	yes	characteristic
205	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
206	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
207	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
208	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
209	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
210	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
211	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
212	C₄×D₄×C₆₇	—	2	2	no	—
213	C₄×D₄×C₆₇	—	2	1	no	—
214	C₄×D₄×C₆₇	—	2	1	no	—
215	C₄×D₄×C₆₇	—	2	2	no	—
216	C₄×D₄×C₆₇	—	2	1	no	—
217	C₄×D₄×C₆₇	—	2	2	no	—
218	C₄×D₄×C₆₇	—	2	1	no	—
219	C₄×D₄×C₆₇	—	2	1	no	—
220	C₄×D₄×C₆₇	—	2	2	no	—
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	1	no	—
223	C₄×D₄×C₆₇	—	2	1	no	—
224	C₄×D₄×C₆₇	—	2	2	no	—
225	C₄×D₄×C₆₇	—	2	2	no	—
226	C₄×D₄×C₆₇	—	2	2	no	—
227	C₄×D₄×C₆₇	—	2	2	no	—
228	C₄×D₄×C₆₇	—	2	1	no	—
229	C₄×D₄×C₆₇	—	2	2	no	—
230	C₄×D₄×C₆₇	—	2	1	no	—
231	C₄×D₄×C₆₇	—	2	2	no	—
232	C₄×D₄×C₆₇	D₄	1	2	yes	—
233	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
234	C₄×D₄×C₆₇	D₄	1	1	yes	characteristic
235	C₄×D₄×C₆₇	D₄	1	2	yes	—
236	C₄×D₄×C₆₇	C₂³	1	2	yes	—
237	C₄×D₄×C₆₇	C₂³	1	2	yes	—
238	C₄×D₄×C₆₇	C₂³	1	2	yes	—
239	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	C₂³	1	2	yes	—
241	C₄×D₄×C₆₇	C₂³	1	2	yes	—
242	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
244	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
245	#117×C₆₇	—	2	2	no	—
246	#117×C₆₇	—	2	1	no	—
247	#117×C₆₇	—	2	2	no	—
248	#117×C₆₇	—	2	1	no	—
249	#117×C₆₇	—	2	2	no	—
250	#117×C₆₇	—	2	1	no	—
251	#117×C₆₇	—	2	2	no	—
252	#117×C₆₇	C₂³	1	2	yes	—
253	#117×C₆₇	C₂³	1	1	yes	characteristic
254	#117×C₆₇	C₂³	1	1	yes	characteristic
255	#117×C₆₇	C₂³	1	1	yes	characteristic
256	#117×C₆₇	C₂³	1	2	yes	—
257	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
258	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
259	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
260	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
261	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
262	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
263	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
264	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
265	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
266	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
267	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
268	C₂×C₄²×C₆₇	—	2	1	no	—
269	C₂×C₄²×C₆₇	—	2	1	no	—
270	C₂×C₄²×C₆₇	—	2	2	no	—
271	C₂×C₄²×C₆₇	—	2	1	no	—
272	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
273	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
274	#107×C₆₇	C₂³	1	1	yes	characteristic
275	#107×C₆₇	C₂³	1	2	yes	—
276	#107×C₆₇	C₂³	1	2	yes	—
277	#107×C₆₇	C₂³	1	2	yes	—
278	#107×C₆₇	C₂³	1	2	yes	—
279	#107×C₆₇	C₂³	1	1	yes	characteristic
280	#106×C₆₇	C₂³	1	1	yes	characteristic
281	#106×C₆₇	C₂³	1	2	yes	—
282	#106×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	2	yes	—
284	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
285	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
286	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	#103×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	1	yes	characteristic
290	#103×C₆₇	C₂³	1	1	yes	characteristic
291	#103×C₆₇	C₂³	1	1	yes	characteristic
292	#103×C₆₇	C₂³	1	1	yes	characteristic
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	2	yes	—
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	2	yes	—
298	#102×C₆₇	C₂³	1	2	yes	—
299	#102×C₆₇	C₂³	1	1	yes	characteristic
300	#102×C₆₇	C₂³	1	1	yes	characteristic
301	#102×C₆₇	C₂³	1	2	yes	—
302	#102×C₆₇	C₂³	1	2	yes	—
303	#102×C₆₇	C₂³	1	2	yes	—
304	#102×C₆₇	C₂³	1	2	yes	—
305	#102×C₆₇	C₂³	1	1	yes	characteristic
306	#102×C₆₇	C₂³	1	1	yes	characteristic
307	#102×C₆₇	C₂³	1	2	yes	—
308	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
309	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
310	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
311	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
312	#97×C₆₇	C₂³	1	1	yes	characteristic
313	#97×C₆₇	C₂³	1	1	yes	characteristic
314	#97×C₆₇	C₂³	1	1	yes	characteristic
315	#97×C₆₇	C₂³	1	1	yes	characteristic
316	#97×C₆₇	C₂³	1	2	yes	—
317	C₄×C₈×C₆₇	C₂³	1	2	yes	—
318	C₂⁴×C₆₇	—	2	2	no	—
319	C₂⁴×C₆₇	—	2	1	no	—
320	#41×C₆₇	—	2	8	no	—
321	#41×C₆₇	—	2	4	no	—
322	#41×C₆₇	—	2	4	no	—
323	#41×C₆₇	—	2	2	no	—
324	#41×C₆₇	—	2	2	no	—
325	#41×C₆₇	—	2	2	no	—
326	#41×C₆₇	—	2	2	no	—
327	#41×C₆₇	—	2	2	no	—
328	#41×C₆₇	#41	1	4	yes	—
329	C₂×Q₈×C₆₇	—	2	1	no	—
330	C₂×Q₈×C₆₇	—	2	2	no	—
331	C₂×Q₈×C₆₇	—	2	2	no	—
332	C₂×Q₈×C₆₇	—	2	2	no	—
333	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
334	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
335	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
336	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
337	C₂×D₄×C₆₇	—	2	16	no	—
338	C₂×D₄×C₆₇	—	2	8	no	—
339	C₂×D₄×C₆₇	—	2	2	no	—
340	C₂×D₄×C₆₇	—	2	1	no	—
341	C₂×D₄×C₆₇	—	2	4	no	—
342	C₂×D₄×C₆₇	—	2	4	no	—
343	C₂×D₄×C₆₇	—	2	1	no	—
344	C₂×D₄×C₆₇	—	2	2	no	—
345	C₂×D₄×C₆₇	—	2	2	no	—
346	C₂×D₄×C₆₇	—	2	1	no	—
347	C₂×D₄×C₆₇	—	2	2	no	—
348	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
349	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
350	C₂×D₄×C₆₇	#41	1	4	yes	—
351	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
352	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
353	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
354	C₂²×C₄×C₆₇	—	2	2	no	—
355	C₂²×C₄×C₆₇	—	2	1	no	—
356	C₂²×C₄×C₆₇	—	2	1	no	—
357	C₂²×C₄×C₆₇	—	2	1	no	—
358	C₂²×C₄×C₆₇	—	2	2	no	—
359	C₂²×C₄×C₆₇	—	2	1	no	—
360	C₂²×C₄×C₆₇	—	2	1	no	—
361	C₂²×C₄×C₆₇	—	2	1	no	—
362	C₂²×C₄×C₆₇	—	2	1	no	—
363	C₂²×C₄×C₆₇	—	2	2	no	—
364	C₂²×C₄×C₆₇	—	2	1	no	—
365	C₂²×C₄×C₆₇	—	2	2	no	—
366	C₂²×C₄×C₆₇	—	2	1	no	—
367	C₂²×C₄×C₆₇	—	2	2	no	—
368	C₂²×C₄×C₆₇	—	2	2	no	—
369	C₂²×C₄×C₆₇	—	2	2	no	—
370	C₂²×C₄×C₆₇	—	8	2	no	—
371	C₂²×C₄×C₆₇	—	8	4	no	—
372	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
373	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
374	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
376	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
378	Q₁₆×C₆₇	—	2	2	no	—
379	Q₁₆×C₆₇	—	2	4	no	—
380	SD₁₆×C₆₇	—	2	2	no	—
381	SD₁₆×C₆₇	—	2	4	no	—
382	SD₁₆×C₆₇	—	2	4	no	—
383	SD₁₆×C₆₇	—	2	2	no	—
384	SD₁₆×C₆₇	—	2	4	no	—
385	SD₁₆×C₆₇	—	2	4	no	—
386	D₈×C₆₇	—	2	2	no	—
387	D₈×C₆₇	—	2	4	no	—
388	M₁₆×C₆₇	—	2	2	no	—
389	M₁₆×C₆₇	—	2	2	no	—
390	C₂×C₈×C₆₇	—	2	2	no	—
391	C₂×C₈×C₆₇	—	2	2	no	—
392	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
393	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
398	C₄⋊C₄×C₆₇	—	2	1	no	—
399	C₄⋊C₄×C₆₇	—	2	2	no	—
400	C₄⋊C₄×C₆₇	—	2	2	no	—
401	C₄⋊C₄×C₆₇	—	2	1	no	—
402	C₄⋊C₄×C₆₇	—	2	2	no	—
403	C₄⋊C₄×C₆₇	—	2	2	no	—
404	C₄⋊C₄×C₆₇	—	2	1	no	—
405	C₄⋊C₄×C₆₇	—	2	1	no	—
406	C₄⋊C₄×C₆₇	—	2	1	no	—
407	C₄⋊C₄×C₆₇	—	2	1	no	—
408	C₄⋊C₄×C₆₇	—	2	2	no	—
409	C₄⋊C₄×C₆₇	—	2	2	no	—
410	C₄⋊C₄×C₆₇	—	2	2	no	—
411	C₄⋊C₄×C₆₇	—	2	2	no	—
412	C₄⋊C₄×C₆₇	—	2	2	no	—
413	C₄⋊C₄×C₆₇	—	2	2	no	—
414	C₄⋊C₄×C₆₇	—	2	2	no	—
415	C₄⋊C₄×C₆₇	—	2	2	no	—
416	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
417	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
418	C₄⋊C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
419	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
420	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
422	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
423	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
424	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
425	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
426	C₂²⋊C₄×C₆₇	—	2	2	no	—
427	C₂²⋊C₄×C₆₇	—	2	1	no	—
428	C₂²⋊C₄×C₆₇	—	2	2	no	—
429	C₂²⋊C₄×C₆₇	—	2	2	no	—
430	C₂²⋊C₄×C₆₇	—	2	1	no	—
431	C₂²⋊C₄×C₆₇	—	2	2	no	—
432	C₂²⋊C₄×C₆₇	—	2	1	no	—
433	C₂²⋊C₄×C₆₇	—	2	2	no	—
434	C₂²⋊C₄×C₆₇	—	2	2	no	—
435	C₂²⋊C₄×C₆₇	—	2	1	no	—
436	C₂²⋊C₄×C₆₇	—	2	2	no	—
437	C₂²⋊C₄×C₆₇	—	2	2	no	—
438	C₂²⋊C₄×C₆₇	—	2	2	no	—
439	C₂²⋊C₄×C₆₇	—	2	1	no	—
440	C₂²⋊C₄×C₆₇	—	2	1	no	—
441	C₂²⋊C₄×C₆₇	—	2	2	no	—
442	C₂²⋊C₄×C₆₇	—	2	2	no	—
443	C₂²⋊C₄×C₆₇	—	2	2	no	—
444	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
445	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
446	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
447	C₄²×C₆₇	—	2	1	no	—
448	C₄²×C₆₇	—	2	1	no	—
449	C₄²×C₆₇	—	2	2	no	—
450	C₄²×C₆₇	—	2	2	no	—
451	C₄²×C₆₇	—	2	1	no	—
452	C₄²×C₆₇	—	2	2	no	—
453	C₄²×C₆₇	—	2	1	no	—
454	C₄²×C₆₇	—	2	1	no	—
455	C₄²×C₆₇	—	2	1	no	—
456	C₄²×C₆₇	—	2	2	no	—
457	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
458	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
459	C₄²×C₆₇	C₂×D₄	1	2	yes	—
460	C₄²×C₆₇	C₂×D₄	1	2	yes	—
461	C₄²×C₆₇	C₂⁴	1	2	yes	—
462	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
463	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
464	C₂³×C₆₇	—	2	8	no	—
465	C₂³×C₆₇	—	2	2	no	—
466	C₂³×C₆₇	—	2	1	no	—
467	C₂³×C₆₇	—	2	4	no	—
468	C₂³×C₆₇	—	2	1	no	—
469	C₂³×C₆₇	—	8	1	no	—
470	C₂³×C₆₇	—	8	2	no	—
471	C₂³×C₆₇	—	8	1	no	—
472	C₂³×C₆₇	—	8	2	no	—
473	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
474	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
475	Q₈×C₆₇	—	2	2	no	—
476	Q₈×C₆₇	—	2	1	no	—
477	Q₈×C₆₇	—	2	2	no	—
478	Q₈×C₆₇	—	2	1	no	—
479	Q₈×C₆₇	—	2	2	no	—
480	Q₈×C₆₇	—	2	1	no	—
481	Q₈×C₆₇	—	4	2	no	—
482	Q₈×C₆₇	—	8	2	no	—
483	Q₈×C₆₇	C₂×#41	1	2	yes	—
484	D₄×C₆₇	—	2	8	no	—
485	D₄×C₆₇	—	2	8	no	—
486	D₄×C₆₇	—	2	4	no	—
487	D₄×C₆₇	—	2	4	no	—
488	D₄×C₆₇	—	2	2	no	—
489	D₄×C₆₇	—	2	4	no	—
490	D₄×C₆₇	—	2	2	no	—
491	D₄×C₆₇	—	2	1	no	—
492	D₄×C₆₇	—	2	1	no	—
493	D₄×C₆₇	—	2	1	no	—
494	D₄×C₆₇	—	4	2	no	—
495	D₄×C₆₇	—	8	2	no	—
496	D₄×C₆₇	C₂×#41	1	2	yes	—
497	D₄×C₆₇	C₂×#41	1	4	yes	—
498	C₂×C₄×C₆₇	—	2	8	no	—
499	C₂×C₄×C₆₇	—	2	1	no	—
500	C₂×C₄×C₆₇	—	2	4	no	—
501	C₂×C₄×C₆₇	—	2	2	no	—
502	C₂×C₄×C₆₇	—	2	2	no	—
503	C₂×C₄×C₆₇	—	2	1	no	—
504	C₂×C₄×C₆₇	—	2	1	no	—
505	C₂×C₄×C₆₇	—	2	2	no	—
506	C₂×C₄×C₆₇	—	2	1	no	—
507	C₂×C₄×C₆₇	—	2	1	no	—
508	C₂×C₄×C₆₇	—	2	2	no	—
509	C₂×C₄×C₆₇	—	2	1	no	—
510	C₂×C₄×C₆₇	—	2	2	no	—
511	C₂×C₄×C₆₇	—	4	1	no	—
512	C₂×C₄×C₆₇	—	4	2	no	—
513	C₂×C₄×C₆₇	—	4	1	no	—
514	C₂×C₄×C₆₇	—	4	2	no	—
515	C₂×C₄×C₆₇	—	4	2	no	—
516	C₂×C₄×C₆₇	—	4	4	no	—
517	C₂×C₄×C₆₇	—	4	2	no	—
518	C₂×C₄×C₆₇	—	4	2	no	—
519	C₂×C₄×C₆₇	—	4	2	no	—
520	C₂×C₄×C₆₇	—	8	1	no	—
521	C₂×C₄×C₆₇	—	8	1	no	—
522	C₂×C₄×C₆₇	—	8	2	no	—
523	C₂×C₄×C₆₇	—	8	2	no	—
524	C₂×C₄×C₆₇	—	8	2	no	—
525	C₂×C₄×C₆₇	—	8	2	no	—
526	C₂×C₄×C₆₇	—	8	1	no	—
527	C₂×C₄×C₆₇	—	8	1	no	—
528	C₂×C₄×C₆₇	—	8	2	no	—
529	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
530	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
531	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
532	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
533	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
534	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
535	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
536	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
537	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
538	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
539	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
540	C₈×C₆₇	—	2	1	no	—
541	C₈×C₆₇	—	2	1	no	—
542	C₈×C₆₇	—	2	1	no	—
543	C₈×C₆₇	—	2	1	no	—
544	C₈×C₆₇	—	2	2	no	—
545	C₈×C₆₇	—	2	2	no	—
546	C₂²×C₆₇	—	2	1	no	—
547	C₂²×C₆₇	—	2	1	no	—
548	C₂²×C₆₇	—	2	2	no	—
549	C₂²×C₆₇	—	2	2	no	—
550	C₂²×C₆₇	—	2	2	no	—
551	C₂²×C₆₇	—	2	4	no	—
552	C₂²×C₆₇	—	2	2	no	—
553	C₂²×C₆₇	—	4	2	no	—
554	C₂²×C₆₇	—	4	1	no	—
555	C₂²×C₆₇	—	4	2	no	—
556	C₂²×C₆₇	—	4	1	no	—
557	C₂²×C₆₇	—	4	1	no	—
558	C₂²×C₆₇	—	4	1	no	—
559	C₂²×C₆₇	—	4	1	no	—
560	C₂²×C₆₇	—	8	4	no	—
561	C₂²×C₆₇	—	8	8	no	—
562	C₂²×C₆₇	#525	1	2	yes	—
563	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
564	C₄×C₆₇	—	2	1	no	—
565	C₄×C₆₇	—	2	1	no	—
566	C₄×C₆₇	—	2	2	no	—
567	C₄×C₆₇	—	2	1	no	—
568	C₄×C₆₇	—	2	1	no	—
569	C₄×C₆₇	—	2	2	no	—
570	C₄×C₆₇	—	2	2	no	—
571	C₄×C₆₇	—	2	2	no	—
572	C₄×C₆₇	—	4	2	no	—
573	C₄×C₆₇	—	4	1	no	—
574	C₄×C₆₇	—	4	2	no	—
575	C₄×C₆₇	—	4	1	no	—
576	C₄×C₆₇	—	4	1	no	—
577	C₄×C₆₇	—	4	1	no	—
578	C₄×C₆₇	—	4	1	no	—
579	C₄×C₆₇	—	4	2	no	—
580	C₄×C₆₇	#525	1	2	yes	—
581	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
582	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
583	#60575	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
584	C₂×C₆₇	—	2	2	no	—
585	C₂×C₆₇	—	4	2	no	—
586	C₂×C₆₇	—	4	4	no	—
587	C₂×C₆₇	—	4	2	no	—
588	C₂×C₆₇	—	8	1	no	—
589	C₂×C₆₇	C₂×#525	1	1	yes	characteristic
590	C₂×C₆₇	#3585	1	1	yes	characteristic
591	C₂×C₆₇	#3586	1	1	yes	characteristic
592	#3461	C₂×C₆₇	1	1	yes	characteristic, complemented
593	C₄×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
594	#3124	C₂×C₆₇	1	2	yes	complemented
595	#3123	C₂×C₆₇	1	2	yes	complemented
596	#3120	C₂×C₆₇	1	2	yes	complemented
597	#3118	C₂×C₆₇	1	2	yes	complemented
598	#3116	C₂×C₆₇	1	2	yes	complemented
599	#3114	C₂×C₆₇	1	2	yes	complemented
600	#3111	C₂×C₆₇	1	2	yes	complemented
601	#3110	C₂×C₆₇	1	2	yes	complemented
602	#3098	C₂×C₆₇	1	1	yes	characteristic, complemented
603	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
604	#3083	C₂×C₆₇	1	1	yes	characteristic, complemented
605	#3081	C₂×C₆₇	1	1	yes	characteristic, complemented
606	#3046	C₂×C₆₇	1	1	yes	characteristic, complemented
607	#3042	C₂×C₆₇	1	1	yes	characteristic, complemented
608	#3012	C₂×C₆₇	1	1	yes	characteristic
609	#3009	C₂×C₆₇	1	1	yes	characteristic, complemented
610	C₄×#137	C₂×C₆₇	1	1	yes	characteristic, complemented
611	C₄×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
612	#2943	C₂×C₆₇	1	1	yes	characteristic, complemented
613	C₂×#440	C₂×C₆₇	1	1	yes	characteristic, complemented
614	#2923	C₂×C₆₇	1	1	yes	characteristic, complemented
615	C₆₇	#60575	1	1	yes	characteristic, direct product factor, Sylow
616	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
617	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic
618	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
619	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
620	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
621	#544	C₂²×C₆₇	1	1	yes	characteristic, complemented
622	#542	—	2	1	no	—
623	#542	C₂²×C₆₇	1	2	yes	complemented
624	#541	—	2	1	no	—
625	#541	C₂²×C₆₇	1	2	yes	complemented
626	#539	—	2	2	no	—
627	#537	C₂²×C₆₇	1	1	yes	characteristic
628	#536	C₂²×C₆₇	1	1	yes	characteristic
629	#536	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#533	—	2	1	no	—
631	#533	C₂²×C₆₇	1	2	yes	complemented
632	#529	—	2	2	no	—
633	#529	—	2	1	no	—
634	#529	C₂²×C₆₇	1	2	yes	complemented
635	#520	—	2	1	no	—
636	#520	C₂²×C₆₇	1	1	yes	characteristic
637	#520	C₂²×C₆₇	1	2	yes	—
638	#520	C₂²×C₆₇	1	1	yes	characteristic
639	#518	—	2	2	no	—
640	#518	—	2	1	no	—
641	#518	C₂²×C₆₇	1	1	yes	characteristic
642	#518	C₂²×C₆₇	1	2	yes	—
643	C₄×#41	—	2	1	no	—
644	C₄×#41	C₂²×C₆₇	1	2	yes	—
645	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
646	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
647	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
648	C₂×C₄×Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
649	C₂×C₄×D₄	—	2	2	no	—
650	C₂×C₄×D₄	—	2	1	no	—
651	C₂×C₄×D₄	C₂²×C₆₇	1	2	yes	—
652	C₂×C₄×D₄	C₂²×C₆₇	1	1	yes	characteristic
653	#485	C₂²×C₆₇	1	2	yes	complemented
654	#485	C₂²×C₆₇	1	2	yes	complemented
655	#485	C₂²×C₆₇	1	2	yes	complemented
656	#484	C₂²×C₆₇	1	2	yes	complemented
657	#484	C₂²×C₆₇	1	2	yes	complemented
658	#483	C₂²×C₆₇	1	2	yes	complemented
659	#482	C₂²×C₆₇	1	2	yes	complemented
660	#480	C₂²×C₆₇	1	2	yes	complemented
661	#479	C₂²×C₆₇	1	2	yes	complemented
662	#478	C₂²×C₆₇	1	2	yes	complemented
663	#478	C₂²×C₆₇	1	2	yes	complemented
664	#478	C₂²×C₆₇	1	2	yes	complemented
665	#477	C₂²×C₆₇	1	2	yes	complemented
666	#476	C₂²×C₆₇	1	2	yes	complemented
667	#474	C₂²×C₆₇	1	2	yes	complemented
668	#474	C₂²×C₆₇	1	2	yes	complemented
669	#464	C₂²×C₆₇	1	2	yes	complemented
670	#463	C₂²×C₆₇	1	2	yes	complemented
671	#463	C₂²×C₆₇	1	2	yes	complemented
672	#463	C₂²×C₆₇	1	2	yes	complemented
673	#462	C₂²×C₆₇	1	2	yes	complemented
674	#461	C₂²×C₆₇	1	2	yes	complemented
675	#461	C₂²×C₆₇	1	2	yes	complemented
676	#461	C₂²×C₆₇	1	2	yes	complemented
677	#452	C₂²×C₆₇	1	2	yes	—
678	#452	C₂²×C₆₇	1	2	yes	—
679	#452	C₂²×C₆₇	1	2	yes	—
680	#450	C₂²×C₆₇	1	2	yes	—
681	#450	C₂²×C₆₇	1	2	yes	—
682	#450	C₂²×C₆₇	1	2	yes	—
683	#449	C₂²×C₆₇	1	2	yes	—
684	#447	C₂²×C₆₇	1	2	yes	—
685	#442	C₂²×C₆₇	1	2	yes	complemented
686	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
687	#442	C₂²×C₆₇	1	1	yes	characteristic, complemented
688	#441	C₂²×C₆₇	1	2	yes	complemented
689	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
690	#441	C₂²×C₆₇	1	1	yes	characteristic, complemented
691	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
692	#440	C₂²×C₆₇	1	2	yes	complemented
693	#440	C₂²×C₆₇	1	2	yes	complemented
694	#440	C₂²×C₆₇	1	2	yes	complemented
695	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
696	#440	C₂²×C₆₇	1	2	yes	complemented
697	#440	C₂²×C₆₇	1	2	yes	complemented
698	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
699	#440	C₂²×C₆₇	1	2	yes	complemented
700	#440	C₂²×C₆₇	1	1	yes	characteristic, complemented
701	C₄×Q₁₆	C₂²×C₆₇	1	2	yes	complemented
702	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
703	C₄×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
704	C₄×D₈	C₂²×C₆₇	1	2	yes	complemented
705	#433	C₂²×C₆₇	1	2	yes	complemented
706	#433	C₂²×C₆₇	1	2	yes	complemented
707	#432	C₂²×C₆₇	1	2	yes	complemented
708	#432	C₂²×C₆₇	1	2	yes	complemented
709	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
710	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
711	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
712	C₂×#107	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	#418	C₂²×C₆₇	1	1	yes	characteristic
717	#417	C₂²×C₆₇	1	1	yes	characteristic
718	#417	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	#416	C₂²×C₆₇	1	1	yes	characteristic
720	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
721	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
722	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
723	#408	C₂²×C₆₇	1	1	yes	characteristic
724	#408	C₂²×C₆₇	1	1	yes	characteristic
725	C₄×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	C₂×#97	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	H(5,𝔽₂)	—	2	4	no	—
728	H(5,𝔽₂)	—	2	4	no	—
729	C₂×#41	—	2	1	no	—
730	C₂×#41	C₂³×C₆₇	1	2	yes	—
731	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
732	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
733	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
734	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
735	C₂²×D₄	—	2	2	no	—
736	C₂²×D₄	—	2	1	no	—
737	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
738	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
739	C₂³×C₄	—	2	1	no	—
740	C₂³×C₄	—	2	2	no	—
741	#137	—	2	4	no	—
742	AGL(1,ℤ/8)	—	2	4	no	—
743	#135	—	2	4	no	—
744	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
745	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
746	C₂×SD₁₆	—	2	4	no	—
747	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
748	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
749	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
750	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
751	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
752	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
753	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
754	C₂×D₈	C₂³×C₆₇	1	2	yes	—
755	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
756	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
757	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
758	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
759	C₄⋊Q₈	—	2	1	no	—
760	C₄⋊Q₈	—	2	1	no	—
761	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
762	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#126	—	2	2	no	—
766	#126	—	2	2	no	—
767	#125	—	2	2	no	—
768	#125	—	2	1	no	—
769	#125	—	2	2	no	—
770	#125	—	2	2	no	—
771	#125	C₂³×C₆₇	1	2	yes	—
772	#124	—	2	1	no	—
773	#124	—	2	2	no	—
774	#124	C₂³×C₆₇	1	2	yes	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	C₂²⋊Q₈	—	2	1	no	—
780	C₂²⋊Q₈	—	2	2	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	1	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	—	2	2	no	—
785	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
786	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
787	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
788	#121	—	2	2	no	—
789	#121	—	2	1	no	—
790	#121	C₂³×C₆₇	1	2	yes	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	2	1	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
796	C₄×Q₈	D₄×C₆₇	1	1	yes	characteristic
797	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
798	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
799	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
800	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
801	C₄×Q₈	C₂³×C₆₇	1	2	yes	—
802	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
803	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	2	no	—
808	C₄×D₄	—	2	1	no	—
809	C₄×D₄	—	2	2	no	—
810	C₄×D₄	—	2	1	no	—
811	C₄×D₄	—	2	1	no	—
812	C₄×D₄	—	2	2	no	—
813	C₄×D₄	—	2	2	no	—
814	C₄×D₄	—	2	1	no	—
815	C₄×D₄	—	2	1	no	—
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	2	no	—
822	C₄×D₄	—	2	1	no	—
823	C₄×D₄	—	2	2	no	—
824	C₄×D₄	D₄×C₆₇	1	2	yes	—
825	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
826	C₄×D₄	D₄×C₆₇	1	1	yes	characteristic
827	C₄×D₄	D₄×C₆₇	1	2	yes	—
828	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
829	C₄×D₄	C₂³×C₆₇	1	2	yes	—
830	C₄×D₄	C₂³×C₆₇	1	2	yes	—
831	C₄×D₄	C₂³×C₆₇	1	2	yes	—
832	C₄×D₄	C₂³×C₆₇	1	2	yes	—
833	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
834	C₄×D₄	C₂³×C₆₇	1	2	yes	—
835	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
836	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
837	#117	—	2	2	no	—
838	#117	—	2	1	no	—
839	#117	—	2	2	no	—
840	#117	—	2	1	no	—
841	#117	—	2	2	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	C₂³×C₆₇	1	1	yes	characteristic
845	#117	C₂³×C₆₇	1	2	yes	—
846	#117	C₂³×C₆₇	1	1	yes	characteristic
847	#117	C₂³×C₆₇	1	1	yes	characteristic
848	#117	C₂³×C₆₇	1	2	yes	—
849	C₂×C₄⋊C₄	—	2	1	no	—
850	C₂×C₄⋊C₄	—	2	2	no	—
851	C₂×C₄⋊C₄	—	2	1	no	—
852	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
853	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
854	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	2	2	no	—
858	C₂×C₂²⋊C₄	—	2	2	no	—
859	C₂×C₂²⋊C₄	—	2	2	no	—
860	C₂×C₄²	—	2	1	no	—
861	C₂×C₄²	—	2	1	no	—
862	C₂×C₄²	—	2	2	no	—
863	C₂×C₄²	—	2	1	no	—
864	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
865	C₂×C₄²	C₂³×C₆₇	1	2	yes	—
866	#107	C₂³×C₆₇	1	2	yes	—
867	#107	C₂³×C₆₇	1	2	yes	—
868	#107	C₂³×C₆₇	1	1	yes	characteristic
869	#107	C₂³×C₆₇	1	1	yes	characteristic
870	#107	C₂³×C₆₇	1	2	yes	—
871	#107	C₂³×C₆₇	1	2	yes	—
872	#106	C₂³×C₆₇	1	1	yes	characteristic
873	#106	C₂³×C₆₇	1	1	yes	characteristic
874	#106	C₂³×C₆₇	1	2	yes	—
875	#106	C₂³×C₆₇	1	2	yes	—
876	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
877	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
878	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
879	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
880	#103	C₂³×C₆₇	1	2	yes	—
881	#103	C₂³×C₆₇	1	2	yes	—
882	#103	C₂³×C₆₇	1	1	yes	characteristic
883	#103	C₂³×C₆₇	1	1	yes	characteristic
884	#103	C₂³×C₆₇	1	1	yes	characteristic
885	#103	C₂³×C₆₇	1	1	yes	characteristic
886	#103	C₂³×C₆₇	1	2	yes	—
887	#103	C₂³×C₆₇	1	2	yes	—
888	#103	C₂³×C₆₇	1	2	yes	—
889	#103	C₂³×C₆₇	1	2	yes	—
890	#102	C₂³×C₆₇	1	2	yes	—
891	#102	C₂³×C₆₇	1	2	yes	—
892	#102	C₂³×C₆₇	1	1	yes	characteristic
893	#102	C₂³×C₆₇	1	1	yes	characteristic
894	#102	C₂³×C₆₇	1	1	yes	characteristic
895	#102	C₂³×C₆₇	1	1	yes	characteristic
896	#102	C₂³×C₆₇	1	2	yes	—
897	#102	C₂³×C₆₇	1	2	yes	—
898	#102	C₂³×C₆₇	1	2	yes	—
899	#102	C₂³×C₆₇	1	2	yes	—
900	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
901	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
902	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
903	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
904	#97	C₂³×C₆₇	1	1	yes	characteristic
905	#97	C₂³×C₆₇	1	1	yes	characteristic
906	#97	C₂³×C₆₇	1	1	yes	characteristic
907	#97	C₂³×C₆₇	1	1	yes	characteristic
908	#97	C₂³×C₆₇	1	2	yes	—
909	C₄×C₈	C₂³×C₆₇	1	2	yes	—
910	C₂⁴	—	2	2	no	—
911	C₂⁴	—	2	1	no	—
912	#41	—	2	8	no	—
913	#41	—	2	4	no	—
914	#41	—	2	4	no	—
915	#41	—	2	2	no	—
916	#41	—	2	2	no	—
917	#41	—	2	2	no	—
918	#41	—	2	2	no	—
919	#41	—	2	2	no	—
920	#41	#41×C₆₇	1	4	yes	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	2	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
926	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
927	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
928	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
929	C₂×D₄	—	2	16	no	—
930	C₂×D₄	—	2	8	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	1	no	—
933	C₂×D₄	—	2	4	no	—
934	C₂×D₄	—	2	4	no	—
935	C₂×D₄	—	2	1	no	—
936	C₂×D₄	—	2	2	no	—
937	C₂×D₄	—	2	2	no	—
938	C₂×D₄	—	2	1	no	—
939	C₂×D₄	—	2	2	no	—
940	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
941	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
942	C₂×D₄	#41×C₆₇	1	4	yes	—
943	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
944	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
945	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
946	C₂²×C₄	—	2	2	no	—
947	C₂²×C₄	—	2	1	no	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	1	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	2	1	no	—
952	C₂²×C₄	—	2	1	no	—
953	C₂²×C₄	—	2	1	no	—
954	C₂²×C₄	—	2	1	no	—
955	C₂²×C₄	—	2	2	no	—
956	C₂²×C₄	—	2	1	no	—
957	C₂²×C₄	—	2	2	no	—
958	C₂²×C₄	—	2	1	no	—
959	C₂²×C₄	—	2	2	no	—
960	C₂²×C₄	—	2	2	no	—
961	C₂²×C₄	—	2	2	no	—
962	C₂²×C₄	—	8	2	no	—
963	C₂²×C₄	—	8	4	no	—
964	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
965	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
966	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
967	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
968	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
969	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
970	Q₁₆	—	2	2	no	—
971	Q₁₆	—	2	4	no	—
972	SD₁₆	—	2	2	no	—
973	SD₁₆	—	2	4	no	—
974	SD₁₆	—	2	4	no	—
975	SD₁₆	—	2	2	no	—
976	SD₁₆	—	2	4	no	—
977	SD₁₆	—	2	4	no	—
978	D₈	—	2	2	no	—
979	D₈	—	2	4	no	—
980	M₁₆	—	2	2	no	—
981	M₁₆	—	2	2	no	—
982	C₂×C₈	—	2	2	no	—
983	C₂×C₈	—	2	2	no	—
984	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
985	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
986	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
987	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
990	C₄⋊C₄	—	2	1	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	1	no	—
994	C₄⋊C₄	—	2	2	no	—
995	C₄⋊C₄	—	2	2	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	2	1	no	—
999	C₄⋊C₄	—	2	1	no	—
1000	C₄⋊C₄	—	2	2	no	—
1001	C₄⋊C₄	—	2	2	no	—
1002	C₄⋊C₄	—	2	2	no	—
1003	C₄⋊C₄	—	2	2	no	—
1004	C₄⋊C₄	—	2	2	no	—
1005	C₄⋊C₄	—	2	2	no	—
1006	C₄⋊C₄	—	2	2	no	—
1007	C₄⋊C₄	—	2	2	no	—
1008	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1009	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1010	C₄⋊C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1011	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1012	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1013	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1014	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1015	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1016	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1017	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	1	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	1	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	1	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	2	2	no	—
1027	C₂²⋊C₄	—	2	1	no	—
1028	C₂²⋊C₄	—	2	2	no	—
1029	C₂²⋊C₄	—	2	2	no	—
1030	C₂²⋊C₄	—	2	2	no	—
1031	C₂²⋊C₄	—	2	1	no	—
1032	C₂²⋊C₄	—	2	1	no	—
1033	C₂²⋊C₄	—	2	2	no	—
1034	C₂²⋊C₄	—	2	2	no	—
1035	C₂²⋊C₄	—	2	2	no	—
1036	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1037	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1038	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1039	C₄²	—	2	1	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	2	no	—
1042	C₄²	—	2	2	no	—
1043	C₄²	—	2	1	no	—
1044	C₄²	—	2	2	no	—
1045	C₄²	—	2	1	no	—
1046	C₄²	—	2	1	no	—
1047	C₄²	—	2	1	no	—
1048	C₄²	—	2	2	no	—
1049	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1050	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1051	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1052	C₄²	C₂×D₄×C₆₇	1	2	yes	—
1053	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1055	C₄²	C₂⁴×C₆₇	1	2	yes	—
1056	C₂³	—	2	8	no	—
1057	C₂³	—	2	2	no	—
1058	C₂³	—	2	1	no	—
1059	C₂³	—	2	4	no	—
1060	C₂³	—	2	1	no	—
1061	C₂³	—	8	1	no	—
1062	C₂³	—	8	2	no	—
1063	C₂³	—	8	1	no	—
1064	C₂³	—	8	2	no	—
1065	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1066	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1067	Q₈	—	2	2	no	—
1068	Q₈	—	2	1	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	1	no	—
1071	Q₈	—	2	2	no	—
1072	Q₈	—	2	1	no	—
1073	Q₈	—	4	2	no	—
1074	Q₈	—	8	2	no	—
1075	Q₈	C₂×#41×C₆₇	1	2	yes	—
1076	D₄	—	2	8	no	—
1077	D₄	—	2	8	no	—
1078	D₄	—	2	4	no	—
1079	D₄	—	2	4	no	—
1080	D₄	—	2	2	no	—
1081	D₄	—	2	4	no	—
1082	D₄	—	2	2	no	—
1083	D₄	—	2	1	no	—
1084	D₄	—	2	1	no	—
1085	D₄	—	2	1	no	—
1086	D₄	—	4	2	no	—
1087	D₄	—	8	2	no	—
1088	D₄	C₂×#41×C₆₇	1	2	yes	—
1089	D₄	C₂×#41×C₆₇	1	4	yes	—
1090	C₂×C₄	—	2	8	no	—
1091	C₂×C₄	—	2	1	no	—
1092	C₂×C₄	—	2	4	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	2	no	—
1098	C₂×C₄	—	2	1	no	—
1099	C₂×C₄	—	2	1	no	—
1100	C₂×C₄	—	2	2	no	—
1101	C₂×C₄	—	2	1	no	—
1102	C₂×C₄	—	2	2	no	—
1103	C₂×C₄	—	4	1	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	4	1	no	—
1106	C₂×C₄	—	4	2	no	—
1107	C₂×C₄	—	4	4	no	—
1108	C₂×C₄	—	4	2	no	—
1109	C₂×C₄	—	4	2	no	—
1110	C₂×C₄	—	4	2	no	—
1111	C₂×C₄	—	4	2	no	—
1112	C₂×C₄	—	8	2	no	—
1113	C₂×C₄	—	8	2	no	—
1114	C₂×C₄	—	8	2	no	—
1115	C₂×C₄	—	8	1	no	—
1116	C₂×C₄	—	8	1	no	—
1117	C₂×C₄	—	8	2	no	—
1118	C₂×C₄	—	8	1	no	—
1119	C₂×C₄	—	8	2	no	—
1120	C₂×C₄	—	8	1	no	—
1121	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1122	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1123	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1124	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1125	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1126	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1127	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1128	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1129	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1130	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1131	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1132	C₈	—	2	1	no	—
1133	C₈	—	2	1	no	—
1134	C₈	—	2	1	no	—
1135	C₈	—	2	1	no	—
1136	C₈	—	2	2	no	—
1137	C₈	—	2	2	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	1	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	2	2	no	—
1143	C₂²	—	2	4	no	—
1144	C₂²	—	2	2	no	—
1145	C₂²	—	4	2	no	—
1146	C₂²	—	4	1	no	—
1147	C₂²	—	4	2	no	—
1148	C₂²	—	4	1	no	—
1149	C₂²	—	4	1	no	—
1150	C₂²	—	4	1	no	—
1151	C₂²	—	4	1	no	—
1152	C₂²	—	8	4	no	—
1153	C₂²	—	8	8	no	—
1154	C₂²	#525×C₆₇	1	2	yes	—
1155	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	1	no	—
1158	C₄	—	2	2	no	—
1159	C₄	—	2	1	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	2	no	—
1163	C₄	—	2	2	no	—
1164	C₄	—	4	2	no	—
1165	C₄	—	4	1	no	—
1166	C₄	—	4	2	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	4	1	no	—
1169	C₄	—	4	1	no	—
1170	C₄	—	4	1	no	—
1171	C₄	—	4	2	no	—
1172	C₄	#525×C₆₇	1	2	yes	—
1173	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1174	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	4	4	no	—
1178	C₂	—	4	2	no	—
1179	C₂	—	8	1	no	—
1180	C₂	C₂×#525×C₆₇	1	1	yes	characteristic
1181	C₂	C₆₇×#3585	1	1	yes	characteristic
1182	C₂	C₆₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
prime radical	C₆₇×#3012	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄×#41×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3461	C₂	semidirect
2. C₄×H(5,𝔽₂)×C₆₇	C₂	semidirect
3. C₆₇×#3124	C₂	semidirect
4. C₆₇×#3123	C₂	semidirect
5. C₆₇×#3120	C₂	semidirect
6. C₆₇×#3118	C₂	semidirect
7. C₆₇×#3116	C₂	semidirect
8. C₆₇×#3114	C₂	semidirect
9. C₆₇×#3111	C₂	semidirect
10. C₆₇×#3110	C₂	semidirect
11. C₆₇×#3098	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3083	C₂	semidirect
14. C₆₇×#3081	C₂	semidirect
15. C₆₇×#3046	C₂	semidirect
16. C₆₇×#3042	C₂	semidirect
18. C₆₇×#3009	C₂	semidirect
19. C₄×#137×C₆₇	C₂	semidirect
20. C₄×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
21. C₆₇×#2943	C₂	semidirect
22. C₂×#440×C₆₇	C₂	semidirect
23. C₆₇×#2923	C₂	semidirect
29. #544×C₆₇	C₂²	semidirect
31. #542×C₆₇	C₂²	semidirect
33. #541×C₆₇	C₂²	semidirect
37. #536×C₆₇	C₂²	semidirect
39. #533×C₆₇	C₂²	semidirect
42. #529×C₆₇	C₂²	semidirect
55. C₄×#41×C₆₇	C₂²	semidirect
56. C₂×C₄×Q₈×C₆₇	C₂²	semidirect
61. #485×C₆₇	C₂²	semidirect
62. #485×C₆₇	C₂²	semidirect
63. #485×C₆₇	C₂²	semidirect
64. #484×C₆₇	C₂²	semidirect
65. #484×C₆₇	C₂²	semidirect
66. #483×C₆₇	C₂²	semidirect
67. #482×C₆₇	C₂²	semidirect
68. #480×C₆₇	C₂²	semidirect
69. #479×C₆₇	C₂²	semidirect
70. #478×C₆₇	C₂²	semidirect
71. #478×C₆₇	C₂²	semidirect
72. #478×C₆₇	C₂²	semidirect
73. #477×C₆₇	C₂²	semidirect
74. #476×C₆₇	C₂²	semidirect
75. #474×C₆₇	C₂²	semidirect
76. #474×C₆₇	C₂²	semidirect
77. #464×C₆₇	C₂²	semidirect
78. #463×C₆₇	C₂²	semidirect
79. #463×C₆₇	C₂²	semidirect
80. #463×C₆₇	C₂²	semidirect
81. #462×C₆₇	C₂²	semidirect
82. #461×C₆₇	C₂²	semidirect
83. #461×C₆₇	C₂²	semidirect
84. #461×C₆₇	C₂²	semidirect
93. #442×C₆₇	C₂²	semidirect
94. #442×C₆₇	C₂²	semidirect
95. #442×C₆₇	C₂²	semidirect
96. #441×C₆₇	C₂²	semidirect
97. #441×C₆₇	C₂²	semidirect
98. #441×C₆₇	C₂²	semidirect
99. #440×C₆₇	C₂²	semidirect
100. #440×C₆₇	C₂²	semidirect
101. #440×C₆₇	C₂²	semidirect
102. #440×C₆₇	C₂²	semidirect
103. #440×C₆₇	C₂²	semidirect
104. #440×C₆₇	C₂²	semidirect
105. #440×C₆₇	C₂²	semidirect
106. #440×C₆₇	C₂²	semidirect
107. #440×C₆₇	C₂²	semidirect
108. #440×C₆₇	C₂²	semidirect
109. C₄×Q₁₆×C₆₇	C₂²	semidirect
110. C₄×SD₁₆×C₆₇	C₂²	semidirect
111. C₄×SD₁₆×C₆₇	C₂²	semidirect
112. C₄×D₈×C₆₇	C₂²	semidirect
113. #433×C₆₇	C₂²	semidirect
114. #433×C₆₇	C₂²	semidirect
115. #432×C₆₇	C₂²	semidirect
116. #432×C₆₇	C₂²	semidirect
117. #428×C₆₇	C₂²	semidirect
118. #428×C₆₇	C₂²	semidirect
119. #427×C₆₇	C₂²	semidirect
120. C₂×#107×C₆₇	C₂²	semidirect
121. #424×C₆₇	C₂²	semidirect
122. #424×C₆₇	C₂²	semidirect
123. #419×C₆₇	C₂²	semidirect
126. #417×C₆₇	C₂²	semidirect
128. #416×C₆₇	C₂²	semidirect
129. C₂×#103×C₆₇	C₂²	semidirect
133. C₄×M₁₆×C₆₇	C₂²	semidirect
134. C₂×#97×C₆₇	C₂²	semidirect
583. #60575	C₆₇	direct (N × H)
592. #3461	C₂×C₆₇	semidirect
593. C₄×H(5,𝔽₂)	C₂×C₆₇	semidirect
594. #3124	C₂×C₆₇	semidirect
595. #3123	C₂×C₆₇	semidirect
596. #3120	C₂×C₆₇	semidirect
597. #3118	C₂×C₆₇	semidirect
598. #3116	C₂×C₆₇	semidirect
599. #3114	C₂×C₆₇	semidirect
600. #3111	C₂×C₆₇	semidirect
601. #3110	C₂×C₆₇	semidirect
602. #3098	C₂×C₆₇	semidirect
603. #3097	C₂×C₆₇	semidirect
604. #3083	C₂×C₆₇	semidirect
605. #3081	C₂×C₆₇	semidirect
606. #3046	C₂×C₆₇	semidirect
607. #3042	C₂×C₆₇	semidirect
609. #3009	C₂×C₆₇	semidirect
610. C₄×#137	C₂×C₆₇	semidirect
611. C₄×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
612. #2943	C₂×C₆₇	semidirect
613. C₂×#440	C₂×C₆₇	semidirect
614. #2923	C₂×C₆₇	semidirect
615. C₆₇	#60575	direct (N × H)
621. #544	C₂²×C₆₇	semidirect
623. #542	C₂²×C₆₇	semidirect
625. #541	C₂²×C₆₇	semidirect
629. #536	C₂²×C₆₇	semidirect
631. #533	C₂²×C₆₇	semidirect
634. #529	C₂²×C₆₇	semidirect
647. C₄×#41	C₂²×C₆₇	semidirect
648. C₂×C₄×Q₈	C₂²×C₆₇	semidirect
653. #485	C₂²×C₆₇	semidirect
654. #485	C₂²×C₆₇	semidirect
655. #485	C₂²×C₆₇	semidirect
656. #484	C₂²×C₆₇	semidirect
657. #484	C₂²×C₆₇	semidirect
658. #483	C₂²×C₆₇	semidirect
659. #482	C₂²×C₆₇	semidirect
660. #480	C₂²×C₆₇	semidirect
661. #479	C₂²×C₆₇	semidirect
662. #478	C₂²×C₆₇	semidirect
663. #478	C₂²×C₆₇	semidirect
664. #478	C₂²×C₆₇	semidirect
665. #477	C₂²×C₆₇	semidirect
666. #476	C₂²×C₆₇	semidirect
667. #474	C₂²×C₆₇	semidirect
668. #474	C₂²×C₆₇	semidirect
669. #464	C₂²×C₆₇	semidirect
670. #463	C₂²×C₆₇	semidirect
671. #463	C₂²×C₆₇	semidirect
672. #463	C₂²×C₆₇	semidirect
673. #462	C₂²×C₆₇	semidirect
674. #461	C₂²×C₆₇	semidirect
675. #461	C₂²×C₆₇	semidirect
676. #461	C₂²×C₆₇	semidirect
685. #442	C₂²×C₆₇	semidirect
686. #442	C₂²×C₆₇	semidirect
687. #442	C₂²×C₆₇	semidirect
688. #441	C₂²×C₆₇	semidirect
689. #441	C₂²×C₆₇	semidirect
690. #441	C₂²×C₆₇	semidirect
691. #440	C₂²×C₆₇	semidirect
692. #440	C₂²×C₆₇	semidirect
693. #440	C₂²×C₆₇	semidirect
694. #440	C₂²×C₆₇	semidirect
695. #440	C₂²×C₆₇	semidirect
696. #440	C₂²×C₆₇	semidirect
697. #440	C₂²×C₆₇	semidirect
698. #440	C₂²×C₆₇	semidirect
699. #440	C₂²×C₆₇	semidirect
700. #440	C₂²×C₆₇	semidirect
701. C₄×Q₁₆	C₂²×C₆₇	semidirect
702. C₄×SD₁₆	C₂²×C₆₇	semidirect
703. C₄×SD₁₆	C₂²×C₆₇	semidirect
704. C₄×D₈	C₂²×C₆₇	semidirect
705. #433	C₂²×C₆₇	semidirect
706. #433	C₂²×C₆₇	semidirect
707. #432	C₂²×C₆₇	semidirect
708. #432	C₂²×C₆₇	semidirect
709. #428	C₂²×C₆₇	semidirect
710. #428	C₂²×C₆₇	semidirect
711. #427	C₂²×C₆₇	semidirect
712. C₂×#107	C₂²×C₆₇	semidirect
713. #424	C₂²×C₆₇	semidirect
714. #424	C₂²×C₆₇	semidirect
715. #419	C₂²×C₆₇	semidirect
718. #417	C₂²×C₆₇	semidirect
720. #416	C₂²×C₆₇	semidirect
721. C₂×#103	C₂²×C₆₇	semidirect
725. C₄×M₁₆	C₂²×C₆₇	semidirect
726. C₂×#97	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×#3461	2
C₄×H(5,𝔽₂)×C₆₇	2
C₆₇×#3124	2
C₆₇×#3123	2
C₆₇×#3120	2
C₆₇×#3118	2
C₆₇×#3116	2
C₆₇×#3114	2
C₆₇×#3111	2
C₆₇×#3110	2
C₆₇×#3098	2
C₆₇×#3097	2
C₆₇×#3083	2
C₆₇×#3081	2
C₆₇×#3046	2
C₆₇×#3042	2
C₆₇×#3012	2
C₆₇×#3009	2
C₄×#137×C₆₇	2
C₄×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#2943	2
C₂×#440×C₆₇	2
C₆₇×#2923	2
#60575	67

Subgroups — C67×#60575 #30739826

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#60575 #30739826