Subgroups — C₆₇×#61215 #30740466

Order 17152.

2200 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×#3511	C₂	1	1	yes	maximal, characteristic, complemented
2	C₆₇×#3498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×#3333	C₂	1	2	yes	maximal, complemented
4	C₆₇×#3332	C₂	1	2	yes	maximal, complemented
5	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
6	C₆₇×#3324	C₂	1	2	yes	maximal, complemented
7	C₆₇×#3305	C₂	1	2	yes	maximal, complemented
8	C₆₇×#3304	C₂	1	2	yes	maximal, complemented
9	C₆₇×#3295	C₂	1	2	yes	maximal, complemented
10	C₆₇×#3294	C₂	1	2	yes	maximal, complemented
11	C₂×#486×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₆₇×#3096	C₂	1	2	yes	maximal, complemented
13	C₆₇×#3079	C₂	1	1	yes	maximal, characteristic, complemented
14	C₆₇×#3062	C₂	1	2	yes	maximal, complemented
15	C₆₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
16	C₆₇×#3012	C₂	1	2	yes	maximal, complemented
17	C₄×#135×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
18	C₆₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
19	C₆₇×#2897	C₂	1	2	yes	maximal, complemented
20	C₂×H(5,𝔽₂)×C₆₇	C₂²	1	2	yes	—
21	C₂×AGL(1,ℤ/8)×C₆₇	C₂²	1	2	yes	complemented
22	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×#131×C₆₇	C₂²	1	2	yes	complemented
24	#556×C₆₇	C₂²	1	2	yes	complemented
25	#555×C₆₇	C₂²	1	2	yes	complemented
26	#554×C₆₇	C₂²	1	2	yes	complemented
27	#553×C₆₇	—	2	2	no	—
28	#550×C₆₇	C₂²	1	2	yes	—
29	#550×C₆₇	C₂²	1	2	yes	—
30	#548×C₆₇	—	2	2	no	—
31	#547×C₆₇	C₂²	1	2	yes	complemented
32	D₄²×C₆₇	—	2	2	no	—
33	D₄²×C₆₇	—	2	2	no	—
34	D₄²×C₆₇	C₂²	1	2	yes	—
35	D₄²×C₆₇	C₂²	1	2	yes	—
36	#542×C₆₇	—	2	2	no	—
37	#537×C₆₇	C₂²	1	2	yes	complemented
38	#535×C₆₇	—	2	2	no	—
39	#535×C₆₇	C₂²	1	2	yes	—
40	#533×C₆₇	—	2	1	no	—
41	#532×C₆₇	—	2	1	no	—
42	#532×C₆₇	—	2	1	no	—
43	#532×C₆₇	C₂²	1	1	yes	characteristic
44	C₂×C₄⋊Q₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
45	C₂×#127×C₆₇	—	2	1	no	—
46	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
47	#520×C₆₇	C₂²	1	2	yes	complemented
48	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic
49	C₄×#41×C₆₇	C₂²	1	1	yes	characteristic, complemented
50	#486×C₆₇	C₂²	1	2	yes	complemented
51	#486×C₆₇	C₂²	1	2	yes	complemented
52	#486×C₆₇	C₂²	1	2	yes	complemented
53	#486×C₆₇	C₂²	1	2	yes	complemented
54	#482×C₆₇	C₂²	1	4	yes	complemented
55	#482×C₆₇	C₂²	1	4	yes	complemented
56	#481×C₆₇	C₂²	1	4	yes	complemented
57	#480×C₆₇	C₂²	1	4	yes	complemented
58	#477×C₆₇	C₂²	1	2	yes	complemented
59	#476×C₆₇	C₂²	1	2	yes	complemented
60	#475×C₆₇	C₂²	1	2	yes	complemented
61	#474×C₆₇	C₂²	1	2	yes	complemented
62	#469×C₆₇	C₂²	1	4	yes	complemented
63	#468×C₆₇	C₂²	1	4	yes	complemented
64	#466×C₆₇	C₂²	1	4	yes	complemented
65	#465×C₆₇	C₂²	1	4	yes	complemented
66	#460×C₆₇	C₂²	1	2	yes	complemented
67	#460×C₆₇	C₂²	1	2	yes	complemented
68	#459×C₆₇	C₂²	1	2	yes	complemented
69	#459×C₆₇	C₂²	1	2	yes	complemented
70	#452×C₆₇	C₂²	1	4	yes	complemented
71	#450×C₆₇	C₂²	1	4	yes	complemented
72	#449×C₆₇	C₂²	1	4	yes	complemented
73	#447×C₆₇	C₂²	1	4	yes	complemented
74	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
75	C₄×Q₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
76	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
78	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
79	C₄×SD₁₆×C₆₇	C₂²	1	1	yes	characteristic, complemented
80	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
82	#436×C₆₇	C₂²	1	2	yes	complemented
83	#436×C₆₇	C₂²	1	2	yes	complemented
84	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
85	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
86	#428×C₆₇	C₂²	1	2	yes	complemented
87	#427×C₆₇	C₂²	1	1	yes	characteristic, complemented
88	#423×C₆₇	C₂²	1	1	yes	characteristic, complemented
89	#418×C₆₇	C₂²	1	2	yes	complemented
90	#418×C₆₇	C₂²	1	4	yes	complemented
91	#417×C₆₇	C₂²	1	2	yes	—
92	#417×C₆₇	C₂²	1	4	yes	complemented
93	#416×C₆₇	C₂²	1	1	yes	characteristic
94	#416×C₆₇	C₂²	1	4	yes	complemented
95	#416×C₆₇	C₂²	1	1	yes	characteristic, complemented
96	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
97	C₂×#102×C₆₇	C₂²	1	4	yes	complemented
98	C₂×#102×C₆₇	C₂²	1	2	yes	complemented
99	#408×C₆₇	C₂²	1	2	yes	complemented
100	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic, complemented
101	H(5,𝔽₂)×C₆₇	—	2	8	no	—
102	H(5,𝔽₂)×C₆₇	—	4	4	no	—
103	C₂×#41×C₆₇	—	2	2	no	—
104	C₂×#41×C₆₇	—	2	2	no	—
105	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
106	C₂×#41×C₆₇	C₂³	1	4	yes	—
107	C₂×#41×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×#41×C₆₇	C₂³	1	2	yes	—
109	C₂²×Q₈×C₆₇	—	2	1	no	—
110	C₂²×D₄×C₆₇	—	2	2	no	—
111	C₂²×D₄×C₆₇	—	2	4	no	—
112	C₂²×D₄×C₆₇	—	2	2	no	—
113	C₂²×D₄×C₆₇	—	2	2	no	—
114	C₂²×D₄×C₆₇	—	2	1	no	—
115	C₂²×D₄×C₆₇	—	2	1	no	—
116	C₂²×D₄×C₆₇	C₂³	1	2	yes	—
117	C₂²×D₄×C₆₇	C₂³	1	4	yes	—
118	AGL(1,ℤ/8)×C₆₇	—	4	4	no	—
119	#135×C₆₇	—	2	4	no	—
120	C₂×Q₁₆×C₆₇	C₂³	1	1	yes	characteristic
121	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
122	C₂×SD₁₆×C₆₇	C₂³	1	1	yes	characteristic
123	C₂×SD₁₆×C₆₇	C₂³	1	4	yes	—
124	C₂×D₈×C₆₇	C₂³	1	1	yes	characteristic
125	C₂×D₈×C₆₇	C₂³	1	4	yes	—
126	#131×C₆₇	—	4	4	no	—
127	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
128	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
129	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
132	C₄⋊Q₈×C₆₇	—	2	1	no	—
133	C₄⋊Q₈×C₆₇	—	2	1	no	—
134	C₄⋊Q₈×C₆₇	D₄	1	1	yes	characteristic
135	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
136	C₄⋊Q₈×C₆₇	C₂³	1	2	yes	—
137	#127×C₆₇	—	2	2	no	—
138	#127×C₆₇	—	2	2	no	—
139	#127×C₆₇	—	2	2	no	—
140	#127×C₆₇	—	2	1	no	—
141	#127×C₆₇	—	2	1	no	—
142	#127×C₆₇	D₄	1	1	yes	characteristic
143	#127×C₆₇	C₂³	1	2	yes	—
144	#127×C₆₇	C₂³	1	2	yes	—
145	#126×C₆₇	—	2	4	no	—
146	#125×C₆₇	—	2	2	no	—
147	#124×C₆₇	—	2	2	no	—
148	#124×C₆₇	—	2	2	no	—
149	#124×C₆₇	—	2	4	no	—
150	#124×C₆₇	D₄	1	2	yes	—
151	#123×C₆₇	—	2	4	no	—
152	C₂²⋊Q₈×C₆₇	—	2	2	no	—
153	C₂²⋊Q₈×C₆₇	—	2	2	no	—
154	C₂²⋊Q₈×C₆₇	—	2	4	no	—
155	C₂²⋊Q₈×C₆₇	C₂³	1	4	yes	—
156	#121×C₆₇	—	2	2	no	—
157	#121×C₆₇	—	2	2	no	—
158	#121×C₆₇	—	2	4	no	—
159	#121×C₆₇	—	2	2	no	—
160	#121×C₆₇	—	2	2	no	—
161	#121×C₆₇	—	2	4	no	—
162	#121×C₆₇	—	2	4	no	—
163	#121×C₆₇	D₄	1	2	yes	—
164	#121×C₆₇	D₄	1	2	yes	—
165	#121×C₆₇	C₂³	1	4	yes	—
166	#121×C₆₇	C₂³	1	4	yes	—
167	#121×C₆₇	C₂³	1	4	yes	—
168	#120×C₆₇	—	2	4	no	—
169	#120×C₆₇	—	2	4	no	—
170	#120×C₆₇	—	2	4	no	—
171	C₄×Q₈×C₆₇	—	2	2	no	—
172	C₄×Q₈×C₆₇	—	2	2	no	—
173	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
174	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
175	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
176	C₄×Q₈×C₆₇	C₂³	1	1	yes	characteristic
177	C₄×D₄×C₆₇	—	2	2	no	—
178	C₄×D₄×C₆₇	—	2	4	no	—
179	C₄×D₄×C₆₇	—	2	2	no	—
180	C₄×D₄×C₆₇	—	2	1	no	—
181	C₄×D₄×C₆₇	—	2	1	no	—
182	C₄×D₄×C₆₇	—	2	1	no	—
183	C₄×D₄×C₆₇	—	2	1	no	—
184	C₄×D₄×C₆₇	—	2	2	no	—
185	C₄×D₄×C₆₇	—	2	2	no	—
186	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
187	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
188	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
189	C₄×D₄×C₆₇	C₂³	1	1	yes	characteristic
190	C₄×D₄×C₆₇	C₂³	1	2	yes	—
191	C₄×D₄×C₆₇	C₂³	1	2	yes	—
192	#117×C₆₇	—	2	2	no	—
193	#117×C₆₇	—	2	1	no	—
194	#117×C₆₇	—	2	1	no	—
195	#117×C₆₇	C₂³	1	4	yes	—
196	#117×C₆₇	C₂³	1	1	yes	characteristic
197	#117×C₆₇	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
199	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄×C₆₇	C₂³	1	2	yes	—
201	C₂×C₄²×C₆₇	—	2	1	no	—
202	C₂×C₄²×C₆₇	—	2	1	no	—
203	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
204	#107×C₆₇	C₂³	1	4	yes	—
205	#107×C₆₇	C₂³	1	1	yes	characteristic
206	#107×C₆₇	C₂³	1	1	yes	characteristic
207	#106×C₆₇	C₂³	1	4	yes	—
208	#106×C₆₇	C₂³	1	1	yes	characteristic
209	#106×C₆₇	C₂³	1	1	yes	characteristic
210	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
211	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
212	#103×C₆₇	C₂³	1	4	yes	—
213	#103×C₆₇	C₂³	1	1	yes	characteristic
214	#103×C₆₇	C₂³	1	1	yes	characteristic
215	#103×C₆₇	C₂³	1	1	yes	characteristic
216	#103×C₆₇	C₂³	1	1	yes	characteristic
217	#102×C₆₇	C₂³	1	4	yes	—
218	#102×C₆₇	C₂³	1	4	yes	—
219	#102×C₆₇	C₂³	1	4	yes	—
220	#102×C₆₇	C₂³	1	4	yes	—
221	#102×C₆₇	C₂³	1	4	yes	—
222	#102×C₆₇	C₂³	1	4	yes	—
223	#102×C₆₇	C₂³	1	1	yes	characteristic
224	#102×C₆₇	C₂³	1	4	yes	—
225	#102×C₆₇	C₂³	1	1	yes	characteristic
226	#102×C₆₇	C₂³	1	1	yes	characteristic
227	#102×C₆₇	C₂³	1	1	yes	characteristic
228	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
229	C₂²⋊C₈×C₆₇	C₂³	1	4	yes	—
230	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
231	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
232	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
233	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
234	C₂⁴×C₆₇	—	2	4	no	—
235	C₂⁴×C₆₇	—	2	2	no	—
236	#41×C₆₇	—	2	4	no	—
237	#41×C₆₇	—	2	4	no	—
238	#41×C₆₇	—	2	2	no	—
239	#41×C₆₇	—	2	8	no	—
240	#41×C₆₇	—	2	2	no	—
241	#41×C₆₇	—	2	2	no	—
242	#41×C₆₇	—	4	4	no	—
243	#41×C₆₇	—	4	8	no	—
244	#41×C₆₇	—	8	4	no	—
245	#41×C₆₇	#41	1	4	yes	complemented
246	C₂×Q₈×C₆₇	—	2	2	no	—
247	C₂×Q₈×C₆₇	—	2	2	no	—
248	C₂×Q₈×C₆₇	—	8	2	no	—
249	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
250	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
251	C₂×Q₈×C₆₇	C₂⁴	1	1	yes	characteristic
252	C₂×D₄×C₆₇	—	2	1	no	—
253	C₂×D₄×C₆₇	—	2	8	no	—
254	C₂×D₄×C₆₇	—	2	1	no	—
255	C₂×D₄×C₆₇	—	2	4	no	—
256	C₂×D₄×C₆₇	—	2	4	no	—
257	C₂×D₄×C₆₇	—	2	4	no	—
258	C₂×D₄×C₆₇	—	2	4	no	—
259	C₂×D₄×C₆₇	—	2	2	no	—
260	C₂×D₄×C₆₇	—	2	2	no	—
261	C₂×D₄×C₆₇	—	2	4	no	—
262	C₂×D₄×C₆₇	—	2	2	no	—
263	C₂×D₄×C₆₇	—	2	2	no	—
264	C₂×D₄×C₆₇	—	2	2	no	—
265	C₂×D₄×C₆₇	—	2	4	no	—
266	C₂×D₄×C₆₇	—	2	4	no	—
267	C₂×D₄×C₆₇	—	4	4	no	—
268	C₂×D₄×C₆₇	—	4	8	no	—
269	C₂×D₄×C₆₇	—	4	16	no	—
270	C₂×D₄×C₆₇	—	8	2	no	—
271	C₂×D₄×C₆₇	—	8	2	no	—
272	C₂×D₄×C₆₇	—	8	4	no	—
273	C₂×D₄×C₆₇	—	8	4	no	—
274	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
275	C₂×D₄×C₆₇	C₂×D₄	1	4	yes	—
276	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
277	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
278	C₂×D₄×C₆₇	C₂⁴	1	4	yes	—
279	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
280	C₂×D₄×C₆₇	C₂⁴	1	1	yes	characteristic
281	C₂²×C₄×C₆₇	—	2	1	no	—
282	C₂²×C₄×C₆₇	—	2	2	no	—
283	C₂²×C₄×C₆₇	—	2	4	no	—
284	C₂²×C₄×C₆₇	—	2	1	no	—
285	C₂²×C₄×C₆₇	—	2	1	no	—
286	C₂²×C₄×C₆₇	—	2	1	no	—
287	C₂²×C₄×C₆₇	—	2	1	no	—
288	C₂²×C₄×C₆₇	—	2	1	no	—
289	C₂²×C₄×C₆₇	—	2	4	no	—
290	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
291	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
292	C₂²×C₄×C₆₇	C₂⁴	1	4	yes	—
293	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
294	Q₁₆×C₆₇	—	2	2	no	—
295	SD₁₆×C₆₇	—	2	2	no	—
296	SD₁₆×C₆₇	—	2	2	no	—
297	SD₁₆×C₆₇	—	4	4	no	—
298	D₈×C₆₇	—	2	2	no	—
299	D₈×C₆₇	—	4	4	no	—
300	M₁₆×C₆₇	—	2	4	no	—
301	M₁₆×C₆₇	—	4	4	no	—
302	C₂×C₈×C₆₇	—	2	2	no	—
303	C₂×C₈×C₆₇	—	2	2	no	—
304	C₂×C₈×C₆₇	—	4	4	no	—
305	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
306	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
307	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
309	C₂×C₈×C₆₇	C₂⁴	1	4	yes	—
310	C₄⋊C₄×C₆₇	—	2	2	no	—
311	C₄⋊C₄×C₆₇	—	2	2	no	—
312	C₄⋊C₄×C₆₇	—	2	2	no	—
313	C₄⋊C₄×C₆₇	—	2	4	no	—
314	C₄⋊C₄×C₆₇	—	2	1	no	—
315	C₄⋊C₄×C₆₇	—	2	1	no	—
316	C₄⋊C₄×C₆₇	—	2	1	no	—
317	C₄⋊C₄×C₆₇	—	2	1	no	—
318	C₄⋊C₄×C₆₇	—	2	4	no	—
319	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
320	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
321	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
322	C₄⋊C₄×C₆₇	C₂⁴	1	4	yes	—
323	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
324	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
325	C₄⋊C₄×C₆₇	C₂⁴	1	1	yes	characteristic
326	C₂²⋊C₄×C₆₇	—	2	1	no	—
327	C₂²⋊C₄×C₆₇	—	2	1	no	—
328	C₂²⋊C₄×C₆₇	—	2	4	no	—
329	C₂²⋊C₄×C₆₇	—	2	4	no	—
330	C₂²⋊C₄×C₆₇	—	2	1	no	—
331	C₂²⋊C₄×C₆₇	—	2	1	no	—
332	C₂²⋊C₄×C₆₇	—	2	1	no	—
333	C₂²⋊C₄×C₆₇	—	2	1	no	—
334	C₂²⋊C₄×C₆₇	—	2	4	no	—
335	C₂²⋊C₄×C₆₇	—	2	4	no	—
336	C₂²⋊C₄×C₆₇	—	2	4	no	—
337	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
338	C₂²⋊C₄×C₆₇	C₂×D₄	1	4	yes	—
339	C₄²×C₆₇	—	2	1	no	—
340	C₄²×C₆₇	—	2	1	no	—
341	C₄²×C₆₇	—	2	1	no	—
342	C₄²×C₆₇	—	2	1	no	—
343	C₄²×C₆₇	—	2	1	no	—
344	C₄²×C₆₇	—	2	1	no	—
345	C₄²×C₆₇	—	2	4	no	—
346	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
347	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
348	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
349	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
350	C₂³×C₆₇	—	2	1	no	—
351	C₂³×C₆₇	—	2	1	no	—
352	C₂³×C₆₇	—	2	4	no	—
353	C₂³×C₆₇	—	4	8	no	—
354	C₂³×C₆₇	—	4	4	no	—
355	C₂³×C₆₇	—	8	2	no	—
356	C₂³×C₆₇	—	8	2	no	—
357	C₂³×C₆₇	—	8	4	no	—
358	C₂³×C₆₇	—	8	4	no	—
359	C₂³×C₆₇	C₂²×D₄	1	4	yes	—
360	C₂³×C₆₇	C₂²×D₄	1	1	yes	characteristic
361	Q₈×C₆₇	—	2	4	no	—
362	Q₈×C₆₇	—	2	1	no	—
363	Q₈×C₆₇	—	2	1	no	—
364	Q₈×C₆₇	—	2	1	no	—
365	Q₈×C₆₇	—	4	4	no	—
366	Q₈×C₆₇	—	8	2	no	—
367	Q₈×C₆₇	C₂×#41	1	2	yes	—
368	D₄×C₆₇	—	2	4	no	—
369	D₄×C₆₇	—	2	8	no	—
370	D₄×C₆₇	—	2	4	no	—
371	D₄×C₆₇	—	2	4	no	—
372	D₄×C₆₇	—	2	4	no	—
373	D₄×C₆₇	—	2	1	no	—
374	D₄×C₆₇	—	2	4	no	—
375	D₄×C₆₇	—	2	1	no	—
376	D₄×C₆₇	—	2	1	no	—
377	D₄×C₆₇	—	2	4	no	—
378	D₄×C₆₇	—	4	8	no	—
379	D₄×C₆₇	—	4	8	no	—
380	D₄×C₆₇	—	4	2	no	—
381	D₄×C₆₇	—	4	4	no	—
382	D₄×C₆₇	—	4	4	no	—
383	D₄×C₆₇	—	4	4	no	—
384	D₄×C₆₇	—	8	2	no	—
385	D₄×C₆₇	—	8	2	no	—
386	D₄×C₆₇	—	8	4	no	—
387	D₄×C₆₇	—	8	4	no	—
388	D₄×C₆₇	—	8	4	no	—
389	D₄×C₆₇	C₂×#41	1	2	yes	—
390	C₂×C₄×C₆₇	—	2	1	no	—
391	C₂×C₄×C₆₇	—	2	4	no	—
392	C₂×C₄×C₆₇	—	2	2	no	—
393	C₂×C₄×C₆₇	—	2	2	no	—
394	C₂×C₄×C₆₇	—	2	4	no	—
395	C₂×C₄×C₆₇	—	2	4	no	—
396	C₂×C₄×C₆₇	—	2	1	no	—
397	C₂×C₄×C₆₇	—	2	1	no	—
398	C₂×C₄×C₆₇	—	2	1	no	—
399	C₂×C₄×C₆₇	—	2	1	no	—
400	C₂×C₄×C₆₇	—	2	1	no	—
401	C₂×C₄×C₆₇	—	2	4	no	—
402	C₂×C₄×C₆₇	—	4	8	no	—
403	C₂×C₄×C₆₇	—	4	2	no	—
404	C₂×C₄×C₆₇	—	4	2	no	—
405	C₂×C₄×C₆₇	—	4	2	no	—
406	C₂×C₄×C₆₇	—	4	2	no	—
407	C₂×C₄×C₆₇	—	4	2	no	—
408	C₂×C₄×C₆₇	—	8	2	no	—
409	C₂×C₄×C₆₇	—	8	4	no	—
410	C₂×C₄×C₆₇	C₂²×D₄	1	4	yes	—
411	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
412	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
413	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
414	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
415	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
416	C₂×C₄×C₆₇	C₂×#41	1	2	yes	—
417	C₂×C₄×C₆₇	H(5,𝔽₂)	1	2	yes	—
418	C₂×C₄×C₆₇	C₂⁵	1	1	yes	characteristic
419	C₈×C₆₇	—	2	1	no	—
420	C₈×C₆₇	—	2	1	no	—
421	C₈×C₆₇	—	2	1	no	—
422	C₈×C₆₇	—	2	1	no	—
423	C₈×C₆₇	—	2	4	no	—
424	C₂²×C₆₇	—	2	1	no	—
425	C₂²×C₆₇	—	2	1	no	—
426	C₂²×C₆₇	—	2	4	no	—
427	C₂²×C₆₇	—	2	2	no	—
428	C₂²×C₆₇	—	2	4	no	—
429	C₂²×C₆₇	—	2	4	no	—
430	C₂²×C₆₇	—	4	1	no	—
431	C₂²×C₆₇	—	4	1	no	—
432	C₂²×C₆₇	—	4	4	no	—
433	C₂²×C₆₇	—	4	1	no	—
434	C₂²×C₆₇	—	4	1	no	—
435	C₂²×C₆₇	—	4	4	no	—
436	C₂²×C₆₇	—	4	1	no	—
437	C₂²×C₆₇	—	4	4	no	—
438	C₂²×C₆₇	—	16	4	no	—
439	C₂²×C₆₇	—	16	8	no	—
440	C₂²×C₆₇	#546	1	2	yes	—
441	C₂²×C₆₇	C₂³×D₄	1	1	yes	characteristic
442	C₄×C₆₇	—	2	2	no	—
443	C₄×C₆₇	—	2	4	no	—
444	C₄×C₆₇	—	2	1	no	—
445	C₄×C₆₇	—	2	1	no	—
446	C₄×C₆₇	—	4	1	no	—
447	C₄×C₆₇	—	4	1	no	—
448	C₄×C₆₇	—	4	1	no	—
449	C₄×C₆₇	—	4	4	no	—
450	C₄×C₆₇	—	4	1	no	—
451	C₄×C₆₇	—	4	1	no	—
452	C₄×C₆₇	#546	1	2	yes	—
453	C₄×C₆₇	#576	1	2	yes	—
454	C₄×C₆₇	#577	1	2	yes	—
455	C₄×C₆₇	C₂²×#41	1	1	yes	characteristic
456	C₄×C₆₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
457	#61215	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
458	C₂×C₆₇	—	2	2	no	—
459	C₂×C₆₇	—	4	4	no	—
460	C₂×C₆₇	—	4	2	no	—
461	C₂×C₆₇	—	8	1	no	—
462	C₂×C₆₇	—	8	4	no	—
463	C₂×C₆₇	C₂×#546	1	1	yes	characteristic
464	C₂×C₆₇	C₂×#576	1	1	yes	characteristic
465	C₂×C₆₇	C₂×#577	1	1	yes	characteristic
466	#3511	C₂×C₆₇	1	1	yes	characteristic, complemented
467	#3498	C₂×C₆₇	1	1	yes	characteristic, complemented
468	#3333	C₂×C₆₇	1	2	yes	complemented
469	#3332	C₂×C₆₇	1	2	yes	complemented
470	#3325	C₂×C₆₇	1	2	yes	complemented
471	#3324	C₂×C₆₇	1	2	yes	complemented
472	#3305	C₂×C₆₇	1	2	yes	complemented
473	#3304	C₂×C₆₇	1	2	yes	complemented
474	#3295	C₂×C₆₇	1	2	yes	complemented
475	#3294	C₂×C₆₇	1	2	yes	complemented
476	C₂×#486	C₂×C₆₇	1	1	yes	characteristic, complemented
477	#3096	C₂×C₆₇	1	2	yes	complemented
478	#3079	C₂×C₆₇	1	1	yes	characteristic, complemented
479	#3062	C₂×C₆₇	1	2	yes	complemented
480	#3038	C₂×C₆₇	1	1	yes	characteristic, complemented
481	#3012	C₂×C₆₇	1	2	yes	complemented
482	C₄×#135	C₂×C₆₇	1	1	yes	characteristic, complemented
483	#2931	C₂×C₆₇	1	1	yes	characteristic, complemented
484	#2897	C₂×C₆₇	1	2	yes	complemented
485	C₆₇	#61215	1	1	yes	characteristic, direct product factor, Sylow
486	C₂×H(5,𝔽₂)	C₂²×C₆₇	1	2	yes	—
487	C₂×AGL(1,ℤ/8)	C₂²×C₆₇	1	2	yes	complemented
488	C₂×#135	C₂²×C₆₇	1	1	yes	characteristic
489	C₂×#131	C₂²×C₆₇	1	2	yes	complemented
490	#556	C₂²×C₆₇	1	2	yes	complemented
491	#555	C₂²×C₆₇	1	2	yes	complemented
492	#554	C₂²×C₆₇	1	2	yes	complemented
493	#553	—	2	2	no	—
494	#550	C₂²×C₆₇	1	2	yes	—
495	#550	C₂²×C₆₇	1	2	yes	—
496	#548	—	2	2	no	—
497	#547	C₂²×C₆₇	1	2	yes	complemented
498	D₄²	—	2	2	no	—
499	D₄²	—	2	2	no	—
500	D₄²	C₂²×C₆₇	1	2	yes	—
501	D₄²	C₂²×C₆₇	1	2	yes	—
502	#542	—	2	2	no	—
503	#537	C₂²×C₆₇	1	2	yes	complemented
504	#535	—	2	2	no	—
505	#535	C₂²×C₆₇	1	2	yes	—
506	#533	—	2	1	no	—
507	#532	—	2	1	no	—
508	#532	—	2	1	no	—
509	#532	C₂²×C₆₇	1	1	yes	characteristic
510	C₂×C₄⋊Q₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
511	C₂×#127	—	2	1	no	—
512	C₂×#127	C₂²×C₆₇	1	1	yes	characteristic
513	#520	C₂²×C₆₇	1	2	yes	complemented
514	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic
515	C₄×#41	C₂²×C₆₇	1	1	yes	characteristic, complemented
516	#486	C₂²×C₆₇	1	2	yes	complemented
517	#486	C₂²×C₆₇	1	2	yes	complemented
518	#486	C₂²×C₆₇	1	2	yes	complemented
519	#486	C₂²×C₆₇	1	2	yes	complemented
520	#482	C₂²×C₆₇	1	4	yes	complemented
521	#482	C₂²×C₆₇	1	4	yes	complemented
522	#481	C₂²×C₆₇	1	4	yes	complemented
523	#480	C₂²×C₆₇	1	4	yes	complemented
524	#477	C₂²×C₆₇	1	2	yes	complemented
525	#476	C₂²×C₆₇	1	2	yes	complemented
526	#475	C₂²×C₆₇	1	2	yes	complemented
527	#474	C₂²×C₆₇	1	2	yes	complemented
528	#469	C₂²×C₆₇	1	4	yes	complemented
529	#468	C₂²×C₆₇	1	4	yes	complemented
530	#466	C₂²×C₆₇	1	4	yes	complemented
531	#465	C₂²×C₆₇	1	4	yes	complemented
532	#460	C₂²×C₆₇	1	2	yes	complemented
533	#460	C₂²×C₆₇	1	2	yes	complemented
534	#459	C₂²×C₆₇	1	2	yes	complemented
535	#459	C₂²×C₆₇	1	2	yes	complemented
536	#452	C₂²×C₆₇	1	4	yes	complemented
537	#450	C₂²×C₆₇	1	4	yes	complemented
538	#449	C₂²×C₆₇	1	4	yes	complemented
539	#447	C₂²×C₆₇	1	4	yes	complemented
540	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
541	C₄×Q₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
542	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
543	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
544	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
545	C₄×SD₁₆	C₂²×C₆₇	1	1	yes	characteristic, complemented
546	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
547	C₄×D₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
548	#436	C₂²×C₆₇	1	2	yes	complemented
549	#436	C₂²×C₆₇	1	2	yes	complemented
550	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
551	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
552	#428	C₂²×C₆₇	1	2	yes	complemented
553	#427	C₂²×C₆₇	1	1	yes	characteristic, complemented
554	#423	C₂²×C₆₇	1	1	yes	characteristic, complemented
555	#418	C₂²×C₆₇	1	2	yes	complemented
556	#418	C₂²×C₆₇	1	4	yes	complemented
557	#417	C₂²×C₆₇	1	2	yes	—
558	#417	C₂²×C₆₇	1	4	yes	complemented
559	#416	C₂²×C₆₇	1	1	yes	characteristic
560	#416	C₂²×C₆₇	1	4	yes	complemented
561	#416	C₂²×C₆₇	1	1	yes	characteristic, complemented
562	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
563	C₂×#102	C₂²×C₆₇	1	2	yes	complemented
564	C₂×#102	C₂²×C₆₇	1	4	yes	complemented
565	#408	C₂²×C₆₇	1	2	yes	complemented
566	C₂×C₄×C₈	C₂²×C₆₇	1	1	yes	characteristic, complemented
567	H(5,𝔽₂)	—	2	8	no	—
568	H(5,𝔽₂)	—	4	4	no	—
569	C₂×#41	—	2	2	no	—
570	C₂×#41	—	2	2	no	—
571	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
572	C₂×#41	C₂³×C₆₇	1	4	yes	—
573	C₂×#41	C₂³×C₆₇	1	1	yes	characteristic
574	C₂×#41	C₂³×C₆₇	1	2	yes	—
575	C₂²×Q₈	—	2	1	no	—
576	C₂²×D₄	—	2	2	no	—
577	C₂²×D₄	—	2	4	no	—
578	C₂²×D₄	—	2	2	no	—
579	C₂²×D₄	—	2	2	no	—
580	C₂²×D₄	—	2	1	no	—
581	C₂²×D₄	—	2	1	no	—
582	C₂²×D₄	C₂³×C₆₇	1	2	yes	—
583	C₂²×D₄	C₂³×C₆₇	1	4	yes	—
584	AGL(1,ℤ/8)	—	4	4	no	—
585	#135	—	2	4	no	—
586	C₂×Q₁₆	C₂³×C₆₇	1	1	yes	characteristic
587	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
588	C₂×SD₁₆	C₂³×C₆₇	1	1	yes	characteristic
589	C₂×SD₁₆	C₂³×C₆₇	1	4	yes	—
590	C₂×D₈	C₂³×C₆₇	1	1	yes	characteristic
591	C₂×D₈	C₂³×C₆₇	1	4	yes	—
592	#131	—	4	4	no	—
593	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
594	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
595	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
596	C₂²×C₈	C₂³×C₆₇	1	1	yes	characteristic
597	C₂²×C₈	C₂³×C₆₇	1	4	yes	—
598	C₄⋊Q₈	—	2	1	no	—
599	C₄⋊Q₈	—	2	1	no	—
600	C₄⋊Q₈	D₄×C₆₇	1	1	yes	characteristic
601	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
602	C₄⋊Q₈	C₂³×C₆₇	1	2	yes	—
603	#127	—	2	2	no	—
604	#127	—	2	2	no	—
605	#127	—	2	2	no	—
606	#127	—	2	1	no	—
607	#127	—	2	1	no	—
608	#127	D₄×C₆₇	1	1	yes	characteristic
609	#127	C₂³×C₆₇	1	2	yes	—
610	#127	C₂³×C₆₇	1	2	yes	—
611	#126	—	2	4	no	—
612	#125	—	2	2	no	—
613	#124	—	2	2	no	—
614	#124	—	2	2	no	—
615	#124	—	2	4	no	—
616	#124	D₄×C₆₇	1	2	yes	—
617	#123	—	2	4	no	—
618	C₂²⋊Q₈	—	2	2	no	—
619	C₂²⋊Q₈	—	2	2	no	—
620	C₂²⋊Q₈	—	2	4	no	—
621	C₂²⋊Q₈	C₂³×C₆₇	1	4	yes	—
622	#121	—	2	2	no	—
623	#121	—	2	2	no	—
624	#121	—	2	4	no	—
625	#121	—	2	2	no	—
626	#121	—	2	2	no	—
627	#121	—	2	4	no	—
628	#121	—	2	4	no	—
629	#121	D₄×C₆₇	1	2	yes	—
630	#121	D₄×C₆₇	1	2	yes	—
631	#121	C₂³×C₆₇	1	4	yes	—
632	#121	C₂³×C₆₇	1	4	yes	—
633	#121	C₂³×C₆₇	1	4	yes	—
634	#120	—	2	4	no	—
635	#120	—	2	4	no	—
636	#120	—	2	4	no	—
637	C₄×Q₈	—	2	2	no	—
638	C₄×Q₈	—	2	2	no	—
639	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
640	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
641	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
642	C₄×Q₈	C₂³×C₆₇	1	1	yes	characteristic
643	C₄×D₄	—	2	2	no	—
644	C₄×D₄	—	2	4	no	—
645	C₄×D₄	—	2	2	no	—
646	C₄×D₄	—	2	1	no	—
647	C₄×D₄	—	2	1	no	—
648	C₄×D₄	—	2	1	no	—
649	C₄×D₄	—	2	1	no	—
650	C₄×D₄	—	2	2	no	—
651	C₄×D₄	—	2	2	no	—
652	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
653	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
654	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
655	C₄×D₄	C₂³×C₆₇	1	1	yes	characteristic
656	C₄×D₄	C₂³×C₆₇	1	2	yes	—
657	C₄×D₄	C₂³×C₆₇	1	2	yes	—
658	#117	—	2	2	no	—
659	#117	—	2	1	no	—
660	#117	—	2	1	no	—
661	#117	C₂³×C₆₇	1	1	yes	characteristic
662	#117	C₂³×C₆₇	1	1	yes	characteristic
663	#117	C₂³×C₆₇	1	4	yes	—
664	C₂×C₄⋊C₄	—	2	1	no	—
665	C₂×C₄⋊C₄	C₂³×C₆₇	1	2	yes	—
666	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
667	C₂×C₄²	—	2	1	no	—
668	C₂×C₄²	—	2	1	no	—
669	C₂×C₄²	C₂³×C₆₇	1	1	yes	characteristic
670	#107	C₂³×C₆₇	1	1	yes	characteristic
671	#107	C₂³×C₆₇	1	1	yes	characteristic
672	#107	C₂³×C₆₇	1	4	yes	—
673	#106	C₂³×C₆₇	1	1	yes	characteristic
674	#106	C₂³×C₆₇	1	1	yes	characteristic
675	#106	C₂³×C₆₇	1	4	yes	—
676	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
677	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
678	#103	C₂³×C₆₇	1	1	yes	characteristic
679	#103	C₂³×C₆₇	1	1	yes	characteristic
680	#103	C₂³×C₆₇	1	4	yes	—
681	#103	C₂³×C₆₇	1	1	yes	characteristic
682	#103	C₂³×C₆₇	1	1	yes	characteristic
683	#102	C₂³×C₆₇	1	1	yes	characteristic
684	#102	C₂³×C₆₇	1	4	yes	—
685	#102	C₂³×C₆₇	1	4	yes	—
686	#102	C₂³×C₆₇	1	4	yes	—
687	#102	C₂³×C₆₇	1	4	yes	—
688	#102	C₂³×C₆₇	1	4	yes	—
689	#102	C₂³×C₆₇	1	4	yes	—
690	#102	C₂³×C₆₇	1	1	yes	characteristic
691	#102	C₂³×C₆₇	1	4	yes	—
692	#102	C₂³×C₆₇	1	1	yes	characteristic
693	#102	C₂³×C₆₇	1	1	yes	characteristic
694	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
695	C₂²⋊C₈	C₂³×C₆₇	1	4	yes	—
696	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
697	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
698	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
699	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
700	C₂⁴	—	2	4	no	—
701	C₂⁴	—	2	2	no	—
702	#41	—	2	4	no	—
703	#41	—	2	4	no	—
704	#41	—	2	2	no	—
705	#41	—	2	8	no	—
706	#41	—	2	2	no	—
707	#41	—	2	2	no	—
708	#41	—	4	4	no	—
709	#41	—	4	8	no	—
710	#41	—	8	4	no	—
711	#41	#41×C₆₇	1	4	yes	complemented
712	C₂×Q₈	—	2	2	no	—
713	C₂×Q₈	—	2	2	no	—
714	C₂×Q₈	—	8	2	no	—
715	C₂×Q₈	C₂×D₄×C₆₇	1	2	yes	—
716	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
717	C₂×Q₈	C₂⁴×C₆₇	1	1	yes	characteristic
718	C₂×D₄	—	2	1	no	—
719	C₂×D₄	—	2	8	no	—
720	C₂×D₄	—	2	1	no	—
721	C₂×D₄	—	2	4	no	—
722	C₂×D₄	—	2	4	no	—
723	C₂×D₄	—	2	4	no	—
724	C₂×D₄	—	2	4	no	—
725	C₂×D₄	—	2	2	no	—
726	C₂×D₄	—	2	2	no	—
727	C₂×D₄	—	2	4	no	—
728	C₂×D₄	—	2	2	no	—
729	C₂×D₄	—	2	2	no	—
730	C₂×D₄	—	2	2	no	—
731	C₂×D₄	—	2	4	no	—
732	C₂×D₄	—	2	4	no	—
733	C₂×D₄	—	4	4	no	—
734	C₂×D₄	—	4	8	no	—
735	C₂×D₄	—	4	16	no	—
736	C₂×D₄	—	8	2	no	—
737	C₂×D₄	—	8	2	no	—
738	C₂×D₄	—	8	4	no	—
739	C₂×D₄	—	8	4	no	—
740	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
741	C₂×D₄	C₂×D₄×C₆₇	1	4	yes	—
742	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
743	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
744	C₂×D₄	C₂⁴×C₆₇	1	4	yes	—
745	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
746	C₂×D₄	C₂⁴×C₆₇	1	1	yes	characteristic
747	C₂²×C₄	—	2	1	no	—
748	C₂²×C₄	—	2	2	no	—
749	C₂²×C₄	—	2	4	no	—
750	C₂²×C₄	—	2	1	no	—
751	C₂²×C₄	—	2	1	no	—
752	C₂²×C₄	—	2	1	no	—
753	C₂²×C₄	—	2	1	no	—
754	C₂²×C₄	—	2	1	no	—
755	C₂²×C₄	—	2	4	no	—
756	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
757	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
758	C₂²×C₄	C₂⁴×C₆₇	1	4	yes	—
759	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
760	Q₁₆	—	2	2	no	—
761	SD₁₆	—	2	2	no	—
762	SD₁₆	—	2	2	no	—
763	SD₁₆	—	4	4	no	—
764	D₈	—	2	2	no	—
765	D₈	—	4	4	no	—
766	M₁₆	—	2	4	no	—
767	M₁₆	—	4	4	no	—
768	C₂×C₈	—	2	2	no	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	4	4	no	—
771	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
772	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
773	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
774	C₂×C₈	C₂⁴×C₆₇	1	1	yes	characteristic
775	C₂×C₈	C₂⁴×C₆₇	1	4	yes	—
776	C₄⋊C₄	—	2	2	no	—
777	C₄⋊C₄	—	2	2	no	—
778	C₄⋊C₄	—	2	2	no	—
779	C₄⋊C₄	—	2	4	no	—
780	C₄⋊C₄	—	2	1	no	—
781	C₄⋊C₄	—	2	1	no	—
782	C₄⋊C₄	—	2	1	no	—
783	C₄⋊C₄	—	2	1	no	—
784	C₄⋊C₄	—	2	4	no	—
785	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
786	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
787	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
788	C₄⋊C₄	C₂⁴×C₆₇	1	4	yes	—
789	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂⁴×C₆₇	1	1	yes	characteristic
792	C₂²⋊C₄	—	2	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	2	4	no	—
795	C₂²⋊C₄	—	2	4	no	—
796	C₂²⋊C₄	—	2	1	no	—
797	C₂²⋊C₄	—	2	1	no	—
798	C₂²⋊C₄	—	2	1	no	—
799	C₂²⋊C₄	—	2	1	no	—
800	C₂²⋊C₄	—	2	4	no	—
801	C₂²⋊C₄	—	2	4	no	—
802	C₂²⋊C₄	—	2	4	no	—
803	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
804	C₂²⋊C₄	C₂×D₄×C₆₇	1	4	yes	—
805	C₄²	—	2	1	no	—
806	C₄²	—	2	1	no	—
807	C₄²	—	2	1	no	—
808	C₄²	—	2	1	no	—
809	C₄²	—	2	1	no	—
810	C₄²	—	2	1	no	—
811	C₄²	—	2	4	no	—
812	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
813	C₄²	C₂×D₄×C₆₇	1	1	yes	characteristic
814	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
815	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
816	C₂³	—	2	1	no	—
817	C₂³	—	2	1	no	—
818	C₂³	—	2	4	no	—
819	C₂³	—	4	8	no	—
820	C₂³	—	4	4	no	—
821	C₂³	—	8	2	no	—
822	C₂³	—	8	2	no	—
823	C₂³	—	8	4	no	—
824	C₂³	—	8	4	no	—
825	C₂³	C₂²×D₄×C₆₇	1	4	yes	—
826	C₂³	C₂²×D₄×C₆₇	1	1	yes	characteristic
827	Q₈	—	2	4	no	—
828	Q₈	—	2	1	no	—
829	Q₈	—	2	1	no	—
830	Q₈	—	2	1	no	—
831	Q₈	—	4	4	no	—
832	Q₈	—	8	2	no	—
833	Q₈	C₂×#41×C₆₇	1	2	yes	—
834	D₄	—	2	4	no	—
835	D₄	—	2	8	no	—
836	D₄	—	2	4	no	—
837	D₄	—	2	4	no	—
838	D₄	—	2	4	no	—
839	D₄	—	2	1	no	—
840	D₄	—	2	4	no	—
841	D₄	—	2	1	no	—
842	D₄	—	2	1	no	—
843	D₄	—	2	4	no	—
844	D₄	—	4	8	no	—
845	D₄	—	4	8	no	—
846	D₄	—	4	2	no	—
847	D₄	—	4	4	no	—
848	D₄	—	4	4	no	—
849	D₄	—	4	4	no	—
850	D₄	—	8	2	no	—
851	D₄	—	8	2	no	—
852	D₄	—	8	4	no	—
853	D₄	—	8	4	no	—
854	D₄	—	8	4	no	—
855	D₄	C₂×#41×C₆₇	1	2	yes	—
856	C₂×C₄	—	2	1	no	—
857	C₂×C₄	—	2	4	no	—
858	C₂×C₄	—	2	2	no	—
859	C₂×C₄	—	2	2	no	—
860	C₂×C₄	—	2	4	no	—
861	C₂×C₄	—	2	4	no	—
862	C₂×C₄	—	2	1	no	—
863	C₂×C₄	—	2	1	no	—
864	C₂×C₄	—	2	1	no	—
865	C₂×C₄	—	2	1	no	—
866	C₂×C₄	—	2	1	no	—
867	C₂×C₄	—	2	4	no	—
868	C₂×C₄	—	4	8	no	—
869	C₂×C₄	—	4	2	no	—
870	C₂×C₄	—	4	2	no	—
871	C₂×C₄	—	4	2	no	—
872	C₂×C₄	—	4	2	no	—
873	C₂×C₄	—	4	2	no	—
874	C₂×C₄	—	8	2	no	—
875	C₂×C₄	—	8	4	no	—
876	C₂×C₄	C₂²×D₄×C₆₇	1	4	yes	—
877	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
878	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
879	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
880	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
881	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
882	C₂×C₄	C₂×#41×C₆₇	1	2	yes	—
883	C₂×C₄	H(5,𝔽₂)×C₆₇	1	2	yes	—
884	C₂×C₄	C₂⁵×C₆₇	1	1	yes	characteristic
885	C₈	—	2	1	no	—
886	C₈	—	2	1	no	—
887	C₈	—	2	1	no	—
888	C₈	—	2	1	no	—
889	C₈	—	2	4	no	—
890	C₂²	—	2	1	no	—
891	C₂²	—	2	1	no	—
892	C₂²	—	2	4	no	—
893	C₂²	—	2	4	no	—
894	C₂²	—	2	4	no	—
895	C₂²	—	2	2	no	—
896	C₂²	—	4	1	no	—
897	C₂²	—	4	1	no	—
898	C₂²	—	4	1	no	—
899	C₂²	—	4	4	no	—
900	C₂²	—	4	1	no	—
901	C₂²	—	4	4	no	—
902	C₂²	—	4	4	no	—
903	C₂²	—	4	1	no	—
904	C₂²	—	16	4	no	—
905	C₂²	—	16	8	no	—
906	C₂²	#546×C₆₇	1	2	yes	—
907	C₂²	C₂³×D₄×C₆₇	1	1	yes	characteristic
908	C₄	—	2	1	no	—
909	C₄	—	2	1	no	—
910	C₄	—	2	2	no	—
911	C₄	—	2	4	no	—
912	C₄	—	4	1	no	—
913	C₄	—	4	1	no	—
914	C₄	—	4	4	no	—
915	C₄	—	4	1	no	—
916	C₄	—	4	1	no	—
917	C₄	—	4	1	no	—
918	C₄	#546×C₆₇	1	2	yes	—
919	C₄	#576×C₆₇	1	2	yes	—
920	C₄	#577×C₆₇	1	2	yes	—
921	C₄	C₂²×#41×C₆₇	1	1	yes	characteristic
922	C₄	C₂×H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
923	C₂	—	2	2	no	—
924	C₂	—	4	4	no	—
925	C₂	—	4	2	no	—
926	C₂	—	8	4	no	—
927	C₂	—	8	1	no	—
928	C₂	C₂×#546×C₆₇	1	1	yes	characteristic
929	C₂	C₂×#576×C₆₇	1	1	yes	characteristic
930	C₂	C₂×#577×C₆₇	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×#3511	C₂	semidirect
2. C₆₇×#3498	C₂	semidirect
3. C₆₇×#3333	C₂	semidirect
4. C₆₇×#3332	C₂	semidirect
5. C₆₇×#3325	C₂	semidirect
6. C₆₇×#3324	C₂	semidirect
7. C₆₇×#3305	C₂	semidirect
8. C₆₇×#3304	C₂	semidirect
9. C₆₇×#3295	C₂	semidirect
10. C₆₇×#3294	C₂	semidirect
11. C₂×#486×C₆₇	C₂	semidirect
12. C₆₇×#3096	C₂	semidirect
13. C₆₇×#3079	C₂	semidirect
14. C₆₇×#3062	C₂	semidirect
15. C₆₇×#3038	C₂	semidirect
16. C₆₇×#3012	C₂	semidirect
17. C₄×#135×C₆₇	C₂	semidirect
18. C₆₇×#2931	C₂	semidirect
19. C₆₇×#2897	C₂	semidirect
21. C₂×AGL(1,ℤ/8)×C₆₇	C₂²	semidirect
23. C₂×#131×C₆₇	C₂²	semidirect
24. #556×C₆₇	C₂²	semidirect
25. #555×C₆₇	C₂²	semidirect
26. #554×C₆₇	C₂²	semidirect
31. #547×C₆₇	C₂²	semidirect
37. #537×C₆₇	C₂²	semidirect
44. C₂×C₄⋊Q₈×C₆₇	C₂²	semidirect
47. #520×C₆₇	C₂²	semidirect
49. C₄×#41×C₆₇	C₂²	semidirect
50. #486×C₆₇	C₂²	semidirect
51. #486×C₆₇	C₂²	semidirect
52. #486×C₆₇	C₂²	semidirect
53. #486×C₆₇	C₂²	semidirect
54. #482×C₆₇	C₂²	semidirect
55. #482×C₆₇	C₂²	semidirect
56. #481×C₆₇	C₂²	semidirect
57. #480×C₆₇	C₂²	semidirect
58. #477×C₆₇	C₂²	semidirect
59. #476×C₆₇	C₂²	semidirect
60. #475×C₆₇	C₂²	semidirect
61. #474×C₆₇	C₂²	semidirect
62. #469×C₆₇	C₂²	semidirect
63. #468×C₆₇	C₂²	semidirect
64. #466×C₆₇	C₂²	semidirect
65. #465×C₆₇	C₂²	semidirect
66. #460×C₆₇	C₂²	semidirect
67. #460×C₆₇	C₂²	semidirect
68. #459×C₆₇	C₂²	semidirect
69. #459×C₆₇	C₂²	semidirect
70. #452×C₆₇	C₂²	semidirect
71. #450×C₆₇	C₂²	semidirect
72. #449×C₆₇	C₂²	semidirect
73. #447×C₆₇	C₂²	semidirect
74. C₄×Q₁₆×C₆₇	C₂²	semidirect
75. C₄×Q₁₆×C₆₇	C₂²	semidirect
76. C₄×SD₁₆×C₆₇	C₂²	semidirect
77. C₄×SD₁₆×C₆₇	C₂²	semidirect
78. C₄×SD₁₆×C₆₇	C₂²	semidirect
79. C₄×SD₁₆×C₆₇	C₂²	semidirect
80. C₄×D₈×C₆₇	C₂²	semidirect
81. C₄×D₈×C₆₇	C₂²	semidirect
82. #436×C₆₇	C₂²	semidirect
83. #436×C₆₇	C₂²	semidirect
84. C₈×D₄×C₆₇	C₂²	semidirect
85. C₈×D₄×C₆₇	C₂²	semidirect
86. #428×C₆₇	C₂²	semidirect
87. #427×C₆₇	C₂²	semidirect
88. #423×C₆₇	C₂²	semidirect
89. #418×C₆₇	C₂²	semidirect
90. #418×C₆₇	C₂²	semidirect
92. #417×C₆₇	C₂²	semidirect
94. #416×C₆₇	C₂²	semidirect
95. #416×C₆₇	C₂²	semidirect
96. C₂×#102×C₆₇	C₂²	semidirect
97. C₂×#102×C₆₇	C₂²	semidirect
98. C₂×#102×C₆₇	C₂²	semidirect
99. #408×C₆₇	C₂²	semidirect
100. C₂×C₄×C₈×C₆₇	C₂²	semidirect
245. #41×C₆₇	#41	semidirect
457. #61215	C₆₇	direct (N × H)
466. #3511	C₂×C₆₇	semidirect
467. #3498	C₂×C₆₇	semidirect
468. #3333	C₂×C₆₇	semidirect
469. #3332	C₂×C₆₇	semidirect
470. #3325	C₂×C₆₇	semidirect
471. #3324	C₂×C₆₇	semidirect
472. #3305	C₂×C₆₇	semidirect
473. #3304	C₂×C₆₇	semidirect
474. #3295	C₂×C₆₇	semidirect
475. #3294	C₂×C₆₇	semidirect
476. C₂×#486	C₂×C₆₇	semidirect
477. #3096	C₂×C₆₇	semidirect
478. #3079	C₂×C₆₇	semidirect
479. #3062	C₂×C₆₇	semidirect
480. #3038	C₂×C₆₇	semidirect
481. #3012	C₂×C₆₇	semidirect
482. C₄×#135	C₂×C₆₇	semidirect
483. #2931	C₂×C₆₇	semidirect
484. #2897	C₂×C₆₇	semidirect
485. C₆₇	#61215	direct (N × H)
487. C₂×AGL(1,ℤ/8)	C₂²×C₆₇	semidirect
489. C₂×#131	C₂²×C₆₇	semidirect
490. #556	C₂²×C₆₇	semidirect
491. #555	C₂²×C₆₇	semidirect
492. #554	C₂²×C₆₇	semidirect
497. #547	C₂²×C₆₇	semidirect
503. #537	C₂²×C₆₇	semidirect
510. C₂×C₄⋊Q₈	C₂²×C₆₇	semidirect
513. #520	C₂²×C₆₇	semidirect
515. C₄×#41	C₂²×C₆₇	semidirect
516. #486	C₂²×C₆₇	semidirect
517. #486	C₂²×C₆₇	semidirect
518. #486	C₂²×C₆₇	semidirect
519. #486	C₂²×C₆₇	semidirect
520. #482	C₂²×C₆₇	semidirect
521. #482	C₂²×C₆₇	semidirect
522. #481	C₂²×C₆₇	semidirect
523. #480	C₂²×C₆₇	semidirect
524. #477	C₂²×C₆₇	semidirect
525. #476	C₂²×C₆₇	semidirect
526. #475	C₂²×C₆₇	semidirect
527. #474	C₂²×C₆₇	semidirect
528. #469	C₂²×C₆₇	semidirect
529. #468	C₂²×C₆₇	semidirect
530. #466	C₂²×C₆₇	semidirect
531. #465	C₂²×C₆₇	semidirect
532. #460	C₂²×C₆₇	semidirect
533. #460	C₂²×C₆₇	semidirect
534. #459	C₂²×C₆₇	semidirect
535. #459	C₂²×C₆₇	semidirect
536. #452	C₂²×C₆₇	semidirect
537. #450	C₂²×C₆₇	semidirect
538. #449	C₂²×C₆₇	semidirect
539. #447	C₂²×C₆₇	semidirect
540. C₄×Q₁₆	C₂²×C₆₇	semidirect
541. C₄×Q₁₆	C₂²×C₆₇	semidirect
542. C₄×SD₁₆	C₂²×C₆₇	semidirect
543. C₄×SD₁₆	C₂²×C₆₇	semidirect
544. C₄×SD₁₆	C₂²×C₆₇	semidirect
545. C₄×SD₁₆	C₂²×C₆₇	semidirect
546. C₄×D₈	C₂²×C₆₇	semidirect
547. C₄×D₈	C₂²×C₆₇	semidirect
548. #436	C₂²×C₆₇	semidirect
549. #436	C₂²×C₆₇	semidirect
550. C₈×D₄	C₂²×C₆₇	semidirect
551. C₈×D₄	C₂²×C₆₇	semidirect
552. #428	C₂²×C₆₇	semidirect
553. #427	C₂²×C₆₇	semidirect
554. #423	C₂²×C₆₇	semidirect
555. #418	C₂²×C₆₇	semidirect
556. #418	C₂²×C₆₇	semidirect
558. #417	C₂²×C₆₇	semidirect
560. #416	C₂²×C₆₇	semidirect
561. #416	C₂²×C₆₇	semidirect
562. C₂×#102	C₂²×C₆₇	semidirect
563. C₂×#102	C₂²×C₆₇	semidirect
564. C₂×#102	C₂²×C₆₇	semidirect
565. #408	C₂²×C₆₇	semidirect
566. C₂×C₄×C₈	C₂²×C₆₇	semidirect
711. #41	#41×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3511	2
C₆₇×#3498	2
C₆₇×#3333	2
C₆₇×#3332	2
C₆₇×#3325	2
C₆₇×#3324	2
C₆₇×#3305	2
C₆₇×#3304	2
C₆₇×#3295	2
C₆₇×#3294	2
C₂×#486×C₆₇	2
C₆₇×#3096	2
C₆₇×#3079	2
C₆₇×#3062	2
C₆₇×#3038	2
C₆₇×#3012	2
C₄×#135×C₆₇	2
C₆₇×#2931	2
C₆₇×#2897	2
#61215	67

Subgroups — C67×#61215 #30740466

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#61215 #30740466