Subgroups — C₆₇×#61216 #30740467

Order 17152.

2060 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3512	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3500	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3327	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3326	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3323	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3322	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3301	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3300	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3297	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3296	C₂	1	2	yes	maximal, complemented
11	C₂×#488×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3097	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3096	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3080	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3063	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3062	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3040	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#3013	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#3012	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
21	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
22	C₆₇×#2898	C₂	1	1	yes	maximal, characteristic, complemented
23	C₆₇×#2897	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic
25	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	#553×C₆₇	—	2	2	no	—
32	#553×C₆₇	—	2	2	no	—
33	#553×C₆₇	C₂²	1	2	yes	complemented
34	#553×C₆₇	C₂²	1	2	yes	complemented
35	#552×C₆₇	C₂²	1	2	yes	complemented
36	#552×C₆₇	C₂²	1	2	yes	complemented
37	#548×C₆₇	C₂²	1	2	yes	—
38	#548×C₆₇	C₂²	1	2	yes	—
39	#546×C₆₇	—	2	2	no	—
40	#546×C₆₇	—	2	2	no	—
41	#546×C₆₇	C₂²	1	2	yes	—
42	#546×C₆₇	C₂²	1	2	yes	—
43	#541×C₆₇	—	2	1	no	—
44	#540×C₆₇	—	2	1	no	—
45	#537×C₆₇	C₂²	1	1	yes	characteristic
46	#537×C₆₇	C₂²	1	1	yes	characteristic, complemented
47	#536×C₆₇	—	2	1	no	—
48	#536×C₆₇	C₂²	1	1	yes	characteristic
49	#535×C₆₇	—	2	1	no	—
50	#535×C₆₇	C₂²	1	1	yes	characteristic
51	#532×C₆₇	—	2	1	no	—
52	#532×C₆₇	C₂²	1	1	yes	characteristic
53	#529×C₆₇	—	2	1	no	—
54	#529×C₆₇	—	2	1	no	—
55	C₂×#125×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	C₂×#124×C₆₇	—	2	1	no	—
57	C₂×#124×C₆₇	C₂²	1	1	yes	characteristic
58	#520×C₆₇	C₂²	1	1	yes	characteristic
59	#520×C₆₇	C₂²	1	1	yes	characteristic, complemented
60	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
61	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
62	#488×C₆₇	C₂²	1	2	yes	complemented
63	#488×C₆₇	C₂²	1	2	yes	complemented
64	#488×C₆₇	C₂²	1	2	yes	complemented
65	#488×C₆₇	C₂²	1	2	yes	complemented
66	#485×C₆₇	C₂²	1	2	yes	complemented
67	#485×C₆₇	C₂²	1	2	yes	complemented
68	#484×C₆₇	C₂²	1	2	yes	complemented
69	#483×C₆₇	C₂²	1	2	yes	complemented
70	#482×C₆₇	C₂²	1	2	yes	complemented
71	#482×C₆₇	C₂²	1	2	yes	complemented
72	#481×C₆₇	C₂²	1	2	yes	complemented
73	#480×C₆₇	C₂²	1	2	yes	complemented
74	#479×C₆₇	C₂²	1	2	yes	complemented
75	#479×C₆₇	C₂²	1	2	yes	complemented
76	#478×C₆₇	C₂²	1	2	yes	complemented
77	#478×C₆₇	C₂²	1	2	yes	complemented
78	#470×C₆₇	C₂²	1	2	yes	complemented
79	#469×C₆₇	C₂²	1	2	yes	complemented
80	#468×C₆₇	C₂²	1	2	yes	complemented
81	#468×C₆₇	C₂²	1	2	yes	complemented
82	#467×C₆₇	C₂²	1	2	yes	complemented
83	#466×C₆₇	C₂²	1	2	yes	complemented
84	#465×C₆₇	C₂²	1	2	yes	complemented
85	#465×C₆₇	C₂²	1	2	yes	complemented
86	#464×C₆₇	C₂²	1	2	yes	complemented
87	#464×C₆₇	C₂²	1	2	yes	complemented
88	#463×C₆₇	C₂²	1	2	yes	complemented
89	#463×C₆₇	C₂²	1	2	yes	complemented
90	#452×C₆₇	C₂²	1	2	yes	—
91	#452×C₆₇	C₂²	1	2	yes	complemented
92	#451×C₆₇	C₂²	1	2	yes	complemented
93	#450×C₆₇	C₂²	1	2	yes	—
94	#449×C₆₇	C₂²	1	2	yes	—
95	#449×C₆₇	C₂²	1	2	yes	complemented
96	#448×C₆₇	C₂²	1	2	yes	complemented
97	#447×C₆₇	C₂²	1	2	yes	—
98	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
102	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
103	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
104	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
106	#436×C₆₇	C₂²	1	2	yes	complemented
107	#436×C₆₇	C₂²	1	2	yes	complemented
108	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
109	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
110	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
111	#428×C₆₇	C₂²	1	1	yes	characteristic, complemented
112	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
113	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
114	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
115	#419×C₆₇	C₂²	1	2	yes	complemented
116	#418×C₆₇	C₂²	1	1	yes	characteristic
117	#418×C₆₇	C₂²	1	2	yes	—
118	#417×C₆₇	C₂²	1	1	yes	characteristic
119	#417×C₆₇	C₂²	1	1	yes	characteristic
120	#417×C₆₇	C₂²	1	2	yes	—
121	#417×C₆₇	C₂²	1	2	yes	complemented
122	#416×C₆₇	C₂²	1	2	yes	—
123	#416×C₆₇	C₂²	1	1	yes	characteristic
124	#416×C₆₇	C₂²	1	2	yes	complemented
125	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
126	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
127	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
128	C₂×#103×C₆₇	C₂²	1	1	yes	characteristic, complemented
129	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
130	C₂×#102×C₆₇	C₂²	1	2	yes	—
131	C₂×#102×C₆₇	C₂²	1	1	yes	characteristic
132	#408×C₆₇	C₂²	1	1	yes	characteristic
133	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
134	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
135	2₋¹⁺⁴×C₆₇	—	2	4	no	—
136	2₋¹⁺⁴×C₆₇	—	4	2	no	—
137	H(5,𝔽₂)×C₆₇	—	2	4	no	—
138	H(5,𝔽₂)×C₆₇	—	4	2	no	—
139	C₂×#41×C₆₇	—	2	1	no	—
140	C₂×#41×C₆₇	—	2	1	no	—
141	C₂×#41×C₆₇	—	2	2	no	—
142	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
143	C₂×#41×C₆₇	C₂³	1	2	yes	—
144	C₂×#41×C₆₇	C₂³	1	2	yes	—
145	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
146	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
147	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
148	C₂²×Q₈×C₆₇	—	2	1	no	—
149	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
150	C₂²×Q₈×C₆₇	C₂³	1	2	yes	—
151	C₂²×D₄×C₆₇	—	2	1	no	—
152	C₂²×D₄×C₆₇	—	2	2	no	—
153	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
154	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
155	#137×C₆₇	—	4	2	no	—
156	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
157	#135×C₆₇	—	2	4	no	—
158	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
159	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	—
160	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
161	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
162	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
163	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
164	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
165	C₂×D₈×C₆₇	C₂³	1	2	yes	—
166	#131×C₆₇	—	4	2	no	—
167	#131×C₆₇	—	4	2	no	—
168	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
169	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
170	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
173	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
174	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
175	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
176	C₄⋊Q₈×C₆₇	—	2	1	no	—
177	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
178	#127×C₆₇	—	2	1	no	—
179	#127×C₆₇	D₄	1	1	yes	characteristic
180	#126×C₆₇	—	2	2	no	—
181	#126×C₆₇	—	2	2	no	—
182	#126×C₆₇	—	2	2	no	—
183	#126×C₆₇	—	2	2	no	—
184	#125×C₆₇	—	2	2	no	—
185	#125×C₆₇	—	2	2	no	—
186	#125×C₆₇	—	2	1	no	—
187	#125×C₆₇	—	2	1	no	—
188	#125×C₆₇	C₂³	1	2	yes	—
189	#125×C₆₇	C₂³	1	2	yes	—
190	#124×C₆₇	—	2	1	no	—
191	#124×C₆₇	—	2	1	no	—
192	#124×C₆₇	—	2	2	no	—
193	#124×C₆₇	—	2	2	no	—
194	#124×C₆₇	—	2	1	no	—
195	#124×C₆₇	—	2	1	no	—
196	#124×C₆₇	D₄	1	1	yes	characteristic
197	#124×C₆₇	D₄	1	1	yes	characteristic
198	#124×C₆₇	C₂³	1	2	yes	—
199	#124×C₆₇	C₂³	1	2	yes	—
200	#123×C₆₇	—	2	2	no	—
201	#123×C₆₇	—	2	2	no	—
202	#123×C₆₇	—	2	2	no	—
203	#123×C₆₇	—	2	2	no	—
204	#123×C₆₇	—	2	2	no	—
205	#123×C₆₇	—	2	2	no	—
206	#123×C₆₇	—	2	2	no	—
207	C₂²⋊Q₈×C₆₇	—	2	1	no	—
208	C₂²⋊Q₈×C₆₇	—	2	1	no	—
209	C₂²⋊Q₈×C₆₇	—	2	2	no	—
210	C₂²⋊Q₈×C₆₇	—	2	2	no	—
211	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
212	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
213	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
214	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
215	#121×C₆₇	—	2	1	no	—
216	#121×C₆₇	—	2	1	no	—
217	#121×C₆₇	—	2	2	no	—
218	#121×C₆₇	—	2	2	no	—
219	#121×C₆₇	—	2	2	no	—
220	#121×C₆₇	—	2	2	no	—
221	#121×C₆₇	—	2	2	no	—
222	#121×C₆₇	—	2	2	no	—
223	#121×C₆₇	—	2	2	no	—
224	#121×C₆₇	—	2	2	no	—
225	#121×C₆₇	D₄	1	2	yes	—
226	#121×C₆₇	D₄	1	2	yes	—
227	#121×C₆₇	C₂³	1	2	yes	—
228	#121×C₆₇	C₂³	1	2	yes	—
229	#121×C₆₇	C₂³	1	2	yes	—
230	#121×C₆₇	C₂³	1	2	yes	—
231	#120×C₆₇	—	2	2	no	—
232	#120×C₆₇	—	2	2	no	—
233	#120×C₆₇	—	2	2	no	—
234	C₄×Q₈×C₆₇	—	2	1	no	—
235	C₄×Q₈×C₆₇	—	2	1	no	—
236	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
237	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
238	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
239	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
240	C₄×D₄×C₆₇	—	2	1	no	—
241	C₄×D₄×C₆₇	—	2	2	no	—
242	C₄×D₄×C₆₇	—	2	1	no	—
243	C₄×D₄×C₆₇	—	2	2	no	—
244	C₄×D₄×C₆₇	—	2	1	no	—
245	C₄×D₄×C₆₇	—	2	1	no	—
246	C₄×D₄×C₆₇	—	2	1	no	—
247	C₄×D₄×C₆₇	—	2	1	no	—
248	C₄×D₄×C₆₇	—	2	2	no	—
249	C₄×D₄×C₆₇	—	2	2	no	—
250	C₄×D₄×C₆₇	—	2	2	no	—
251	C₄×D₄×C₆₇	—	2	2	no	—
252	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
254	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
255	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
256	C₄×D₄×C₆₇	C₂³	1	2	yes	—
257	C₄×D₄×C₆₇	C₂³	1	2	yes	—
258	#117×C₆₇	—	2	2	no	—
259	#117×C₆₇	—	2	2	no	—
260	#117×C₆₇	—	2	1	no	—
261	#117×C₆₇	—	2	1	no	—
262	#117×C₆₇	C₂³	1	2	yes	—
263	#117×C₆₇	C₂³	1	2	yes	—
264	#117×C₆₇	C₂³	1	1	yes	characteristic
265	#117×C₆₇	C₂³	1	1	yes	characteristic
266	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
267	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
268	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
269	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
270	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
271	C₂×C₄⋊C₄×C₆₇	C₂³	1	1	yes	characteristic
272	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
273	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
274	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
275	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
276	C₂×C₄²×C₆₇	—	2	1	no	—
277	C₂×C₄²×C₆₇	—	2	1	no	—
278	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
279	#107×C₆₇	C₂³	1	2	yes	—
280	#107×C₆₇	C₂³	1	2	yes	—
281	#107×C₆₇	C₂³	1	1	yes	characteristic
282	#107×C₆₇	C₂³	1	1	yes	characteristic
283	#106×C₆₇	C₂³	1	2	yes	—
284	#106×C₆₇	C₂³	1	2	yes	—
285	#106×C₆₇	C₂³	1	1	yes	characteristic
286	#106×C₆₇	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
288	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
289	#103×C₆₇	C₂³	1	2	yes	—
290	#103×C₆₇	C₂³	1	2	yes	—
291	#103×C₆₇	C₂³	1	2	yes	—
292	#103×C₆₇	C₂³	1	2	yes	—
293	#103×C₆₇	C₂³	1	2	yes	—
294	#103×C₆₇	C₂³	1	2	yes	—
295	#103×C₆₇	C₂³	1	1	yes	characteristic
296	#103×C₆₇	C₂³	1	2	yes	—
297	#103×C₆₇	C₂³	1	1	yes	characteristic
298	#103×C₆₇	C₂³	1	2	yes	—
299	#103×C₆₇	C₂³	1	1	yes	characteristic
300	#103×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	2	yes	—
306	#102×C₆₇	C₂³	1	2	yes	—
307	#102×C₆₇	C₂³	1	1	yes	characteristic
308	#102×C₆₇	C₂³	1	2	yes	—
309	#102×C₆₇	C₂³	1	1	yes	characteristic
310	#102×C₆₇	C₂³	1	2	yes	—
311	#102×C₆₇	C₂³	1	1	yes	characteristic
312	#102×C₆₇	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
314	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
315	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
316	C₂²⋊C₈×C₆₇	C₂³	1	2	yes	—
317	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
318	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
319	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
320	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
321	C₂⁴×C₆₇	—	2	2	no	—
322	C₂⁴×C₆₇	—	2	1	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	—	2	4	no	—
329	#41×C₆₇	—	2	4	no	—
330	#41×C₆₇	—	2	2	no	—
331	#41×C₆₇	—	2	2	no	—
332	#41×C₆₇	—	4	2	no	—
333	#41×C₆₇	—	4	2	no	—
334	#41×C₆₇	—	4	4	no	—
335	#41×C₆₇	—	4	4	no	—
336	#41×C₆₇	—	4	8	no	—
337	#41×C₆₇	#41	1	4	yes	—
338	C₂×Q₈×C₆₇	—	2	2	no	—
339	C₂×Q₈×C₆₇	—	2	1	no	—
340	C₂×Q₈×C₆₇	—	2	4	no	—
341	C₂×Q₈×C₆₇	—	2	2	no	—
342	C₂×Q₈×C₆₇	—	2	2	no	—
343	C₂×Q₈×C₆₇	—	4	2	no	—
344	C₂×Q₈×C₆₇	—	4	4	no	—
345	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
346	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
348	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂×D₄×C₆₇	—	2	1	no	—
351	C₂×D₄×C₆₇	—	2	4	no	—
352	C₂×D₄×C₆₇	—	2	1	no	—
353	C₂×D₄×C₆₇	—	2	2	no	—
354	C₂×D₄×C₆₇	—	2	2	no	—
355	C₂×D₄×C₆₇	—	2	2	no	—
356	C₂×D₄×C₆₇	—	2	2	no	—
357	C₂×D₄×C₆₇	—	2	2	no	—
358	C₂×D₄×C₆₇	—	2	2	no	—
359	C₂×D₄×C₆₇	—	2	2	no	—
360	C₂×D₄×C₆₇	—	2	1	no	—
361	C₂×D₄×C₆₇	—	2	2	no	—
362	C₂×D₄×C₆₇	—	2	2	no	—
363	C₂×D₄×C₆₇	—	4	2	no	—
364	C₂×D₄×C₆₇	—	4	4	no	—
365	C₂×D₄×C₆₇	—	4	8	no	—
366	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
367	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
368	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
369	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
370	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
371	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
372	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
373	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
374	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
375	C₂²×C₄×C₆₇	—	2	1	no	—
376	C₂²×C₄×C₆₇	—	2	1	no	—
377	C₂²×C₄×C₆₇	—	2	2	no	—
378	C₂²×C₄×C₆₇	—	2	1	no	—
379	C₂²×C₄×C₆₇	—	2	1	no	—
380	C₂²×C₄×C₆₇	—	2	2	no	—
381	C₂²×C₄×C₆₇	—	2	2	no	—
382	C₂²×C₄×C₆₇	—	2	1	no	—
383	C₂²×C₄×C₆₇	—	2	2	no	—
384	C₂²×C₄×C₆₇	—	2	2	no	—
385	C₂²×C₄×C₆₇	—	2	1	no	—
386	C₂²×C₄×C₆₇	—	2	1	no	—
387	C₂²×C₄×C₆₇	—	2	1	no	—
388	C₂²×C₄×C₆₇	—	2	1	no	—
389	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
390	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
391	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
392	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
393	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
394	Q₁₆×C₆₇	—	2	2	no	—
395	Q₁₆×C₆₇	—	4	2	no	—
396	SD₁₆×C₆₇	—	2	2	no	—
397	SD₁₆×C₆₇	—	2	2	no	—
398	SD₁₆×C₆₇	—	4	2	no	—
399	SD₁₆×C₆₇	—	4	2	no	—
400	D₈×C₆₇	—	2	2	no	—
401	D₈×C₆₇	—	4	2	no	—
402	M₁₆×C₆₇	—	2	2	no	—
403	M₁₆×C₆₇	—	2	2	no	—
404	M₁₆×C₆₇	—	4	2	no	—
405	M₁₆×C₆₇	—	4	2	no	—
406	C₂×C₈×C₆₇	—	2	2	no	—
407	C₂×C₈×C₆₇	—	2	2	no	—
408	C₂×C₈×C₆₇	—	4	2	no	—
409	C₂×C₈×C₆₇	—	4	2	no	—
410	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
411	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
412	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
413	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
414	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
415	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
416	C₄⋊C₄×C₆₇	—	2	2	no	—
417	C₄⋊C₄×C₆₇	—	2	2	no	—
418	C₄⋊C₄×C₆₇	—	2	2	no	—
419	C₄⋊C₄×C₆₇	—	2	2	no	—
420	C₄⋊C₄×C₆₇	—	2	1	no	—
421	C₄⋊C₄×C₆₇	—	2	1	no	—
422	C₄⋊C₄×C₆₇	—	2	2	no	—
423	C₄⋊C₄×C₆₇	—	2	2	no	—
424	C₄⋊C₄×C₆₇	—	2	1	no	—
425	C₄⋊C₄×C₆₇	—	2	1	no	—
426	C₄⋊C₄×C₆₇	—	2	1	no	—
427	C₄⋊C₄×C₆₇	—	2	1	no	—
428	C₄⋊C₄×C₆₇	—	2	2	no	—
429	C₄⋊C₄×C₆₇	—	2	2	no	—
430	C₄⋊C₄×C₆₇	—	2	2	no	—
431	C₄⋊C₄×C₆₇	—	2	2	no	—
432	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
433	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
434	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
435	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
436	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
437	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
438	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
440	C₂²⋊C₄×C₆₇	—	2	2	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	—	2	1	no	—
445	C₂²⋊C₄×C₆₇	—	2	1	no	—
446	C₂²⋊C₄×C₆₇	—	2	2	no	—
447	C₂²⋊C₄×C₆₇	—	2	2	no	—
448	C₂²⋊C₄×C₆₇	—	2	2	no	—
449	C₂²⋊C₄×C₆₇	—	2	2	no	—
450	C₂²⋊C₄×C₆₇	—	2	2	no	—
451	C₂²⋊C₄×C₆₇	—	2	2	no	—
452	C₂²⋊C₄×C₆₇	—	2	2	no	—
453	C₂²⋊C₄×C₆₇	—	2	2	no	—
454	C₂²⋊C₄×C₆₇	—	2	1	no	—
455	C₂²⋊C₄×C₆₇	—	2	1	no	—
456	C₂²⋊C₄×C₆₇	—	2	1	no	—
457	C₂²⋊C₄×C₆₇	—	2	1	no	—
458	C₂²⋊C₄×C₆₇	—	2	2	no	—
459	C₂²⋊C₄×C₆₇	—	2	2	no	—
460	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
461	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
462	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
463	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
464	C₄²×C₆₇	—	2	1	no	—
465	C₄²×C₆₇	—	2	1	no	—
466	C₄²×C₆₇	—	2	1	no	—
467	C₄²×C₆₇	—	2	1	no	—
468	C₄²×C₆₇	—	2	1	no	—
469	C₄²×C₆₇	—	2	1	no	—
470	C₄²×C₆₇	—	2	2	no	—
471	C₄²×C₆₇	—	2	2	no	—
472	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
473	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
474	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
475	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
476	C₂³×C₆₇	—	2	1	no	—
477	C₂³×C₆₇	—	2	1	no	—
478	C₂³×C₆₇	—	2	2	no	—
479	C₂³×C₆₇	—	4	4	no	—
480	C₂³×C₆₇	—	4	2	no	—
481	C₂³×C₆₇	—	8	1	no	—
482	C₂³×C₆₇	—	8	1	no	—
483	C₂³×C₆₇	—	8	2	no	—
484	C₂³×C₆₇	—	8	2	no	—
485	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
486	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
487	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
488	Q₈×C₆₇	—	2	2	no	—
489	Q₈×C₆₇	—	2	2	no	—
490	Q₈×C₆₇	—	2	1	no	—
491	Q₈×C₆₇	—	2	1	no	—
492	Q₈×C₆₇	—	2	2	no	—
493	Q₈×C₆₇	—	2	1	no	—
494	Q₈×C₆₇	—	2	2	no	—
495	Q₈×C₆₇	—	4	4	no	—
496	Q₈×C₆₇	—	4	2	no	—
497	Q₈×C₆₇	C₂×#41	1	2	yes	—
498	D₄×C₆₇	—	2	4	no	—
499	D₄×C₆₇	—	2	4	no	—
500	D₄×C₆₇	—	2	4	no	—
501	D₄×C₆₇	—	2	2	no	—
502	D₄×C₆₇	—	2	2	no	—
503	D₄×C₆₇	—	2	1	no	—
504	D₄×C₆₇	—	2	2	no	—
505	D₄×C₆₇	—	2	1	no	—
506	D₄×C₆₇	—	2	1	no	—
507	D₄×C₆₇	—	2	2	no	—
508	D₄×C₆₇	—	4	2	no	—
509	D₄×C₆₇	—	4	2	no	—
510	D₄×C₆₇	—	4	4	no	—
511	D₄×C₆₇	—	4	4	no	—
512	D₄×C₆₇	—	4	4	no	—
513	D₄×C₆₇	—	4	2	no	—
514	D₄×C₆₇	—	4	2	no	—
515	D₄×C₆₇	—	8	2	no	—
516	D₄×C₆₇	—	8	2	no	—
517	D₄×C₆₇	—	8	2	no	—
518	D₄×C₆₇	—	8	2	no	—
519	D₄×C₆₇	C₂×#41	1	2	yes	—
520	C₂×C₄×C₆₇	—	2	1	no	—
521	C₂×C₄×C₆₇	—	2	4	no	—
522	C₂×C₄×C₆₇	—	2	2	no	—
523	C₂×C₄×C₆₇	—	2	2	no	—
524	C₂×C₄×C₆₇	—	2	2	no	—
525	C₂×C₄×C₆₇	—	2	2	no	—
526	C₂×C₄×C₆₇	—	2	1	no	—
527	C₂×C₄×C₆₇	—	2	1	no	—
528	C₂×C₄×C₆₇	—	2	1	no	—
529	C₂×C₄×C₆₇	—	2	1	no	—
530	C₂×C₄×C₆₇	—	2	1	no	—
531	C₂×C₄×C₆₇	—	2	2	no	—
532	C₂×C₄×C₆₇	—	2	2	no	—
533	C₂×C₄×C₆₇	—	2	2	no	—
534	C₂×C₄×C₆₇	—	4	1	no	—
535	C₂×C₄×C₆₇	—	4	1	no	—
536	C₂×C₄×C₆₇	—	4	4	no	—
537	C₂×C₄×C₆₇	—	4	4	no	—
538	C₂×C₄×C₆₇	—	4	4	no	—
539	C₂×C₄×C₆₇	—	4	2	no	—
540	C₂×C₄×C₆₇	—	4	2	no	—
541	C₂×C₄×C₆₇	—	8	1	no	—
542	C₂×C₄×C₆₇	—	8	1	no	—
543	C₂×C₄×C₆₇	—	8	1	no	—
544	C₂×C₄×C₆₇	—	8	1	no	—
545	C₂×C₄×C₆₇	—	8	2	no	—
546	C₂×C₄×C₆₇	—	8	2	no	—
547	C₂×C₄×C₆₇	—	8	1	no	—
548	C₂×C₄×C₆₇	—	8	1	no	—
549	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
550	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
551	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
552	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
553	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
554	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
555	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
556	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
557	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
558	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
559	C₈×C₆₇	—	2	1	no	—
560	C₈×C₆₇	—	2	1	no	—
561	C₈×C₆₇	—	2	1	no	—
562	C₈×C₆₇	—	2	1	no	—
563	C₈×C₆₇	—	2	2	no	—
564	C₈×C₆₇	—	2	2	no	—
565	C₂²×C₆₇	—	2	1	no	—
566	C₂²×C₆₇	—	2	1	no	—
567	C₂²×C₆₇	—	2	2	no	—
568	C₂²×C₆₇	—	2	2	no	—
569	C₂²×C₆₇	—	2	2	no	—
570	C₂²×C₆₇	—	2	2	no	—
571	C₂²×C₆₇	—	2	2	no	—
572	C₂²×C₆₇	—	2	2	no	—
573	C₂²×C₆₇	—	2	2	no	—
574	C₂²×C₆₇	—	4	1	no	—
575	C₂²×C₆₇	—	4	1	no	—
576	C₂²×C₆₇	—	4	1	no	—
577	C₂²×C₆₇	—	4	1	no	—
578	C₂²×C₆₇	—	4	2	no	—
579	C₂²×C₆₇	—	4	2	no	—
580	C₂²×C₆₇	—	4	2	no	—
581	C₂²×C₆₇	—	4	1	no	—
582	C₂²×C₆₇	—	16	2	no	—
583	C₂²×C₆₇	—	16	4	no	—
584	C₂²×C₆₇	#546	1	2	yes	—
585	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
586	C₄×C₆₇	—	2	1	no	—
587	C₄×C₆₇	—	2	1	no	—
588	C₄×C₆₇	—	2	1	no	—
589	C₄×C₆₇	—	2	1	no	—
590	C₄×C₆₇	—	2	2	no	—
591	C₄×C₆₇	—	2	2	no	—
592	C₄×C₆₇	—	2	2	no	—
593	C₄×C₆₇	—	4	1	no	—
594	C₄×C₆₇	—	4	1	no	—
595	C₄×C₆₇	—	4	2	no	—
596	C₄×C₆₇	—	4	2	no	—
597	C₄×C₆₇	—	4	1	no	—
598	C₄×C₆₇	—	4	1	no	—
599	C₄×C₆₇	—	4	2	no	—
600	C₄×C₆₇	—	4	1	no	—
601	C₄×C₆₇	#546	1	2	yes	—
602	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
603	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
604	#61216	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
605	C₂×C₆₇	—	2	2	no	—
606	C₂×C₆₇	—	4	2	no	—
607	C₂×C₆₇	—	4	2	no	—
608	C₂×C₆₇	—	4	2	no	—
609	C₂×C₆₇	—	8	1	no	—
610	C₂×C₆₇	—	8	2	no	—
611	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
612	C₂×C₆₇	#3584	1	1	yes	characteristic
613	C₂×C₆₇	#3584	1	1	yes	characteristic
614	#3512	C₂×C₆₇	1	1	yes	characteristic, complemented
615	#3500	C₂×C₆₇	1	1	yes	characteristic, complemented
616	#3327	C₂×C₆₇	1	2	yes	complemented
617	#3326	C₂×C₆₇	1	2	yes	complemented
618	#3323	C₂×C₆₇	1	2	yes	complemented
619	#3322	C₂×C₆₇	1	2	yes	complemented
620	#3301	C₂×C₆₇	1	2	yes	complemented
621	#3300	C₂×C₆₇	1	2	yes	complemented
622	#3297	C₂×C₆₇	1	2	yes	complemented
623	#3296	C₂×C₆₇	1	2	yes	complemented
624	C₂×#488	C₂×C₆₇	1	1	yes	characteristic, complemented
625	#3097	C₂×C₆₇	1	1	yes	characteristic, complemented
626	#3096	C₂×C₆₇	1	1	yes	characteristic, complemented
627	#3080	C₂×C₆₇	1	1	yes	characteristic, complemented
628	#3063	C₂×C₆₇	1	1	yes	characteristic, complemented
629	#3062	C₂×C₆₇	1	1	yes	characteristic, complemented
630	#3040	C₂×C₆₇	1	1	yes	characteristic, complemented
631	#3013	C₂×C₆₇	1	1	yes	characteristic, complemented
632	#3012	C₂×C₆₇	1	1	yes	characteristic, complemented
633	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
634	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
635	#2898	C₂×C₆₇	1	1	yes	characteristic, complemented
636	#2897	C₂×C₆₇	1	1	yes	characteristic, complemented
637	C₆₇	#61216	1	1	yes	characteristic, direct product factor, Sylow
638	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic
639	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
640	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
641	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
642	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
643	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic
644	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
645	#553	—	2	2	no	—
646	#553	—	2	2	no	—
647	#553	C₂²×C₆₇	1	2	yes	complemented
648	#553	C₂²×C₆₇	1	2	yes	complemented
649	#552	C₂²×C₆₇	1	2	yes	complemented
650	#552	C₂²×C₆₇	1	2	yes	complemented
651	#548	C₂²×C₆₇	1	2	yes	—
652	#548	C₂²×C₆₇	1	2	yes	—
653	#546	—	2	2	no	—
654	#546	—	2	2	no	—
655	#546	C₂²×C₆₇	1	2	yes	—
656	#546	C₂²×C₆₇	1	2	yes	—
657	#541	—	2	1	no	—
658	#540	—	2	1	no	—
659	#537	C₂²×C₆₇	1	1	yes	characteristic
660	#537	C₂²×C₆₇	1	1	yes	characteristic, complemented
661	#536	—	2	1	no	—
662	#536	C₂²×C₆₇	1	1	yes	characteristic
663	#535	—	2	1	no	—
664	#535	C₂²×C₆₇	1	1	yes	characteristic
665	#532	—	2	1	no	—
666	#532	C₂²×C₆₇	1	1	yes	characteristic
667	#529	—	2	1	no	—
668	#529	—	2	1	no	—
669	C₂×#125	C₂²×C₆₇	1	1	yes	characteristic, complemented
670	C₂×#124	—	2	1	no	—
671	C₂×#124	C₂²×C₆₇	1	1	yes	characteristic
672	#520	C₂²×C₆₇	1	1	yes	characteristic
673	#520	C₂²×C₆₇	1	1	yes	characteristic, complemented
674	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
675	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
676	#488	C₂²×C₆₇	1	2	yes	complemented
677	#488	C₂²×C₆₇	1	2	yes	complemented
678	#488	C₂²×C₆₇	1	2	yes	complemented
679	#488	C₂²×C₆₇	1	2	yes	complemented
680	#485	C₂²×C₆₇	1	2	yes	complemented
681	#485	C₂²×C₆₇	1	2	yes	complemented
682	#484	C₂²×C₆₇	1	2	yes	complemented
683	#483	C₂²×C₆₇	1	2	yes	complemented
684	#482	C₂²×C₆₇	1	2	yes	complemented
685	#482	C₂²×C₆₇	1	2	yes	complemented
686	#481	C₂²×C₆₇	1	2	yes	complemented
687	#480	C₂²×C₆₇	1	2	yes	complemented
688	#479	C₂²×C₆₇	1	2	yes	complemented
689	#479	C₂²×C₆₇	1	2	yes	complemented
690	#478	C₂²×C₆₇	1	2	yes	complemented
691	#478	C₂²×C₆₇	1	2	yes	complemented
692	#470	C₂²×C₆₇	1	2	yes	complemented
693	#469	C₂²×C₆₇	1	2	yes	complemented
694	#468	C₂²×C₆₇	1	2	yes	complemented
695	#468	C₂²×C₆₇	1	2	yes	complemented
696	#467	C₂²×C₆₇	1	2	yes	complemented
697	#466	C₂²×C₆₇	1	2	yes	complemented
698	#465	C₂²×C₆₇	1	2	yes	complemented
699	#465	C₂²×C₆₇	1	2	yes	complemented
700	#464	C₂²×C₆₇	1	2	yes	complemented
701	#464	C₂²×C₆₇	1	2	yes	complemented
702	#463	C₂²×C₆₇	1	2	yes	complemented
703	#463	C₂²×C₆₇	1	2	yes	complemented
704	#452	C₂²×C₆₇	1	2	yes	—
705	#452	C₂²×C₆₇	1	2	yes	complemented
706	#451	C₂²×C₆₇	1	2	yes	complemented
707	#450	C₂²×C₆₇	1	2	yes	—
708	#449	C₂²×C₆₇	1	2	yes	—
709	#449	C₂²×C₆₇	1	2	yes	complemented
710	#448	C₂²×C₆₇	1	2	yes	complemented
711	#447	C₂²×C₆₇	1	2	yes	—
712	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
713	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
714	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
715	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
716	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
717	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
718	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
719	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
720	#436	C₂²×C₆₇	1	2	yes	complemented
721	#436	C₂²×C₆₇	1	2	yes	complemented
722	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
723	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
724	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
725	#428	C₂²×C₆₇	1	1	yes	characteristic, complemented
726	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
727	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
728	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
729	#419	C₂²×C₆₇	1	2	yes	complemented
730	#418	C₂²×C₆₇	1	1	yes	characteristic
731	#418	C₂²×C₆₇	1	2	yes	—
732	#417	C₂²×C₆₇	1	1	yes	characteristic
733	#417	C₂²×C₆₇	1	1	yes	characteristic
734	#417	C₂²×C₆₇	1	2	yes	—
735	#417	C₂²×C₆₇	1	2	yes	complemented
736	#416	C₂²×C₆₇	1	1	yes	characteristic
737	#416	C₂²×C₆₇	1	2	yes	—
738	#416	C₂²×C₆₇	1	2	yes	complemented
739	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
740	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
741	C₂×#103	C₂²×C₆₇	1	1	yes	characteristic, complemented
742	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
743	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
744	C₂×#102	C₂²×C₆₇	1	1	yes	characteristic
745	C₂×#102	C₂²×C₆₇	1	2	yes	—
746	#408	C₂²×C₆₇	1	1	yes	characteristic
747	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
748	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
749	2₋¹⁺⁴	—	2	4	no	—
750	2₋¹⁺⁴	—	4	2	no	—
751	H(5,𝔽₂)	—	2	4	no	—
752	H(5,𝔽₂)	—	4	2	no	—
753	C₂×#41	—	2	1	no	—
754	C₂×#41	—	2	1	no	—
755	C₂×#41	—	2	2	no	—
756	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
757	C₂×#41	C₂³×C₆₇	1	2	yes	—
758	C₂×#41	C₂³×C₆₇	1	2	yes	—
759	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
760	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
761	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
762	C₂²×Q₈	—	2	1	no	—
763	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
764	C₂²×Q₈	C₂³×C₆₇	1	2	yes	—
765	C₂²×D₄	—	2	1	no	—
766	C₂²×D₄	—	2	2	no	—
767	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
768	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
769	#137	—	4	2	no	—
770	AGL(1,ℤ/8)	—	4	2	no	—
771	#135	—	2	4	no	—
772	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
773	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	—
774	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
775	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
776	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
777	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
778	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
779	C₂×D₈	C₂³×C₆₇	1	2	yes	—
780	#131	—	4	2	no	—
781	#131	—	4	2	no	—
782	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
783	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
784	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
785	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
786	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
787	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
788	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
789	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
790	C₄⋊Q₈	—	2	1	no	—
791	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
792	#127	—	2	1	no	—
793	#127	D₄×C₆₇	1	1	yes	characteristic
794	#126	—	2	2	no	—
795	#126	—	2	2	no	—
796	#126	—	2	2	no	—
797	#126	—	2	2	no	—
798	#125	—	2	2	no	—
799	#125	—	2	2	no	—
800	#125	—	2	1	no	—
801	#125	—	2	1	no	—
802	#125	C₂³×C₆₇	1	2	yes	—
803	#125	C₂³×C₆₇	1	2	yes	—
804	#124	—	2	1	no	—
805	#124	—	2	1	no	—
806	#124	—	2	2	no	—
807	#124	—	2	2	no	—
808	#124	—	2	1	no	—
809	#124	—	2	1	no	—
810	#124	D₄×C₆₇	1	1	yes	characteristic
811	#124	D₄×C₆₇	1	1	yes	characteristic
812	#124	C₂³×C₆₇	1	2	yes	—
813	#124	C₂³×C₆₇	1	2	yes	—
814	#123	—	2	2	no	—
815	#123	—	2	2	no	—
816	#123	—	2	2	no	—
817	#123	—	2	2	no	—
818	#123	—	2	2	no	—
819	#123	—	2	2	no	—
820	#123	—	2	2	no	—
821	C₂²⋊Q₈	—	2	1	no	—
822	C₂²⋊Q₈	—	2	1	no	—
823	C₂²⋊Q₈	—	2	2	no	—
824	C₂²⋊Q₈	—	2	2	no	—
825	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
826	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
827	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
828	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
829	#121	—	2	1	no	—
830	#121	—	2	1	no	—
831	#121	—	2	2	no	—
832	#121	—	2	2	no	—
833	#121	—	2	2	no	—
834	#121	—	2	2	no	—
835	#121	—	2	2	no	—
836	#121	—	2	2	no	—
837	#121	—	2	2	no	—
838	#121	—	2	2	no	—
839	#121	D₄×C₆₇	1	2	yes	—
840	#121	D₄×C₆₇	1	2	yes	—
841	#121	C₂³×C₆₇	1	2	yes	—
842	#121	C₂³×C₆₇	1	2	yes	—
843	#121	C₂³×C₆₇	1	2	yes	—
844	#121	C₂³×C₆₇	1	2	yes	—
845	#120	—	2	2	no	—
846	#120	—	2	2	no	—
847	#120	—	2	2	no	—
848	C₄×Q₈	—	2	1	no	—
849	C₄×Q₈	—	2	1	no	—
850	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
851	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
852	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
853	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
854	C₄×D₄	—	2	1	no	—
855	C₄×D₄	—	2	2	no	—
856	C₄×D₄	—	2	1	no	—
857	C₄×D₄	—	2	2	no	—
858	C₄×D₄	—	2	1	no	—
859	C₄×D₄	—	2	1	no	—
860	C₄×D₄	—	2	1	no	—
861	C₄×D₄	—	2	1	no	—
862	C₄×D₄	—	2	2	no	—
863	C₄×D₄	—	2	2	no	—
864	C₄×D₄	—	2	2	no	—
865	C₄×D₄	—	2	2	no	—
866	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
867	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
868	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
869	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
870	C₄×D₄	C₂³×C₆₇	1	2	yes	—
871	C₄×D₄	C₂³×C₆₇	1	2	yes	—
872	#117	—	2	2	no	—
873	#117	—	2	2	no	—
874	#117	—	2	1	no	—
875	#117	—	2	1	no	—
876	#117	C₂³×C₆₇	1	1	yes	characteristic
877	#117	C₂³×C₆₇	1	1	yes	characteristic
878	#117	C₂³×C₆₇	1	2	yes	—
879	#117	C₂³×C₆₇	1	2	yes	—
880	C₂×C₄⋊C₄	—	2	1	no	—
881	C₂×C₄⋊C₄	—	2	1	no	—
882	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
883	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
884	C₂×C₄⋊C₄	C₂³×C₆₇	1	1	yes	characteristic
885	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
886	C₂×C₂²⋊C₄	—	2	1	no	—
887	C₂×C₂²⋊C₄	—	2	1	no	—
888	C₂×C₂²⋊C₄	—	2	2	no	—
889	C₂×C₂²⋊C₄	—	2	2	no	—
890	C₂×C₄²	—	2	1	no	—
891	C₂×C₄²	—	2	1	no	—
892	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
893	#107	C₂³×C₆₇	1	1	yes	characteristic
894	#107	C₂³×C₆₇	1	1	yes	characteristic
895	#107	C₂³×C₆₇	1	2	yes	—
896	#107	C₂³×C₆₇	1	2	yes	—
897	#106	C₂³×C₆₇	1	1	yes	characteristic
898	#106	C₂³×C₆₇	1	1	yes	characteristic
899	#106	C₂³×C₆₇	1	2	yes	—
900	#106	C₂³×C₆₇	1	2	yes	—
901	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
902	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
903	#103	C₂³×C₆₇	1	1	yes	characteristic
904	#103	C₂³×C₆₇	1	2	yes	—
905	#103	C₂³×C₆₇	1	2	yes	—
906	#103	C₂³×C₆₇	1	2	yes	—
907	#103	C₂³×C₆₇	1	2	yes	—
908	#103	C₂³×C₆₇	1	2	yes	—
909	#103	C₂³×C₆₇	1	2	yes	—
910	#103	C₂³×C₆₇	1	1	yes	characteristic
911	#103	C₂³×C₆₇	1	2	yes	—
912	#103	C₂³×C₆₇	1	2	yes	—
913	#103	C₂³×C₆₇	1	1	yes	characteristic
914	#103	C₂³×C₆₇	1	1	yes	characteristic
915	#102	C₂³×C₆₇	1	1	yes	characteristic
916	#102	C₂³×C₆₇	1	2	yes	—
917	#102	C₂³×C₆₇	1	2	yes	—
918	#102	C₂³×C₆₇	1	2	yes	—
919	#102	C₂³×C₆₇	1	2	yes	—
920	#102	C₂³×C₆₇	1	2	yes	—
921	#102	C₂³×C₆₇	1	2	yes	—
922	#102	C₂³×C₆₇	1	1	yes	characteristic
923	#102	C₂³×C₆₇	1	2	yes	—
924	#102	C₂³×C₆₇	1	2	yes	—
925	#102	C₂³×C₆₇	1	1	yes	characteristic
926	#102	C₂³×C₆₇	1	1	yes	characteristic
927	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
928	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
929	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
930	C₂²⋊C₈	C₂³×C₆₇	1	2	yes	—
931	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
932	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
933	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
934	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
935	C₂⁴	—	2	2	no	—
936	C₂⁴	—	2	1	no	—
937	#41	—	2	2	no	—
938	#41	—	2	2	no	—
939	#41	—	2	2	no	—
940	#41	—	2	2	no	—
941	#41	—	2	2	no	—
942	#41	—	2	4	no	—
943	#41	—	2	4	no	—
944	#41	—	2	2	no	—
945	#41	—	2	2	no	—
946	#41	—	4	2	no	—
947	#41	—	4	2	no	—
948	#41	—	4	4	no	—
949	#41	—	4	4	no	—
950	#41	—	4	8	no	—
951	#41	#41×C₆₇	1	4	yes	—
952	C₂×Q₈	—	2	2	no	—
953	C₂×Q₈	—	2	1	no	—
954	C₂×Q₈	—	2	4	no	—
955	C₂×Q₈	—	2	2	no	—
956	C₂×Q₈	—	2	2	no	—
957	C₂×Q₈	—	4	2	no	—
958	C₂×Q₈	—	4	4	no	—
959	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
960	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
961	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
962	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
963	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	2	4	no	—
966	C₂×D₄	—	2	1	no	—
967	C₂×D₄	—	2	2	no	—
968	C₂×D₄	—	2	2	no	—
969	C₂×D₄	—	2	2	no	—
970	C₂×D₄	—	2	2	no	—
971	C₂×D₄	—	2	2	no	—
972	C₂×D₄	—	2	2	no	—
973	C₂×D₄	—	2	2	no	—
974	C₂×D₄	—	2	1	no	—
975	C₂×D₄	—	2	2	no	—
976	C₂×D₄	—	2	2	no	—
977	C₂×D₄	—	4	2	no	—
978	C₂×D₄	—	4	4	no	—
979	C₂×D₄	—	4	8	no	—
980	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
981	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
982	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
983	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
984	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
985	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
986	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
987	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
988	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
989	C₂²×C₄	—	2	1	no	—
990	C₂²×C₄	—	2	1	no	—
991	C₂²×C₄	—	2	2	no	—
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	2	no	—
995	C₂²×C₄	—	2	2	no	—
996	C₂²×C₄	—	2	1	no	—
997	C₂²×C₄	—	2	2	no	—
998	C₂²×C₄	—	2	2	no	—
999	C₂²×C₄	—	2	1	no	—
1000	C₂²×C₄	—	2	1	no	—
1001	C₂²×C₄	—	2	1	no	—
1002	C₂²×C₄	—	2	1	no	—
1003	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1004	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
1005	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1006	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
1007	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	4	2	no	—
1010	SD₁₆	—	2	2	no	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	4	2	no	—
1013	SD₁₆	—	4	2	no	—
1014	D₈	—	2	2	no	—
1015	D₈	—	4	2	no	—
1016	M₁₆	—	2	2	no	—
1017	M₁₆	—	2	2	no	—
1018	M₁₆	—	4	2	no	—
1019	M₁₆	—	4	2	no	—
1020	C₂×C₈	—	2	2	no	—
1021	C₂×C₈	—	2	2	no	—
1022	C₂×C₈	—	4	2	no	—
1023	C₂×C₈	—	4	2	no	—
1024	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1025	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1026	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1027	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
1028	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1029	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
1030	C₄⋊C₄	—	2	2	no	—
1031	C₄⋊C₄	—	2	2	no	—
1032	C₄⋊C₄	—	2	2	no	—
1033	C₄⋊C₄	—	2	2	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	2	no	—
1037	C₄⋊C₄	—	2	2	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	2	1	no	—
1042	C₄⋊C₄	—	2	2	no	—
1043	C₄⋊C₄	—	2	2	no	—
1044	C₄⋊C₄	—	2	2	no	—
1045	C₄⋊C₄	—	2	2	no	—
1046	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1047	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1048	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1049	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1050	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1051	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
1052	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1053	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
1054	C₂²⋊C₄	—	2	2	no	—
1055	C₂²⋊C₄	—	2	2	no	—
1056	C₂²⋊C₄	—	2	2	no	—
1057	C₂²⋊C₄	—	2	2	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	2	no	—
1061	C₂²⋊C₄	—	2	2	no	—
1062	C₂²⋊C₄	—	2	2	no	—
1063	C₂²⋊C₄	—	2	2	no	—
1064	C₂²⋊C₄	—	2	2	no	—
1065	C₂²⋊C₄	—	2	2	no	—
1066	C₂²⋊C₄	—	2	2	no	—
1067	C₂²⋊C₄	—	2	2	no	—
1068	C₂²⋊C₄	—	2	1	no	—
1069	C₂²⋊C₄	—	2	1	no	—
1070	C₂²⋊C₄	—	2	1	no	—
1071	C₂²⋊C₄	—	2	1	no	—
1072	C₂²⋊C₄	—	2	2	no	—
1073	C₂²⋊C₄	—	2	2	no	—
1074	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1075	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1076	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1077	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	2	1	no	—
1084	C₄²	—	2	2	no	—
1085	C₄²	—	2	2	no	—
1086	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1087	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
1088	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1089	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
1090	C₂³	—	2	1	no	—
1091	C₂³	—	2	1	no	—
1092	C₂³	—	2	2	no	—
1093	C₂³	—	4	4	no	—
1094	C₂³	—	4	2	no	—
1095	C₂³	—	8	1	no	—
1096	C₂³	—	8	1	no	—
1097	C₂³	—	8	2	no	—
1098	C₂³	—	8	2	no	—
1099	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1100	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
1101	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
1102	Q₈	—	2	2	no	—
1103	Q₈	—	2	2	no	—
1104	Q₈	—	2	1	no	—
1105	Q₈	—	2	1	no	—
1106	Q₈	—	2	2	no	—
1107	Q₈	—	2	1	no	—
1108	Q₈	—	2	2	no	—
1109	Q₈	—	4	4	no	—
1110	Q₈	—	4	2	no	—
1111	Q₈	C₂×#41×C₆₇	1	2	yes	—
1112	D₄	—	2	4	no	—
1113	D₄	—	2	4	no	—
1114	D₄	—	2	4	no	—
1115	D₄	—	2	2	no	—
1116	D₄	—	2	2	no	—
1117	D₄	—	2	1	no	—
1118	D₄	—	2	2	no	—
1119	D₄	—	2	1	no	—
1120	D₄	—	2	1	no	—
1121	D₄	—	2	2	no	—
1122	D₄	—	4	2	no	—
1123	D₄	—	4	2	no	—
1124	D₄	—	4	4	no	—
1125	D₄	—	4	4	no	—
1126	D₄	—	4	4	no	—
1127	D₄	—	4	2	no	—
1128	D₄	—	4	2	no	—
1129	D₄	—	8	2	no	—
1130	D₄	—	8	2	no	—
1131	D₄	—	8	2	no	—
1132	D₄	—	8	2	no	—
1133	D₄	C₂×#41×C₆₇	1	2	yes	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	4	no	—
1136	C₂×C₄	—	2	2	no	—
1137	C₂×C₄	—	2	2	no	—
1138	C₂×C₄	—	2	2	no	—
1139	C₂×C₄	—	2	2	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	1	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	2	no	—
1146	C₂×C₄	—	2	2	no	—
1147	C₂×C₄	—	2	2	no	—
1148	C₂×C₄	—	4	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	4	no	—
1151	C₂×C₄	—	4	4	no	—
1152	C₂×C₄	—	4	4	no	—
1153	C₂×C₄	—	4	2	no	—
1154	C₂×C₄	—	4	2	no	—
1155	C₂×C₄	—	8	1	no	—
1156	C₂×C₄	—	8	1	no	—
1157	C₂×C₄	—	8	1	no	—
1158	C₂×C₄	—	8	1	no	—
1159	C₂×C₄	—	8	2	no	—
1160	C₂×C₄	—	8	2	no	—
1161	C₂×C₄	—	8	1	no	—
1162	C₂×C₄	—	8	1	no	—
1163	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1164	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1165	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1166	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1167	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1168	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1169	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1170	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
1171	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1172	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1173	C₈	—	2	1	no	—
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	2	no	—
1178	C₈	—	2	2	no	—
1179	C₂²	—	2	1	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	2	no	—
1182	C₂²	—	2	2	no	—
1183	C₂²	—	2	2	no	—
1184	C₂²	—	2	2	no	—
1185	C₂²	—	2	2	no	—
1186	C₂²	—	2	2	no	—
1187	C₂²	—	2	2	no	—
1188	C₂²	—	4	1	no	—
1189	C₂²	—	4	1	no	—
1190	C₂²	—	4	1	no	—
1191	C₂²	—	4	1	no	—
1192	C₂²	—	4	2	no	—
1193	C₂²	—	4	2	no	—
1194	C₂²	—	4	2	no	—
1195	C₂²	—	4	1	no	—
1196	C₂²	—	16	2	no	—
1197	C₂²	—	16	4	no	—
1198	C₂²	#546×C₆₇	1	2	yes	—
1199	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	2	no	—
1206	C₄	—	2	2	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	2	no	—
1210	C₄	—	4	2	no	—
1211	C₄	—	4	1	no	—
1212	C₄	—	4	1	no	—
1213	C₄	—	4	2	no	—
1214	C₄	—	4	1	no	—
1215	C₄	#546×C₆₇	1	2	yes	—
1216	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
1217	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1218	C₂	—	2	2	no	—
1219	C₂	—	4	2	no	—
1220	C₂	—	4	2	no	—
1221	C₂	—	4	2	no	—
1222	C₂	—	8	2	no	—
1223	C₂	—	8	1	no	—
1224	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
1225	C₂	C₆₇×#3584	1	1	yes	characteristic
1226	C₂	C₆₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₆₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ #532×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3512	C₂	semidirect
2. C₆₇×#3500	C₂	semidirect
3. C₆₇×#3327	C₂	semidirect
4. C₆₇×#3326	C₂	semidirect
5. C₆₇×#3323	C₂	semidirect
6. C₆₇×#3322	C₂	semidirect
7. C₆₇×#3301	C₂	semidirect
8. C₆₇×#3300	C₂	semidirect
9. C₆₇×#3297	C₂	semidirect
10. C₆₇×#3296	C₂	semidirect
11. C₂×#488×C₆₇	C₂	semidirect
12. C₆₇×#3097	C₂	semidirect
13. C₆₇×#3096	C₂	semidirect
14. C₆₇×#3080	C₂	semidirect
15. C₆₇×#3063	C₂	semidirect
16. C₆₇×#3062	C₂	semidirect
17. C₆₇×#3040	C₂	semidirect
18. C₆₇×#3013	C₂	semidirect
19. C₆₇×#3012	C₂	semidirect
20. C₄×#135×C₆₇	C₂	semidirect
21. C₆₇×#2931	C₂	semidirect
22. C₆₇×#2898	C₂	semidirect
23. C₆₇×#2897	C₂	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
30. C₂×#131×C₆₇	C₂²	semidirect
33. #553×C₆₇	C₂²	semidirect
34. #553×C₆₇	C₂²	semidirect
35. #552×C₆₇	C₂²	semidirect
36. #552×C₆₇	C₂²	semidirect
46. #537×C₆₇	C₂²	semidirect
55. C₂×#125×C₆₇	C₂²	semidirect
59. #520×C₆₇	C₂²	semidirect
61. C₄×#41×C₆₇	C₂²	semidirect
62. #488×C₆₇	C₂²	semidirect
63. #488×C₆₇	C₂²	semidirect
64. #488×C₆₇	C₂²	semidirect
65. #488×C₆₇	C₂²	semidirect
66. #485×C₆₇	C₂²	semidirect
67. #485×C₆₇	C₂²	semidirect
68. #484×C₆₇	C₂²	semidirect
69. #483×C₆₇	C₂²	semidirect
70. #482×C₆₇	C₂²	semidirect
71. #482×C₆₇	C₂²	semidirect
72. #481×C₆₇	C₂²	semidirect
73. #480×C₆₇	C₂²	semidirect
74. #479×C₆₇	C₂²	semidirect
75. #479×C₆₇	C₂²	semidirect
76. #478×C₆₇	C₂²	semidirect
77. #478×C₆₇	C₂²	semidirect
78. #470×C₆₇	C₂²	semidirect
79. #469×C₆₇	C₂²	semidirect
80. #468×C₆₇	C₂²	semidirect
81. #468×C₆₇	C₂²	semidirect
82. #467×C₆₇	C₂²	semidirect
83. #466×C₆₇	C₂²	semidirect
84. #465×C₆₇	C₂²	semidirect
85. #465×C₆₇	C₂²	semidirect
86. #464×C₆₇	C₂²	semidirect
87. #464×C₆₇	C₂²	semidirect
88. #463×C₆₇	C₂²	semidirect
89. #463×C₆₇	C₂²	semidirect
91. #452×C₆₇	C₂²	semidirect
92. #451×C₆₇	C₂²	semidirect
95. #449×C₆₇	C₂²	semidirect
96. #448×C₆₇	C₂²	semidirect
98. C₄×Q₁₆×C₆₇	C₂²	semidirect
99. C₄×Q₁₆×C₆₇	C₂²	semidirect
100. C₄×SD₁₆×C₆₇	C₂²	semidirect
101. C₄×SD₁₆×C₆₇	C₂²	semidirect
102. C₄×SD₁₆×C₆₇	C₂²	semidirect
103. C₄×SD₁₆×C₆₇	C₂²	semidirect
104. C₄×D₈×C₆₇	C₂²	semidirect
105. C₄×D₈×C₆₇	C₂²	semidirect
106. #436×C₆₇	C₂²	semidirect
107. #436×C₆₇	C₂²	semidirect
108. C₈×D₄×C₆₇	C₂²	semidirect
109. C₈×D₄×C₆₇	C₂²	semidirect
110. #428×C₆₇	C₂²	semidirect
111. #428×C₆₇	C₂²	semidirect
112. #427×C₆₇	C₂²	semidirect
113. #423×C₆₇	C₂²	semidirect
114. #419×C₆₇	C₂²	semidirect
115. #419×C₆₇	C₂²	semidirect
121. #417×C₆₇	C₂²	semidirect
124. #416×C₆₇	C₂²	semidirect
125. #416×C₆₇	C₂²	semidirect
126. C₂×#103×C₆₇	C₂²	semidirect
127. C₂×#103×C₆₇	C₂²	semidirect
128. C₂×#103×C₆₇	C₂²	semidirect
133. #408×C₆₇	C₂²	semidirect
134. C₂×C₄×C₈×C₆₇	C₂²	semidirect
604. #61216	C₆₇	direct (N × H)
614. #3512	C₂×C₆₇	semidirect
615. #3500	C₂×C₆₇	semidirect
616. #3327	C₂×C₆₇	semidirect
617. #3326	C₂×C₆₇	semidirect
618. #3323	C₂×C₆₇	semidirect
619. #3322	C₂×C₆₇	semidirect
620. #3301	C₂×C₆₇	semidirect
621. #3300	C₂×C₆₇	semidirect
622. #3297	C₂×C₆₇	semidirect
623. #3296	C₂×C₆₇	semidirect
624. C₂×#488	C₂×C₆₇	semidirect
625. #3097	C₂×C₆₇	semidirect
626. #3096	C₂×C₆₇	semidirect
627. #3080	C₂×C₆₇	semidirect
628. #3063	C₂×C₆₇	semidirect
629. #3062	C₂×C₆₇	semidirect
630. #3040	C₂×C₆₇	semidirect
631. #3013	C₂×C₆₇	semidirect
632. #3012	C₂×C₆₇	semidirect
633. C₄×#135	C₂×C₆₇	semidirect
634. #2931	C₂×C₆₇	semidirect
635. #2898	C₂×C₆₇	semidirect
636. #2897	C₂×C₆₇	semidirect
637. C₆₇	#61216	direct (N × H)
640. C₂×#137	C₂²×C₆₇	semidirect
644. C₂×#131	C₂²×C₆₇	semidirect
647. #553	C₂²×C₆₇	semidirect
648. #553	C₂²×C₆₇	semidirect
649. #552	C₂²×C₆₇	semidirect
650. #552	C₂²×C₆₇	semidirect
660. #537	C₂²×C₆₇	semidirect
669. C₂×#125	C₂²×C₆₇	semidirect
673. #520	C₂²×C₆₇	semidirect
675. C₄×#41	C₂²×C₆₇	semidirect
676. #488	C₂²×C₆₇	semidirect
677. #488	C₂²×C₆₇	semidirect
678. #488	C₂²×C₆₇	semidirect
679. #488	C₂²×C₆₇	semidirect
680. #485	C₂²×C₆₇	semidirect
681. #485	C₂²×C₆₇	semidirect
682. #484	C₂²×C₆₇	semidirect
683. #483	C₂²×C₆₇	semidirect
684. #482	C₂²×C₆₇	semidirect
685. #482	C₂²×C₆₇	semidirect
686. #481	C₂²×C₆₇	semidirect
687. #480	C₂²×C₆₇	semidirect
688. #479	C₂²×C₆₇	semidirect
689. #479	C₂²×C₆₇	semidirect
690. #478	C₂²×C₆₇	semidirect
691. #478	C₂²×C₆₇	semidirect
692. #470	C₂²×C₆₇	semidirect
693. #469	C₂²×C₆₇	semidirect
694. #468	C₂²×C₆₇	semidirect
695. #468	C₂²×C₆₇	semidirect
696. #467	C₂²×C₆₇	semidirect
697. #466	C₂²×C₆₇	semidirect
698. #465	C₂²×C₆₇	semidirect
699. #465	C₂²×C₆₇	semidirect
700. #464	C₂²×C₆₇	semidirect
701. #464	C₂²×C₆₇	semidirect
702. #463	C₂²×C₆₇	semidirect
703. #463	C₂²×C₆₇	semidirect
705. #452	C₂²×C₆₇	semidirect
706. #451	C₂²×C₆₇	semidirect
709. #449	C₂²×C₆₇	semidirect
710. #448	C₂²×C₆₇	semidirect
712. C₄×Q₁₆	C₂²×C₆₇	semidirect
713. C₄×Q₁₆	C₂²×C₆₇	semidirect
714. C₄×SD₁₆	C₂²×C₆₇	semidirect
715. C₄×SD₁₆	C₂²×C₆₇	semidirect
716. C₄×SD₁₆	C₂²×C₆₇	semidirect
717. C₄×SD₁₆	C₂²×C₆₇	semidirect
718. C₄×D₈	C₂²×C₆₇	semidirect
719. C₄×D₈	C₂²×C₆₇	semidirect
720. #436	C₂²×C₆₇	semidirect
721. #436	C₂²×C₆₇	semidirect
722. C₈×D₄	C₂²×C₆₇	semidirect
723. C₈×D₄	C₂²×C₆₇	semidirect
724. #428	C₂²×C₆₇	semidirect
725. #428	C₂²×C₆₇	semidirect
726. #427	C₂²×C₆₇	semidirect
727. #423	C₂²×C₆₇	semidirect
728. #419	C₂²×C₆₇	semidirect
729. #419	C₂²×C₆₇	semidirect
735. #417	C₂²×C₆₇	semidirect
738. #416	C₂²×C₆₇	semidirect
739. #416	C₂²×C₆₇	semidirect
740. C₂×#103	C₂²×C₆₇	semidirect
741. C₂×#103	C₂²×C₆₇	semidirect
742. C₂×#103	C₂²×C₆₇	semidirect
747. #408	C₂²×C₆₇	semidirect
748. C₂×C₄×C₈	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×#3512	2
C₆₇×#3500	2
C₆₇×#3327	2
C₆₇×#3326	2
C₆₇×#3323	2
C₆₇×#3322	2
C₆₇×#3301	2
C₆₇×#3300	2
C₆₇×#3297	2
C₆₇×#3296	2
C₂×#488×C₆₇	2
C₆₇×#3097	2
C₆₇×#3096	2
C₆₇×#3080	2
C₆₇×#3063	2
C₆₇×#3062	2
C₆₇×#3040	2
C₆₇×#3013	2
C₆₇×#3012	2
C₄×#135×C₆₇	2
C₆₇×#2931	2
C₆₇×#2898	2
C₆₇×#2897	2
#61216	67

Subgroups — C67×#61216 #30740467

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61216 #30740467