Subgroups — C₆₇×#61059 #30740310

Order 17152.

2878 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#577×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#3484	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3275	C₂	1	4	yes	maximal, complemented
6	C₆₇×#3274	C₂	1	4	yes	maximal, complemented
7	C₆₇×#3268	C₂	1	4	yes	maximal, complemented
8	C₆₇×#3265	C₂	1	4	yes	maximal, complemented
9	C₆₇×#3155	C₂	1	1	yes	maximal, characteristic, complemented
10	C₆₇×#3058	C₂	1	1	yes	maximal, characteristic, complemented
11	C₆₇×#3054	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3043	C₂	1	1	yes	maximal, characteristic, complemented
13	C₆₇×#3041	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3010	C₂	1	1	yes	maximal, characteristic, complemented
15	C₆₇×#3008	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3005	C₂	1	1	yes	maximal, characteristic, complemented
17	C₆₇×#3003	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2949	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2930	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×2₋¹⁺⁴×C₆₇	C₂²	1	1	yes	characteristic, complemented
21	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	1	yes	characteristic
22	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
23	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
24	#577×C₆₇	—	2	8	no	—
25	C₂×#137×C₆₇	C₂²	1	1	yes	characteristic, complemented
26	C₂×#137×C₆₇	C₂²	1	2	yes	complemented
27	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
28	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
30	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	4	yes	complemented
31	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
34	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂×#135×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic
37	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
39	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
40	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic, complemented
42	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
43	#550×C₆₇	—	2	2	no	—
44	#550×C₆₇	C₂²	1	4	yes	complemented
45	#548×C₆₇	—	2	2	no	—
46	#548×C₆₇	C₂²	1	4	yes	complemented
47	#546×C₆₇	—	2	2	no	—
48	#546×C₆₇	C₂²	1	4	yes	complemented
49	D₄²×C₆₇	—	2	2	no	—
50	D₄²×C₆₇	C₂²	1	4	yes	complemented
51	#535×C₆₇	—	2	2	no	—
52	#535×C₆₇	C₂²	1	1	yes	characteristic
53	#535×C₆₇	C₂²	1	1	yes	characteristic
54	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
55	#535×C₆₇	C₂²	1	1	yes	characteristic, complemented
56	#534×C₆₇	—	2	2	no	—
57	#525×C₆₇	—	2	2	no	—
58	#525×C₆₇	C₂²	1	1	yes	characteristic
59	#525×C₆₇	C₂²	1	1	yes	characteristic
60	#525×C₆₇	C₂²	1	1	yes	characteristic, complemented
61	C₂×#120×C₆₇	—	2	2	no	—
62	#519×C₆₇	C₂²	1	1	yes	characteristic, complemented
63	#518×C₆₇	C₂²	1	1	yes	characteristic
64	#496×C₆₇	C₂²	1	2	yes	complemented
65	#496×C₆₇	C₂²	1	2	yes	complemented
66	#495×C₆₇	C₂²	1	2	yes	complemented
67	#493×C₆₇	C₂²	1	2	yes	complemented
68	#470×C₆₇	C₂²	1	2	yes	complemented
69	#469×C₆₇	C₂²	1	4	yes	complemented
70	#469×C₆₇	C₂²	1	2	yes	complemented
71	#468×C₆₇	C₂²	1	2	yes	complemented
72	#468×C₆₇	C₂²	1	2	yes	complemented
73	#466×C₆₇	C₂²	1	4	yes	complemented
74	#464×C₆₇	C₂²	1	4	yes	complemented
75	#463×C₆₇	C₂²	1	4	yes	complemented
76	#460×C₆₇	C₂²	1	4	yes	complemented
77	#459×C₆₇	C₂²	1	4	yes	complemented
78	#452×C₆₇	C₂²	1	4	yes	complemented
79	#450×C₆₇	C₂²	1	4	yes	complemented
80	#449×C₆₇	C₂²	1	4	yes	complemented
81	#449×C₆₇	C₂²	1	4	yes	complemented
82	#449×C₆₇	C₂²	1	4	yes	complemented
83	#448×C₆₇	C₂²	1	4	yes	complemented
84	#447×C₆₇	C₂²	1	4	yes	complemented
85	#447×C₆₇	C₂²	1	4	yes	complemented
86	#440×C₆₇	C₂²	1	4	yes	complemented
87	C₄×SD₁₆×C₆₇	C₂²	1	4	yes	complemented
88	#436×C₆₇	C₂²	1	4	yes	complemented
89	#435×C₆₇	C₂²	1	4	yes	complemented
90	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
91	#424×C₆₇	C₂²	1	1	yes	characteristic, complemented
92	#419×C₆₇	C₂²	1	1	yes	characteristic, complemented
93	#418×C₆₇	C₂²	1	1	yes	characteristic
94	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
95	#418×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
97	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
98	#408×C₆₇	C₂²	1	1	yes	characteristic, complemented
99	#407×C₆₇	C₂²	1	1	yes	characteristic, complemented
100	#405×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	C₂⁵×C₆₇	—	2	1	no	—
102	2₋¹⁺⁴×C₆₇	—	2	4	no	—
103	2₋¹⁺⁴×C₆₇	—	4	2	no	—
104	H(5,𝔽₂)×C₆₇	—	2	4	no	—
105	H(5,𝔽₂)×C₆₇	—	4	2	no	—
106	C₂×#41×C₆₇	—	2	1	no	—
107	C₂×#41×C₆₇	—	2	2	no	—
108	C₂×#41×C₆₇	—	2	1	no	—
109	C₂×#41×C₆₇	—	2	2	no	—
110	C₂×#41×C₆₇	—	2	4	no	—
111	C₂×#41×C₆₇	—	4	2	no	—
112	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
113	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
114	C₂×#41×C₆₇	C₂³	1	2	yes	—
115	C₂×#41×C₆₇	C₂³	1	4	yes	—
116	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
117	C₂×#41×C₆₇	C₂³	1	2	yes	complemented
118	C₂²×Q₈×C₆₇	—	2	1	no	—
119	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
120	C₂²×Q₈×C₆₇	C₂³	1	2	yes	complemented
121	C₂²×D₄×C₆₇	—	2	4	no	—
122	C₂²×D₄×C₆₇	—	2	1	no	—
123	C₂²×D₄×C₆₇	—	2	2	no	—
124	C₂²×D₄×C₆₇	—	2	1	no	—
125	C₂²×D₄×C₆₇	—	2	4	no	—
126	C₂²×D₄×C₆₇	—	2	1	no	—
127	C₂²×D₄×C₆₇	—	2	2	no	—
128	C₂²×D₄×C₆₇	—	4	2	no	—
129	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
132	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₆₇	—	2	1	no	—
135	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
136	#137×C₆₇	—	2	4	no	—
137	#137×C₆₇	—	2	8	no	—
138	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
139	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
140	AGL(1,ℤ/8)×C₆₇	—	2	16	no	—
141	AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
142	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
143	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
144	#135×C₆₇	—	2	8	no	—
145	#135×C₆₇	—	2	4	no	—
146	C₂×Q₁₆×C₆₇	C₂³	1	2	yes	complemented
147	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
148	C₂×SD₁₆×C₆₇	—	2	4	no	—
149	C₂×SD₁₆×C₆₇	—	2	8	no	—
150	C₂×SD₁₆×C₆₇	D₄	1	8	yes	complemented
151	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
152	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
153	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
154	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
155	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	—
156	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
157	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
158	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic, complemented
159	C₂×SD₁₆×C₆₇	C₂³	1	2	yes	complemented
160	C₂×D₈×C₆₇	—	2	4	no	—
161	C₂×D₈×C₆₇	—	2	4	no	—
162	C₂×D₈×C₆₇	C₂³	1	4	yes	—
163	C₂×D₈×C₆₇	C₂³	1	2	yes	—
164	C₂×D₈×C₆₇	C₂³	1	2	yes	—
165	C₂×D₈×C₆₇	C₂³	1	2	yes	—
166	C₂×D₈×C₆₇	C₂³	1	2	yes	—
167	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic, complemented
168	C₂×D₈×C₆₇	C₂³	1	2	yes	complemented
169	#131×C₆₇	—	2	4	no	—
170	C₂×M₁₆×C₆₇	—	2	4	no	—
171	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
172	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
173	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
174	C₂×M₁₆×C₆₇	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₆₇	C₂³	1	2	yes	complemented
176	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₆₇	C₂³	1	2	yes	complemented
179	#127×C₆₇	—	2	4	no	—
180	#127×C₆₇	—	2	1	no	—
181	#127×C₆₇	—	2	1	no	—
182	#127×C₆₇	C₂³	1	2	yes	—
183	#127×C₆₇	C₂³	1	2	yes	complemented
184	#124×C₆₇	—	2	1	no	—
185	#124×C₆₇	—	2	1	no	—
186	#124×C₆₇	—	2	4	no	—
187	#124×C₆₇	C₂³	1	2	yes	—
188	#124×C₆₇	C₂³	1	2	yes	complemented
189	#123×C₆₇	—	2	1	no	—
190	#123×C₆₇	—	2	1	no	—
191	#123×C₆₇	—	2	4	no	—
192	#123×C₆₇	D₄	1	2	yes	—
193	C₂²⋊Q₈×C₆₇	—	2	4	no	—
194	C₂²⋊Q₈×C₆₇	D₄	1	2	yes	—
195	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
196	C₂²⋊Q₈×C₆₇	C₂³	1	2	yes	—
197	#121×C₆₇	—	2	4	no	—
198	#121×C₆₇	—	2	4	no	—
199	#121×C₆₇	—	2	2	no	—
200	#121×C₆₇	—	2	2	no	—
201	#121×C₆₇	—	2	4	no	—
202	#121×C₆₇	—	2	4	no	—
203	#121×C₆₇	—	2	4	no	—
204	#121×C₆₇	D₄	1	2	yes	—
205	#121×C₆₇	C₂³	1	4	yes	—
206	#121×C₆₇	C₂³	1	2	yes	—
207	#121×C₆₇	C₂³	1	2	yes	—
208	#121×C₆₇	C₂³	1	4	yes	complemented
209	#120×C₆₇	—	2	1	no	—
210	#120×C₆₇	—	2	1	no	—
211	#120×C₆₇	—	2	2	no	—
212	#120×C₆₇	—	2	4	no	—
213	#120×C₆₇	—	2	2	no	—
214	#120×C₆₇	—	2	2	no	—
215	#120×C₆₇	—	2	4	no	—
216	#120×C₆₇	—	2	2	no	—
217	#120×C₆₇	—	2	4	no	—
218	#120×C₆₇	D₄	1	2	yes	—
219	C₄×Q₈×C₆₇	—	2	2	no	—
220	C₄×Q₈×C₆₇	C₂³	1	4	yes	complemented
221	C₄×D₄×C₆₇	—	2	2	no	—
222	C₄×D₄×C₆₇	—	2	2	no	—
223	C₄×D₄×C₆₇	—	2	2	no	—
224	C₄×D₄×C₆₇	—	2	4	no	—
225	C₄×D₄×C₆₇	—	2	4	no	—
226	C₄×D₄×C₆₇	C₂³	1	4	yes	—
227	C₄×D₄×C₆₇	C₂³	1	4	yes	—
228	#117×C₆₇	—	2	2	no	—
229	#117×C₆₇	C₂³	1	1	yes	characteristic
230	#117×C₆₇	C₂³	1	1	yes	characteristic
231	#117×C₆₇	C₂³	1	1	yes	characteristic
232	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
233	C₂×C₂²⋊C₄×C₆₇	—	2	4	no	—
234	#107×C₆₇	C₂³	1	2	yes	complemented
235	#106×C₆₇	C₂³	1	2	yes	complemented
236	C₄⋊C₈×C₆₇	C₂³	1	4	yes	complemented
237	#103×C₆₇	C₂³	1	2	yes	complemented
238	#103×C₆₇	C₂³	1	4	yes	complemented
239	#103×C₆₇	C₂³	1	2	yes	complemented
240	#102×C₆₇	C₂³	1	4	yes	—
241	#102×C₆₇	C₂³	1	4	yes	—
242	#102×C₆₇	C₂³	1	2	yes	complemented
243	#102×C₆₇	C₂³	1	4	yes	complemented
244	#102×C₆₇	C₂³	1	2	yes	complemented
245	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
246	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	complemented
247	#97×C₆₇	C₂³	1	2	yes	complemented
248	C₄×C₈×C₆₇	C₂³	1	2	yes	complemented
249	C₂⁴×C₆₇	—	2	1	no	—
250	C₂⁴×C₆₇	—	2	4	no	—
251	C₂⁴×C₆₇	—	2	1	no	—
252	C₂⁴×C₆₇	—	2	1	no	—
253	C₂⁴×C₆₇	—	2	2	no	—
254	C₂⁴×C₆₇	—	4	4	no	—
255	C₂⁴×C₆₇	—	8	4	no	—
256	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
257	#41×C₆₇	—	2	2	no	—
258	#41×C₆₇	—	2	2	no	—
259	#41×C₆₇	—	2	4	no	—
260	#41×C₆₇	—	2	8	no	—
261	#41×C₆₇	—	2	4	no	—
262	#41×C₆₇	—	2	2	no	—
263	#41×C₆₇	—	2	2	no	—
264	#41×C₆₇	—	2	2	no	—
265	#41×C₆₇	—	2	2	no	—
266	#41×C₆₇	—	4	4	no	—
267	#41×C₆₇	—	4	2	no	—
268	#41×C₆₇	—	4	2	no	—
269	#41×C₆₇	—	4	8	no	—
270	#41×C₆₇	—	4	8	no	—
271	#41×C₆₇	—	4	4	no	—
272	#41×C₆₇	—	4	4	no	—
273	C₂×Q₈×C₆₇	—	2	1	no	—
274	C₂×Q₈×C₆₇	—	2	2	no	—
275	C₂×Q₈×C₆₇	—	2	2	no	—
276	C₂×Q₈×C₆₇	—	2	4	no	—
277	C₂×Q₈×C₆₇	—	4	2	no	—
278	C₂×Q₈×C₆₇	—	4	4	no	—
279	C₂×Q₈×C₆₇	C₂×D₄	1	1	yes	characteristic
280	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	complemented
281	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
282	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
283	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
284	C₂×D₄×C₆₇	—	2	4	no	—
285	C₂×D₄×C₆₇	—	2	8	no	—
286	C₂×D₄×C₆₇	—	2	2	no	—
287	C₂×D₄×C₆₇	—	2	1	no	—
288	C₂×D₄×C₆₇	—	2	1	no	—
289	C₂×D₄×C₆₇	—	2	2	no	—
290	C₂×D₄×C₆₇	—	2	4	no	—
291	C₂×D₄×C₆₇	—	2	2	no	—
292	C₂×D₄×C₆₇	—	2	2	no	—
293	C₂×D₄×C₆₇	—	2	4	no	—
294	C₂×D₄×C₆₇	—	2	4	no	—
295	C₂×D₄×C₆₇	—	2	1	no	—
296	C₂×D₄×C₆₇	—	2	2	no	—
297	C₂×D₄×C₆₇	—	2	2	no	—
298	C₂×D₄×C₆₇	—	2	2	no	—
299	C₂×D₄×C₆₇	—	2	4	no	—
300	C₂×D₄×C₆₇	—	2	1	no	—
301	C₂×D₄×C₆₇	—	2	1	no	—
302	C₂×D₄×C₆₇	—	2	4	no	—
303	C₂×D₄×C₆₇	—	2	4	no	—
304	C₂×D₄×C₆₇	—	2	2	no	—
305	C₂×D₄×C₆₇	—	2	2	no	—
306	C₂×D₄×C₆₇	—	2	2	no	—
307	C₂×D₄×C₆₇	—	4	4	no	—
308	C₂×D₄×C₆₇	—	4	2	no	—
309	C₂×D₄×C₆₇	—	4	8	no	—
310	C₂×D₄×C₆₇	—	4	4	no	—
311	C₂×D₄×C₆₇	—	4	4	no	—
312	C₂×D₄×C₆₇	—	4	4	no	—
313	C₂×D₄×C₆₇	—	4	8	no	—
314	C₂×D₄×C₆₇	—	8	8	no	—
315	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
316	C₂×D₄×C₆₇	C₂×D₄	1	1	yes	characteristic
317	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
318	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
319	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
320	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
323	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
324	C₂²×C₄×C₆₇	—	2	1	no	—
325	C₂²×C₄×C₆₇	—	2	2	no	—
326	C₂²×C₄×C₆₇	—	2	2	no	—
327	C₂²×C₄×C₆₇	—	2	2	no	—
328	C₂²×C₄×C₆₇	—	2	2	no	—
329	C₂²×C₄×C₆₇	—	2	1	no	—
330	C₂²×C₄×C₆₇	—	2	1	no	—
331	C₂²×C₄×C₆₇	—	2	2	no	—
332	C₂²×C₄×C₆₇	—	2	4	no	—
333	C₂²×C₄×C₆₇	—	2	4	no	—
334	C₂²×C₄×C₆₇	—	4	4	no	—
335	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
336	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
339	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
340	Q₁₆×C₆₇	—	2	4	no	—
341	Q₁₆×C₆₇	—	2	2	no	—
342	SD₁₆×C₆₇	—	2	8	no	—
343	SD₁₆×C₆₇	—	2	4	no	—
344	SD₁₆×C₆₇	—	2	4	no	—
345	SD₁₆×C₆₇	—	2	2	no	—
346	SD₁₆×C₆₇	—	2	2	no	—
347	SD₁₆×C₆₇	—	4	2	no	—
348	SD₁₆×C₆₇	—	4	2	no	—
349	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
350	SD₁₆×C₆₇	C₂×D₄	1	8	yes	complemented
351	D₈×C₆₇	—	2	8	no	—
352	D₈×C₆₇	—	2	4	no	—
353	D₈×C₆₇	—	2	4	no	—
354	D₈×C₆₇	—	2	4	no	—
355	D₈×C₆₇	—	2	2	no	—
356	D₈×C₆₇	—	4	2	no	—
357	D₈×C₆₇	—	4	2	no	—
358	M₁₆×C₆₇	—	2	2	no	—
359	M₁₆×C₆₇	—	2	2	no	—
360	M₁₆×C₆₇	—	2	4	no	—
361	M₁₆×C₆₇	—	2	4	no	—
362	M₁₆×C₆₇	—	2	4	no	—
363	C₂×C₈×C₆₇	—	2	2	no	—
364	C₂×C₈×C₆₇	—	2	4	no	—
365	C₂×C₈×C₆₇	C₂×D₄	1	4	yes	complemented
366	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
367	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
368	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
369	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₆₇	—	2	4	no	—
372	C₄⋊C₄×C₆₇	—	2	2	no	—
373	C₄⋊C₄×C₆₇	—	2	2	no	—
374	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
375	C₄⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
376	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
377	C₄⋊C₄×C₆₇	C₂⁴	1	2	yes	—
378	C₂²⋊C₄×C₆₇	—	2	1	no	—
379	C₂²⋊C₄×C₆₇	—	2	2	no	—
380	C₂²⋊C₄×C₆₇	—	2	1	no	—
381	C₂²⋊C₄×C₆₇	—	2	2	no	—
382	C₂²⋊C₄×C₆₇	—	2	4	no	—
383	C₂²⋊C₄×C₆₇	—	2	4	no	—
384	C₂²⋊C₄×C₆₇	—	2	4	no	—
385	C₂²⋊C₄×C₆₇	—	2	2	no	—
386	C₂²⋊C₄×C₆₇	—	2	2	no	—
387	C₂²⋊C₄×C₆₇	—	2	4	no	—
388	C₂²⋊C₄×C₆₇	—	2	4	no	—
389	C₂²⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
390	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
391	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
392	C₄²×C₆₇	—	2	4	no	—
393	C₄²×C₆₇	—	2	1	no	—
394	C₄²×C₆₇	—	2	1	no	—
395	C₄²×C₆₇	C₂⁴	1	2	yes	—
396	C₂³×C₆₇	—	2	2	no	—
397	C₂³×C₆₇	—	2	2	no	—
398	C₂³×C₆₇	—	2	4	no	—
399	C₂³×C₆₇	—	2	2	no	—
400	C₂³×C₆₇	—	2	2	no	—
401	C₂³×C₆₇	—	2	1	no	—
402	C₂³×C₆₇	—	2	1	no	—
403	C₂³×C₆₇	—	4	2	no	—
404	C₂³×C₆₇	—	4	8	no	—
405	C₂³×C₆₇	—	4	4	no	—
406	C₂³×C₆₇	—	4	8	no	—
407	C₂³×C₆₇	—	4	2	no	—
408	C₂³×C₆₇	—	4	2	no	—
409	C₂³×C₆₇	—	8	2	no	—
410	C₂³×C₆₇	—	8	2	no	—
411	C₂³×C₆₇	—	8	2	no	—
412	C₂³×C₆₇	—	8	4	no	—
413	C₂³×C₆₇	—	8	4	no	—
414	C₂³×C₆₇	—	8	16	no	—
415	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
416	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
417	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
418	Q₈×C₆₇	—	2	4	no	—
419	Q₈×C₆₇	—	2	2	no	—
420	Q₈×C₆₇	—	2	2	no	—
421	Q₈×C₆₇	—	2	1	no	—
422	Q₈×C₆₇	—	2	1	no	—
423	Q₈×C₆₇	—	2	1	no	—
424	Q₈×C₆₇	—	2	1	no	—
425	Q₈×C₆₇	—	4	4	no	—
426	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
427	D₄×C₆₇	—	2	4	no	—
428	D₄×C₆₇	—	2	4	no	—
429	D₄×C₆₇	—	2	2	no	—
430	D₄×C₆₇	—	2	2	no	—
431	D₄×C₆₇	—	2	1	no	—
432	D₄×C₆₇	—	2	2	no	—
433	D₄×C₆₇	—	2	1	no	—
434	D₄×C₆₇	—	2	2	no	—
435	D₄×C₆₇	—	2	1	no	—
436	D₄×C₆₇	—	2	1	no	—
437	D₄×C₆₇	—	2	2	no	—
438	D₄×C₆₇	—	2	2	no	—
439	D₄×C₆₇	—	4	4	no	—
440	D₄×C₆₇	—	4	8	no	—
441	D₄×C₆₇	—	4	4	no	—
442	D₄×C₆₇	—	4	8	no	—
443	D₄×C₆₇	—	4	4	no	—
444	D₄×C₆₇	—	4	4	no	—
445	D₄×C₆₇	—	4	4	no	—
446	D₄×C₆₇	—	4	2	no	—
447	D₄×C₆₇	—	4	2	no	—
448	D₄×C₆₇	—	4	2	no	—
449	D₄×C₆₇	—	4	2	no	—
450	D₄×C₆₇	—	8	4	no	—
451	D₄×C₆₇	—	8	4	no	—
452	D₄×C₆₇	—	8	4	no	—
453	D₄×C₆₇	—	8	2	no	—
454	D₄×C₆₇	—	8	4	no	—
455	D₄×C₆₇	C₂²×D₄	1	4	yes	—
456	C₂×C₄×C₆₇	—	2	2	no	—
457	C₂×C₄×C₆₇	—	2	4	no	—
458	C₂×C₄×C₆₇	—	2	2	no	—
459	C₂×C₄×C₆₇	—	2	4	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	1	no	—
467	C₂×C₄×C₆₇	—	2	1	no	—
468	C₂×C₄×C₆₇	—	4	8	no	—
469	C₂×C₄×C₆₇	—	4	4	no	—
470	C₂×C₄×C₆₇	—	4	4	no	—
471	C₂×C₄×C₆₇	—	4	4	no	—
472	C₂×C₄×C₆₇	—	4	2	no	—
473	C₂×C₄×C₆₇	—	4	2	no	—
474	C₂×C₄×C₆₇	—	8	4	no	—
475	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
476	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
477	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
478	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
480	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
481	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
482	C₈×C₆₇	—	2	2	no	—
483	C₈×C₆₇	—	2	2	no	—
484	C₈×C₆₇	—	2	2	no	—
485	C₈×C₆₇	C₂²×D₄	1	2	yes	—
486	C₈×C₆₇	C₂²×D₄	1	2	yes	—
487	C₂²×C₆₇	—	2	2	no	—
488	C₂²×C₆₇	—	2	2	no	—
489	C₂²×C₆₇	—	2	4	no	—
490	C₂²×C₆₇	—	2	2	no	—
491	C₂²×C₆₇	—	2	2	no	—
492	C₂²×C₆₇	—	2	2	no	—
493	C₂²×C₆₇	—	2	4	no	—
494	C₂²×C₆₇	—	4	4	no	—
495	C₂²×C₆₇	—	4	4	no	—
496	C₂²×C₆₇	—	4	2	no	—
497	C₂²×C₆₇	—	4	2	no	—
498	C₂²×C₆₇	—	4	4	no	—
499	C₂²×C₆₇	—	4	4	no	—
500	C₂²×C₆₇	—	4	1	no	—
501	C₂²×C₆₇	—	4	2	no	—
502	C₂²×C₆₇	—	4	1	no	—
503	C₂²×C₆₇	—	4	2	no	—
504	C₂²×C₆₇	—	8	4	no	—
505	C₂²×C₆₇	—	8	4	no	—
506	C₂²×C₆₇	—	8	4	no	—
507	C₂²×C₆₇	—	8	16	no	—
508	C₂²×C₆₇	—	16	4	no	—
509	C₂²×C₆₇	D₄²	1	2	yes	—
510	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
511	C₄×C₆₇	—	2	4	no	—
512	C₄×C₆₇	—	2	2	no	—
513	C₄×C₆₇	—	2	4	no	—
514	C₄×C₆₇	—	2	2	no	—
515	C₄×C₆₇	—	4	2	no	—
516	C₄×C₆₇	—	4	2	no	—
517	C₄×C₆₇	—	4	1	no	—
518	C₄×C₆₇	—	4	1	no	—
519	C₄×C₆₇	D₄²	1	2	yes	—
520	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
521	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
522	#61059	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
523	C₂×C₆₇	—	2	2	no	—
524	C₂×C₆₇	—	4	2	no	—
525	C₂×C₆₇	—	4	2	no	—
526	C₂×C₆₇	—	4	4	no	—
527	C₂×C₆₇	—	8	1	no	—
528	C₂×C₆₇	—	8	2	no	—
529	C₂×C₆₇	—	8	2	no	—
530	C₂×C₆₇	—	8	1	no	—
531	C₂×C₆₇	C₂×D₄²	1	1	yes	characteristic
532	C₂×C₆₇	#3585	1	2	yes	—
533	C₂×#577	C₂×C₆₇	1	1	yes	characteristic, complemented
534	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
535	#3487	C₂×C₆₇	1	1	yes	characteristic, complemented
536	#3484	C₂×C₆₇	1	1	yes	characteristic, complemented
537	#3275	C₂×C₆₇	1	4	yes	complemented
538	#3274	C₂×C₆₇	1	4	yes	complemented
539	#3268	C₂×C₆₇	1	4	yes	complemented
540	#3265	C₂×C₆₇	1	4	yes	complemented
541	#3155	C₂×C₆₇	1	1	yes	characteristic, complemented
542	#3058	C₂×C₆₇	1	1	yes	characteristic, complemented
543	#3054	C₂×C₆₇	1	1	yes	characteristic, complemented
544	#3043	C₂×C₆₇	1	1	yes	characteristic, complemented
545	#3041	C₂×C₆₇	1	1	yes	characteristic, complemented
546	#3010	C₂×C₆₇	1	1	yes	characteristic, complemented
547	#3008	C₂×C₆₇	1	1	yes	characteristic, complemented
548	#3005	C₂×C₆₇	1	1	yes	characteristic, complemented
549	#3003	C₂×C₆₇	1	1	yes	characteristic, complemented
550	#2949	C₂×C₆₇	1	1	yes	characteristic, complemented
551	#2930	C₂×C₆₇	1	1	yes	characteristic, complemented
552	C₆₇	#61059	1	1	yes	characteristic, direct product factor, Sylow
553	C₂×2₋¹⁺⁴	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	1	yes	characteristic
555	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
556	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
557	#577	—	2	8	no	—
558	C₂×#137	C₂²×C₆₇	1	1	yes	characteristic, complemented
559	C₂×#137	C₂²×C₆₇	1	2	yes	complemented
560	C₂×AGL(1,ℤ/8)	—	2	8	no	—
561	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic
562	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
563	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	4	yes	complemented
564	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
565	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	1	yes	characteristic, complemented
566	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
567	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic, complemented
568	C₂×#135	C₂²×C₆₇	1	2	yes	complemented
569	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic
570	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
571	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
572	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic
573	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
574	C₂×#131	C₂²×C₆₇	1	1	yes	characteristic, complemented
575	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
576	#550	—	2	2	no	—
577	#550	C₂²×C₆₇	1	4	yes	complemented
578	#548	—	2	2	no	—
579	#548	C₂²×C₆₇	1	4	yes	complemented
580	#546	—	2	2	no	—
581	#546	C₂²×C₆₇	1	4	yes	complemented
582	D₄²	—	2	2	no	—
583	D₄²	C₂²×C₆₇	1	4	yes	complemented
584	#535	—	2	2	no	—
585	#535	C₂²×C₆₇	1	1	yes	characteristic
586	#535	C₂²×C₆₇	1	1	yes	characteristic
587	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
588	#535	C₂²×C₆₇	1	1	yes	characteristic, complemented
589	#534	—	2	2	no	—
590	#525	—	2	2	no	—
591	#525	C₂²×C₆₇	1	1	yes	characteristic
592	#525	C₂²×C₆₇	1	1	yes	characteristic
593	#525	C₂²×C₆₇	1	1	yes	characteristic, complemented
594	C₂×#120	—	2	2	no	—
595	#519	C₂²×C₆₇	1	1	yes	characteristic, complemented
596	#518	C₂²×C₆₇	1	1	yes	characteristic
597	#496	C₂²×C₆₇	1	2	yes	complemented
598	#496	C₂²×C₆₇	1	2	yes	complemented
599	#495	C₂²×C₆₇	1	2	yes	complemented
600	#493	C₂²×C₆₇	1	2	yes	complemented
601	#470	C₂²×C₆₇	1	2	yes	complemented
602	#469	C₂²×C₆₇	1	4	yes	complemented
603	#469	C₂²×C₆₇	1	2	yes	complemented
604	#468	C₂²×C₆₇	1	2	yes	complemented
605	#468	C₂²×C₆₇	1	2	yes	complemented
606	#466	C₂²×C₆₇	1	4	yes	complemented
607	#464	C₂²×C₆₇	1	4	yes	complemented
608	#463	C₂²×C₆₇	1	4	yes	complemented
609	#460	C₂²×C₆₇	1	4	yes	complemented
610	#459	C₂²×C₆₇	1	4	yes	complemented
611	#452	C₂²×C₆₇	1	4	yes	complemented
612	#450	C₂²×C₆₇	1	4	yes	complemented
613	#449	C₂²×C₆₇	1	4	yes	complemented
614	#449	C₂²×C₆₇	1	4	yes	complemented
615	#449	C₂²×C₆₇	1	4	yes	complemented
616	#448	C₂²×C₆₇	1	4	yes	complemented
617	#447	C₂²×C₆₇	1	4	yes	complemented
618	#447	C₂²×C₆₇	1	4	yes	complemented
619	#440	C₂²×C₆₇	1	4	yes	complemented
620	C₄×SD₁₆	C₂²×C₆₇	1	4	yes	complemented
621	#436	C₂²×C₆₇	1	4	yes	complemented
622	#435	C₂²×C₆₇	1	4	yes	complemented
623	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
624	#424	C₂²×C₆₇	1	1	yes	characteristic, complemented
625	#419	C₂²×C₆₇	1	1	yes	characteristic, complemented
626	#418	C₂²×C₆₇	1	1	yes	characteristic
627	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
628	#418	C₂²×C₆₇	1	1	yes	characteristic, complemented
629	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
630	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
631	#408	C₂²×C₆₇	1	1	yes	characteristic, complemented
632	#407	C₂²×C₆₇	1	1	yes	characteristic, complemented
633	#405	C₂²×C₆₇	1	1	yes	characteristic, complemented
634	C₂⁵	—	2	1	no	—
635	2₋¹⁺⁴	—	2	4	no	—
636	2₋¹⁺⁴	—	4	2	no	—
637	H(5,𝔽₂)	—	2	4	no	—
638	H(5,𝔽₂)	—	4	2	no	—
639	C₂×#41	—	2	1	no	—
640	C₂×#41	—	2	2	no	—
641	C₂×#41	—	2	1	no	—
642	C₂×#41	—	2	2	no	—
643	C₂×#41	—	2	4	no	—
644	C₂×#41	—	4	2	no	—
645	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
646	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
647	C₂×#41	C₂³×C₆₇	1	2	yes	—
648	C₂×#41	C₂³×C₆₇	1	4	yes	—
649	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
650	C₂×#41	C₂³×C₆₇	1	2	yes	complemented
651	C₂²×Q₈	—	2	1	no	—
652	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
653	C₂²×Q₈	C₂³×C₆₇	1	2	yes	complemented
654	C₂²×D₄	—	2	4	no	—
655	C₂²×D₄	—	2	1	no	—
656	C₂²×D₄	—	2	2	no	—
657	C₂²×D₄	—	2	1	no	—
658	C₂²×D₄	—	2	4	no	—
659	C₂²×D₄	—	2	1	no	—
660	C₂²×D₄	—	2	2	no	—
661	C₂²×D₄	—	4	2	no	—
662	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
663	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
664	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
665	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
666	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
667	C₂³×C₄	—	2	1	no	—
668	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
669	#137	—	2	4	no	—
670	#137	—	2	8	no	—
671	AGL(1,ℤ/8)	—	2	4	no	—
672	AGL(1,ℤ/8)	—	2	16	no	—
673	AGL(1,ℤ/8)	—	2	16	no	—
674	AGL(1,ℤ/8)	—	2	8	no	—
675	AGL(1,ℤ/8)	—	4	2	no	—
676	AGL(1,ℤ/8)	—	4	2	no	—
677	#135	—	2	8	no	—
678	#135	—	2	4	no	—
679	C₂×Q₁₆	C₂³×C₆₇	1	2	yes	complemented
680	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
681	C₂×SD₁₆	—	2	4	no	—
682	C₂×SD₁₆	—	2	8	no	—
683	C₂×SD₁₆	D₄×C₆₇	1	8	yes	complemented
684	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
686	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	—
689	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
690	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
691	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic, complemented
692	C₂×SD₁₆	C₂³×C₆₇	1	2	yes	complemented
693	C₂×D₈	—	2	4	no	—
694	C₂×D₈	—	2	4	no	—
695	C₂×D₈	C₂³×C₆₇	1	4	yes	—
696	C₂×D₈	C₂³×C₆₇	1	2	yes	—
697	C₂×D₈	C₂³×C₆₇	1	2	yes	—
698	C₂×D₈	C₂³×C₆₇	1	2	yes	—
699	C₂×D₈	C₂³×C₆₇	1	2	yes	—
700	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic, complemented
701	C₂×D₈	C₂³×C₆₇	1	2	yes	complemented
702	#131	—	2	4	no	—
703	C₂×M₁₆	—	2	4	no	—
704	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
705	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
706	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
707	C₂×M₁₆	C₂³×C₆₇	1	1	yes	characteristic
708	C₂×M₁₆	C₂³×C₆₇	1	2	yes	complemented
709	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
710	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
711	C₂²×C₈	C₂³×C₆₇	1	2	yes	complemented
712	#127	—	2	4	no	—
713	#127	—	2	1	no	—
714	#127	—	2	1	no	—
715	#127	C₂³×C₆₇	1	2	yes	—
716	#127	C₂³×C₆₇	1	2	yes	complemented
717	#124	—	2	1	no	—
718	#124	—	2	1	no	—
719	#124	—	2	4	no	—
720	#124	C₂³×C₆₇	1	2	yes	—
721	#124	C₂³×C₆₇	1	2	yes	complemented
722	#123	—	2	1	no	—
723	#123	—	2	1	no	—
724	#123	—	2	4	no	—
725	#123	D₄×C₆₇	1	2	yes	—
726	C₂²⋊Q₈	—	2	4	no	—
727	C₂²⋊Q₈	D₄×C₆₇	1	2	yes	—
728	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
729	C₂²⋊Q₈	C₂³×C₆₇	1	2	yes	—
730	#121	—	2	4	no	—
731	#121	—	2	4	no	—
732	#121	—	2	2	no	—
733	#121	—	2	2	no	—
734	#121	—	2	4	no	—
735	#121	—	2	4	no	—
736	#121	—	2	4	no	—
737	#121	D₄×C₆₇	1	2	yes	—
738	#121	C₂³×C₆₇	1	2	yes	—
739	#121	C₂³×C₆₇	1	2	yes	—
740	#121	C₂³×C₆₇	1	4	yes	—
741	#121	C₂³×C₆₇	1	4	yes	complemented
742	#120	—	2	1	no	—
743	#120	—	2	1	no	—
744	#120	—	2	2	no	—
745	#120	—	2	4	no	—
746	#120	—	2	2	no	—
747	#120	—	2	2	no	—
748	#120	—	2	4	no	—
749	#120	—	2	2	no	—
750	#120	—	2	4	no	—
751	#120	D₄×C₆₇	1	2	yes	—
752	C₄×Q₈	—	2	2	no	—
753	C₄×Q₈	C₂³×C₆₇	1	4	yes	complemented
754	C₄×D₄	—	2	2	no	—
755	C₄×D₄	—	2	2	no	—
756	C₄×D₄	—	2	2	no	—
757	C₄×D₄	—	2	4	no	—
758	C₄×D₄	—	2	4	no	—
759	C₄×D₄	C₂³×C₆₇	1	4	yes	—
760	C₄×D₄	C₂³×C₆₇	1	4	yes	—
761	#117	—	2	2	no	—
762	#117	C₂³×C₆₇	1	1	yes	characteristic
763	#117	C₂³×C₆₇	1	1	yes	characteristic
764	#117	C₂³×C₆₇	1	1	yes	characteristic
765	C₂×C₂²⋊C₄	—	2	2	no	—
766	C₂×C₂²⋊C₄	—	2	4	no	—
767	#107	C₂³×C₆₇	1	2	yes	complemented
768	#106	C₂³×C₆₇	1	2	yes	complemented
769	C₄⋊C₈	C₂³×C₆₇	1	4	yes	complemented
770	#103	C₂³×C₆₇	1	2	yes	complemented
771	#103	C₂³×C₆₇	1	2	yes	complemented
772	#103	C₂³×C₆₇	1	4	yes	complemented
773	#102	C₂³×C₆₇	1	4	yes	—
774	#102	C₂³×C₆₇	1	4	yes	—
775	#102	C₂³×C₆₇	1	2	yes	complemented
776	#102	C₂³×C₆₇	1	2	yes	complemented
777	#102	C₂³×C₆₇	1	4	yes	complemented
778	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
779	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	complemented
780	#97	C₂³×C₆₇	1	2	yes	complemented
781	C₄×C₈	C₂³×C₆₇	1	2	yes	complemented
782	C₂⁴	—	2	1	no	—
783	C₂⁴	—	2	4	no	—
784	C₂⁴	—	2	1	no	—
785	C₂⁴	—	2	1	no	—
786	C₂⁴	—	2	2	no	—
787	C₂⁴	—	4	4	no	—
788	C₂⁴	—	8	4	no	—
789	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
790	#41	—	2	2	no	—
791	#41	—	2	2	no	—
792	#41	—	2	4	no	—
793	#41	—	2	8	no	—
794	#41	—	2	4	no	—
795	#41	—	2	2	no	—
796	#41	—	2	2	no	—
797	#41	—	2	2	no	—
798	#41	—	2	2	no	—
799	#41	—	4	4	no	—
800	#41	—	4	2	no	—
801	#41	—	4	2	no	—
802	#41	—	4	8	no	—
803	#41	—	4	8	no	—
804	#41	—	4	4	no	—
805	#41	—	4	4	no	—
806	C₂×Q₈	—	2	1	no	—
807	C₂×Q₈	—	2	2	no	—
808	C₂×Q₈	—	2	2	no	—
809	C₂×Q₈	—	2	4	no	—
810	C₂×Q₈	—	4	2	no	—
811	C₂×Q₈	—	4	4	no	—
812	C₂×Q₈	C₂×D₄×C₆₇	1	1	yes	characteristic
813	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	complemented
814	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
815	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
816	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
817	C₂×D₄	—	2	4	no	—
818	C₂×D₄	—	2	8	no	—
819	C₂×D₄	—	2	2	no	—
820	C₂×D₄	—	2	1	no	—
821	C₂×D₄	—	2	1	no	—
822	C₂×D₄	—	2	2	no	—
823	C₂×D₄	—	2	4	no	—
824	C₂×D₄	—	2	2	no	—
825	C₂×D₄	—	2	2	no	—
826	C₂×D₄	—	2	4	no	—
827	C₂×D₄	—	2	4	no	—
828	C₂×D₄	—	2	1	no	—
829	C₂×D₄	—	2	2	no	—
830	C₂×D₄	—	2	2	no	—
831	C₂×D₄	—	2	2	no	—
832	C₂×D₄	—	2	4	no	—
833	C₂×D₄	—	2	1	no	—
834	C₂×D₄	—	2	1	no	—
835	C₂×D₄	—	2	4	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	4	no	—
841	C₂×D₄	—	4	2	no	—
842	C₂×D₄	—	4	8	no	—
843	C₂×D₄	—	4	4	no	—
844	C₂×D₄	—	4	4	no	—
845	C₂×D₄	—	4	4	no	—
846	C₂×D₄	—	4	8	no	—
847	C₂×D₄	—	8	8	no	—
848	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
849	C₂×D₄	C₂×D₄×C₆₇	1	1	yes	characteristic
850	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
851	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
852	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
853	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
854	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
855	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
856	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
857	C₂²×C₄	—	2	1	no	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	2	2	no	—
860	C₂²×C₄	—	2	2	no	—
861	C₂²×C₄	—	2	2	no	—
862	C₂²×C₄	—	2	1	no	—
863	C₂²×C₄	—	2	1	no	—
864	C₂²×C₄	—	2	2	no	—
865	C₂²×C₄	—	2	4	no	—
866	C₂²×C₄	—	2	4	no	—
867	C₂²×C₄	—	4	4	no	—
868	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
869	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
870	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
871	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
872	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
873	Q₁₆	—	2	4	no	—
874	Q₁₆	—	2	2	no	—
875	SD₁₆	—	2	8	no	—
876	SD₁₆	—	2	4	no	—
877	SD₁₆	—	2	4	no	—
878	SD₁₆	—	2	2	no	—
879	SD₁₆	—	2	2	no	—
880	SD₁₆	—	4	2	no	—
881	SD₁₆	—	4	2	no	—
882	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
883	SD₁₆	C₂×D₄×C₆₇	1	8	yes	complemented
884	D₈	—	2	8	no	—
885	D₈	—	2	4	no	—
886	D₈	—	2	4	no	—
887	D₈	—	2	4	no	—
888	D₈	—	2	2	no	—
889	D₈	—	4	2	no	—
890	D₈	—	4	2	no	—
891	M₁₆	—	2	2	no	—
892	M₁₆	—	2	2	no	—
893	M₁₆	—	2	4	no	—
894	M₁₆	—	2	4	no	—
895	M₁₆	—	2	4	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	4	no	—
898	C₂×C₈	C₂×D₄×C₆₇	1	4	yes	complemented
899	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
900	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
901	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
902	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
904	C₄⋊C₄	—	2	4	no	—
905	C₄⋊C₄	—	2	2	no	—
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
908	C₄⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
909	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
910	C₄⋊C₄	C₂⁴×C₆₇	1	2	yes	—
911	C₂²⋊C₄	—	2	1	no	—
912	C₂²⋊C₄	—	2	2	no	—
913	C₂²⋊C₄	—	2	1	no	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	4	no	—
916	C₂²⋊C₄	—	2	4	no	—
917	C₂²⋊C₄	—	2	4	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	2	2	no	—
920	C₂²⋊C₄	—	2	4	no	—
921	C₂²⋊C₄	—	2	4	no	—
922	C₂²⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
923	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
924	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
925	C₄²	—	2	4	no	—
926	C₄²	—	2	1	no	—
927	C₄²	—	2	1	no	—
928	C₄²	C₂⁴×C₆₇	1	2	yes	—
929	C₂³	—	2	2	no	—
930	C₂³	—	2	2	no	—
931	C₂³	—	2	4	no	—
932	C₂³	—	2	2	no	—
933	C₂³	—	2	2	no	—
934	C₂³	—	2	1	no	—
935	C₂³	—	2	1	no	—
936	C₂³	—	4	2	no	—
937	C₂³	—	4	8	no	—
938	C₂³	—	4	4	no	—
939	C₂³	—	4	8	no	—
940	C₂³	—	4	2	no	—
941	C₂³	—	4	2	no	—
942	C₂³	—	8	2	no	—
943	C₂³	—	8	2	no	—
944	C₂³	—	8	4	no	—
945	C₂³	—	8	2	no	—
946	C₂³	—	8	4	no	—
947	C₂³	—	8	16	no	—
948	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
949	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
950	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
951	Q₈	—	2	4	no	—
952	Q₈	—	2	2	no	—
953	Q₈	—	2	2	no	—
954	Q₈	—	2	1	no	—
955	Q₈	—	2	1	no	—
956	Q₈	—	2	1	no	—
957	Q₈	—	2	1	no	—
958	Q₈	—	4	4	no	—
959	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
960	D₄	—	2	4	no	—
961	D₄	—	2	4	no	—
962	D₄	—	2	2	no	—
963	D₄	—	2	2	no	—
964	D₄	—	2	1	no	—
965	D₄	—	2	2	no	—
966	D₄	—	2	1	no	—
967	D₄	—	2	2	no	—
968	D₄	—	2	1	no	—
969	D₄	—	2	1	no	—
970	D₄	—	2	2	no	—
971	D₄	—	2	2	no	—
972	D₄	—	4	4	no	—
973	D₄	—	4	8	no	—
974	D₄	—	4	4	no	—
975	D₄	—	4	8	no	—
976	D₄	—	4	4	no	—
977	D₄	—	4	4	no	—
978	D₄	—	4	4	no	—
979	D₄	—	4	2	no	—
980	D₄	—	4	2	no	—
981	D₄	—	4	2	no	—
982	D₄	—	4	2	no	—
983	D₄	—	8	4	no	—
984	D₄	—	8	4	no	—
985	D₄	—	8	4	no	—
986	D₄	—	8	4	no	—
987	D₄	—	8	2	no	—
988	D₄	C₂²×D₄×C₆₇	1	4	yes	—
989	C₂×C₄	—	2	2	no	—
990	C₂×C₄	—	2	4	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	4	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	2	2	no	—
998	C₂×C₄	—	2	2	no	—
999	C₂×C₄	—	2	1	no	—
1000	C₂×C₄	—	2	1	no	—
1001	C₂×C₄	—	4	8	no	—
1002	C₂×C₄	—	4	4	no	—
1003	C₂×C₄	—	4	4	no	—
1004	C₂×C₄	—	4	4	no	—
1005	C₂×C₄	—	4	2	no	—
1006	C₂×C₄	—	4	2	no	—
1007	C₂×C₄	—	8	4	no	—
1008	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
1009	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1010	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1011	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
1012	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
1013	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
1014	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
1015	C₈	—	2	2	no	—
1016	C₈	—	2	2	no	—
1017	C₈	—	2	2	no	—
1018	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1019	C₈	C₂²×D₄×C₆₇	1	2	yes	—
1020	C₂²	—	2	2	no	—
1021	C₂²	—	2	2	no	—
1022	C₂²	—	2	4	no	—
1023	C₂²	—	2	2	no	—
1024	C₂²	—	2	2	no	—
1025	C₂²	—	2	2	no	—
1026	C₂²	—	2	4	no	—
1027	C₂²	—	4	4	no	—
1028	C₂²	—	4	4	no	—
1029	C₂²	—	4	2	no	—
1030	C₂²	—	4	2	no	—
1031	C₂²	—	4	4	no	—
1032	C₂²	—	4	4	no	—
1033	C₂²	—	4	1	no	—
1034	C₂²	—	4	2	no	—
1035	C₂²	—	4	1	no	—
1036	C₂²	—	4	2	no	—
1037	C₂²	—	8	4	no	—
1038	C₂²	—	8	4	no	—
1039	C₂²	—	8	4	no	—
1040	C₂²	—	8	16	no	—
1041	C₂²	—	16	4	no	—
1042	C₂²	D₄²×C₆₇	1	2	yes	—
1043	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
1044	C₄	—	2	4	no	—
1045	C₄	—	2	2	no	—
1046	C₄	—	2	4	no	—
1047	C₄	—	2	2	no	—
1048	C₄	—	4	2	no	—
1049	C₄	—	4	2	no	—
1050	C₄	—	4	1	no	—
1051	C₄	—	4	1	no	—
1052	C₄	D₄²×C₆₇	1	2	yes	—
1053	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
1054	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
1055	C₂	—	2	2	no	—
1056	C₂	—	4	2	no	—
1057	C₂	—	4	2	no	—
1058	C₂	—	4	4	no	—
1059	C₂	—	8	2	no	—
1060	C₂	—	8	2	no	—
1061	C₂	—	8	1	no	—
1062	C₂	—	8	1	no	—
1063	C₂	C₂×D₄²×C₆₇	1	1	yes	characteristic
1064	C₂	C₆₇×#3585	1	2	yes	—

	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 ◁ #525×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#577×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₆₇×#3487	C₂	semidirect
4. C₆₇×#3484	C₂	semidirect
5. C₆₇×#3275	C₂	semidirect
6. C₆₇×#3274	C₂	semidirect
7. C₆₇×#3268	C₂	semidirect
8. C₆₇×#3265	C₂	semidirect
9. C₆₇×#3155	C₂	semidirect
10. C₆₇×#3058	C₂	semidirect
11. C₆₇×#3054	C₂	semidirect
12. C₆₇×#3043	C₂	semidirect
13. C₆₇×#3041	C₂	semidirect
14. C₆₇×#3010	C₂	semidirect
15. C₆₇×#3008	C₂	semidirect
16. C₆₇×#3005	C₂	semidirect
17. C₆₇×#3003	C₂	semidirect
18. C₆₇×#2949	C₂	semidirect
19. C₆₇×#2930	C₂	semidirect
20. C₂×2₋¹⁺⁴×C₆₇	C₂²	semidirect
22. C₂²×#41×C₆₇	C₂²	semidirect
25. C₂×#137×C₆₇	C₂²	semidirect
26. C₂×#137×C₆₇	C₂²	semidirect
29. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
30. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
31. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
32. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
33. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
34. C₂×#135×C₆₇	C₂²	semidirect
35. C₂×#135×C₆₇	C₂²	semidirect
37. C₂²×SD₁₆×C₆₇	C₂²	semidirect
38. C₂²×SD₁₆×C₆₇	C₂²	semidirect
40. C₂²×D₈×C₆₇	C₂²	semidirect
41. C₂×#131×C₆₇	C₂²	semidirect
42. C₂²×M₁₆×C₆₇	C₂²	semidirect
44. #550×C₆₇	C₂²	semidirect
46. #548×C₆₇	C₂²	semidirect
48. #546×C₆₇	C₂²	semidirect
50. D₄²×C₆₇	C₂²	semidirect
54. #535×C₆₇	C₂²	semidirect
55. #535×C₆₇	C₂²	semidirect
60. #525×C₆₇	C₂²	semidirect
62. #519×C₆₇	C₂²	semidirect
64. #496×C₆₇	C₂²	semidirect
65. #496×C₆₇	C₂²	semidirect
66. #495×C₆₇	C₂²	semidirect
67. #493×C₆₇	C₂²	semidirect
68. #470×C₆₇	C₂²	semidirect
69. #469×C₆₇	C₂²	semidirect
70. #469×C₆₇	C₂²	semidirect
71. #468×C₆₇	C₂²	semidirect
72. #468×C₆₇	C₂²	semidirect
73. #466×C₆₇	C₂²	semidirect
74. #464×C₆₇	C₂²	semidirect
75. #463×C₆₇	C₂²	semidirect
76. #460×C₆₇	C₂²	semidirect
77. #459×C₆₇	C₂²	semidirect
78. #452×C₆₇	C₂²	semidirect
79. #450×C₆₇	C₂²	semidirect
80. #449×C₆₇	C₂²	semidirect
81. #449×C₆₇	C₂²	semidirect
82. #449×C₆₇	C₂²	semidirect
83. #448×C₆₇	C₂²	semidirect
84. #447×C₆₇	C₂²	semidirect
85. #447×C₆₇	C₂²	semidirect
86. #440×C₆₇	C₂²	semidirect
87. C₄×SD₁₆×C₆₇	C₂²	semidirect
88. #436×C₆₇	C₂²	semidirect
89. #435×C₆₇	C₂²	semidirect
90. #427×C₆₇	C₂²	semidirect
91. #424×C₆₇	C₂²	semidirect
92. #419×C₆₇	C₂²	semidirect
94. #418×C₆₇	C₂²	semidirect
95. #418×C₆₇	C₂²	semidirect
96. #416×C₆₇	C₂²	semidirect
97. #416×C₆₇	C₂²	semidirect
98. #408×C₆₇	C₂²	semidirect
99. #407×C₆₇	C₂²	semidirect
100. #405×C₆₇	C₂²	semidirect
117. C₂×#41×C₆₇	C₂³	semidirect
120. C₂²×Q₈×C₆₇	C₂³	semidirect
146. C₂×Q₁₆×C₆₇	C₂³	semidirect
147. C₂×Q₁₆×C₆₇	C₂³	semidirect
150. C₂×SD₁₆×C₆₇	D₄	semidirect
156. C₂×SD₁₆×C₆₇	C₂³	semidirect
157. C₂×SD₁₆×C₆₇	C₂³	semidirect
158. C₂×SD₁₆×C₆₇	C₂³	semidirect
159. C₂×SD₁₆×C₆₇	C₂³	semidirect
167. C₂×D₈×C₆₇	C₂³	semidirect
168. C₂×D₈×C₆₇	C₂³	semidirect
175. C₂×M₁₆×C₆₇	C₂³	semidirect
178. C₂²×C₈×C₆₇	C₂³	semidirect
183. #127×C₆₇	C₂³	semidirect
188. #124×C₆₇	C₂³	semidirect
208. #121×C₆₇	C₂³	semidirect
220. C₄×Q₈×C₆₇	C₂³	semidirect
234. #107×C₆₇	C₂³	semidirect
235. #106×C₆₇	C₂³	semidirect
236. C₄⋊C₈×C₆₇	C₂³	semidirect
237. #103×C₆₇	C₂³	semidirect
238. #103×C₆₇	C₂³	semidirect
239. #103×C₆₇	C₂³	semidirect
242. #102×C₆₇	C₂³	semidirect
243. #102×C₆₇	C₂³	semidirect
244. #102×C₆₇	C₂³	semidirect
246. C₂²⋊C₈×C₆₇	C₂³	semidirect
247. #97×C₆₇	C₂³	semidirect
248. C₄×C₈×C₆₇	C₂³	semidirect
280. C₂×Q₈×C₆₇	C₂×D₄	semidirect
349. SD₁₆×C₆₇	C₂×D₄	semidirect
350. SD₁₆×C₆₇	C₂×D₄	semidirect
365. C₂×C₈×C₆₇	C₂×D₄	semidirect
522. #61059	C₆₇	direct (N × H)
533. C₂×#577	C₂×C₆₇	semidirect
534. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
535. #3487	C₂×C₆₇	semidirect
536. #3484	C₂×C₆₇	semidirect
537. #3275	C₂×C₆₇	semidirect
538. #3274	C₂×C₆₇	semidirect
539. #3268	C₂×C₆₇	semidirect
540. #3265	C₂×C₆₇	semidirect
541. #3155	C₂×C₆₇	semidirect
542. #3058	C₂×C₆₇	semidirect
543. #3054	C₂×C₆₇	semidirect
544. #3043	C₂×C₆₇	semidirect
545. #3041	C₂×C₆₇	semidirect
546. #3010	C₂×C₆₇	semidirect
547. #3008	C₂×C₆₇	semidirect
548. #3005	C₂×C₆₇	semidirect
549. #3003	C₂×C₆₇	semidirect
550. #2949	C₂×C₆₇	semidirect
551. #2930	C₂×C₆₇	semidirect
552. C₆₇	#61059	direct (N × H)
553. C₂×2₋¹⁺⁴	C₂²×C₆₇	semidirect
555. C₂²×#41	C₂²×C₆₇	semidirect
558. C₂×#137	C₂²×C₆₇	semidirect
559. C₂×#137	C₂²×C₆₇	semidirect
562. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
563. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
564. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
565. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
566. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
567. C₂×#135	C₂²×C₆₇	semidirect
568. C₂×#135	C₂²×C₆₇	semidirect
570. C₂²×SD₁₆	C₂²×C₆₇	semidirect
571. C₂²×SD₁₆	C₂²×C₆₇	semidirect
573. C₂²×D₈	C₂²×C₆₇	semidirect
574. C₂×#131	C₂²×C₆₇	semidirect
575. C₂²×M₁₆	C₂²×C₆₇	semidirect
577. #550	C₂²×C₆₇	semidirect
579. #548	C₂²×C₆₇	semidirect
581. #546	C₂²×C₆₇	semidirect
583. D₄²	C₂²×C₆₇	semidirect
587. #535	C₂²×C₆₇	semidirect
588. #535	C₂²×C₆₇	semidirect
593. #525	C₂²×C₆₇	semidirect
595. #519	C₂²×C₆₇	semidirect
597. #496	C₂²×C₆₇	semidirect
598. #496	C₂²×C₆₇	semidirect
599. #495	C₂²×C₆₇	semidirect
600. #493	C₂²×C₆₇	semidirect
601. #470	C₂²×C₆₇	semidirect
602. #469	C₂²×C₆₇	semidirect
603. #469	C₂²×C₆₇	semidirect
604. #468	C₂²×C₆₇	semidirect
605. #468	C₂²×C₆₇	semidirect
606. #466	C₂²×C₆₇	semidirect
607. #464	C₂²×C₆₇	semidirect
608. #463	C₂²×C₆₇	semidirect
609. #460	C₂²×C₆₇	semidirect
610. #459	C₂²×C₆₇	semidirect
611. #452	C₂²×C₆₇	semidirect
612. #450	C₂²×C₆₇	semidirect
613. #449	C₂²×C₆₇	semidirect
614. #449	C₂²×C₆₇	semidirect
615. #449	C₂²×C₆₇	semidirect
616. #448	C₂²×C₆₇	semidirect
617. #447	C₂²×C₆₇	semidirect
618. #447	C₂²×C₆₇	semidirect
619. #440	C₂²×C₆₇	semidirect
620. C₄×SD₁₆	C₂²×C₆₇	semidirect
621. #436	C₂²×C₆₇	semidirect
622. #435	C₂²×C₆₇	semidirect
623. #427	C₂²×C₆₇	semidirect
624. #424	C₂²×C₆₇	semidirect
625. #419	C₂²×C₆₇	semidirect
627. #418	C₂²×C₆₇	semidirect
628. #418	C₂²×C₆₇	semidirect
629. #416	C₂²×C₆₇	semidirect
630. #416	C₂²×C₆₇	semidirect
631. #408	C₂²×C₆₇	semidirect
632. #407	C₂²×C₆₇	semidirect
633. #405	C₂²×C₆₇	semidirect
650. C₂×#41	C₂³×C₆₇	semidirect
653. C₂²×Q₈	C₂³×C₆₇	semidirect
679. C₂×Q₁₆	C₂³×C₆₇	semidirect
680. C₂×Q₁₆	C₂³×C₆₇	semidirect
683. C₂×SD₁₆	D₄×C₆₇	semidirect
689. C₂×SD₁₆	C₂³×C₆₇	semidirect
690. C₂×SD₁₆	C₂³×C₆₇	semidirect
691. C₂×SD₁₆	C₂³×C₆₇	semidirect
692. C₂×SD₁₆	C₂³×C₆₇	semidirect
700. C₂×D₈	C₂³×C₆₇	semidirect
701. C₂×D₈	C₂³×C₆₇	semidirect
708. C₂×M₁₆	C₂³×C₆₇	semidirect
711. C₂²×C₈	C₂³×C₆₇	semidirect
716. #127	C₂³×C₆₇	semidirect
721. #124	C₂³×C₆₇	semidirect
741. #121	C₂³×C₆₇	semidirect
753. C₄×Q₈	C₂³×C₆₇	semidirect
767. #107	C₂³×C₆₇	semidirect
768. #106	C₂³×C₆₇	semidirect
769. C₄⋊C₈	C₂³×C₆₇	semidirect
770. #103	C₂³×C₆₇	semidirect
771. #103	C₂³×C₆₇	semidirect
772. #103	C₂³×C₆₇	semidirect
775. #102	C₂³×C₆₇	semidirect
776. #102	C₂³×C₆₇	semidirect
777. #102	C₂³×C₆₇	semidirect
779. C₂²⋊C₈	C₂³×C₆₇	semidirect
780. #97	C₂³×C₆₇	semidirect
781. C₄×C₈	C₂³×C₆₇	semidirect
813. C₂×Q₈	C₂×D₄×C₆₇	semidirect
882. SD₁₆	C₂×D₄×C₆₇	semidirect
883. SD₁₆	C₂×D₄×C₆₇	semidirect
898. C₂×C₈	C₂×D₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#577×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₆₇×#3487	2
C₆₇×#3484	2
C₆₇×#3275	2
C₆₇×#3274	2
C₆₇×#3268	2
C₆₇×#3265	2
C₆₇×#3155	2
C₆₇×#3058	2
C₆₇×#3054	2
C₆₇×#3043	2
C₆₇×#3041	2
C₆₇×#3010	2
C₆₇×#3008	2
C₆₇×#3005	2
C₆₇×#3003	2
C₆₇×#2949	2
C₆₇×#2930	2
#61059	67

Subgroups — C67×#61059 #30740310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61059 #30740310