Subgroups — C₂×C₆₇×#3012 #30739615

Order 17152.

5126 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×H(5,𝔽₂)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×AGL(1,ℤ/8)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#537×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₆₇×#3012	C₂	1	16	yes	maximal, direct product factor
6	C₂×#452×C₆₇	C₂	1	2	yes	maximal, complemented
7	C₂×#449×C₆₇	C₂	1	2	yes	maximal, complemented
8	C₂×#450×C₆₇	C₂	1	2	yes	maximal, complemented
9	C₂×#447×C₆₇	C₂	1	2	yes	maximal, complemented
10	C₂×#417×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×#102×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×H(5,𝔽₂)×C₆₇	—	2	4	no	—
14	C₂×H(5,𝔽₂)×C₆₇	—	2	8	no	—
15	C₂×H(5,𝔽₂)×C₆₇	—	2	8	no	—
16	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	8	yes	complemented
17	C₂²×#41×C₆₇	—	2	1	no	—
18	C₂²×#41×C₆₇	C₂²	1	2	yes	—
19	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
20	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
21	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
22	C₂³×D₄×C₆₇	—	2	2	no	—
23	C₂³×D₄×C₆₇	—	2	1	no	—
24	C₂³×D₄×C₆₇	C₂²	1	2	yes	—
25	C₂³×D₄×C₆₇	C₂²	1	1	yes	characteristic
26	C₂×AGL(1,ℤ/8)×C₆₇	—	2	8	no	—
27	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	8	yes	complemented
28	C₂×#135×C₆₇	—	2	8	no	—
29	C₂×#135×C₆₇	C₂²	1	8	yes	complemented
30	C₂²×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
31	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
32	C₂²×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
33	C₂²×SD₁₆×C₆₇	C₂²	1	2	yes	complemented
34	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
35	C₂²×D₈×C₆₇	C₂²	1	2	yes	complemented
36	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
37	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
38	#537×C₆₇	—	2	4	no	—
39	#537×C₆₇	C₂²	1	8	yes	complemented
40	C₂×C₂²⋊Q₈×C₆₇	—	2	1	no	—
41	C₂×C₂²⋊Q₈×C₆₇	C₂²	1	2	yes	complemented
42	C₂×#121×C₆₇	—	2	1	no	—
43	C₂×#121×C₆₇	—	2	2	no	—
44	C₂×#121×C₆₇	C₂²	1	2	yes	complemented
45	C₂²×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic, complemented
46	#452×C₆₇	C₂²	1	16	yes	complemented
47	#450×C₆₇	C₂²	1	16	yes	complemented
48	#449×C₆₇	C₂²	1	16	yes	complemented
49	#447×C₆₇	C₂²	1	16	yes	complemented
50	#417×C₆₇	C₂²	1	8	yes	complemented
51	C₂×#103×C₆₇	C₂²	1	2	yes	complemented
52	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
53	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
54	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
55	C₂×#102×C₆₇	C₂²	1	8	yes	complemented
56	#408×C₆₇	C₂²	1	8	yes	complemented
57	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
58	C₂×C₂²⋊C₈×C₆₇	C₂²	1	2	yes	complemented
59	C₂⁵×C₆₇	—	2	2	no	—
60	C₂⁵×C₆₇	—	2	1	no	—
61	H(5,𝔽₂)×C₆₇	—	2	64	no	—
62	H(5,𝔽₂)×C₆₇	—	2	32	no	—
63	H(5,𝔽₂)×C₆₇	—	2	32	no	—
64	C₂×#41×C₆₇	—	2	16	no	—
65	C₂×#41×C₆₇	—	2	8	no	—
66	C₂×#41×C₆₇	—	2	8	no	—
67	C₂×#41×C₆₇	—	2	8	no	—
68	C₂×#41×C₆₇	—	2	4	no	—
69	C₂×#41×C₆₇	—	2	4	no	—
70	C₂×#41×C₆₇	—	2	2	no	—
71	C₂×#41×C₆₇	—	2	4	no	—
72	C₂×#41×C₆₇	—	2	4	no	—
73	C₂×#41×C₆₇	—	2	2	no	—
74	C₂×#41×C₆₇	—	2	4	no	—
75	C₂×#41×C₆₇	—	2	4	no	—
76	C₂×#41×C₆₇	D₄	1	4	yes	—
77	C₂×#41×C₆₇	D₄	1	8	yes	complemented
78	C₂×#41×C₆₇	C₂³	1	8	yes	—
79	C₂×#41×C₆₇	C₂³	1	4	yes	—
80	C₂×#41×C₆₇	C₂³	1	4	yes	—
81	C₂×#41×C₆₇	C₂³	1	4	yes	complemented
82	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
83	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
84	C₂²×Q₈×C₆₇	C₂³	1	1	yes	characteristic
85	C₂²×D₄×C₆₇	—	2	32	no	—
86	C₂²×D₄×C₆₇	—	2	16	no	—
87	C₂²×D₄×C₆₇	—	2	2	no	—
88	C₂²×D₄×C₆₇	—	2	1	no	—
89	C₂²×D₄×C₆₇	—	2	16	no	—
90	C₂²×D₄×C₆₇	—	2	8	no	—
91	C₂²×D₄×C₆₇	—	2	8	no	—
92	C₂²×D₄×C₆₇	—	2	8	no	—
93	C₂²×D₄×C₆₇	—	2	1	no	—
94	C₂²×D₄×C₆₇	—	2	2	no	—
95	C₂²×D₄×C₆₇	—	2	2	no	—
96	C₂²×D₄×C₆₇	—	2	1	no	—
97	C₂²×D₄×C₆₇	—	2	4	no	—
98	C₂²×D₄×C₆₇	—	2	2	no	—
99	C₂²×D₄×C₆₇	—	2	4	no	—
100	C₂²×D₄×C₆₇	D₄	1	2	yes	—
101	C₂²×D₄×C₆₇	D₄	1	1	yes	characteristic
102	C₂²×D₄×C₆₇	D₄	1	8	yes	complemented
103	C₂²×D₄×C₆₇	C₂³	1	8	yes	—
104	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
105	C₂²×D₄×C₆₇	C₂³	1	1	yes	characteristic
106	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
107	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
108	C₂³×C₄×C₆₇	—	2	2	no	—
109	C₂³×C₄×C₆₇	—	2	1	no	—
110	C₂³×C₄×C₆₇	—	2	1	no	—
111	C₂³×C₄×C₆₇	—	2	1	no	—
112	C₂³×C₄×C₆₇	C₂³	1	2	yes	—
113	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
114	AGL(1,ℤ/8)×C₆₇	—	2	32	no	—
115	#135×C₆₇	—	2	32	no	—
116	C₂×Q₁₆×C₆₇	—	2	4	no	—
117	C₂×Q₁₆×C₆₇	C₂³	1	4	yes	complemented
118	C₂×SD₁₆×C₆₇	—	2	4	no	—
119	C₂×SD₁₆×C₆₇	—	2	4	no	—
120	C₂×SD₁₆×C₆₇	—	2	8	no	—
121	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
122	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	complemented
123	C₂×SD₁₆×C₆₇	C₂³	1	8	yes	complemented
124	C₂×D₈×C₆₇	—	2	4	no	—
125	C₂×D₈×C₆₇	—	2	8	no	—
126	C₂×D₈×C₆₇	C₂³	1	8	yes	complemented
127	C₂×D₈×C₆₇	C₂³	1	4	yes	complemented
128	C₂×M₁₆×C₆₇	—	2	4	no	—
129	C₂×M₁₆×C₆₇	C₂³	1	4	yes	complemented
130	C₂²×C₈×C₆₇	—	2	4	no	—
131	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
134	C₂²×C₈×C₆₇	C₂³	1	4	yes	complemented
135	C₂²⋊Q₈×C₆₇	—	2	8	no	—
136	C₂²⋊Q₈×C₆₇	—	2	4	no	—
137	C₂²⋊Q₈×C₆₇	C₂³	1	8	yes	complemented
138	#121×C₆₇	—	2	8	no	—
139	#121×C₆₇	—	2	16	no	—
140	#121×C₆₇	—	2	4	no	—
141	#121×C₆₇	C₂³	1	8	yes	complemented
142	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
143	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
144	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
145	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	complemented
147	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
148	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
149	#103×C₆₇	C₂³	1	8	yes	complemented
150	#102×C₆₇	C₂³	1	8	yes	complemented
151	#102×C₆₇	C₂³	1	8	yes	complemented
152	#102×C₆₇	C₂³	1	8	yes	complemented
153	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
154	C₂²⋊C₈×C₆₇	C₂³	1	8	yes	complemented
155	C₂⁴×C₆₇	—	2	16	no	—
156	C₂⁴×C₆₇	—	2	2	no	—
157	C₂⁴×C₆₇	—	2	1	no	—
158	C₂⁴×C₆₇	—	2	8	no	—
159	C₂⁴×C₆₇	—	2	8	no	—
160	C₂⁴×C₆₇	—	2	4	no	—
161	C₂⁴×C₆₇	—	2	1	no	—
162	C₂⁴×C₆₇	—	8	2	no	—
163	C₂⁴×C₆₇	—	8	2	no	—
164	C₂⁴×C₆₇	—	8	4	no	—
165	C₂⁴×C₆₇	—	8	4	no	—
166	C₂⁴×C₆₇	C₂×D₄	1	2	yes	—
167	C₂⁴×C₆₇	C₂×D₄	1	1	yes	characteristic
168	#41×C₆₇	—	2	64	no	—
169	#41×C₆₇	—	2	32	no	—
170	#41×C₆₇	—	2	16	no	—
171	#41×C₆₇	—	2	16	no	—
172	#41×C₆₇	—	2	16	no	—
173	#41×C₆₇	—	2	16	no	—
174	#41×C₆₇	—	2	8	no	—
175	#41×C₆₇	—	2	8	no	—
176	#41×C₆₇	—	2	8	no	—
177	#41×C₆₇	—	2	8	no	—
178	#41×C₆₇	—	2	8	no	—
179	#41×C₆₇	—	4	8	no	—
180	#41×C₆₇	C₂×D₄	1	16	yes	complemented
181	C₂×Q₈×C₆₇	—	2	4	no	—
182	C₂×Q₈×C₆₇	—	2	2	no	—
183	C₂×Q₈×C₆₇	—	2	1	no	—
184	C₂×Q₈×C₆₇	—	2	1	no	—
185	C₂×Q₈×C₆₇	—	2	2	no	—
186	C₂×Q₈×C₆₇	—	2	2	no	—
187	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
188	C₂×Q₈×C₆₇	C₂×D₄	1	4	yes	—
189	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
190	C₂×Q₈×C₆₇	C₂⁴	1	2	yes	—
191	C₂×D₄×C₆₇	—	2	16	no	—
192	C₂×D₄×C₆₇	—	2	16	no	—
193	C₂×D₄×C₆₇	—	2	128	no	—
194	C₂×D₄×C₆₇	—	2	64	no	—
195	C₂×D₄×C₆₇	—	2	32	no	—
196	C₂×D₄×C₆₇	—	2	8	no	—
197	C₂×D₄×C₆₇	—	2	8	no	—
198	C₂×D₄×C₆₇	—	2	8	no	—
199	C₂×D₄×C₆₇	—	2	4	no	—
200	C₂×D₄×C₆₇	—	2	16	no	—
201	C₂×D₄×C₆₇	—	2	16	no	—
202	C₂×D₄×C₆₇	—	2	4	no	—
203	C₂×D₄×C₆₇	—	2	8	no	—
204	C₂×D₄×C₆₇	—	2	4	no	—
205	C₂×D₄×C₆₇	—	2	8	no	—
206	C₂×D₄×C₆₇	—	2	16	no	—
207	C₂×D₄×C₆₇	—	2	8	no	—
208	C₂×D₄×C₆₇	—	2	4	no	—
209	C₂×D₄×C₆₇	—	2	1	no	—
210	C₂×D₄×C₆₇	—	2	2	no	—
211	C₂×D₄×C₆₇	—	2	4	no	—
212	C₂×D₄×C₆₇	—	2	2	no	—
213	C₂×D₄×C₆₇	—	2	8	no	—
214	C₂×D₄×C₆₇	—	2	2	no	—
215	C₂×D₄×C₆₇	—	2	2	no	—
216	C₂×D₄×C₆₇	—	2	1	no	—
217	C₂×D₄×C₆₇	—	4	4	no	—
218	C₂×D₄×C₆₇	—	8	4	no	—
219	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
220	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
221	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
222	C₂×D₄×C₆₇	C₂×D₄	1	8	yes	—
223	C₂×D₄×C₆₇	C₂×D₄	1	16	yes	complemented
224	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
225	C₂×D₄×C₆₇	C₂⁴	1	2	yes	—
226	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
227	C₂²×C₄×C₆₇	—	2	16	no	—
228	C₂²×C₄×C₆₇	—	2	1	no	—
229	C₂²×C₄×C₆₇	—	2	8	no	—
230	C₂²×C₄×C₆₇	—	2	8	no	—
231	C₂²×C₄×C₆₇	—	2	4	no	—
232	C₂²×C₄×C₆₇	—	2	4	no	—
233	C₂²×C₄×C₆₇	—	2	4	no	—
234	C₂²×C₄×C₆₇	—	2	2	no	—
235	C₂²×C₄×C₆₇	—	2	1	no	—
236	C₂²×C₄×C₆₇	—	2	4	no	—
237	C₂²×C₄×C₆₇	—	2	4	no	—
238	C₂²×C₄×C₆₇	—	4	4	no	—
239	C₂²×C₄×C₆₇	—	8	2	no	—
240	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
241	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
242	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
243	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
244	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
245	C₂²×C₄×C₆₇	C₂×D₄	1	4	yes	—
246	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
247	C₂²×C₄×C₆₇	C₂⁴	1	2	yes	—
248	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
249	Q₁₆×C₆₇	—	2	8	no	—
250	SD₁₆×C₆₇	—	2	8	no	—
251	SD₁₆×C₆₇	—	2	8	no	—
252	SD₁₆×C₆₇	—	2	16	no	—
253	D₈×C₆₇	—	2	8	no	—
254	D₈×C₆₇	—	2	16	no	—
255	M₁₆×C₆₇	—	2	8	no	—
256	C₂×C₈×C₆₇	—	2	2	no	—
257	C₂×C₈×C₆₇	—	2	2	no	—
258	C₂×C₈×C₆₇	—	2	8	no	—
259	C₂×C₈×C₆₇	—	2	4	no	—
260	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
261	C₂×C₈×C₆₇	C₂⁴	1	2	yes	—
262	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
263	C₄⋊C₄×C₆₇	—	2	2	no	—
264	C₄⋊C₄×C₆₇	—	2	4	no	—
265	C₄⋊C₄×C₆₇	—	2	8	no	—
266	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
267	C₂²⋊C₄×C₆₇	—	2	8	no	—
268	C₂²⋊C₄×C₆₇	—	2	8	no	—
269	C₂³×C₆₇	—	2	2	no	—
270	C₂³×C₆₇	—	2	2	no	—
271	C₂³×C₆₇	—	2	32	no	—
272	C₂³×C₆₇	—	2	4	no	—
273	C₂³×C₆₇	—	2	8	no	—
274	C₂³×C₆₇	—	2	4	no	—
275	C₂³×C₆₇	—	2	4	no	—
276	C₂³×C₆₇	—	2	4	no	—
277	C₂³×C₆₇	—	2	4	no	—
278	C₂³×C₆₇	—	2	2	no	—
279	C₂³×C₆₇	—	2	16	no	—
280	C₂³×C₆₇	—	2	2	no	—
281	C₂³×C₆₇	—	4	4	no	—
282	C₂³×C₆₇	—	4	2	no	—
283	C₂³×C₆₇	—	4	4	no	—
284	C₂³×C₆₇	—	4	2	no	—
285	C₂³×C₆₇	—	4	2	no	—
286	C₂³×C₆₇	—	4	2	no	—
287	C₂³×C₆₇	—	4	2	no	—
288	C₂³×C₆₇	—	8	16	no	—
289	C₂³×C₆₇	—	8	4	no	—
290	C₂³×C₆₇	—	8	4	no	—
291	C₂³×C₆₇	—	8	8	no	—
292	C₂³×C₆₇	—	8	8	no	—
293	C₂³×C₆₇	—	8	32	no	—
294	C₂³×C₆₇	#120	1	4	yes	—
295	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
296	C₂³×C₆₇	C₂²×D₄	1	2	yes	—
297	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
298	Q₈×C₆₇	—	2	4	no	—
299	Q₈×C₆₇	—	2	8	no	—
300	Q₈×C₆₇	—	2	2	no	—
301	Q₈×C₆₇	—	2	2	no	—
302	Q₈×C₆₇	—	2	2	no	—
303	Q₈×C₆₇	—	4	2	no	—
304	Q₈×C₆₇	C₂²×D₄	1	4	yes	—
305	D₄×C₆₇	—	2	32	no	—
306	D₄×C₆₇	—	2	32	no	—
307	D₄×C₆₇	—	2	16	no	—
308	D₄×C₆₇	—	2	16	no	—
309	D₄×C₆₇	—	2	8	no	—
310	D₄×C₆₇	—	2	4	no	—
311	D₄×C₆₇	—	2	8	no	—
312	D₄×C₆₇	—	2	16	no	—
313	D₄×C₆₇	—	2	4	no	—
314	D₄×C₆₇	—	2	2	no	—
315	D₄×C₆₇	—	2	2	no	—
316	D₄×C₆₇	—	2	2	no	—
317	D₄×C₆₇	—	4	8	no	—
318	D₄×C₆₇	—	4	2	no	—
319	D₄×C₆₇	—	8	8	no	—
320	D₄×C₆₇	C₂²×D₄	1	4	yes	—
321	D₄×C₆₇	C₂²×D₄	1	8	yes	—
322	C₂×C₄×C₆₇	—	2	32	no	—
323	C₂×C₄×C₆₇	—	2	4	no	—
324	C₂×C₄×C₆₇	—	2	4	no	—
325	C₂×C₄×C₆₇	—	2	2	no	—
326	C₂×C₄×C₆₇	—	2	16	no	—
327	C₂×C₄×C₆₇	—	2	8	no	—
328	C₂×C₄×C₆₇	—	2	4	no	—
329	C₂×C₄×C₆₇	—	2	4	no	—
330	C₂×C₄×C₆₇	—	2	4	no	—
331	C₂×C₄×C₆₇	—	2	2	no	—
332	C₂×C₄×C₆₇	—	4	2	no	—
333	C₂×C₄×C₆₇	—	4	4	no	—
334	C₂×C₄×C₆₇	—	4	8	no	—
335	C₂×C₄×C₆₇	—	8	4	no	—
336	C₂×C₄×C₆₇	#120	1	4	yes	—
337	C₂×C₄×C₆₇	#120	1	8	yes	—
338	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
339	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
340	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
341	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
342	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
343	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
344	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
345	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
346	C₈×C₆₇	—	2	2	no	—
347	C₈×C₆₇	—	2	2	no	—
348	C₈×C₆₇	—	2	4	no	—
349	C₂²×C₆₇	—	2	8	no	—
350	C₂²×C₆₇	—	2	2	no	—
351	C₂²×C₆₇	—	2	2	no	—
352	C₂²×C₆₇	—	2	4	no	—
353	C₂²×C₆₇	—	2	8	no	—
354	C₂²×C₆₇	—	2	4	no	—
355	C₂²×C₆₇	—	2	4	no	—
356	C₂²×C₆₇	—	2	4	no	—
357	C₂²×C₆₇	—	4	8	no	—
358	C₂²×C₆₇	—	4	16	no	—
359	C₂²×C₆₇	—	4	8	no	—
360	C₂²×C₆₇	—	4	4	no	—
361	C₂²×C₆₇	—	4	2	no	—
362	C₂²×C₆₇	—	4	4	no	—
363	C₂²×C₆₇	—	4	2	no	—
364	C₂²×C₆₇	—	4	2	no	—
365	C₂²×C₆₇	—	4	2	no	—
366	C₂²×C₆₇	—	4	2	no	—
367	C₂²×C₆₇	—	8	16	no	—
368	C₂²×C₆₇	—	8	32	no	—
369	C₂²×C₆₇	—	8	4	no	—
370	C₂²×C₆₇	C₂×#120	1	4	yes	—
371	C₂²×C₆₇	C₂×#120	1	2	yes	—
372	C₂²×C₆₇	#576	1	2	yes	—
373	C₂²×C₆₇	#577	1	2	yes	—
374	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
375	C₄×C₆₇	—	2	4	no	—
376	C₄×C₆₇	—	2	4	no	—
377	C₄×C₆₇	—	4	2	no	—
378	C₄×C₆₇	—	4	4	no	—
379	C₄×C₆₇	C₂×#120	1	4	yes	—
380	C₄×C₆₇	C₂×#120	1	2	yes	—
381	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
382	C₄×C₆₇	C₂³×D₄	1	1	yes	characteristic
383	C₂×#3012	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
384	C₂×C₆₇	—	2	4	no	—
385	C₂×C₆₇	—	4	4	no	—
386	C₂×C₆₇	—	4	8	no	—
387	C₂×C₆₇	—	4	4	no	—
388	C₂×C₆₇	—	8	2	no	—
389	C₂×C₆₇	#3012	1	4	yes	direct product factor
390	C₂×C₆₇	C₂²×#120	1	1	yes	characteristic
391	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
392	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
393	C₂²×H(5,𝔽₂)	C₂×C₆₇	1	1	yes	characteristic, complemented
394	C₂²×AGL(1,ℤ/8)	C₂×C₆₇	1	1	yes	characteristic, complemented
395	C₂²×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
396	C₂×#537	C₂×C₆₇	1	1	yes	characteristic, complemented
397	#3012	C₂×C₆₇	1	16	yes	direct product factor
398	C₂×#452	C₂×C₆₇	1	2	yes	complemented
399	C₂×#449	C₂×C₆₇	1	2	yes	complemented
400	C₂×#450	C₂×C₆₇	1	2	yes	complemented
401	C₂×#447	C₂×C₆₇	1	2	yes	complemented
402	C₂×#417	C₂×C₆₇	1	1	yes	characteristic, complemented
403	C₂²×#102	C₂×C₆₇	1	1	yes	characteristic, complemented
404	C₂×#408	C₂×C₆₇	1	1	yes	characteristic, complemented
405	C₆₇	C₂×#3012	1	1	yes	characteristic, direct product factor, Sylow
406	C₂×H(5,𝔽₂)	—	2	4	no	—
407	C₂×H(5,𝔽₂)	—	2	8	no	—
408	C₂×H(5,𝔽₂)	—	2	8	no	—
409	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	8	yes	complemented
410	C₂²×#41	—	2	1	no	—
411	C₂²×#41	C₂²×C₆₇	1	2	yes	—
412	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
413	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
414	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
415	C₂³×D₄	—	2	2	no	—
416	C₂³×D₄	—	2	1	no	—
417	C₂³×D₄	C₂²×C₆₇	1	2	yes	—
418	C₂³×D₄	C₂²×C₆₇	1	1	yes	characteristic
419	C₂×AGL(1,ℤ/8)	—	2	8	no	—
420	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	8	yes	complemented
421	C₂×#135	—	2	8	no	—
422	C₂×#135	C₂²×C₆₇	1	8	yes	complemented
423	C₂²×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
424	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
425	C₂²×SD₁₆	C₂²×C₆₇	1	2	yes	complemented
426	C₂²×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
427	C₂²×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
428	C₂²×D₈	C₂²×C₆₇	1	2	yes	complemented
429	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
430	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
431	#537	—	2	4	no	—
432	#537	C₂²×C₆₇	1	8	yes	complemented
433	C₂×C₂²⋊Q₈	—	2	1	no	—
434	C₂×C₂²⋊Q₈	C₂²×C₆₇	1	2	yes	complemented
435	C₂×#121	—	2	1	no	—
436	C₂×#121	—	2	2	no	—
437	C₂×#121	C₂²×C₆₇	1	2	yes	complemented
438	C₂²×C₄⋊C₄	C₂²×C₆₇	1	1	yes	characteristic, complemented
439	#452	C₂²×C₆₇	1	16	yes	complemented
440	#450	C₂²×C₆₇	1	16	yes	complemented
441	#449	C₂²×C₆₇	1	16	yes	complemented
442	#447	C₂²×C₆₇	1	16	yes	complemented
443	#417	C₂²×C₆₇	1	8	yes	complemented
444	C₂×#103	C₂²×C₆₇	1	2	yes	complemented
445	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
446	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
447	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
448	C₂×#102	C₂²×C₆₇	1	8	yes	complemented
449	#408	C₂²×C₆₇	1	8	yes	complemented
450	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
451	C₂×C₂²⋊C₈	C₂²×C₆₇	1	2	yes	complemented
452	C₂⁵	—	2	2	no	—
453	C₂⁵	—	2	1	no	—
454	H(5,𝔽₂)	—	2	64	no	—
455	H(5,𝔽₂)	—	2	32	no	—
456	H(5,𝔽₂)	—	2	32	no	—
457	C₂×#41	—	2	16	no	—
458	C₂×#41	—	2	8	no	—
459	C₂×#41	—	2	8	no	—
460	C₂×#41	—	2	8	no	—
461	C₂×#41	—	2	4	no	—
462	C₂×#41	—	2	4	no	—
463	C₂×#41	—	2	2	no	—
464	C₂×#41	—	2	4	no	—
465	C₂×#41	—	2	4	no	—
466	C₂×#41	—	2	2	no	—
467	C₂×#41	—	2	4	no	—
468	C₂×#41	—	2	4	no	—
469	C₂×#41	D₄×C₆₇	1	4	yes	—
470	C₂×#41	D₄×C₆₇	1	8	yes	complemented
471	C₂×#41	C₂³×C₆₇	1	8	yes	—
472	C₂×#41	C₂³×C₆₇	1	4	yes	—
473	C₂×#41	C₂³×C₆₇	1	4	yes	—
474	C₂×#41	C₂³×C₆₇	1	4	yes	complemented
475	C₂²×Q₈	D₄×C₆₇	1	1	yes	characteristic
476	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
477	C₂²×Q₈	C₂³×C₆₇	1	1	yes	characteristic
478	C₂²×D₄	—	2	32	no	—
479	C₂²×D₄	—	2	16	no	—
480	C₂²×D₄	—	2	2	no	—
481	C₂²×D₄	—	2	1	no	—
482	C₂²×D₄	—	2	16	no	—
483	C₂²×D₄	—	2	8	no	—
484	C₂²×D₄	—	2	8	no	—
485	C₂²×D₄	—	2	8	no	—
486	C₂²×D₄	—	2	1	no	—
487	C₂²×D₄	—	2	2	no	—
488	C₂²×D₄	—	2	2	no	—
489	C₂²×D₄	—	2	1	no	—
490	C₂²×D₄	—	2	4	no	—
491	C₂²×D₄	—	2	2	no	—
492	C₂²×D₄	—	2	4	no	—
493	C₂²×D₄	D₄×C₆₇	1	2	yes	—
494	C₂²×D₄	D₄×C₆₇	1	1	yes	characteristic
495	C₂²×D₄	D₄×C₆₇	1	8	yes	complemented
496	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
497	C₂²×D₄	C₂³×C₆₇	1	8	yes	—
498	C₂²×D₄	C₂³×C₆₇	1	1	yes	characteristic
499	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
500	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
501	C₂³×C₄	—	2	2	no	—
502	C₂³×C₄	—	2	1	no	—
503	C₂³×C₄	—	2	1	no	—
504	C₂³×C₄	—	2	1	no	—
505	C₂³×C₄	C₂³×C₆₇	1	2	yes	—
506	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
507	AGL(1,ℤ/8)	—	2	32	no	—
508	#135	—	2	32	no	—
509	C₂×Q₁₆	—	2	4	no	—
510	C₂×Q₁₆	C₂³×C₆₇	1	4	yes	complemented
511	C₂×SD₁₆	—	2	4	no	—
512	C₂×SD₁₆	—	2	4	no	—
513	C₂×SD₁₆	—	2	8	no	—
514	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
515	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	complemented
516	C₂×SD₁₆	C₂³×C₆₇	1	8	yes	complemented
517	C₂×D₈	—	2	4	no	—
518	C₂×D₈	—	2	8	no	—
519	C₂×D₈	C₂³×C₆₇	1	4	yes	complemented
520	C₂×D₈	C₂³×C₆₇	1	8	yes	complemented
521	C₂×M₁₆	—	2	4	no	—
522	C₂×M₁₆	C₂³×C₆₇	1	4	yes	complemented
523	C₂²×C₈	—	2	4	no	—
524	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
525	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
526	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
527	C₂²×C₈	C₂³×C₆₇	1	4	yes	complemented
528	C₂²⋊Q₈	—	2	8	no	—
529	C₂²⋊Q₈	—	2	4	no	—
530	C₂²⋊Q₈	C₂³×C₆₇	1	8	yes	complemented
531	#121	—	2	8	no	—
532	#121	—	2	16	no	—
533	#121	—	2	4	no	—
534	#121	C₂³×C₆₇	1	8	yes	complemented
535	C₂×C₄⋊C₄	—	2	1	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	—	2	2	no	—
538	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
539	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	complemented
540	C₂×C₂²⋊C₄	—	2	2	no	—
541	C₂×C₂²⋊C₄	—	2	2	no	—
542	#103	C₂³×C₆₇	1	8	yes	complemented
543	#102	C₂³×C₆₇	1	8	yes	complemented
544	#102	C₂³×C₆₇	1	8	yes	complemented
545	#102	C₂³×C₆₇	1	8	yes	complemented
546	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
547	C₂²⋊C₈	C₂³×C₆₇	1	8	yes	complemented
548	C₂⁴	—	2	16	no	—
549	C₂⁴	—	2	2	no	—
550	C₂⁴	—	2	1	no	—
551	C₂⁴	—	2	8	no	—
552	C₂⁴	—	2	8	no	—
553	C₂⁴	—	2	4	no	—
554	C₂⁴	—	2	1	no	—
555	C₂⁴	—	8	2	no	—
556	C₂⁴	—	8	2	no	—
557	C₂⁴	—	8	4	no	—
558	C₂⁴	—	8	4	no	—
559	C₂⁴	C₂×D₄×C₆₇	1	2	yes	—
560	C₂⁴	C₂×D₄×C₆₇	1	1	yes	characteristic
561	#41	—	2	64	no	—
562	#41	—	2	32	no	—
563	#41	—	2	16	no	—
564	#41	—	2	16	no	—
565	#41	—	2	16	no	—
566	#41	—	2	16	no	—
567	#41	—	2	8	no	—
568	#41	—	2	8	no	—
569	#41	—	2	8	no	—
570	#41	—	2	8	no	—
571	#41	—	2	8	no	—
572	#41	—	4	8	no	—
573	#41	C₂×D₄×C₆₇	1	16	yes	complemented
574	C₂×Q₈	—	2	4	no	—
575	C₂×Q₈	—	2	2	no	—
576	C₂×Q₈	—	2	1	no	—
577	C₂×Q₈	—	2	1	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	—	2	2	no	—
580	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
581	C₂×Q₈	C₂×D₄×C₆₇	1	4	yes	—
582	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
583	C₂×Q₈	C₂⁴×C₆₇	1	2	yes	—
584	C₂×D₄	—	2	16	no	—
585	C₂×D₄	—	2	16	no	—
586	C₂×D₄	—	2	128	no	—
587	C₂×D₄	—	2	64	no	—
588	C₂×D₄	—	2	32	no	—
589	C₂×D₄	—	2	8	no	—
590	C₂×D₄	—	2	8	no	—
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	2	4	no	—
593	C₂×D₄	—	2	16	no	—
594	C₂×D₄	—	2	16	no	—
595	C₂×D₄	—	2	4	no	—
596	C₂×D₄	—	2	8	no	—
597	C₂×D₄	—	2	4	no	—
598	C₂×D₄	—	2	8	no	—
599	C₂×D₄	—	2	16	no	—
600	C₂×D₄	—	2	8	no	—
601	C₂×D₄	—	2	4	no	—
602	C₂×D₄	—	2	1	no	—
603	C₂×D₄	—	2	2	no	—
604	C₂×D₄	—	2	4	no	—
605	C₂×D₄	—	2	2	no	—
606	C₂×D₄	—	2	8	no	—
607	C₂×D₄	—	2	2	no	—
608	C₂×D₄	—	2	2	no	—
609	C₂×D₄	—	2	1	no	—
610	C₂×D₄	—	4	4	no	—
611	C₂×D₄	—	8	4	no	—
612	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
613	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
614	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
615	C₂×D₄	C₂×D₄×C₆₇	1	8	yes	—
616	C₂×D₄	C₂×D₄×C₆₇	1	16	yes	complemented
617	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
618	C₂×D₄	C₂⁴×C₆₇	1	2	yes	—
619	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
620	C₂²×C₄	—	2	16	no	—
621	C₂²×C₄	—	2	1	no	—
622	C₂²×C₄	—	2	8	no	—
623	C₂²×C₄	—	2	8	no	—
624	C₂²×C₄	—	2	4	no	—
625	C₂²×C₄	—	2	4	no	—
626	C₂²×C₄	—	2	4	no	—
627	C₂²×C₄	—	2	2	no	—
628	C₂²×C₄	—	2	1	no	—
629	C₂²×C₄	—	2	4	no	—
630	C₂²×C₄	—	2	4	no	—
631	C₂²×C₄	—	4	4	no	—
632	C₂²×C₄	—	8	2	no	—
633	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
634	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
635	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
636	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
637	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
638	C₂²×C₄	C₂×D₄×C₆₇	1	4	yes	—
639	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
640	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
641	C₂²×C₄	C₂⁴×C₆₇	1	2	yes	—
642	Q₁₆	—	2	8	no	—
643	SD₁₆	—	2	8	no	—
644	SD₁₆	—	2	8	no	—
645	SD₁₆	—	2	16	no	—
646	D₈	—	2	8	no	—
647	D₈	—	2	16	no	—
648	M₁₆	—	2	8	no	—
649	C₂×C₈	—	2	2	no	—
650	C₂×C₈	—	2	2	no	—
651	C₂×C₈	—	2	8	no	—
652	C₂×C₈	—	2	4	no	—
653	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
654	C₂×C₈	C₂⁴×C₆₇	1	2	yes	—
655	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
656	C₄⋊C₄	—	2	2	no	—
657	C₄⋊C₄	—	2	4	no	—
658	C₄⋊C₄	—	2	8	no	—
659	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
660	C₂²⋊C₄	—	2	8	no	—
661	C₂²⋊C₄	—	2	8	no	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	2	32	no	—
665	C₂³	—	2	4	no	—
666	C₂³	—	2	8	no	—
667	C₂³	—	2	4	no	—
668	C₂³	—	2	4	no	—
669	C₂³	—	2	4	no	—
670	C₂³	—	2	4	no	—
671	C₂³	—	2	2	no	—
672	C₂³	—	2	16	no	—
673	C₂³	—	2	2	no	—
674	C₂³	—	4	4	no	—
675	C₂³	—	4	2	no	—
676	C₂³	—	4	4	no	—
677	C₂³	—	4	2	no	—
678	C₂³	—	4	2	no	—
679	C₂³	—	4	2	no	—
680	C₂³	—	4	2	no	—
681	C₂³	—	8	16	no	—
682	C₂³	—	8	4	no	—
683	C₂³	—	8	4	no	—
684	C₂³	—	8	8	no	—
685	C₂³	—	8	8	no	—
686	C₂³	—	8	32	no	—
687	C₂³	#120×C₆₇	1	4	yes	—
688	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
689	C₂³	C₂²×D₄×C₆₇	1	2	yes	—
690	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
691	Q₈	—	2	4	no	—
692	Q₈	—	2	8	no	—
693	Q₈	—	2	2	no	—
694	Q₈	—	2	2	no	—
695	Q₈	—	2	2	no	—
696	Q₈	—	4	2	no	—
697	Q₈	C₂²×D₄×C₆₇	1	4	yes	—
698	D₄	—	2	32	no	—
699	D₄	—	2	32	no	—
700	D₄	—	2	16	no	—
701	D₄	—	2	16	no	—
702	D₄	—	2	8	no	—
703	D₄	—	2	4	no	—
704	D₄	—	2	8	no	—
705	D₄	—	2	16	no	—
706	D₄	—	2	4	no	—
707	D₄	—	2	2	no	—
708	D₄	—	2	2	no	—
709	D₄	—	2	2	no	—
710	D₄	—	4	8	no	—
711	D₄	—	4	2	no	—
712	D₄	—	8	8	no	—
713	D₄	C₂²×D₄×C₆₇	1	4	yes	—
714	D₄	C₂²×D₄×C₆₇	1	8	yes	—
715	C₂×C₄	—	2	32	no	—
716	C₂×C₄	—	2	4	no	—
717	C₂×C₄	—	2	4	no	—
718	C₂×C₄	—	2	2	no	—
719	C₂×C₄	—	2	16	no	—
720	C₂×C₄	—	2	8	no	—
721	C₂×C₄	—	2	4	no	—
722	C₂×C₄	—	2	4	no	—
723	C₂×C₄	—	2	4	no	—
724	C₂×C₄	—	2	2	no	—
725	C₂×C₄	—	4	2	no	—
726	C₂×C₄	—	4	4	no	—
727	C₂×C₄	—	4	8	no	—
728	C₂×C₄	—	8	4	no	—
729	C₂×C₄	#120×C₆₇	1	4	yes	—
730	C₂×C₄	#120×C₆₇	1	8	yes	—
731	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
732	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
733	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
734	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
735	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
736	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
737	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
738	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
739	C₈	—	2	2	no	—
740	C₈	—	2	2	no	—
741	C₈	—	2	4	no	—
742	C₂²	—	2	8	no	—
743	C₂²	—	2	2	no	—
744	C₂²	—	2	2	no	—
745	C₂²	—	2	4	no	—
746	C₂²	—	2	4	no	—
747	C₂²	—	2	4	no	—
748	C₂²	—	2	8	no	—
749	C₂²	—	2	4	no	—
750	C₂²	—	4	8	no	—
751	C₂²	—	4	16	no	—
752	C₂²	—	4	8	no	—
753	C₂²	—	4	4	no	—
754	C₂²	—	4	2	no	—
755	C₂²	—	4	4	no	—
756	C₂²	—	4	2	no	—
757	C₂²	—	4	2	no	—
758	C₂²	—	4	2	no	—
759	C₂²	—	4	2	no	—
760	C₂²	—	8	16	no	—
761	C₂²	—	8	32	no	—
762	C₂²	—	8	4	no	—
763	C₂²	C₂×#120×C₆₇	1	4	yes	—
764	C₂²	C₂×#120×C₆₇	1	2	yes	—
765	C₂²	#576×C₆₇	1	2	yes	—
766	C₂²	#577×C₆₇	1	2	yes	—
767	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
768	C₄	—	2	4	no	—
769	C₄	—	2	4	no	—
770	C₄	—	4	4	no	—
771	C₄	—	4	2	no	—
772	C₄	C₂×#120×C₆₇	1	4	yes	—
773	C₄	C₂×#120×C₆₇	1	2	yes	—
774	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
775	C₄	C₂³×D₄×C₆₇	1	1	yes	characteristic
776	C₂	—	2	4	no	—
777	C₂	—	4	4	no	—
778	C₂	—	4	8	no	—
779	C₂	—	4	4	no	—
780	C₂	—	8	2	no	—
781	C₂	C₆₇×#3012	1	4	yes	direct product factor
782	C₂	C₂²×#120×C₆₇	1	1	yes	characteristic
783	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
784	C₂	C₂×#577×C₆₇	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂²×H(5,𝔽₂)×C₆₇	C₂	semidirect
2. C₂²×AGL(1,ℤ/8)×C₆₇	C₂	semidirect
3. C₂²×#135×C₆₇	C₂	semidirect
4. C₂×#537×C₆₇	C₂	semidirect
5. C₆₇×#3012	C₂	direct (N × H)
6. C₂×#452×C₆₇	C₂	semidirect
7. C₂×#449×C₆₇	C₂	semidirect
8. C₂×#450×C₆₇	C₂	semidirect
9. C₂×#447×C₆₇	C₂	semidirect
10. C₂×#417×C₆₇	C₂	semidirect
11. C₂²×#102×C₆₇	C₂	semidirect
12. C₂×#408×C₆₇	C₂	semidirect
16. C₂×H(5,𝔽₂)×C₆₇	C₂²	semidirect
21. C₂²×#41×C₆₇	C₂²	semidirect
27. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
29. C₂×#135×C₆₇	C₂²	semidirect
30. C₂²×Q₁₆×C₆₇	C₂²	semidirect
31. C₂²×SD₁₆×C₆₇	C₂²	semidirect
32. C₂²×SD₁₆×C₆₇	C₂²	semidirect
33. C₂²×SD₁₆×C₆₇	C₂²	semidirect
34. C₂²×D₈×C₆₇	C₂²	semidirect
35. C₂²×D₈×C₆₇	C₂²	semidirect
36. C₂²×M₁₆×C₆₇	C₂²	semidirect
37. C₂³×C₈×C₆₇	C₂²	semidirect
39. #537×C₆₇	C₂²	semidirect
41. C₂×C₂²⋊Q₈×C₆₇	C₂²	semidirect
44. C₂×#121×C₆₇	C₂²	semidirect
45. C₂²×C₄⋊C₄×C₆₇	C₂²	semidirect
46. #452×C₆₇	C₂²	semidirect
47. #450×C₆₇	C₂²	semidirect
48. #449×C₆₇	C₂²	semidirect
49. #447×C₆₇	C₂²	semidirect
50. #417×C₆₇	C₂²	semidirect
51. C₂×#103×C₆₇	C₂²	semidirect
52. C₂×#102×C₆₇	C₂²	semidirect
53. C₂×#102×C₆₇	C₂²	semidirect
54. C₂×#102×C₆₇	C₂²	semidirect
55. C₂×#102×C₆₇	C₂²	semidirect
56. #408×C₆₇	C₂²	semidirect
57. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
58. C₂×C₂²⋊C₈×C₆₇	C₂²	semidirect
77. C₂×#41×C₆₇	D₄	semidirect
81. C₂×#41×C₆₇	C₂³	semidirect
102. C₂²×D₄×C₆₇	D₄	semidirect
117. C₂×Q₁₆×C₆₇	C₂³	semidirect
121. C₂×SD₁₆×C₆₇	C₂³	semidirect
122. C₂×SD₁₆×C₆₇	C₂³	semidirect
123. C₂×SD₁₆×C₆₇	C₂³	semidirect
126. C₂×D₈×C₆₇	C₂³	semidirect
127. C₂×D₈×C₆₇	C₂³	semidirect
129. C₂×M₁₆×C₆₇	C₂³	semidirect
134. C₂²×C₈×C₆₇	C₂³	semidirect
137. C₂²⋊Q₈×C₆₇	C₂³	semidirect
141. #121×C₆₇	C₂³	semidirect
146. C₂×C₄⋊C₄×C₆₇	C₂³	semidirect
149. #103×C₆₇	C₂³	semidirect
150. #102×C₆₇	C₂³	semidirect
151. #102×C₆₇	C₂³	semidirect
152. #102×C₆₇	C₂³	semidirect
153. C₂²⋊C₈×C₆₇	C₂³	semidirect
154. C₂²⋊C₈×C₆₇	C₂³	semidirect
180. #41×C₆₇	C₂×D₄	semidirect
223. C₂×D₄×C₆₇	C₂×D₄	semidirect
383. C₂×#3012	C₆₇	direct (N × H)
389. C₂×C₆₇	#3012	direct (N × H)
393. C₂²×H(5,𝔽₂)	C₂×C₆₇	semidirect
394. C₂²×AGL(1,ℤ/8)	C₂×C₆₇	semidirect
395. C₂²×#135	C₂×C₆₇	semidirect
396. C₂×#537	C₂×C₆₇	semidirect
397. #3012	C₂×C₆₇	direct (N × H)
398. C₂×#452	C₂×C₆₇	semidirect
399. C₂×#449	C₂×C₆₇	semidirect
400. C₂×#450	C₂×C₆₇	semidirect
401. C₂×#447	C₂×C₆₇	semidirect
402. C₂×#417	C₂×C₆₇	semidirect
403. C₂²×#102	C₂×C₆₇	semidirect
404. C₂×#408	C₂×C₆₇	semidirect
405. C₆₇	C₂×#3012	direct (N × H)
409. C₂×H(5,𝔽₂)	C₂²×C₆₇	semidirect
414. C₂²×#41	C₂²×C₆₇	semidirect
420. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
422. C₂×#135	C₂²×C₆₇	semidirect
423. C₂²×Q₁₆	C₂²×C₆₇	semidirect
424. C₂²×SD₁₆	C₂²×C₆₇	semidirect
425. C₂²×SD₁₆	C₂²×C₆₇	semidirect
426. C₂²×SD₁₆	C₂²×C₆₇	semidirect
427. C₂²×D₈	C₂²×C₆₇	semidirect
428. C₂²×D₈	C₂²×C₆₇	semidirect
429. C₂²×M₁₆	C₂²×C₆₇	semidirect
430. C₂³×C₈	C₂²×C₆₇	semidirect
432. #537	C₂²×C₆₇	semidirect
434. C₂×C₂²⋊Q₈	C₂²×C₆₇	semidirect
437. C₂×#121	C₂²×C₆₇	semidirect
438. C₂²×C₄⋊C₄	C₂²×C₆₇	semidirect
439. #452	C₂²×C₆₇	semidirect
440. #450	C₂²×C₆₇	semidirect
441. #449	C₂²×C₆₇	semidirect
442. #447	C₂²×C₆₇	semidirect
443. #417	C₂²×C₆₇	semidirect
444. C₂×#103	C₂²×C₆₇	semidirect
445. C₂×#102	C₂²×C₆₇	semidirect
446. C₂×#102	C₂²×C₆₇	semidirect
447. C₂×#102	C₂²×C₆₇	semidirect
448. C₂×#102	C₂²×C₆₇	semidirect
449. #408	C₂²×C₆₇	semidirect
450. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
451. C₂×C₂²⋊C₈	C₂²×C₆₇	semidirect
470. C₂×#41	D₄×C₆₇	semidirect
474. C₂×#41	C₂³×C₆₇	semidirect
495. C₂²×D₄	D₄×C₆₇	semidirect
510. C₂×Q₁₆	C₂³×C₆₇	semidirect
514. C₂×SD₁₆	C₂³×C₆₇	semidirect
515. C₂×SD₁₆	C₂³×C₆₇	semidirect
516. C₂×SD₁₆	C₂³×C₆₇	semidirect
519. C₂×D₈	C₂³×C₆₇	semidirect
520. C₂×D₈	C₂³×C₆₇	semidirect
522. C₂×M₁₆	C₂³×C₆₇	semidirect
527. C₂²×C₈	C₂³×C₆₇	semidirect
530. C₂²⋊Q₈	C₂³×C₆₇	semidirect
534. #121	C₂³×C₆₇	semidirect
539. C₂×C₄⋊C₄	C₂³×C₆₇	semidirect
542. #103	C₂³×C₆₇	semidirect
543. #102	C₂³×C₆₇	semidirect
544. #102	C₂³×C₆₇	semidirect
545. #102	C₂³×C₆₇	semidirect
546. C₂²⋊C₈	C₂³×C₆₇	semidirect
547. C₂²⋊C₈	C₂³×C₆₇	semidirect
573. #41	C₂×D₄×C₆₇	semidirect
616. C₂×D₄	C₂×D₄×C₆₇	semidirect
781. C₂	C₆₇×#3012	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×H(5,𝔽₂)×C₆₇	2
C₂²×AGL(1,ℤ/8)×C₆₇	2
C₂²×#135×C₆₇	2
C₂×#537×C₆₇	2
C₆₇×#3012	2
C₂×#452×C₆₇	2
C₂×#449×C₆₇	2
C₂×#450×C₆₇	2
C₂×#447×C₆₇	2
C₂×#417×C₆₇	2
C₂²×#102×C₆₇	2
C₂×#408×C₆₇	2
C₂×#3012	67

Subgroups — C2×C67×#3012 #30739615

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#3012 #30739615